In this paper the hybrid approach is presented for the modelling of complex systems that involve many interacting components with different physical properties over different spatial and temporal scales. Such systems are difficult to resolve, since they exhibit high levels of uncertainty. We briefly discuss other modelling strategies and their advantages and disadvantages and then a complete description of the mathematical-computational hybrid framework is given. Then, an application from the field of particulate-based engineering processes is presented and the ability of the framework is demonstrated to accurately represent key granular material processes with the aid of information extracted from different scales.
Bar-YamY., Dynamics of Complex Systems, 1st ed., Addison-Wesley:Reading, Massachusets, 1997.
2.
WeaverW., “Science and complexity”, American Scientist, Vol. 36, pp. 536–544, 1948.
3.
OttinoJ.M., “Complex Systems”, AIChe Journal, Vol.49, pp. 292–299, 2003.
4.
SimonH.A., “The Architecture of Complexity”, Proc. American Philosophical Society, Vol. 106, pp. 467–482, 1962.
5.
ParnasD., “On the criteria to be used in decomposing systems into modules”, Comm. ACM, Vol. 15, pp. 1053–1058, 1972.
6.
HarelD., “Statecharts: A visual formalism of complex systems”, Science of Computer Programming, Vol. 8, pp. 231–274, 1987.
7.
StermanJ., “Learning in and about complex systems”, System Dynamics Review, Vol. 10, pp. 291–230, 1994.
8.
HakenH., Information and self-organization: A macroscopic approach to complex systems, 3rd ed., Springer: Berlin. Heidelberg, New York, 2006.
9.
GuckenheimerJ. and OttinoJ.M., Foundations for complex systems research in the physical sciences and engineering, Report from an NSF Workshop, September 2008.
10.
AchesonD., From calculus to chaos: An introduction to dynamics, 1st ed., Oxford University Press: New York, 1998.
11.
Larsen-FreemanD. and CameronL., Complex Systems and Applied Linguistics, 1st ed., Oxford University Press: New York, 2008.
12.
GonzalezM.C.HindalgoC.A. and BarabásiA.L., “Understanding individual human mobility patterns”, Nature, Vol. 453, pp. 779–782, 2009.
13.
ShaliziC.R., “Methods and techniques of complex systems science: An overview”, in Complex Systems Science in Biomedicine, DeisboekT. S. and KreshJ. Y., Eds., New York: Springer-Verlag, 2006, pp. 33–114.
von NeumannJ., The Theory of Self-Reproducing Automata, BurksA.W. Ed., University of Illinois Press: Champaign IL, 1966.
16.
GheorgheA.V. and VamanuD.V., “Forest fire essentials: A cellular automaton-wise, percolation-oriented model”, International Journal of Critical Infrastructures, Vol. 4, pp. 430–444, 2008.
WolframS., A New Kind of Science, 1st ed., Wolfram Media: Champaign, IL, 2002.
19.
FrischU.HasslacherB. and PomeauY., “Lattice-gas automata for the Navier-Stokes equations”, Physical Review Letters, Vol. 56, pp.1505–1508, 1986.
20.
ChopardB. and DrozM., Cellular Automata Modeling of Physical Systems, 1st ed., Cambridge University Press: Cambridge, 1998.
21.
NorthM.J. and MacalC.M., Managing Business Complexity: Discovering Strategic Solution with Agent-based Modeling and Simulation, 1st ed., Oxford University Press: New York, 2007.
22.
SchellingT., Micromotives and Macrobehavior, 1st ed.WW. Norton & Co., 1978.
23.
TesfatsionL., “Agent-based Computatioal Economics: A Constructive Approach to Economic Theory” in Handbook of Computational Economics: Volume 2, Agent-based Computatioal Economics, TesfatsionL. and JuddK. L., Eds., Amsterdam: Elsevier, 2006, pp. 831–880.
24.
SucciS., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond: 1st ed., Oxford University Press: New York, 2001.
25.
DornP. and HughesD., Self-Organized Criticality in Cellular Automata, MSci Project Report, Imperial College, London, UK, May 2000.
26.
BuchananM. and CaldarelliG., “A networked world”, Physics World, Vol. 23, February 2010, pp. 22–24.
27.
ChristakisN.ChapelleP.StrusevichN.BridleI.BaxterJ.PatelM.K.CrossM.TüzünU.ReedA.R. and BradleyM.S.A., “A hybrid numerical model for predicting segregation during core flow discharge”, Advanced Powder Technology, Vol. 17, pp. 641–662, 2006.
28.
KushnerM.J., “Hybrid modelling of low temperature plasmas for fundamental investigations and equipment design”, Journal of Physics D: Applied Physics, Vol. 42, September 2009, 194013, doi: 10.1088/0022-3727/42/19/194013.
29.
MehtaA. and BarkerG.C., “The dynamics of sand”, Reports on Progress in Physics, 57, 1994, doi: 10.1088/0034-4885/57/4/002.
30.
ChristakisN.ChapelleP. and PatelM.K., “Analysis and Modelling of Heaping Behaviour of Granular Mixtures within a Computational Mechanics Framework”, Advanced Powder Technology, Vol. 17, pp. 383–398, 2006.
31.
ChristakisN.PatelM.K.CrossM.TüzünU.BaxterJ. and Abou-ChakraH., “Predictions of segregation of granular material with the aid of PHYSICA, a 3D unstructured finite volume modelling framework”, International Journal of Numerical Methods in Fluids, Vol. 40, pp. 281–291, 2002.
32.
de GennesP.G., “Reflections on the mechanics of granular matter”, Physica A, Vol. 261, pp. 267–293, 1998.
33.
OttinoJ.M., “Granular matter as a window into collective systems far from equilibrium, complexity and scientific prematurity”, Chemical Engineering Science, Vol. 61, pp. 4165–4171, 2006.
34.
PohlmanN.A.OttinoJ.M. and LueptowR.M., “Unsteady granular flows in a rotating tumbler”, Physical Review E, Vol. 80, 031392, 9 pages, 2009.
35.
TardosG.I., “A flow mechanistic approach to slow, frictional flow of powders”, Powder Technology, Vol. 92, pp. 61–74, 1997.
36.
KarlssonT.KlisinskiM. and RunnesonK., “Finite element simulation of granular material flow in plane soils with complicated geometry”, Powder Technology, Vol. 99, pp. 29–39, 1999.
37.
LangstonP.A.TüzünU. and HeyesD.M., “Discrete element simulation of internal stress and flow fields in funnel flow hoppers”, Powder Technology, Vol. 85, pp. 153–169, 1995.
38.
ClearyP.W. and SawleyM.L., “DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge”, Applied Mathematical Modelling, Vol. 26, pp. 89–111, 2002.
39.
BaxterJ.TüzünU.BurnellJ. and HeyesD.M., “Granular dynamics simulations of two-dimensional heap formation”, Physical Review E., Vol. 55, pp. 3546–3554, 1997.
40.
BaxterJ.Abou-ChakraH.TüzünU. and LampteyB.M., “A DEM simulation and experimental strategy for solving fine powder flow problems”, Chemical Engineering Research & Design, Vol. 78, pp. 1019–1025, 2000.
41.
Abou-ChakraH.TüzünU.BridleI.LeaperM.C.BradleyM.S.A. and ReedA.R., “Assessing the potential of a fine powder to segregate using laser diffraction and sieve particle measuring techniques”, Advanced Powder Technology, Vol. 14, pp. 167–177, 2003.
42.
BaxterJ.GrogerT.Abou-ChakraH.TüzünU.ChristakisN.PatelM.K. and CrossM., “Micro-mechanical parametrisations for continuum modelling of granular material using the discrete element method”, Fifth World Congress on Computational Mechanics, 7–12 July 2002, Vienna, Austria, ISBN3-9501554-0-6, http://wccm.tuwien.ac.at.
43.
ArnoldP.C.MacLeanA.G. and RobertsA.W.SolidsBulk: Storage, Flow and Handling, TUNRA Bulk Solids Handling Research Associates, University of Newcastle, NSW, Australia, 1982.
44.
NeddermanR.M., “The use of the kinematic model to predict the development of the stagnant zone boundary in the batch discharge of a bunker”, Chemical Engineering Science, Vol. 50, pp. 959–965, 1995.
45.
SalmanA.D.HounslowM.J. and VerbaA., “Particle fragmentation in dilute phase pneumatic conveying”, Powder Technology, Vol. 126, pp. 109–115, 2002.
46.
Abou-ChakraH.TüzünU.BridleI.LeaperM.C.BradleyM.S.A. and ReedA.R., “An investigation of particle degradation by impact within a centrifugal accelerator type degradation tester”, Proceedings of IMechE. Journal of Process Mechanical Engineering, Part E., Vol. 217, pp. 257–266, 2003.
47.
AustinL.G., “Introduction to the mathematical description of grinding as a rate process”, Powder Technology, Vol. 5, pp. 1–17, 1971/1972.
48.
ChapelleP.Abou-ChakraH.ChristakisN.PatelM.K.Abu-NaharA.TüzünU. and CrossM., “Computational model for prediction of particle degradation during dilute phase pneumatic conveying: The use of a laboratory scale degradation tester for the determination of degradation propensity”, Advanced Powder Technology, Vol.15, pp. 13–30, 2004.
49.
ChapelleP.ChristakisN.Abou-ChakraH.BridleI.BradleyM.S.A.PatelM.K. and CrossM., “Computational model for prediction of particle degradation during dilute phase pneumatic conveying: Modelling of dilute phase pneumatic conveying”, Advanced Powder Technology, Vol. 15, pp. 31–50, 2004.
50.
LeaperM.C.BradleyM.S.A.CleaverJ.A.S.BridleI.ReedA.R.Abou-ChakraH. and TüzünU., “Constructing an engineering model for moisture migration in bulk solids as a prelude to predicting moisture migration caking”, Advanced Powder Technology, Vol. 13, pp. 411–424, 2002.
51.
LeaperM.C.BradleyM.S.A.CleaverJ.A.S.BridleI.ReedA.R.Abou-ChakraH. and TüzünU., “Measuring the tensile strength of caked sugar produced from humidity cycling”, Proceedings of IMechE. Journal of Process Mechanical Engineering, Part E., Vol. 217, pp. 41–47, 2003.
52.
WangJ.ChristakisN.PatelM.K.LeaperM.C. and CrossM., “A Computational Model of Coupled Heat and Moisture Transfer with Phase Change in Granular Sugar During Varying Environmental Conditions”, Numerical Heat Transfer, Part A, Vol. 45, pp. 751–776, 2004.
53.
TanakaT., “Evaluation the caking strength of powders”, Ind. Eng. Chem. Prod. Res. Dev., Vol. 17, pp. 241–246, 1978.
54.
ChristakisN.WangJ.PatelM.K.BradleyM.S.A.LeaperM.C. and CrossM., “Aggregation and caking processes of granular materials: Continuum model and numerical simulation with application to sugar”, Advanced Powder Technology, Vol. 17, pp. 543–565, 2006.
55.
ChristakisN.ChapelleP.PatelM.K.CrossM.BridleI.Abou-ChakraH. and BaxterJ., “Utilising Computational Fluid Dynamics (CFD) for the Modelling of Granular Material in Large-Scale Engineering Processes”. In: SllotP.M.A.TanC.J.K.DongaraJ.J.HoekstraA.G. (Eds). Lecture Notes in Computer Science 2329: Computational Science-ICCS 2002, Springer-VerlagBerlin Heidelberg, pp. 743–752, 2002.
56.
ChapelleP.ChristakisN.WangJ.StrusevichN.PatelM.K.CrossM.Abou-ChakraH.BaxterJ. and TüzünU., “Application of simulation technologies in the analysis of granular material behaviour during transport and storage”, Proceedings of the I MECH E Part E: Journal of Process Mechanical Engineering, Vol. 219, pp. 43–52, 2005.
57.
SalterG.F., Investigations into the Segregation of Heaps of Particulate Materials with Particular Reference to the Effects of Particle Size, Ph.D. Thesis, University of Greenwich, UK, 1999.
58.
BradleyM.S.A. and MillsD., “Approaches to dealing with the problem of energy loss due to bends”, Proc. 13th Powder & Bulk Conference, Rosemont, Illinois, USA, pp. 705–715, 1988.
59.
HyderL.M., The effect of particle size and density on pressure gradients in horizontal pipelines in lean phase pneumatic conveying, PhD Thesis, University of Greenwich, UK, 1999.
60.
EngblomN., Segregation of powder mixtures in silos with particular reference to dry mineral-based construction materials, PhD Thesis, Abo Akademi University, Finland, 2012.
61.
XuC.L.LiangC.ZhouB. and WangS.M., “HHT analysis of electrostatic fluctuation signals in dense-phase pneumatic conveying of pulverized coal at high pressure”, Chemical Engineering Science, Vol. 65, pp. 1334–1344, 2010.
62.
ZambraC.E.MoragaN.O. and EscudeyM. M., “Heat and mass transfer in unsaturated porous media: Moisture effects in compost piles self-heating”International Journal of Heat and Mass Transfer, Vol. 54, pp. 2801–2810, 2011.
ChristakisN. and VairisA., “An analytical description of the frictional behaviour of a Titanium alloy”, Research Letters in Material Science, ID 92170, 4 pages, 2007, doi: 10.1155/2007/92170.
