Manuscript Topics

Mathematical models constitute a cornerstone of modern scientific inquiry, providing a rigorous framework for describing, analyzing, and predicting the behavior of complex systems across physics, biology, finance, and engineering. By translating empirical observations and theoretical principles into quantitative form, mathematical modeling enables a deeper understanding of underlying mechanisms and interdependencies. Beyond purely theoretical investigations, computational simulations play a central role in practical applications: they allow researchers to explore system dynamics under varying conditions, assess sensitivity to parameters, validate hypotheses, and forecast the evolution of quantities of interest in realistic scenarios.

The aim of this Special Issue is to gather high-quality contributions in the broad domain of mathematical physics, with particular emphasis on the formulation, analysis, and application of diverse classes of mathematical models. Both deterministic models–typically formulated in terms of ordinary differential equations (ODEs) and partial differential equations (PDEs)–and stochastic models–based on stochastic processes or stochastic differential equations (SDEs)–are within scope. Contributions addressing multiscale, multi-physics, or hybrid deterministic–stochastic frameworks are also welcome.

A rigorous investigation of the mathematical structure of the proposed models is strongly encouraged. Relevant topics include, but are not limited to, well-posedness (existence, uniqueness, and regularity of solutions), stability and bifurcation analysis, asymptotic behavior, qualitative properties of solutions, and analytical or semi-analytical techniques. Works that bridge theoretical analysis with computational practice are particularly valued.

To ensure relevance to real-world applications, submissions should incorporate appropriate numerical simulations that illustrate and validate the theoretical findings. A wide range of numerical methodologies may be employed, depending on the problem setting, including finite difference and finite volume schemes, finite element methods, discontinuous Galerkin approaches, spectral methods, and Monte Carlo techniques. Attention to convergence, stability, and computational efficiency is appreciated, especially in high-dimensional or data-intensive contexts.

Whenever possible, models should be calibrated and validated using empirical data. Parameter estimation, inverse problems, uncertainty quantification, and data-driven optimization strategies are therefore of significant interest. Contributions that integrate mathematical modeling with experimental or observational datasets–demonstrating predictive capability and practical impact–are particularly encouraged.

Through this Special Issue, we aim to foster interdisciplinary dialogue and promote advances in the development, analysis, and numerical implementation of mathematical models capable of addressing contemporary challenges in science and engineering.

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