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Stochastic wind sea is an intermediate small-scale physical process responsible for the state of the atmospheric boundary layer and the water upper layer, having dynamics of all scales. To describe behavior of this system, one could use the…
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical…
According to the wave-particle duality (WPD), quantum systems show both particle- and wave-like behavior, and cannot be described using only one of these classical concepts. Identifying quantum features that cannot be reproduced by any…
Particle Swam Optimization is a population-based and gradient-free optimization method developed by mimicking social behaviour observed in nature. Its ability to optimize is not specifically implemented but emerges in the global level from…
A manifestation of the Pauli Exclusion Principle is observed when fermions are trapped in the ground state of a 2D harmonic oscillator trap at very low temperatures. This non-interaction of fermions results in the formation of Pauli…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
The theories of stochastic quantum mechanics and stochastic electrodynamics bring to light important aspects of the quantum dynamics that are concealed in the standard formalism. Here we take further previous work regarding the connection…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Aims. The simulation of three-wave interaction based plasma emission, thought to be the underlying mechanism for Type III solar radio bursts, is a challenging task requiring fully-kinetic, multi-dimensional models. This paper aims to…
One of the most severe limitations in particle accelerators and beam transport are non-linear effects. Techniques to study and possibly suppress some of these detrimental effects exist, the most popular are based on particle tracking and…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
The aim of this textbook is to provide students with basic knowledge of stochastic models that may apply to telecommunications research areas, such as traffic modelling, resource provisioning and traffic management. These study areas are…
The purpose of this article is to explore the role of viscoelastic properties of polymeric solutions on the jet mode in the electrospray process. In this research, several numerical simulations were performed to model the behavior of…
This paper is devoted to three topics. First, proving a measurability theorem for multifunctions with values in non-metrizable spaces, which is required to show that solutions to stochastic wave equations with interval parameters are random…
The Standard Model of particle physics is built on the principle of local gauge symmetry. This work provides a pedagogical introduction for advanced undergraduates by using quantum electrodynamics (QED) as the simplest example of a gauge…
Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…
Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: microphysics of electron resonant scattering by electromagnetic waves and…
During the last decades there has been a relatively extensive attempt to develop the theory of stochastic electrodynamics (SED) with a view to establishing it as the foundation for quantum mechanics. The theory had several important…
We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2. We apply an anticipative Girsanov transformation to transform the system into another one, driven only by…
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…