计算工程、金融与科学
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 constructed on the basis of the modified Landau-Ginzburg theory…
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 based on the Landau theory of phase transformations. Each…
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 phase transformations essential in the modelling of shape…
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 reducible to a stochastic differential equation with…
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 that is reducible to a first passage time (FPT) problem. This…
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 probability density of the time for such a process to cross a…
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 be reduced to estimating the probability of a (stochastic)…
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 conservation law equations is proposed. This framework allows…
We present a quasi-analytic perturbation expansion for multivariate N-dimensional Gaussian integrals. The perturbation expansion is an infinite series of lower-dimensional integrals (one-dimensional in the simplest approximation). This…
We analyze numerical stability of a recursive computation scheme of present value (PV) amd show that the absolute error increases exponentially for positive discount rates. We show that reversing the direction of calculations in the…
We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…
This report aims to present my research updates on distance function wavelets (DFW) based on the fundamental solutions and the general solutions of the Helmholtz, modified Helmholtz, and convection-diffusion equations, which include the…
Slow-moving vehicles relying on crustal magnetic anomaly navigation (MagNav) or vehicles revisiting the same location in a short time - such as those used for surveys in magnetic anomaly mapping - require fixed ground stations within 100 km…
This paper presents a Finite Element Model Updating framework for identifying heterogeneous material distributions in planar Bernoulli-Euler beams based on a rotation-free isogeometric formulation. The procedure follows two steps: First,…
In this study, the effect of ferrite grain size on the mechanical properties and dislocation behavior of dual-phase (DP) steel is investigated using dislocation-based crystal plasticity finite element analysis. DP steel, composed of a soft…
The thermal conductivity of covalent organic frameworks (COFs), an emerging class of nanoporous polymeric materials, is crucial for many applications, yet the link between their structure and thermal properties remains poorly understood.…
In financial time series forecasting, the naive forecast is a notoriously difficult benchmark to surpass because of the stochastic nature of the data. Motivated by this challenge, this study introduces the movement prediction-adjusted naive…
Automated rock classification from mineral composition presents a significant challenge in geological applications, with critical implications for material recycling, resource management, and industrial processing. While existing methods…
Despite continuous advancements in the capabilities of large language models (LLMs), numerical reasoning remains a challenging area. Techniques like chain-of-thought prompting, tree-of-thought prompting, and program-of-thought prompting…
Spinodoid architected materials have drawn significant attention due to their unique nature in stochasticity, aperiodicity, and bi-continuity. Compared to classic periodic truss-, beam- and plate-based lattice architectures, spinodoids are…