Transactions on Computational Science VII

This paper deals with the construction of numerical solution of nonlinear random matrix initial value problems by means of a random Euler scheme. Conditions for the mean square convergence of the method are established avoiding the use of pathwise information. Finally, one includes several illustrative examples where the main statistics properties of the stochastic approximation processes are given.

This paper discusses a discrete-time Geo/G/1 retrial queue with impatient customers and server subject to starting failures. Retrial times are assumed to follow a geometric distribution. For the balking customers case, the generating functions of the orbit size and the system size distributions are obtained. Hence, performance measures of interest are derived and examined numerically. Recursive formulas are built up to facilitate computing important distributions. For the general case, a simulation study is built up to investigate the effect of impatience on the system performance.

In this paper, the diffusion equation under square and cubic nonlinearities and stochastic no homogeneity is solved using the Homotopy-WHEP technique. The use of the homotopy perturbation method in WHEP technique is introduced to deal with non-perturbative systems. The new technique is then used to solve the nonlinear diffusion equation with making comparisons with Homotopy perturbation method (HPM). The method of analysis is illustrated through case studies.

We give an Itô-Stratonovitch formula for the wave equation on a torus, where we have no stochastic process associated to this partial differential equation. This gives a generalization of the classical Itô-Stratonovitch equation for diffusion in semi-group theory established by ourself in [18], [20].

In this paper, a nonlinear diffusion equation is studied under stochastic nonhomogeneity through homogeneous boundary conditions. The analytical solution for the linear case is obtained using the eigenfunction expansion. The Pickard approximation method is used to introduce a first order approximate solution for the nonlinear case. The WHEP technique is also used to obtain approximate solution under different orders and different corrections. Using Mathematica-5, the solution algorithm is operated through first order approximation. The method of solution is illustrated through case studies and figures.

Security continues to be an increasingly important concern in the design of modern systems. Many systems may have security requirements such as protecting the integrity and confidentiality of data and code stored in the system, ensuring integrity of computations, or preventing the execution of unauthorized code. Making security guarantees has become even harder with the emergence of hardware attacks where the attacker has physical access to the system and can bypass any software security mechanisms employed. To this end, researchers have proposed Secure Processor architectures that provide protection against hardware attacks using platform features. In this paper, we analyze three of the currently proposed secure uniprocessor designs in terms of their security, complexity of hardware required and performance overheads: eXecute Only Memory (XOM), Counter mode encryption and Merkle tree based authentication, and Address Independent Seed Encryption and Bonsai Merkle Tree based authentication. We then provide a discussion on the issues in securing multiprocessor systems and survey one design each for Shared Memory Multiprocessors and Distributed Shared Memory Multiprocessors. Finally, we discuss future directions in Secure Processor research which have largely been ignored forming the weakest link in the security afforded by the proposed schemes, namely, Secure booting and Secure configuration. We identify potential issues which can serve to form the foundation of further research in secure processors.

It is known that dispersive/dissipative features of the difference schemes used for simulations may be described by their differential approximations (DA). It is shown, that exact traveling wave solutions of the DA for the nonlinear Burgers equation help us to suggest artificial additions to the schemes to suppress the influence of the scheme dispersion and dissipation. Analytical predictions are confirmed using modifications of some familiar schemes, namely, the Lax-Wendroff, Warming-Beam and the third-order Lax-Wendroff schemes.

The dielectric medium consisting of rigidly polarized molecules is treated as a 3D disordered spin system. For investigation of statistical properties of this system on a scales of space-time periods of standing electromagnetic wave a microscopic approach has been developed. Using Birgoff’s ergodic hypothesis the initial 3D spin-glass problem is reduced to two conditionally separated 1D problems along the external electromagnetic field’s propagation. The first problem describes a quantum dynamics of 1D disordered N-particles system with relaxation in 3D media, while the second one describes a statistical properties of ensemble of disordered steric 1D spin-chains. On the base of constructions which are developed in both problems, is calculated the coefficient of polarizability related with the collective orientational effects of dipoles in external standing electromagnetic field. The Clausius-Mossotti equation for effective dielectric constant on the space-time scale’s of external standing field is generalized. The effective parallel algorithm for computation of stationary dielectric constant is proposed.

We discuss a possible strategy for implementing a grid-based approach to realizing the immense computational resources required to compute reactive molecular scattering cross sections and rate constants.

The paper “New Mathematical Conception and Computation Algorithm for Study of Quantum 3D Disordered Spin System under the Influence of External Field”, on pages 132 - 153 of this publication, has been retracted, because the name of Sergei Flach, appearing as the third author, was used without his permission or knowledge.