Journal of Computational Methods in Sciences and Engineering

We make an endeavor to study and analyze the effect of surface roughness on the performance of a magnetic fluid based squeeze film between conical plates. The lubricant used here is a magnetic fluid and the external magnetic field is oblique to the lower plate. The bearing surfaces are assumed to be transversely rough. The roughness of the bearing surface is modeled by a stochastic random variable with non-zero mean variance and skew-ness. The associated Reynolds' equation is solved with appropriate boundary conditions to get the pressure distribution, which is, then used to obtain the expression for load carrying capacity leading to the computation of the response time. The results are presented graphically as well as in tabular form. It is noticed that although the bearing suffers owing to transverse surface roughness, the load carrying capacity registers an increase in the case of negatively skewed roughness. Even the negative variance causes an increase in the load carrying capacity. It is observed that the reduction in the load carrying capacity induced by the porosity and the standard deviation can be neutralized up to certain extent by the positive effect of the magnetization parameter μ* with suitable values of the semi-vertical angle ω in the case of negatively skewed roughness. A close scrutiny of some of the results presented graphically makes it clear that the positive effect of variance dominates the effect of the skew-ness whose impact is slightly better than that of the magnetization parameter. It is needless to say that the performance of the rough bearing with the magnetic fluid lubricant is definitely better than the one with conventional lubricant. This article reveals that there is a scope for enhancing the performance of the bearing system considerably by choosing a suitable combination of the magnetization parameter and semi-vertical angle of the cone in the case of negatively skewed roughness especially when negative variance is involved.

Consider a planar annulus. A result of Ramm and Shivakumar states that as the inner circle moves toward the outer circle, the principal Dirichlet eigenvalue of the Laplacian decreases. Numerical experiments in that paper clearly verify this result. The purpose of this short note is to fill in a small gap in that paper: the numerical calculation of the principal eigenvalue when the two circles touch. This is a non-trivial numerical problem because the domain has a cusp which is a strong singularity. Adaptive finite element methods have difficulty converging in the presence of such singularities. Our method is to perform a transformation taking the domain to a rectangle, where it is relatively straightforward to compute the principal eigenvalue. We also calculate the minimal (non-zero) eigenvalue of the Neumann problem. Numerically, the Neumann eigenvalue has no such monotonicity property.

We show simulation techniques that enable to computationally bridge from the atomistic up to the mesoscopic scale. To evaluate the efficiency, we use a phase-field method to simulate symmetric thermal dendrites and start the computation at an early stage of solidification related to nucleation. The early structures are taken from the molecular dynamics method. The proposed techniques allow to simulate three dimensional dendrites from the state of nuclei (≈ 50 Å) up to a size proportional to μ m where ternary side-arms start to grow.

Three-party key exchange protocol is one of the most essential cryptographic technique in the secure communication areas. In this protocol, two clients, each shares a human-memorable password, working with a trusted server, can agree a secure session key. Recently, Lu and Cao proposed a new simple three-party key exchange (S-3PAKE) protocol and claimed that it is not only very simple and efficient, but also can survive against various known attacks. However, Nam et al. pointed out that S-3PAKE is vulnerable to both off-line password guessing attack and undetectable on-line password guessing attack. Based on their finding, Nam et al. proposed an improved method to resolve this weakness. They further claimed that so far no off-line password guessing attack has been successful against their proposed protocol. In this paper, we demonstrate that Nam et al.'s improved protocol, unfortunately, is still vulnerable to an undetectable on-line password guessing attack. We therefore propose a simple and powerful method to address this issue. Which results in an improved three-party key exchange protocol that can protect against an undetectable on-line password guessing attack.

To obtain the maximum drag profiles for the surface of an object located in unsteady flow, a shape optimization algorithm based on an adjoint method is presented. The adjoint method is based on the Lagrange multiplier method. Using a first variation of the Lagrange function, stationary conditions can be derived. These conditions consist of state equations, adjoint equations, and sensitivity equations with boundary conditions. The sensitivity equations are derived based on the shape derivative and the material derivative. To achieve the optimal shape based on these stationary conditions, a smoothing technique, a constant volume technique, a node relocation technique, the SUPG/PSPG stabilized method, and the GPBi-CG solver are implemented in the shape optimization algorithm. Using this algorithm, under Stokes flow, we can obtain the Pironneau's result found in the literature (where the optimal shape is of the rugby ball type). Under unsteady flow (i.e. for a Reynolds number of 1000), this algorithm can also construct an optimal shape. Compared an initial cylindrical shape, the drag of the optimal shape under constant volume can be increased by about 218% in the case of a Reynolds number of 1000.

Parastatistical macroscopic classical systems with distinguishable states (cells) and arranged state occupation (IDA-systems) are considered. In one-dimensional case (IDA1-systems) they are shown to be equivalent to the systems with indistinguishable elements and states (II-systems). In two-dimensional case (IDA2-systems) they require special approach. Their microscopic states are associated with one- and two-dimensional Young diagrams, respectively. Macroscopic states are defined as neighbourhoods of microscopic ones. Explicit expressions for probabilities and entropies of macroscopic states are derived. Analysis of equilibrium states reveals shell-type mechanism of growth for IDA-systems.