Educational research into socio-economic dynamics of university graduate employment: Triple analogy-based physics-and-engineering approach to labor market oscillations

1 The state of the art. Concerning graduate employment oscillations and “soft skills” development problem

For the last few years the situation with youth employment and, in particular, with graduate employment has become one of the very acute and highly discussed socio-economic topics worldwide. Recently, this employment-related topic has become the object of numerous socio-political studies. As a result, the employment-related problem has also become the subject for strategy development and higher education policy-related decision-making.

There has also been a wide discussion and criticism of the general efficiency and employability-related quality of university education, associated with the rapid growth of technology-induced “technical” or “technological” unemployment [1]. Peters et al. (2019) have provided a detailed study of the “technological” unemployment problem in the context of the general problem of employment [1]. Peters et al. have noted that even thoughtful planning and careful selection of a particular individual way of strategic university development does not guarantee future sustainable, reliable and trouble-free graduate employment due to the emerging globally imposed problem of technologicalunemployment [1]. Peters et al. have confirmed that the problem of ongoing global replacement of human labor with use of automated machines cannot be considered as a new socio-technical problem [1]. However, a clear understanding of the quickly approaching serious global challenge of technological unemployment has been clearly realized and analyzed only recently.

Berriman et al. (2017) have prepared an economic report, which estimates the socially-negative outlook concerning the growing rate of British unemployment for the next 13-15 years up to early 2030 [2]. They have shown that up to 30% of British workplaces could be potentially reduced due to a growing level of full-scale automation in the approach to 2030 [2]. Berriman et al., 2017 have noted that this forecast is less negative, and even more favorable, in comparison with expected levels of workplace reduction in the USA (38%) or in Germany (35%) [2]. However, the expected level of workplace decrease in Britain (30%) will be higher than in Japan (21%) [2]. Berriman et al., 2017 have predicted that the highest risks of reduced employment are expected in the field of transportation with a 56% of workplace reduction and in the manufacturing sector with a 46% of workplace decrease [2]. Berriman et al., 2017 have forecast that lower levels of risk for future employment will be in the more “human-centered” spheres of healthcare and social work with an expected level for workplace reduction of 17% [2]. Berriman et al., 2017 have emphasized that the main differentiating factor, preventing stuff reduction for specific individual employees, is availability of a university diploma-supported higher education-and-qualification level [2]. I.e. they emphasize that, for individual employees, the risk of future unemployment can be greatly reduced by obtaining a university diploma [2]. Berriman et al. have estimated that the potential automation-induced dismissal risk of unemployment will reach 46% for non-graduate paraprofessional workers [2]. They have also suggested that the risk of unemployment for a worker in the UK will reduce to 12% if the employee obtains a university diploma with a Bachelor’s (BSc.) or higher (MSc, and-or Ph.D.) Degree [2]. Therefore, Berriman et al. have concluded that the availability of higher education diplomas for the individual employees directly improves employment opportunities [2].

Nevertheless, Peters et al. have proposed to do additional research into the perspectives of a technological unemployment in the context of the historical position of education and the ongoing role of global technologization with an emphasis on the political and socio-ideological foundations of social and technical sciences [1]. Peters et al. have noted that, at first sight, the universities are regularly creating and promoting different intellectually attractive “scientific worlds” and “new life opportunities” [1]. However, Peters et al. have added that students are increasingly encouraged to consider the educational space of university education just as a means of achieving their short-term diploma-related pragmatic objectives [1]. They have formulated that modern youth considers universities as places where a neo-liberal education ensures the formation and development of special flexible and soft skills, which are very important for the directly applicable maintenance of a certain type of capitalism [1]. Peters et al., 2019 have also noted that the globally universal problem of technological unemployment, as with other social problems and concerns, has become an exclusively educational problem [1]. Moreover, Peters et al. emphasized that the technological unemployment concern has been reflected in the modern higher education policy as a problem that must be rectified only by efforts of the universities [1]. However, they confirmed that the naïve assumption that higher education alone can successfully solve the problem of technological unemployment is a kind of groundless political construction, which had not fulfilled the expectations [1].

Peters et al. have addressed the number of interconnected problems like automation, robotics and robotic automation-induced unemployment [3]. They have noted that the development of new methodological, philosophical, scientific, sociological, economic, ethical and political approaches for the principal rethinking of existing categories of labor and education will be the best way for successful adaptation and combat of the technological unemployment problem [3]. Peters et al. have suggested that modern society requires new approaches for rethinking the role of university education in the digital (physics-centered) epoch and post-digital (biology-centered) era, which will be characterized with potential massive technological unemployment with a global-scale coverage of the burden distribution [3]. Peters et al. have noted that plenty of attractive employment opportunities simply do not exist in the modern world for everyone [3]. Therefore, Peters et al. have concluded that the higher education cannot be considered as a panacea for this quickly growing problem of technological unemployment [3].

As we have seen, the scientific emphasis in modern educational research is shifting away from direct study of the educational system to a more comprehensive social investigation of society as a nonlinear dynamic system or, more specifically, as a neoliberal social system. In particular, the growing neoliberalism facilitates the transition of educational discourse from the concept of the individual duty and responsibility of the teachers to the social effects of education and graduate employment. This approach assumes that the labor markets will take care of themselves in the case of the sufficient availability of highly qualified and well-trained human resources with the appropriate level of higher professional education of employees. E.g., Peters & Jandrić (2019) noted that the human concept has been changed in modern social studies as well [4]. This means that the “economic” person (“Homo economicus”) transforms into the “collaborating” individual (“Homo collaborans”) [4]. However, Peters & Jandrić have considered that both of these definitions are rather ideal models for possibilities to make a principal socio-economic positioning of an individual human within the socially useful capitalistic boundaries [4].

Additionally, Peters & Jandric have noted the increased blurring of the distinctions between the realities of human life within the physical world and the virtual reality of computer-generated environment as well as between a human being and a computerized machine [4].

Peters & Jandrić have shown the ongoing tendency of a full-scale transition from the primacy of the substances to the predominance of the interactions, which are consistent features for network communications [4]. They have considered the socio-economic network architecture as a completely different type of epistemological set of complex interdependent and functional relationships rather than an individual rational agent [4] and have noted that an individual interest also tends to be compensated by the forms of a jointly shared collective responsibility [4]. Peters & Jandrić, 2019 have shown that there are no scientifically determinable cut-off points within our increasingly interconnected and interdependent socio-economic world [4]. Therefore, they substantiated that classical educational responses, which are based on the conventional concepts of human capital and a traditional (customary) economy, have never resolved the problem of technological unemployment [4].

Hayes (2019) has concluded that the prevailing classical theory of Weberian rationality (Weber’s rationalization) is no longer operational [5]. Hayes expresses concern about the ongoing acceleration of manufacturing efficiency, which has resulted in the achievement of considerable progress through replacement of human workers with automated robotic systems in recent years [5]. As a result, Hayes agreed with Ritzer’s opinion that automation-enhanced continuous staff reductions have resulted in various social forms of human irrationalization [5]. Hayes has emphasized that scientific research into the socio-economic problems of human-centered graduate employment and technology-induced unemployment continues to oscillate between two sharply defined extreme options: the unconditional refusal of modern computerized technologies of full-scale automation for new employment creation and technology-centered determinism [5]. He has drawn attention to the fact that modern neoliberal higher education is focused on the production and dissemination of certain types of “soft” capitalism [5]. Therefore, Hayes has introduced a new Ritzer-inspired term “McPolicy” for the social description of the common rational university policy [5]. Hayes has found similar trends between the latest educational research studies of advanced learning-instruction technologies, graduate employment etc., on the one hand, and marketing strategies for better selling of consumer products, on the other hand, when marketing specialists prefer to anthropomorphize and humanize the consumer goods with the human qualities (e.g. “ambitious” computer or car) [5]. Hayes noted that “McPolicy” term ensures a similar discourse concerning the working university activity of instructors and students [5].

Some researchers (Buntat et al., 2016) believe that there are spheres of the labor market, where the number of employed people will increase despite the presence of technological unemployment [6]. For example, Buntat et al. predict a trend of growing employment in the fields of biomedical engineering, biomedicine and biotechnology [6].

Historically, university engineering graduates have generally found employment that is consistent with their major specialty field, such as control, computer, electrical, electronics, mechanical, industrial, aerospace, chemical, nuclear, mining, civil, etc. Industrial firms generally hired engineers based on their grade reports, particularly in their major field, and the impression made on a human resources (HR) representative in an interview. Results have always been mixed, but there have been a few facts established. One is that the best students do not always make the best engineers. Another is that an HR representative interview is totally inadequate for evaluating a prospective engineer’s capabilities. Therefore, recruitment becomes a sort of crap shoot. And the graduate, who is badly in need of a job, is usually willing to say or do anything necessary to get a job. But the student does not know any truth about the company and the company knows very little about the graduate.

Successful employment of university graduates has always been a complex problem, involving a number of interconnected aspects in the economic, educational, industrial, psychological, social and ethical spheres of human activity. Today the problem has become even more complex in view of growing globalization, ongoing computerization and increasing competition. In addition to all of the above, the relevance and quality of a graduate’s education can have a major effect on finding successful employment. In many cases, the educational system has not kept up with modern industrial trends, leaving graduates ill-equipped to compete for jobs.

Sometimes, a graduate’s chances for successful employment can be enhanced by a slightly more diverse, less specialized graduate curriculum. Better understanding and humanities-inspired rethinking of this problem requires further detailed study of the graduate employment sphere. There are so-called “secondary” abilities of graduate students with “minor” importance like empathy and “soft” skills [7–12], which can have far more impact on successful employment than was previously assumed.

Some modern researchers [13–15] suggest that traditional liberal economics should be more human-centered and, despite growing unemployment, facilitate socialization of people with disabilities through the development of soft, flexible skills and occupations for socially-sensitive groups of invalids [13, 14] and pensioners [15].

The simplest empathy interpretation means person’s sensitivity in communication. More complex empathy understanding assumes mental and moral responsiveness as well as commitment to joint, unite and solidary activity in a team, working under regular pressure.

Quite often educators assume that the “self-existing” process of graduate empathy formation, if there is any, is a personal trait, which develops spontaneously and sporadic for some students, without help from the educational system. However, the value of a graduate’s empathy can be significant to him in the process of seeking employment. An approach for assessing its value and the possibility of providing educational aid to a student’s development of empathy should be considered, based on a firmer scientific foundation than the spontaneous assumption.

A person can learn to cooperate in a joint effort in teamwork and participate in a successful technical project. But, if he can also apply empathy, he can understand the feelings and motivations of others in the project and create a communication on this level, resulting in an even more successful end product. But, in addition, a new relationship between the people involved has been created and can carry over into new projects. The combination of good technical skills and the ability to employ empathy in communication can be extremely valuable in obtaining and retaining good employment [8, 11].

Quite often instructor’s and employer’s empathy help many graduate students to find the point of employment support in complex real situation of the constant uncertainty.

Phenomenological (phenomena-oriented) and psychological empathy studies were addressed in a number of novel approaches [7–12] and other multidisciplinary research studies, conducted and published in recent years and decades. Elliott et al. have proposed meta-analysis-enhanced psychotherapy-inspired empirical estimation of the empathy level with wide use of a judgement scale method [7]. McGregor has considered empathy as a growth factor of personal development [10]. Some researchers have analyzed empathy from a social-political viewpoint. E.g., Patterson has tied together a decrease in empathy with wide dissemination and distribution of a neoliberalism viewpoint [12]. The recent research reports by Elliott et al. [7]; Hill et al. [8]; Korte et al. [9]; McGregor [10]; Nair et al. [11]; Patterson [12] are focused on an interpretation of empathy as a professional skill together with other soft skills [7–12].

Nevertheless, the scientific problems of reliability of the methodology for empathy level evaluation, the measure of its significance, and the level of confidence in applied empathy measurements are actual and important when applied to the impact of empathy on graduate employment.

2 Aims and scope of the paper. Research methods and prime scientific novelty

3 Original mathematical model of graduate student employment

There has to be a labor market reserve (also known as unemployment) for normal functioning of capitalistic market economy. The current volume of this labor market reserve varies depending on the annual turnout of graduated specialists by universities and outflow-induced turnover of highly skilled professional staff into other professions and occupations because of the impossibility for self-fulfillment in their profession, dissatisfaction with salaryetc.

Let us introduce the following notation:

N₀ is the optimum number of professional specialists employed in a specific manufacturing industry, where N₀ = 100%;

n₀ is the “optimum” number of professional specialists who are unemployed or underemployed, as a percentage of the N₀, where the statistically-observed value of n₀ is roughly equal to one-third of N₀: n₀≈30%;

N = N(t) is the actual number of professional specialists employed in the specific manufacturing industry, as a percentage of the N₀;

n = n(t) is the actual number of professional specialists, who are unemployed or underemployed, as a percentage of the N₀.

Employment of university graduates tends to replace mandatory retirement of highly skilled workers on a pension and those leaving their former professions for other reasons, such as feeling of dissatisfaction with low-quality working conditions, relocation into areas where the specific profession or specialty is not required or plays a minimum role, etc.

In this case, the optimum annual turnout of graduated specialists by universities can be estimated by the value of the following quantity (γ · N₀). We can estimate the numerical value of the γ coefficient as γ ≈ 0.03 (1/yr) ≈ 0.03 (1/year), according to the typical distribution of age groups. Therefore, it is possible to propose the following definition of γ coefficient: γ is the ratio of the (annual) number of specialists who dropped out of the specific manufacturing industry (due to mandatory retirement etc.) per unit of time (in a year) to the optimum number of professional specialists employed in a specific manufacturing industry.

If redundant (excessive) unemployment (n(t)– n₀) is positive ((n(t)– n₀) > 0), then the number of redundant (excessive) professional specialists employed in a specific manufacturing industry (N(t)– N₀) increases with time. The entrepreneur has the opportunity to employ more workers, including young professionals, for lower wages, in this case of ((n(t)– n₀) > 0).

In addition, vice versa, if redundant (excessive) unemployment (n(t)– n₀) is negative ((n(t)– n₀) < 0), then the number of redundant (excessive) professional specialists employed in a specific manufacturing industry (N(t)– N₀) decreases with time. The entrepreneur has to scale up wages, while reducing the number of employed workers, e.g. through the denial of employment of entry-level young professionals as a substitute replacement of dropped out staff members for whatever reasons.

Thus, the change in the redundant (excessive) number (N(t)– N₀) of professional specialists employed in a specific manufacturing industry with time is described with the following first differential equation: ( d ( N ( t ) - N 0 ) dt ) = α · ( n ( t ) - n 0 )(1) where α is a constant of proportionality.

The instructor adds that the simplest α proportionality coefficient definition is as follows: α can be defined as the ratio of the rate of change in the redundant number of excessive professional specialists to the value of redundant (excessive) unemployment.

Some technical students argue that engineer is rather not in the position to introduce new narrow-minded self-proposed technical terminology. The instructor partially agrees with this argument but notes that new terminology development is not necessarily a sign of ignorance and lack of engineering literacy. Engineering students should know that occasional engineering-inspired introduction of new technical terminology is a usual practice for engineering specialists, working in the spheres of engineering computations and mathematical modeling of social and technical systems.

If the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry is positive ((N(t)– N₀) > 0), then unemployment decreases with time. The greater the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry, the lower employee wages will be. The lower the wages become, the more experts, including young professionals, will move into alternative professions and occupations for higher salaries in other organizations. Over time, this tendency of a drift and departure of younger professionals to another place of work results in a local reduction in the number of job applicants and a resulting decrease in local unemployment.

In addition, vice versa, if the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry is negative ((N(t)– N₀) < 0), then unemployment increases with time. The lower the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry, the higher employee wages will be. The higher the wages become, the more experts, including young professionals, will take the opportunity to be employed in disciplines of their university major and work in their profession in this organization. Over time, this tendency to enter occupations commensurate with graduates’ skills results in a local increase in the number of job applicants and a resulting increase in local unemployment.

Thus, a change in the number of unemployed professional specialists with time is described with the following second differential equation: ( d ( n ( t ) ) dt ) = ( - β ) · ( N ( t ) - N 0 )(2) where β is a constant of proportionality.

The instructor adds that the simplest β proportionality coefficient definition is as follows: β can be defined as the ratio of the rate of change in unemployment to the redundant number of excessive professional specialists.

The instructor notes that linearized equations (1)-(2) are quite suitable for the first “linear” description of a stable functioning period of economics.

However, there are students who principally disagree with the linear character of the first and the second “economic” differential equations (1)-(2) because they believe that they are in a position to start their cross-disciplinary learning with the analysis of non-linear differential equations for a more complex non-linear economic model.

At this point, the instructor encourages the “quick” students to go ahead of the instructor’s lecture and help him facilitate the advancement of the current class level of understanding. Moreover, these “quick” students are kindly encouraged to propose and solve their own non-linear problems at home and show their computational advances to the instructor and classmates in a future class if they manage “not forget” their novel non-linear models “at home”.

The instructor certainly agrees that the “ideal” regularization of labor market is damaged during an economic crisis. Therefore, an economic crisis study requires additional modifications of the linearized equations (1)-(2) with the possible introduction of non-linear terms and multipliers into the system (1)-(2). However, this analysis surely goes beyond the aims and scopes of the first, introductory lecture, dealing with educational study of the linearized system (1)-(2).

Upon differentiating (1) we obtain the following equation: ( d 2 ( N ( t ) - N 0 ) d t 2 ) = α · ( d ( n ( t ) ) dt )(3)

Substitution of (2) into (3) will result in the following second-order differential equation: ( d 2 ( N ( t ) - N 0 ) d t 2 ) = ( ( - α · β ) · ( N ( t ) - N 0 ) )(4)

We will find an analytical solution of differential equation (4) in the following form: ( N ( t ) - N 0 ) = A · sin ( ω · t )(5) where A is the maximum value (as a percentage of the N₀) of the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry;

and

ω is the cyclic circular (or angular) frequency of oscillations in the number of professional specialists, dim(ω) = [rad/s] = [Angle/Time]: ω = ( α · β )(6)

Equation (5) yields that the actual number N = N(t) of professional specialists occupied in the industry, as a percentage of the N₀, can be determined as follows: N ( t ) = N 0 + A · sin ( ω · t )(7)

Substitution of (7) into (2) yields the following first-order differential equation: ( d ( n ( t ) ) dt ) = ( - β · A ) · sin ( ω · t )(8)

An analytical solution of the last differential equation (8) yields the following algebraic expression for the unknown function n = n(t): n ( t ) = n 0 + ( ( β ω ) · A ) · cos ( ω · t )(9)

This equation (9) for n = n(t) shows the time dependent behavior of the actual number of professional specialists who are underemployed or are working outside their university area of graduation study (as a percentage of the optimum number N₀ of professional specialists).

It is obvious that the number of underemployed professional specialists cannot be negative: n 0 ⩾ ( A · ( β ω ) )(10) or n 0 ⩾ ( A · ( β α ) )(11)

We will introduce the following author-proposed estimation for an unemployment measure: n * ( t ) = ( n ( t ) · N 0 N ( t ) )(12)

Equation (12) determines unemployment as the number of underemployed professional specialists as a percentage of the actual number N = N(t) of specialists employed and occupied in a specific manufacturing industry at this time.

Computational plots in Figs. 1–2 show 2D graphical information on the time variations of the number N = N(t) of successfully industry-employed specialists and the number n = n(t) of underemployed specialists as a percentage of the optimum number of professional specialists as well as the percent of unemployment n^* = n^*(t) for the following numerical values: n₀ = 30%; A = 10%; α = 0.8 (1/year) = 0.8 (1/yr); β = 0.6 (1/year) = 0.6 (1/yr):

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Fig.1

2D computational plots of N = N(t) (upper dark blue sine-shaped curved line), N₀-level (upper purple horizontal line), n = n(t) (lower red cosine-shaped curved line), n^* = n^*(t) (lower green cosine-shaped curved line) and n₀-level (lower blue-grey horizontal line), where the vertical axis values are rated on a percentage basis and the horizontal axis marks show time inyears.

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Fig.2

2D computational circular chart (pie chart) of N = N(t) (outer dark blue circle), n = n(t) (internal red circle) and n^* = n^*(t) (internal green circle), where N₀- and n₀- levels are plotted as purple and blue-grey circles.

N = N(t) is the actual number of professional specialists employed in the specific manufacturing industry, as a percentage of the N₀, where N (t) = N₀ + A · sin(ω · t);

n = n(t) is the actual number of professional specialists, who are underemployed or are working not in employment according to their university area of graduation study, as a percentage of the N₀, where n (t) = n₀ + (A · (β/ω)) · cos(ω · t);

n^* = n^*(t) is the actual number of professional specialists, who are underemployed or are working not in employment according to their university area of graduation study, as a percentage of the actual number N = N(t) of specialists, employed and occupied in a specific manufacturing industry at this time n^* (t) = (((n (t)) · N₀)/(N (t))).

Unemployment n^* = n^*(t) is a kind of a pool of employees. Unemployment n^* = n^*(t) availability is a necessary prerequisite for the successful functioning of the capitalist market economy. Therefore, university graduates need to be prepared to face the real-life situation of unemployment in a manufacturing field related to the academic and professional disciplines that require highly specialized scientific and technical knowledge or advanced skills of their university major at least for a certain period oftime.

In this paper, we have introduced N = N(t) as the actual number of professional specialists employed in a specific manufacturing industry, as a percentage of the optimum number N₀ of professional specialists. E.g., let us say that the optimum number of professionals is equal to ten specialists: N₀ = 10. It is necessary to improve wages for local workers in order to attract professionals when we have low levels of local unemployment n^* = n^*(t).

However, the annual cost of wages always has a limit, which is generally defined by the company’s profit margin and financial condition. I.e., salary costs are not a rubber ball. Therefore, the employer retains only nine (9) out of ten (10) specialists in a technical team and makes no compensation for natural attrition of technical staff due to mandatory retirement etc.

However, it is possible to employ an 11th (eleventh) worker, offering him a lower salary if unemployment n^* = n^*(t) is high. It is highly probably that this 11th (eleventh) worker agrees to employ and to earn a lower salary because he needs a job, he cannot find another job and he often not in a position for a successful alternative employment. Quite often, an employer must officially increase his production in order to employ an 11th (eleventh) worker. Alternatively, an employer may hire an 11th (eleventh) worker only as apprentice in order to prepare the ground for team successors in view of the fact that many staff members will retire soon.

Figure 1 shows that the actual number of professional specialists employed in a specific manufacturing industry (N = N(t)) lags (retards) in phase with the actual number of unemployed professional specialists (n = n(t)) with a phase difference of approximately (π/2).

Figure 1 shows that when an “unemployment” curve (n = n(t)) passes through the point of extremum (i.e. through the point where the unemployment value is minimum or maximum), then the actual number of occupied professional specialists N takes the optimum value N₀.

Figure 1 shows that when a descending “unemployment” curve (n = n(t)) passes through the optimum point n₀, then the actual number of occupied professional specialists (N = N(t)) takes a maximum value.

Figure 1 shows that when an ascending “unemployment” curve (n = n(t)) passes through the optimum point n₀, then the actual number of occupied professional specialists (N = N(t)) takes a minimum value.

Therefore, the actual number of occupied professional specialists (N = N(t)) is expected to decline (reduce) in a quarter of period (T/4), following the achievement of the minimum value in the “unemployment” curve (n = n(t)).

Hence, the actual number of occupied professional specialists (N = N(t)) is expected to increase in a quarter of period (T/4), following the achievement of a maximum value in the “unemployment” curve (n = n(t)).

Figure 1 shows that the curve of (n^* = n^*(t)) insignificantly lags (retards) in phase from the curve of (n = n(t)).

5 Electrical analogy of original mathematical model

The instructor notes that it is possible to ensure a suitable level of engineer-friendly explanation of the author-proposed graduate employment model (1) – (12) through the introduction of a non-obvious electrical analogy between this social process (Figs. 1–2) and electrodynamics of the electrical scheme of an LC-field-effect transistor oscillator (Fig. 3).

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Fig.3

Author-proposed electrical analogy of the graduate employment process using the electrical scheme of an LC-field-effect transistor oscillator for illustrating of the author-developed phenomenological model, shown in formulae (1) and (4).

Let us consider the LC circuit in Fig. 3.

The instructor notes that the total electric current I(t) through the inductance coil is the sum of the following two current components: I ( t ) = i ( t ) + I 0(13) where

I(t) is the total electric current through the inductance coil, dim(I(t)) = [A] = [Ampere];

i(t) is the alternating (variable) AC-component of the total electric current through the inductance coil, dim(i(t)) = [A] = [Ampere];

I₀ is the direct (steady) DC-component of the total electric current through the inductance coil, dim(I₀) = [A] = [Ampere].

The last formula (13) yields the following expression for the alternating (variable) AC-component of the total electric current through the inductance coil: i ( t ) = I ( t ) – I 0 .(14)

The instructor notes that, on the other hand, we can alternatively estimate i(t) in (14) as the rate of change of the electric charge q(t): i ( t ) = ( d ( q ( t ) ) dt )(15) where

q(t) is the electric charge, dim(q(t)) = [C] = [Coulomb].

The instructor adds that the full electric voltage U(t) through the inductance coil is the sum of the following two voltage components: U ( t ) = u ( t ) + U 0 ,(16) where

U(t) is the full electric voltage (electric potential difference) through the inductance coil, dim(U(t)) = [V] = [Volt];

u(t) is the alternating (variable) AC-component of the full electric voltage (ac electric potential difference) through the inductance coil, dim(u(t)) = [V] = [Volt];

U₀ is the direct (steady) DC-component of the full electric voltage (dc electric potential difference) through the inductance coil, dim(U₀) = [V] = [Volt].

The last formula (16) yields the following expression for the alternating (variable) AC-component of the full electric voltage through the inductance coil as: u ( t ) = U ( t ) – U 0 . ( 17 )(17)

Now we define the electric charge q(t) in (15) through u(t) in (17) as q ( t ) = C · u ( t )(18) where C is the electric capacitance, dim(C) =[F] = [Farad].

After substitution of (17) into (18), we have the following new expression for the electric charge as q ( t ) = C · ( U ( t ) - U 0 )(19)

Substitution of (19) into (15) yields that i ( t ) = ( d ( C · ( U ( t ) - U 0 ) ) dt )(20) or i ( t ) = C · ( d ( ( U ( t ) - U 0 ) ) dt )(21)

Substitution of (21) into (14) yields that ( I ( t ) - I 0 ) = C · ( d ( ( U ( t ) - U 0 ) ) dt )(22)

The last equation (22) yields that ( d ( ( U ( t ) - U 0 ) ) dt ) = ( ( 1 C ) · ( I ( t ) - I 0 ) )(23) .

The instructor shows to surprised students that an “economics” equation (1) is very similar to the derived “electrical” equation (23) by writing both these equations together as system (24): { ( d ( N ( t ) - N 0 ) dt ) = ( α · ( n ( t ) - n 0 ) ) , ( d ( ( U ( t ) - U 0 ) ) dt ) = ( ( 1 C ) · ( I ( t ) - I 0 ) ) .(24)

The similarity of the two equations in system (24) means that we can complete the following list of formal algebraic analogies between the “economic” equation (1) and “electrical” equation (23):

N ( t ) ⇔ U ( t ) ; N 0 ⇔ U 0 ; α ⇔ ( 1 / - C ) ; n ( t ) ⇔ I ( t ) ; n 0 ⇔ I 0 .(25)

At this point, the instructor encourages students to propose their ideas regarding the possible definition of the α factor of proportionality in (24) through comparison of the phenomenological equation (1) with the typical differential equation (23) for an electrical LC-circuit in Fig. 3. The instructor notes to students that the constant of proportionality (1/C) [(1/Farad)] in the “electrical” equation (23) was defined as the reciprocal value of electric capacitance C [Farad]. The instructor wonders about the student-preferred simple definition of α coefficient in (1) within the framework of analogy (24) – (25) between the structure of the author-proposed “economic” expression (1) and the well-known “electrical” formula (23).

Now the technical instructor introduces an electrical analogy-based estimation (25) for the second author-proposed “economic” equation (2). The instructor notes that we can estimate the AC-voltage component in (17) for the LC circuit in Fig. 3 through the introduction of Faraday’s law of induction as u ( t ) = ( ( - L ) · ( d ( I ( t ) ) dt ) ) ,(26) where L is the magnetic inductance, dim(L) = [H] = [Henry].

However, there are the students in the class who are not comfortable with the “minus” sign in the “electrical” formula (26) for Fig. 3.

In this regard, the instructor additionally notes that the expression (26) is the generally known Faraday’s formula e ( t ) = ( ( - L ) · ( d ( I ( t ) ) dt ) ) of self-induced emf within inductance coil for the LC circuit in Fig. 3.

This means that the voltage on an inductance coil for the LC circuit in Fig. 3 is u L ( t ) = - e ( t ) = ( ( + L ) · ( d ( I ( t ) ) dt ) ) .

Therefore, the voltmeter-measured voltage on the capacitor for the LC circuit in Fig. 3 is u ( t ) = - u L ( t ) = + e ( t ) = ( ( - L ) · ( d ( I ( t ) ) dt ) ) .

Most curious students would like to know that Maxwell has provided the further generalization of Faraday’s law of induction (26). As a result, Faraday has derived the one of his four vector equations, which establishes the interconnection between the vector of electric field strength E → ( t ) and the rate of time change of the vector of the magnetic flux density B → ( t ) , where dim ( E → ( t ) ) = [ V / - m ] = [ Volt / - Meter ] and dim ( B → ( t ) ) = [ T ] = [ Tesla ] . The integral form of the correspondent Maxwell equation describes the motion of the electromagnetic field and generalizes the formula (26) in the form of the following integral equation: ∮ L ( E → ( t ) · d I → ) = ∫ S ( ∂ ( B → ( t ) ) ∂ t ) d S → , where Φ(t) is the magnetic flux: Φ ( t ) = L · I ( t ) = ∫ S ( B → ( t ) ) d S → , dim(Φ(t)) = [Wb] = [Weber].

After substitution of (17) into (26), we have the following second analogy-related “electrical” expression for the second “economic” equation (2): U ( t ) - U 0 = ( ( - L ) · ( d ( I ( t ) ) dt ) ) .(27)

The last equation (27) yields that ( d ( I ( t ) ) dt ) = ( - 1 L ) · ( U ( t ) - U 0 ) .(28)

The instructor shows to surprised students that the “economic” equation (2) is very similar to the derived “electrical” equation (28) by writing both these equations together as system (29): { ( d ( n ( t ) ) dt ) = ( - β ) · ( N ( t ) - N 0 ) , ( d ( I ( t ) ) dt ) = ( - 1 L ) · ( U ( t ) - U 0 ) .(29)

The similarity of the two equations in system (29) means that we can complete the following list of formal algebraic analogies between the “economic” equation (2) and the “electrical” equation (28): n ( t ) ⇔ I ( t ) ; β ⇔ ( 1 / - L ) ; N ( t ) ⇔ U ( t ) ; N 0 ⇔ U 0 .(30)

At this point, the instructor encourages students to propose their ideas regarding the possible definition of this β factor of proportionality in (2) through comparison of equation (2) with the typical second differential equation (28) for an electrical LC-circuit in Fig. 3. The instructor notes to students that the constant of proportionality (1/L [(1/Henry)]) in the “electrical” equation (28) was defined as the reciprocal value of magnetic inductance L[Henry]. The instructor wonders about the student-preferred simple definition of β coefficient in (2) within the framework of the author-proposed non-obvious analogy (29) – (30) between the structure of the author-proposed “economical” expression (2) and the well-known “electrical” formula (28).

It is possible to make the further “electrical” generalization of the previous “economical” equation (3) through the joint use of both lists of “electro-economical” analogies (25), (30): ( d 2 ( U ( t ) - U 0 ) d t 2 ) = ( 1 C ) · ( d ( I ( t ) ) dt ) .(31)

“Electrical” generalization of the previous “economic” equation (4) according to the rules (25), (30) yields that, because of (23): ( d 2 ( U ( t ) - U 0 ) d t 2 ) = ( ( - 1 ( L · C ) ) · ( U ( t ) - U 0 ) ) .(32)

The “electrical” analogue of the “economic” expression (5) is as follows: ( U ( t ) - U 0 ) = A · sin ( ω · t ) ,(33) where A is the maximum value of the AC-voltage component through the inductance coil for the oscillating circuit, dim(A) = [V] = [Volt];

and

ω is the cyclic circular (or angular) frequency of the electrical oscillations in the LC circuit, where the “electrical” form of equation (6) is as follows: ω = 1 ( L · C )(34)

The “electrical” analogy of the “economic” equation (7) can be written as: U ( t ) = U 0 + A · sin ( ω · t ) .(35)

Use of the rules (25), (30) allows us to write the following “electrical” analogy of (8): ( d ( I ( t ) ) dt ) = ( - ( A L ) ) · sin ( ω · t ) .(36)

We can write an “electrical” analogy of (9) as I ( t ) = I 0 + ( A ( ω · L ) ) · cos ( ω · t ) .(37)

The “electrical” analogies of inequalities (10–11) are as follows: I 0 ⩾ ( A ω · L )(38) or I 0 ⩾ ( A · ( C L ) ) .(39)

It was found that both engineering and economic specialties students find these author-proposed student-friendly “economic-electrical” analogies (24) – (25) & (29) – (30) between (1) – (11) and (23), (28), (31) – (39) as non-obvious and thought-provoking comparisons of social and technical phenomena, which essentially expands the multidisciplinary knowledge of engineering students.

The circuit diagram of an LC-based field-effect transistor oscillator, which electrically illustrates the graduate employment problem, is shown in Fig. 3. It was earlier shown in Fig. 1 that the actual number (N = N(t)) of professional specialists employed in a specific manufacturing industry lags (retards) in phase with the actual number (n = n(t)) of unemployed professional specialists with a phase difference between (N = N(t)) and (n = n(t)) of (π/2). The instructor shows students that similarly in Fig. 3, the capacitor’s C1 voltage (U _C  = U _C (t)), which is measured with a voltmeter V, is a sinusoidal quantity and lags (retards) in phase with the capacitor’s C1 current (I _C  = I _C (t)), which is measured with an ammeter A, with a phase difference between (U _C  = U _C (t)) and (I _C  = I _C (t)) of (π/2).

Hence, the capacitor’s C1 current (I _C  = I _C (t)) is maximum (max(I _C (t))) when the capacitor’s C1 voltage (U _C  = U _C (t)) is zero ( U C * = 0 ) . Analogously, the capacitor’s C1 current (I _C  = I _C (t)) is zero ( I C * = 0 ) when the capacitor’s C1 voltage (U _C  = U _C (t)) reaches its maximum value (max(U _C (t))) in Fig. 3.

The electrical oscillations, generated with the resonant LC-circuit in Fig. 3, are submitted to the gate of transistor VT1. The direction of traversal (sense of rotation) of an oscillating circuit is in a clockwise direction (Fig. 3).

“Socially-saying”, the case of negative capacitor voltage (U _C (t) < 0) in Fig. 3 corresponds to a negative half-wave of the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry (Figs. 1–2). When the capacitor voltage is negative (U _C (t) < 0), then we have a positive sign of the electric potential of the upper sheet (plate) of capacitor C1 (Fig. 3). In this case, a positive voltage is supplied to the control gate of field-effect transistor VT1 (Fig. 3). As a result, the channel conductance is increasing and the drain current is growing (Fig. 3). This growing drain current results in an increase of magnetic field energy of the inductance coil (Fig. 3), which “socially-saying” corresponds to an increase in the redundant (excessive) unemployment (n(t)– n₀) in Figs. 1–2.

“Socially-saying”, the case of positive capacitor voltage (U _C (t) > 0) in Fig. 3 corresponds to a positive half-wave of the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry (Figs. 1–2). When the capacitor voltage is positive (U _C (t) > 0), then we have a negative sign of the electric potential of the upper sheet (plate) of capacitor C1 (Fig. 3). In this case, a negative voltage is supplied to the control gate of the field-effect transistor VT1 (Fig. 3). As a result, the channel conductance is decreasing and the drain current has almost stopped (Fig. 3). Energy losses within the electrically oscillating LC circuit are not compensated (Fig. 3). “Electrically-saying”, the alternating AC-component of the total electric current through the inductance coil is decreasing in this case (Fig. 3). “Socially-saying”, this electrical case corresponds to a decrease in the redundant (excessive) unemployment (n(t)– n₀) in Figs. 1–2.

The instructor notes that the graduate employment problem (Figs. 1–2) is closely associated with self-excited oscillating systems because both the technical structure of professional specialists employees (Figs. 1–2), and the oscillator-tuned circuit of the LC-generator (Fig. 3), and the air accumulator of the hydraulic ram pump (Fig. 4) are examples of self-sustained oscillation (auto-oscillating) systems. To be more specific, it is possible to observe the periodic exchange between the groups of employed and unemployed professional specialists within the professional community of specialists-employees in the “social case” of graduate employment (Figs. 1–2). Analogously, we can see the periodic exchange between the electric-field energy of the capacitor and magnetic-field energy of the inductance coil within the oscillator-tuned circuit of the LC-generator (Fig. 3). Similarly, we can observe the periodic exchange between kinetic energy of the liquid flow and the potential energy of pressure within the air accumulator of the hydraulic ram pump (Fig. 4).

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Fig.4

Author-proposed hydraulic analogy of the graduate employment process using a hydraulic ram pump for illustrating of the author-developed mathematical model, shown in formulae (1) and (4).

The instructor emphasizes that replenishment of the losses (attrition replacement) is a necessary prerequisite for sustainable working of a self-excited system. The loss of experienced staff due to planned or early retirement etc. is replenished with graduate employment of young professional specialists in the social case of the professional community of specialists-employees (Figs. 1–2). The part of lost energy, which is dissipated due to electrical heating of the wires, is replenished with an emf voltage source in the electrical case of the oscillator-tuned circuit of the LC-generator (Fig. 3). The part of energy, which is dissipated due to overcoming of hydraulic resistances (flow friction) and water lifting to the height of the receiver discharge tank E (holding basin E), is replenished with incoming flow (entering flux) from the source tank A in the hydraulic case of the air accumulator of hydraulic ram pump (Fig. 4).

It is time for the technical instructor to introduce the author-proposed hydraulic analogy of the graduate employment process through a didactic analysis of the work of a scheme of a hydraulic ram pump, shown in Fig. 4. The lecturer notes that the hydraulic ram pump is a special type of a hydraulic impact-based pump. The operating principle of this hydraulic shock device working is based on the phenomenon of water hammer action (Fig. 4).

The instructor explains to students that hydraulic fluid (water) is beginning to flow freely from the superior tank A into the joined pipe length B and then water flows freely from the open gate valve 1 (Fig. 4). The gate valve 1 closes after the required pressure has been reached (Fig. 4). However, water from the superior tank A continues to run by inertia for some time after the gate valve 1 has been closed and, as a result, continues to compress the water into the joined pipe length B (Fig. 4). This physical process results in the generation of water pressure fluctuations and hydraulic oscillations as well as the appearance of a hydraulic impact-induced shock wave within the pipe length AB with a period: T water = 2 · ( L c ) ,(40) where

T_water is the period of hydraulic shock wave, dim(T) = [s] = [Time];

L is the length of the pipe length AB, dim(L) = [m] = [Length]; and

c is the shock-wave speed, dim(c) = [m/s] = [Length/Time]: c = 1 ( ( ρ water E water ) · [ 1 + ( ( E water E pipe ) · ( D pipe δ pipe - wall ) ) ] ) ,(41)

where

E_water is the Young’s modulus (modulus of volume elasticity) of the hydraulic fluid, where for a water we have E _water  ≈ 2 · 10⁹  [Pa]; dim ( E water ) = [ Pa ] = [ kg m · s 2 ] = ( ( Mass ) ( Length ) · ( Time ) 2 ) ;

E_pipe is the Young’s modulus (modulus of volume elasticity) of the pipe material, where for a steel pipe we have E _pipe  ≈ 2 · 10¹¹  [Pa]; dim ( E pipe ) = [ Pa ] = [ kg m · s 2 ] = ( ( Mass ) ( Length ) · ( Time ) 2 ) ;

ρ_water is the mass density of the hydraulic fluid (water), where dim ( ρ water ) = [ kg ( m 3 ) ] = ( ( Mass ) ( Length ) 3 ) ;

D_pipe is the pipe diameter, dim(D_pipe) = [m] = (Length);

δ_pipe–wall is the pipe wall thickness, dim(δ_pipe–wall) = [m] = (Length).

The instructor also provides students with a detailed additional explanation concerning the operation modes of the hydraulic scheme working, shown in Fig. 4. In the beginning, we address the first case when gate valve two (2) is fixed in its off state (blocking state). Water flow stops when gate valve one (1) closes (turns-off) under the influence of the incident (approaching) flow. However, the water tries to move by inertia and proceeds, creating forward (delivery) pressure, and experiences continued essential compression for some time after gate valve 1 has been closed. As a result, the end-of-pipe water pressure, near gate valve two (2), increases and a hydraulic shock arises. Once the water has reached the maximum level of compression, then water begins to expand in the direction of tank A. Then the water continues to expand by inertia, forming a zone with a vacuum (under-pressure) in the vicinity of gate valve two (2). As a result, gate valve one (1) opens. Return of the water, which was previously squeezed into tank A, follows immediately after the vacuum phase. However, gate valve one (1) is now opened. Therefore, the fluid flow has increased by taking out the energy due to acceleration in the gravity field. This is followed by the closing movement of gate valve one (1), another new hydraulic impact and the process repeats all over again. Therefore, the hydraulic oscillations are originated within the hydraulic system in Fig. 4, fed by the energy of the passing fluid flow, which is guided toward gate valveone (1).

The instructor notes that the hydraulic oscillatory system in Fig. 4 is similar to the LC-transistor oscillator in Fig. 3. Engineering students should give further thought to the following non-obvious analogies between the electrical scheme in Fig. 3 and the hydraulic scheme in Fig. 4:

the pressure p(t) near gate valve two (2) in “hydraulics” Fig. 4 is analogous to the capacitor voltage U _C (t) in “electric” Fig. 3;

“Socially-saying”, in the employment case, the vacuum pressure (p(t) < p_atm) near gate valve two (2) in Fig. 4 corresponds to a negative half-wave of the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry (Figs. 1–2). When the vacuum pressure (p(t) < p_atm) of the water is near gate valve two (2), then we have an open position for gate valve one (1), which is shown in Fig. 4. In this case, additional (auxiliary) energy is supplied to the hydraulic system from the transient passing water flow in Fig. 4. The instructor adds that, “socially-saying”, for the employment case, this first “hydraulics” pressure regime of (p(t) < p_atm) in Fig. 4 corresponds to an increase in the redundant (excessive) unemployment (n(t)– n₀) in Figs. 1–2.

“Socially-saying”, in the employment case, the high water pressure (p(t) > p_atm) near gate valve two (2) in Fig. 4 corresponds to a positive half-wave of the number of redundant (excessive) professional specialists (N(t)– N₀) employed in a specific manufacturing industry (Figs. 1–2). When the increased positive pressure (p(t) > p_atm) of the water is near gate valve two (2), then we have a closed position for gate valve one (1), shown in Fig. 4. In this case, additional (auxiliary) energy cannot be supplied to the hydraulic system because of the absence of the transient passing water flow through the hydraulic system in Fig. 4. Energy losses for overcoming (against) the frictional forces within the hydraulic oscillating mechanical system are not compensated (Fig. 4). “Hydraulically-saying”, the stream energy of water flow through the hydraulic system in Fig. 4 is decreasing in this case. “Socially-saying”, for the employment case, this second hydraulics pressure regime (p(t) > p_atm) corresponds to a decrease in the redundant (excessive) unemployment (n(t)– n₀) in Figs. 1–2.

The instructor notes that the hydraulics model in Fig. 4 uses the constant pressure component p₀, which is equal to the water column pressure (water head) p₀ = ρ · g · h _A , where h _A is the water level mark in the water tank A. This hydraulics model in Fig. 4 also introduces the constant flow rate component Q₀, which goes in the transit mode towards the air accumulator C.

The instructor notes that the hydraulic oscillatory system in Fig. 4 is similar to the social oscillatory system of employees in Figs. 1–2. Engineering students should give further thought to the following non-obvious analogies between the employment/unemployment oscillations in Figs. 1–2 and the hydraulic scheme in Fig. 4:

the optimum number N₀ of professional specialists employed in a specific manufacturing industry (Figs. 1–2) is analogous to the constant pressure component p₀ of the pipe pressure (Fig. 4);

At this point, the technical instructor should briefly explain to students why we actually need the hydraulic ram pump (Fig. 4) in engineering practice and how this hydraulics model improves our understanding of the graduate employment problem (Figs. 1–2). The instructor notes that water transits into the air accumulator C and compresses the air, located within C, at the moment of achievement of the required level of pressure, which is sufficient for opening gate valve two (2) in Fig. 4. Then the compressed air pushes a part of the water into the above-placed water tank E, when gate valve two (2) closes. The schematic sketch in Fig. 4 shows that the water reservoir E (from the right) is located at a higher elevation than the water reservoir A (from theleft).

Let us give consideration to the oscillations of a liquid column within a water tube with pipe length L and cross-sectional discharge area F_area of the water flow (Fig. 4), where the dimension of F_area is as follows: dim(F_area) = [m²] = (Length²). We simplify the hydraulics model in Fig. 4 by neglecting the loss of pressure head and the additional effects of pipe elasticity.

The instructor notes that it is possible to estimate the bulk compressibility factor β _p of the water with the following formula: β p = - d ( W ( t ) ) ( W 0 · ( dp ( t ) ) ) ,(42) where the “minus” sign indicates that the water volume decreases with increasing water pressure; β _p  = (1/E) = E^-1 is the compressibility of the hydraulic fluid, where for water we have ( β p ) water = ( 1 / - ( E water ) ) = E water - 1 ≈ 5 · 10 - 10 [ P a - 1 ] and the dimension of the column water compressibility is as follows: dim ( β p ) = dim ( 1 E ) = [ 1 Pa ] = [ ( m · s 2 ) kg ] = ( ( Length ) · ( Time ) 2 ( Mass ) ) ;

W₀ = ((F_area) · L) is the fixed value of water volume within the studied water column, located within the chosen pipe, dim(W₀) = [m³] = (Length³);

d(W(t)) is the water volume change, dim(d(W(t))) = [m³] = (Length³);

(d (W (t))/W₀) is the unit volume change of the water, dim(d (W (t))/W₀) = [1];

d(p(t)) is the water pressure change, dim ( d ( p ( t ) ) ) = [ Pa ] = [ kg m · s 2 ] = ( ( Mass ) ( Length ) · ( Time ) 2 ) .

The previous equation (42) yields the following expression for the relative change (d (W (t))/W₀) in water volume under the action of the additional pressure d(p(t)), applied to the water column: d ( W ( t ) ) W 0 = - β p · d ( p ( t ) ) .(43)

Suppose that we multiply both sides of the equation (43) by W₀ = (F_area) · L. We get d ( W ( t ) ) = - β p · W 0 · d ( p ( t ) )(44) or d ( W ( t ) ) = - β p · ( F area ) · L · d ( p ( t ) ) .(45)

Suppose that we multiply both sides of the equation (45) by (1/dt). We get ( d ( W ( t ) ) dt ) = - β p · ( F area ) · L · ( d ( p ( t ) ) dt ) ,(46) where (d (W (t))/dt) = (- 1) · (Q (t)-Q₀) is the rate (velocity) of the water volume change with flow time or the volumetric flow rate, dim(d (W (t))/dt) = dim(Q (t)-Q₀) = [(m³)/s] = [(Length³)/(Time)];

(d (p (t))/dt) = (d (p (t)-p₀)/dt) is the rate of the water pressure change with respect to flow time, dim ( d ( p ( t ) ) dt ) = dim ( d ( p ( t ) - p 0 ) dt ) = [ Pa s ] = [ kg ( m · s 3 ) ] = ( ( Mass ) ( Length ) · ( Time ) ) .

The previous equation (46) yields the following expression for the rate of the water pressure change with time (d (p (t))/dt) = (d (p (t)-p₀)/dt):

( d ( p ( t ) ) dt ) = ( - 1 ) · ( 1 β p · ( F area ) · L ) · ( d ( W ( t ) ) dt ) ,(47)

or

( d ( p ( t ) - p 0 ) dt ) = ( ( 1 β p · ( F area ) · L ) · ( Q ( t ) - Q 0 ) ) .(48)

At this point, the instructor directs the students’ attention to this last “hydraulics” expression (48), which has the analogous structure (24) with the previous “employment-related” formula (1) and the “electrical” equation (23): { ( d ( N ( t ) - N 0 ) dt ) = ( α · ( n ( t ) - n 0 ) ) , ( d ( ( U ( t ) - U 0 ) ) dt ) = ( ( 1 C ) · ( I ( t ) - I 0 ) ) , ( d ( p ( t ) - p 0 ) dt ) = ( ( 1 β p · ( F area ) · L ) · ( Q ( t ) - Q 0 ) ) .(49)

The similarity of the three equations in the last triple system (49) means that we can complete the following expanded list of formal algebraic analogies between the “employment” equation (1), the “electrical” equation (23) and the “hydraulics” equation (48): { N ( t ) ⇔ U ( t ) ⇔ p ( t ) ; N 0 ⇔ U 0 ⇔ p 0 ; n ( t ) ⇔ I ( t ) ⇔ Q ( t ) ; n 0 ⇔ I 0 ⇔ Q 0 ; α ⇔ ( 1 C ) ⇔ ( 1 β p · ( F area ) · L ) .(50)

It is time for the technical instructor to derive the second governing equation of hydraulics-based analogy in Fig. 4 by addressing Newton’s second law of motion: M 0 · a water ( t ) = ∑ i ( R i ( t ) ) ,(51) where

M₀ = (ρ_water · W₀) = (ρ_water · (F_area) · L) is the mass of the studied water column within the water pipe;

a_water (t) = (d (V_water (t))/dt) is the water column acceleration;

∑ _i  (R _i  (t)) = R_water (t) = ((- 1) · (Δp_water (t)) ·  (F_area)) = ((- 1) · (p (t)-p₀) · (F_area)) is the resultant hydrodynamic force or the total flow force, applied to the studied water column.

The last equation (51) yields the following form of Newton’s second law for the water column motion within the pressurized water pipe:

ρ water · ( F area ) · L · ( d ( V water ( t ) ) dt ) = ( - 1 ) · ( p ( t ) - p 0 ) · ( F area ) ,(52) or

( d ( ( F area ) · V water ( t ) ) dt ) = ( - 1 ) · ( 1 ρ water · L ) · ( p ( t ) - p 0 ) · ( F area ) ,(53) or ( d ( Q ( t ) ) dt ) = ( - 1 ) · ( ( F area ) ρ water · L ) · ( p ( t ) - p 0 ) ,(54) where

Q (t) = ((F_area) · V_water (t)) is the rate (velocity) of change of the water volume with flow time or the volumetric flow rate, dim(Q (t)) = dim((F_area) · V_water (t)) = [(m³)/s]   =   [(Length³)/(Time)].

At this point, the instructor directs the students’ attention to this last “hydraulics” expression (54), which has an analogous structure (29) with the previous “employment-related” formula (2) and the “electrical” equation (28): { ( d ( n ( t ) ) dt ) = ( - β ) · ( N ( t ) - N 0 ) , ( d ( I ( t ) ) dt ) = ( - 1 L ) · ( U ( t ) - U 0 ) , ( d ( Q ( t ) ) dt ) = ( - ( ( F area ) ρ water · L ) ) · ( p ( t ) - p 0 ) .(55)

The similarity of the three equations in the last triple system (55) means that we can complete the following expanded list of formal algebraic analogies between the “employment” equation (2), the “electrical” equation (28) and the “hydraulics” equation (54): { N ( t ) ⇔ U ( t ) ⇔ p ( t ) ; N 0 ⇔ U 0 ⇔ p 0 ; n ( t ) ⇔ I ( t ) ⇔ Q ( t ) ; β ⇔ ( 1 L ) ⇔ ( ( F area ) ρ water · L ) .(56)

Both systems (50) and (56) yield the following expanded list of the triple analogies: { N ( t ) ⇔ U ( t ) ⇔ p ( t ) ; N 0 ⇔ U 0 ⇔ p 0 ; n ( t ) ⇔ I ( t ) ⇔ Q ( t ) ; n 0 ⇔ I 0 ⇔ Q 0 ; α ⇔ ( 1 C ) ⇔ ( 1 β p · ( F area ) · L ) ; β ⇔ ( 1 L ) ⇔ ( ( F area ) ρ water · L ) .(57)

The instructor additionally addresses formulae (6), (34) and (56) in order to estimate the circular frequency ω of the correspondent oscillations in the social (Figs. 1–2), the electrical (Fig. 3) and the hydraulics (Fig. 4) systems:

ω = ( α · β ) = 1 ( L · C ) = ( 1 β p · ( F area ) · L ) · ( ( F area ) ρ water · L ) = 1 L · ( 1 ρ water · β p ) .(58)

The last equation (58) yields that the period T of the correspondent oscillations is as follows:

T = ( ( 2 · π ) ω ) = ( ( 2 · π ) ( α · β ) ) = ( 2 · π ) · ( L · C ) = ( 2 · π · L ) · ( ρ water · β p ) .(59)

An author-proposed triple analogy-based description of graduate employment oscillations in the labor market (Figs. 1–6 and formulae (1) – (59)) was explained for undergraduate, graduate and postgraduate students of Donbass State Engineering Academy (DSEA, Kramatorsk, Ukraine), majoring in economics cybernetics, industrial economics, management, mechanical engineering, materials science, metallurgy, control & electrical engineering, computer sciences and information technologies.

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Fig.5

Original author-proposed allegorical sketch, illustrating graduate employment problems, when gingerbread butterball-shaped average character of graduate (shown from the left) has numerous practical difficulties with adaptation to different employer requirements, where some employers’ characters are allegorically shown as cuboid figures (at upper level), pyramid figures (at middle level), and star-shaped figures (at lower level). In finding his employment, graduate student disappointedly wonders: “Is it possible to fit employer requirements?” Upper level-located cuboids clamor about the graduate student and ask each other: “Are you sure he is an engineer?” Middle level-located pyramids sadly conclude about the graduate: “Born to crawl - can not fly!” Lower level-located “creative stars” notice with sorrow: “Apples and oranges, baby doll.” Source: Drawing by co-author Alexander G. Kaikatsishvili. Copyright © 2019 Alexander G. Kaikatsishvili.

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Fig.6

The original author’s allegorical sketch, illustrating graduate employment problems, when the gingerbread butterball-shaped average character of graduate (character shown in the upper left) must make his/her own individual choice and decide whether he/she is prepared to work under pressure upon university graduation. Employee characters are allegorically shown as a verdant young tree (shown in the lower left) and as a drying up black tree without leaves (shown at the right). Employer-determined levels of psycho-emotional comfort are allegorically shown as the lush green surroundings in the sunshine (at the lower left) and as lifeless rocks during a lightning storm (at the right). In finding his targeted employment, the graduate student (upper left) impatiently exclaims: “I need a job upon graduation, because I need a ton of money!” The left-located green tree with hassle-free employment notes: “Well, what could be better than the most comfortable conditions of work?” The right-located black tree, with employment under pressure, sadly notices: “Things have been crazy at work. I am afraid that I won’t work long under pressure! I can’t work like this!” Source: Drawing by co-author Alexander G. Kaikatsishvili. Copyright © 2019 Alexander G. Kaikatsishvili.

The technical instructor can start the lecture with a typical humorous story in order to tune up engineering students towards more attentive listening of employment related topics. For example, two acquainted graduate students occasionally get to talking:

Graduate student 1: Colleagues say that you found a job. Where did you find your employment?

Graduate student 2: I have already gained provisional employment in the Labor Office (Centre for Employment). I’m registering unemployed persons. However, they say that this is a temporary job with employment for a maximum of two years.

Graduate student 1: Anyway, that’s wonderful. People say that nothing lasts longer than the temporary. It is nice if you could find a diploma-related professional employment in your field in two years. However, stay in touch with the job center. You could lose your future professional job for changing economic situation. Therefore, your current employment in the job center sounds as the most secure and sustainable workplace!

It is also important for the instructor to make some preliminary comments concerning social phenomena of unemployment before further description of the lecture material. Unemployment can be determined as a socio-economic phenomenon when the able-bodied active-working population is actively seeking jobs and is prepared to proceed to work but still cannot exercise the human rights of labor due to exclusion from the labor market for various reasons.

Numerous university departments and many other higher education institutions “honestly” promise that “100% of university degree holders will successfully find employment in their field of university-specialized education”. It is possible to add numerous literature references for illustration of these “generous promises” but everyone can “google” this search phrase, access this information in his local language and find dozens of related links to the “100% employment” promises of departments and universities.

Initially, in a lecture, the technical instructor explains to students some “top-priority” secrets. It is important to make a brief disclosure and a strong denial of the official bureaucratic information concerning the “perfect theoretical efficiency” of the higher educational system, which formally reports about “100% level of the graduate employment” and consistently denies the existence of any employment oscillations in the labor market, shown in the Figs. 1–2. This fact usually shocks some undergraduate students who cannot believe that the official academy-provided information about excellent educational efficiency of the specific technical university, which promises “successful professional employment” of “100% of engineering graduates”, is not true. Modernly saying, this official information is rather a “post-truth”. Moreover, it is not a hype of the lecturer. The instructor notes that it is a long established practice when engineering graduates provide a university with fake references from a hypothetical place of “successful employment” in order to get their university graduation diplomas.

Therefore, it is a rather generally known “secret” that only about one-third or one-quarter of engineering graduates are able to pursue their professional employment in the engineering sphere immediately after university graduation. The truth is that in several years after university graduation, there are only occasional cases of successful continuing engineering employment of university graduates in a field related to their graduation major. As a result, the long-term yield of university efficiency is 5–20% of successful targeted employment of engineering graduates.

For example, (Sudakova & Mehedyniuk, 2016) have reported that only 42% of university graduates in Ukraine have obtained specialized employment related to their university degree major [16]. At the same time, 65% of these respondents with current specialized employment and specialized university diplomas confirmed that they would like to retrain and change their employment to alternative job positions as soon as possible [16]. Their desired new positions are many times not remotely related to their major field, for which they had spent many years of university education [16].

In this way, the technical instructor explains to engineering students that employment market-related oscillations in the number of employed/unemployed professional specialists, plotted in Figs. 1–2, are real-life-related oscillations, globally observable in the labor markets in all existing socio-economic systems (Figs. 5–6).

At the second stage of the lecturer’s description, the technical instructor has to serve as a psychotherapist for some part of permanently aggressive and self-assured students, majoring in physics and engineering. These students usually try to sabotage a lecture and to stop the instructor’s explanation with their half-hysterical behavior and standard critical mottos of generally philosophical nature.

The typical examples of these “thought-provo-king” and time-burning statements are as follows:

“Social sciences have neither scientific novelty nor research merit!”

At this point, the technical instructor politely explains that, socially saying, the present educational description is not very ambitious. Engineering students should consider the present didactical material as rather simple intellectual exercise, directed towards an original three-way derivation of the similar analogous oscillatory equations, independently derived from economic (Figs. 1–2 and formulae (1) – (12)), electrical (Fig. 3 and formulae (13) – (39)) and hydraulics (Fig. 4 and formulae (40) – (59)) considerations.

The best way for an instructor to stop these never-ending emotional discussions is to note the following proposition. If the gathered students are so smart, they are kindly encouraged to advise the technical instructor with student-suggested hints, related to physical and mathematical aspects of original instructor’s explanation. Otherwise, if available students are not qualified for constructive suggestions, these people are encouraged to listen to the instructor attentively and without extra comments. Usually all non-relevant extra discussions are successfully stopped at this stage.

At the third stage of the lecturer’s description, he/she addresses the concept of analogous modeling and similarity-based simulation as applied to the subjects of education of scientific disciplines (Kostikov et al., 2017 [17]; Perig, 2017 [18]) and education & educational research (Liuta et al., 2019 [19]; Perig et al., 2017 [20]; Perig, 2018 [21]; Perig et al., 2018 [22]; Perig, 2019 [23]; Perig et al., 2019 [24]; Svyetlichnyy et al., 2019 [25]).

It was surprising to engineering students to see that the dynamics of complex multi-physical behavior of technical systems in the inanimate world and social physics of the non-linear behavior of human society with responsible, rationally thinking human individuals are subject to the same general laws, which can be described with analogous differential equations of a similar mathematical structure.

To save educational time, the lecturer can address this student question through the following intuitive, although rather naïve, but quick and simple explanation. The instructor agrees with students that all humans have individual thinking independently of one another. However, statistically speaking, the lecturer emphasizes that the pattern of statistically significant behavior of a heavy accumulation of individual independent people is mathematically described under one and the same laws of statistical mechanics, which were initially developed for the behavior of the statistical ensemble (assembly) of electrons and atoms. The instructor notes that the differential equations are widely used in scientific and engineering curricula for deterministic expressions of physics-inspired statistical laws. The lecturer adds that both analytical and numerical solutions of the initial-boundary value problems for the differential equations are defined by the initial conditions and the boundary conditions. At this point, the instructor jumps into the following generalized and non-obvious conclusions:

The boundary conditions for an aggregate of electrons are defined by the specific commutation of the elements of the electrical circuit for an LC-field-effect transistor oscillator in Fig. 3;

The next student’s question has been raised as to whether or not the energy conservation law has or has not been violated during the working process of a hydraulic ram pump in Fig. 4. Many engineering students were rather puzzled by the fact that the potential energy of the water, flowing from the lower left tank A into the upper right tank E, increases in Fig. 4. The technical instructor, replying to this fluid-related question, explained that water, passing through the gate valve 1 (one), transfers a part of its energy to the upward propagating DE water flow, which rising into the upper water tank E along the right hand-side located pipe DE in Fig. 4.

The engineering students also asked some clarifying questions such as “How is the steady state regime for electrical oscillations of an LC-field-effect transistor circuit in Fig. 3 established?” This student question can be answered quite simply. The instructor noted that self-induced e.m.f. voltage, which arising within an inductance coil with increasing intensity of drain current, is the trigger for the appearance of electrical oscillations in Fig. 3. This self-induction Faraday voltage generates a capacitor-charging rate.

The engineering students attempted to extend this triple analogy even farther. Students were surprised with the fact that both electrical oscillations, generated during the work of an LC-field-effect transistor oscillator (Fig. 3), and mechanical oscillations, produced during the work of a hydraulic ram pump (Fig. 4), have the constant amplitudes and periods whereas these characteristics are less strictly fixed in the case of unemployment oscillations (Figs. 1–2). In this regard, the lecturer noted that it is possible to regulate the amplitudes and periods of the oscillations in the studied electrical scheme through changing of the condenser capacitance and alteration of the power supply voltage for the electrical circuit in Fig. 3. The instructor suggested that, technically speaking, we could control the amplitudes and periods of the oscillations in the studied hydraulics scheme through the variation of the elevation height of the water tanks and the regulation of the operating threshold levels for the gate valves in Fig. 4.

At this point, naturally, a new student question has been raised as to whether it might be possible to regulate the amplitudes and periods in the unemployment curve oscillations, to minimize unemployment oscillations, and completely eliminate unemployment in Figs. 1–2. The instructor noted that these efforts have been undertaken at the global level. In some countries, there are the socialism-inspired legislative initiatives, which would require mandatory payment of unemployment benefits to unemployed graduate students through the budget of the education establishment from which they had graduated. There are also the similar initiatives that the high cost for reeducation and retraining of unemployed graduate student with a different high-demand specialty would be forcedly covered through the budget of the university, which unemployed person graduated from. Another approach is focused on seeking a way to conclude a trilateral agreement between engineering student, technical university and employing company, when the company pays the university tuition fees and guarantees the graduate employment. The company always has the opportunity to terminate the signed trilateral agreement in the case of unacceptably low levels of educational achievement of the student. The instructor notes that a Chinese case shows some effectiveness of government management of the planned economy for the purpose of unemployment minimization. However, the social attractiveness of the economically successful authoritarian state with persistent human rights violations is rather questionable.

As usually, the fact of graduate employment is an excellent practical opportunity to switch graduate’s attention from individual problems to more constructive direction of social integration (Figs. 5–6).

One of the serious drawbacks of modern university education is the domination of a verbal form of communication during learning and instruction, which leads to negative final results for educators and learners. Highly-specialized classroom education is dominated by analytical and theoretical approaches focused on student understanding of abstract universal concepts, information and ideas. Quite often, this educational information neither contributes to empathy formation nor practically helps engineering students in applied professional activity. Therefore, in our opinion, it is possible to achieve effective formation of a high-level student’s empathy through exceeding the limits of university auditoriums, e.g. through creation of integrated educational, scientific and practical thought incubators, which will help to strengthen the transformation of engineering education into effective small-scale industry. A creative atmosphere of industry/academy complexes will help students acquire both professional and empathy-related skills through regular business communication with colleagues, through prompt solution of applied specific problems, and through development of solidary way of team communication and behavior.

One of the best ways for a company to ultimately recruit highly productive engineers is to develop a cooperative work/study program with one or more universities. The student’s education takes more time to complete, but when he does graduate his chances of finding a good job are greatly increased.

Several good things happen during a work/study program:

The student becomes much more familiar with what his job would be if he were offered a permanent job by this company.

Sometimes the student sees that he should make changes in his course of study to better prepare him for the job. By doing so, he increases his chances for a job upon graduation.

The company gets experience with the student and fellow engineers and supervisors can evaluate the student’s performance on the job.

The company can place the student in several types of jobs during his work /study program, allowing both the company and the student to look “outside the box” of his current specialty and see if he might fit better in something else.

Sometimes graduate’s creativity and talent are well appeared in adjacent spheres to the main student’s specialty. Broadening a student’s education to include courses unrelated to his current major can sometimes be like “taking the blinders off a horse.” He sees something that interests him far more than what he thought his interests were when he enrolled. Of course, he does need to stabilize quickly and do the hard work required to change and not become like a “blind dog in a meat market.” This alternative graduate’s advances in non-major field may practically help graduate person to get successful employment in the best-fitted alternatively available vacancy. E.g., student’s job placement in a creative position of a design artist is a sound example of successful alternative graduate’s employment at IT-company or factory.

A student’s certainty in finding a good job goes up tremendously when he graduates not only as a good student, but one with experience in his desired field. All graduate engineers require “on the job training” before they become useful to a company. A graduate may be an expert in mathematics, physics, chemistry, mechanics, or computer technology, but until he can demonstrate that he can create or accomplish something useful by applying his knowledge, he is of little use to the company. Availability of stable and sustainable student’s interest to practical solution of specific class of applied engineering problems usually helps the further successful graduate’s employment within targeted interest-driven direction.

As usually, practical instructor’s involvement in a regular individual solution of applied scientific-technical problems triggers derivative student’s interest in lecturer’s-inspired subject area with growing possibility of the further successful employment of engaged and devoted graduates. Use of social sciences in this case takes place at the level of continuing engineering education within facultative in-depth study.

Work/study programs are not always available for a variety of reasons, perhaps not supported by the university, no companies with work/study programs, etc. But, even if we stop short of such programs, it is still very helpful and productive to the engineering student to allow and encourage diversity in his education. This should be done, not as a simple addition to the student’s workload, but as an integral part of the curriculum. Educators could make tremendous improvements in engineering education by creating new 21st century curricula with this principle in mind.

9 Importance of soft skills development for successful employment: Can the humanities and social sciences help?

However, a full-scale creation and global implementation of industry-academy collaborative centers is probably an expression of idealized ambitions. So, face-to-face auditorium training still remains the dominant of global technical university system and some isolation of engineering students from communication with applied practical problems of industry will remain in the near future. Therefore, a question presents itself, how it is possible to enhance the level of graduate student empathy under present curricula conditions? And, if so, what might the role of social sciences be in the process of graduate empathy development?

Authors propose that both social sciences and humanities may help graduate students in empathy formation.

However, it is possible to achieve a good social sciences-enhanced impact on university education by applying an effective learning strategy to the system of technical disciplines. It is important to ensure a better understanding of the place of the student specialty among alternative majors and specializations. More rigorous engineering curricula should be not a simple set of unbound technical and social disciplines but should be a unified logical system of interconnected branches of the global system of properly narrated educational disciplines. For example, the modern biologist needs physics in the same way as a modern physicist requires biology because the organic form of matter contains the physical form of matter in indirect sublated form (Hegel’s “Aufhebung”) and this mediated sublated form better discloses the identity of matter. The classical Hegel’s philosophy teaches us that social sciences contain both mechanics, chemistry and biology in a sublated (indirect) form of “Aufhebung”. In fact, social sciences help engineering students understand the surrounding complex world as a whole and to think clearly, significantly and critically.

Social sciences may help engineering students develop more efficient imagination, sensuality and sensibility, which are the sources of creative thinking and empathy of future engineers. Social sciences help stimulate weakly involved segments of the student mind and enhances an engineering student’s understanding of the world as a whole and himself on a basic level. General student understanding of the world at large allows him to see the main trends of development, observe social, economic and political processes and risks, and be able to estimate the usefulness and the necessity for products of student activity. Social sciences-inspired student self-understanding will ensure more effective engineering productivity because proper understanding of one’s personal life and career is the best way to realize who you are and who you are not.

However, at this point we should better explain the necessary enhanced requirements for teaching social sciences in national engineering education curricula. Quite often, many national engineering education systems show a serious imbalance when engineering undergraduates study numerous individual courses of national history, history of national culture, national business language but the philosophy course is restricted to only one single discipline. Moreover, most technical universities are constrained to teaching only the history of philosophy, rather than a philosophy course because there are no available teaching hours of classroom instruction in applied questions of practical philosophy, logic, and the methodology of world cognition. However, student’s mechanical study of numerous historic days and grammatical rules mainly leads to memory training via memorization of large volume of instructional information. Unfortunately, the student’s focus on the acquisition of information restricts both creative thinking, sensibility and empathy.

10 Discussions

The tendency of university education has been to train single-function and narrowly focused specialists. This tendency has a serious disadvantage when narrow focused specialists have been unable to accomplish prompt cross-training and obtain employment in area-rotated major-related alternative fields and occupations. As a result, excess narrowly focused specialists are forced to accept unqualified low-paying downgrading odd-jobs at low-skill and entry-level positions, which are usually “generously” offered to them. A possible solution to this problem would be to provide university graduates with an additional high-demand work specialty (i.e. welder, locksmith, plasterer, plumber, barber, cook, ornamental casting specialist, artistic forging specialist etc.) and related work skills through applied technical education. It is possible to improve the quality of life of graduate students if under-employed university graduates are prepared for temporary employment in a working specialty, which is closely associated to their university major instead of occasional employment in unqualified low-paying odd jobs. This valuable student work experience in a working specialty for several months will considerably improve the graduate’s chances of targeted university major-associated employment in the future.

Graduate students should benefit from a more fundamental in-depth engineering education and must be better informed on all matters relevant to similar and closely related specialties together with specific knowledge in narrow engineering specialization. A broader engineering education should improve a graduate’s employment chances in adjacent specialties where unemployment value n^* = n^*(t) is lower than in main specialty of graduation major.

The combination of practical experience with the nuts and bolts of a specific technical area, such as the aircraft or automotive industries, and a graduate engineering degree is far more productive for both the employer and the employee when it occurs. A good example (although rare) was an air force non-commissioned officer with 15 years’ experience as an aircraft mechanic, crew chief, and instructor. After 15 years, he left the air force and went to the university. He graduated with a BS degree in aeronautical engineering. Because of his degree and his years of practical experience with a variety of aircraft, he was hired as an aeronautical research engineer and did excellent highly productive work for the next 20 years.

The universities should keep the labor market situation with graduate employment under review in the light of regular improvement and timely enhancement of engineering curricula for undergraduate, graduate and postgraduate students. It is possible to improve the quality of life of graduate students and to enhance their chances with specialty-associated targeted employment if universities will participate in a full-scale graduate tracking system with the aim of forecasting the trends in behavior of both graduates and employers. Technical universities should additionally study unemployment periodicity, to make monitoring the labor market perspectives in view of establishment and the opening of new regional industries and enterprises. Universities should make timely corrections of turn-out of specialists within the range of graduation majors. Literally, it is possible to make major curriculum corrections even for the year before graduation of new university-trained specialists. Real university activity toward partially-successful real graduate employment would be much more efficient and important than the commonly-used bureaucratic games when universities usually make formal official declarations that “100% of university graduates successfully employed according to their university major” and university has already received the “formal confirmation of successful 100% targeted employment”. However, it is not a secret that this official information has nothing in common with objective reality.

Instructor adds that the long-term development of a market economy may result into disruption of growth periodicity in a form of a disastrous economic crisis. The states attempted to take action in order to smooth and reduce fluctuations of economic indicators in order to prevent the occurrence of similar economic crises in the years to come. Engineering students should be aware that the fundamentals of state regulation were comprehensively addressed in the numerous existing economic theories, e.g. in Keynesian economics (Keynesianism) and monetarism. The states must take action in order to smooth and reduce fluctuations in the quantity of unemployed citizens by coordinating or directly managing turn-out and employment of university graduated specialists. Wise state regulation of turn-out of university-trained specialists is very important for prevention of crisis-induced social and political instability.

However, most of highly qualified research engineers think it is a total waste of time for engineering students to study all the weird economic theories as a way to choose a well-employed career. Economic ups and downs and the related unemployment are very cyclical, affected by political leanings, wars, trade wars, power struggles etc. At the moment, in April 2019, the US unemployment rate is 3.8%, the lowest in 18 years, resulting in a “tightening” labor force. The usual result is high wages. Sometimes this leads to inflation. Sometimes the government dumps money into such things as building up infrastructure to increase employment. During the great depression of the 1930’s the US government put a lot of money into public works to give people jobs. They built libraries, flood levees, national parks, etc. i.e. things that private enterprise would never do. But high US government spending leads to high US government debt, like USA have now. It is a very complex and never-ending problem.

A student has to use his common sense and be aware of the economic situation he will graduate into. For example, retired NASA engineer would never advise a student now to major in aeronautical engineering like he did. The aircraft US industry has shrunk to about a tenth of what it was in 1960. Majoring in something else is a no-brainer. Less specialization is usually better because a mechanical or electrical engineer will have his specialization guided by his employment. He is placed where he is needed and that will be the start of his specialization. A graduate with a mechanical or electrical or industrial engineering degree and some practical exposure to the trades can easily be trained on the job to meet the employer’s requirements and ensure a long-lasting employment.

11 Conclusions

The problem of graduate unemployment is a widespread problem for young professional specialists, which results in imposing a heavy burden on society with severe socio-economic and psychosocial consequences at the individual and community-societal levels.

Higher education is globally considered as a way to prevent and reduce unemployment at the regional and global labor markets. However, even a higher education diploma does not guarantee sustainable employment for a young professional specialist upon university graduation. An ongoing need for guaranteed gainful employment is not only a problem of individual graduates and universities but this burden also impacts the socio-economic condition of modern society itself.

Paper authors suppose that successful graduate employment requires the completion of the following educational assignments by modern engineering student:

Understanding the fundamental trends in development of economics and technology;

A decline in production takes place during a recession. However, the industrial vertical unions prevent arbitrary termination of employment of workers. Therefore, reduction in the number of employees takes place mainly through attrition from retirements (pensioner retirement). However, company retirement is usually not mandatory and many times is insufficient to offset the decline in employment of young professionals who would like to replace retired specialists. Young professionals have a chance for successful employment mainly in the case of an upturn in production. Therefore, numerous third-world eternally-“developing” countries, who have experienced a permanent economic crisis for many decades, become constant providers of an affordable, cheap and hardworking labor force in the global employment market.

The present paper is the first authors attempt to address the problem of graduate employment oscillations. The paper has a number of the following research limitations, which are associated with boundedness of the aims and scopes of the present scientific article. Ethical issues of graduate student employment fall outside the research focus of the paper. Student-instructor conversation analysis was outside the paper aims and scope as well.

Further social research efforts will be associated with sustainability-related thematization of micro-level of social practice of graduate employment in order to analyze how interviewees construct their individual behavior and interpret the conduct of another with regard to possible graduate employment and unemployment.

Further research efforts will be directed toward analysis of open access data concerning unemployment oscillations over a long period of time in order to verify the author-proposed triple analogy and to propose an immediate unemployment forecast for the near future.

Further research studies in this direction will be associated with the development and analysis of more sophisticated socio-economic models for a quantitative phenomenological description of graduate employment problems. In particular, it sounds attractive and perspective to apply computational techniques of the mathematical theory of parabolic differential equations and to implement the methods of mass transport-related diffusion equations to a simulation of employment-related “diffusion” of employees as they make their labor way from university graduation to the targeted potential workplace. Probably it will be necessary to take into account the different computational cases for the constant and variable values of labor market-related “diffusion coefficients” for the different cases of graduate employment.

Additional computational challenges in further studies will be associated with quantified accounting of new employment-friendly effects, related to the description of individual empathy and soft skills development in engineering graduates. It will be highly interesting to make an additional mathematical description of short-term working and long-term effective soft skills, which provide substantial improvement of the chances and opportunities for successful graduate employment.

Authors’ contributions

All authors participated in the design of this work and performed equally. All authors read and approved the final manuscript.

Competing interests

The authors declare that they have no competing interests.

Conflict of interest

The authors Alexander V. Perig, Nikolai N. Golodenko, Roman S. Martynov, and Alexander G. Kaikatsishvili declare that there is no conflict of interest regarding the publication of this paper.

Data availability statement

Some or all data, models, or code generated or used during the study are available from the corresponding author by request: “Graduate Employment Oscillations 2019.xlsx”

Funding

The authors have no funding to report.