123 citations · 476 across the 44 of their papers we have counts for
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Numerical Model For Vibration Damping Resulting From the First Order Phase Transformations
Linxiang X. Wang, Roderick V. N. Melnik
A numerical model is constructed for modelling macroscale damping effects induced by the first order martensite phase transformations in a shape memory alloy rod. The model is cons…
Simulation of Phase Combinations in Shape Memory Alloys Patches by Hybrid Optimization Methods
Linxiang X. Wang, Roderick V. N. Melnik
In this paper, phase combinations among martensitic variants in shape memory alloys patches and bars are simulated by a hybrid optimization methodology. The mathematical model is b…
Finite Volume Analysis of Nonlinear Thermo-mechanical Dynamics of Shape Memory Alloys
Linxiang X. Wang, Roderick V. N. Melnik
In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic p…
Solving Stochastic Differential Equations with Jump-Diffusion Efficiently: Applications to FPT Problems in Credit Risk
Di Zhang, Roderick V. N. Melnik
The first passage time (FPT) problem is ubiquitous in many applications. In finance, we often have to deal with stochastic processes with jump-diffusion, so that the FTP problem is…
Efficient estimation of default correlation for multivariate jump-diffusion processes
Di Zhang, Roderick V. N. Melnik
Evaluation of default correlation is an important task in credit risk analysis. In many practical situations, it concerns the joint defaults of several correlated firms, the task t…
Monte-Carlo Simulations of the First Passage Time for Multivariate Jump-Diffusion Processes in Financial Applications
Di Zhang, Roderick V. N. Melnik
Many problems in finance require the information on the first passage time (FPT) of a stochastic process. Mathematically, such problems are often reduced to the evaluation of the p…
First Passage Time for Multivariate Jump-diffusion Stochastic Models With Applications in Finance
Di Zhang, Roderick V. N. Melnik
The ``first passage-time'' (FPT) problem is an important problem with a wide range of applications in mathematics, physics, biology and finance. Mathematically, such a problem can…
Coupling Control and Human-Centered Automation in Mathematical Models of Complex Systems
Roderick V. N. Melnik
In this paper we analyze mathematically how human factors can be effectively incorporated into the analysis and control of complex systems. As an example, we focus our discussion a…
Linking Microscopic and Macroscopic Models for Evolution: Markov Chain Network Training and Conservation Law Approximations
Roderick V. N. Melnik
In this paper, a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of Markov chains and the approximation of co…