In this paper, symmetry properties of the basic equations of atmospheric motion are proposed. The results on symmetries show that the basic equations of atmospheric motion are invariant under space-time translation transformation, Galilean translatio...
We consider symmetric fuzzy stochastic differential equations where diffusion and drift terms arise in a symmetric way at both sides of the equations and diffusion parts are driven by fractional Brownian motions. Such equations can be used in real-li...
The physics-informed neural network (PINN) is an effective alternative method for solving differential equations that do not require grid partitioning, making it easy to implement. In this study, using automatic differentiation techniques, the PINN m...
In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations...
In this article, we introduce a Wong–Zakai type stationary approximation to the fractional Brownian motions and provide a sharp rate of convergence in
With many conveniences afforded by advances in smartphone technology, developing advanced data analysis methods for health-related information from smartphone users has become a fast-growing research topic in the healthcare field. Along these lines,...
The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift...
A permanent challenge in physics and other disciplines is to solve Euler–Lagrange equations. Thereby, a beneficial investigation is to continue searching for new procedures to perform this task. A novel Monte Carlo Metropolis framework is prese...
The main purpose of the present paper is to investigate the problem of estimating the time-varying coefficient in a stochastic parabolic equation driven by a sub-fractional Brownian motion. More precisely, we introduce a kernel-type estimator for the...
In this research, we present the analogies between variational calculations in cosmology and in classical mechanics. Our approach is based on the invariants for transformations of affine connections defined on N-dimensional manifolds (special cases a...
We consider the master equation of quantum Brownian motion, and with the application of the group invariant transformation, we show that there exists a surface on which the solution of the master equation is given by an autonomous one-dimensional Sch...
The equations of motion of an isospin-carrying particle in a Yang–Mills and gravitational field were first proposed in 1968 by Kerner, who considered geodesics in a Kaluza–Klein-type framework. Two years later, the flat space Kerner equat...
How to prescribe traction on boundary surface is still an open question in peridynamics. This problem is investigated in this paper. Through introducing the induced body force defined by boundary traction, the Silling’s peridynamic motion equat...
In this investigation, different computational methods for the analytical development and the computer implementation of the differential-algebraic dynamic equations of rigid multibody systems are examined. The analytical formulations considered in t...
We explore a timeless approach to quantum theory, in the form of the Page–Wootters mechanism, in which a gravitational interaction is introduced between the system and a finite-dimensional clock. The clock model used is the recently proposed qu...
This work explores the swimming of ammonoids, cephalopods related to living squids, octopuses, and nautilids and, like the latter, equipped with a coiled external shell. A mathematical model is introduced for theoretical ammonoid conchs. The two diff...
In some problems, partial differential equations are reduced to ordinary differential equations. In special cases, when incorporating randomness, equations can be reduced to systems of stochastic differential Equations (SDEs). Stochastic averaging fo...
Robot manipulators have played an enormous role in the industry during the twenty-first century. Due to the advances in materials science, lightweight manipulators have emerged with low energy consumption and positive economic aspect regardless of th...
When analyzing the dynamic behavior of multi-body elastic systems, a commonly used method is the finite element method conjunctively with Lagrange’s equations. The central problem when approaching such a system is determining the equations of m...
For a stationary potential 2D planar open high-velocity water flow of the ideal liquid, we propose a closed system of nonlinear equations considering the resistance forces to the flow from the channel bottom. Tangential stresses on jet interfaces are...
Ground motion prediction equations are a key element of seismic hazard assessments. Pakistan lacks a robust ground motion prediction equation specifically developed using a Pakistan seismic ground motion databank. In this study, performance assessmen...
The aim of this paper is to find higher order geometrical corrections to the Einstein–Hilbert action that can lead only to second order equations of motion. The metric formalism is used, and static spherically-symmetric and Friedmann–Lemaître space-t...
In this article, the stochastic Davey–Stewartson equations (SDSEs) forced by multiplicative noise are addressed. We use the mapping method to find new rational, elliptic, hyperbolic and trigonometric functions. In addition, we generalize some p...
The aim of this work is to establish and generalize a relationship between fractional partial differential equations (fPDEs) and stochastic differential equations (SDEs) to a wider class of stochastic processes, including fractional Brownian motions...
In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishi’s
Open channel levees are used extensively in hydraulic and environmental engineering applications to protect the surrounding area from inundation. However, levees may fail to produce an unsteady flow that is inherently three dimensional. Such a failur...
This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is e...
In the field of straw recycling, a cotton straw-harvesting mechanism is an important piece of agricultural equipment. The mechanistic analysis method of the harvesting mechanism is a major focus of research and development in this field. Currently, i...
Cyclotron frequency of a crystal electron is, in general, not an easily accessible parameter. Nevertheless, its calculation can be simplified when the symmetry properties of the band structure and those of the motion equations in the magnetic field a...
The purpose of this article was to present the solution for the critical Taylor number in the case of the motion between rotating coaxial cylinders based on the theory of stochastic equations of continuum laws and the equivalence of measures between...
Due to a heightened interest in the field of earthquakes after two moderately sized earthquakes occurred in Gyeongju and Pohang, this study explores which ground motion prediction equations are compatible for the South Korea region. Due to data avail...
This article presents alternative Hamiltonian and Lagrangian formalisms for relativistic mechanics using proper time and proper Lagrangian coordinates in 1 + 1 dimensions as parameters of evolution. The Lagrangian and Hamiltonian formalisms for a hyp...
Conditions for the existence and uniqueness of mild solutions for a system of semilinear impulsive differential equations with infinite fractional Brownian movements and the Wiener process are established. Our approach is based on a novel application...
A classical three-body problem with two planets moving around a central star of variable mass on quasi-periodic orbits is considered. The bodies are assumed to attract each other according to Newton’s law of universal gravitation. The star lose...
A thermodynamic approach to mechanical motion is presented, and it is shown that dissipation of energy is the key process through which mechanical motion becomes observable. By studying charged particles moving in conservative central force fields, i...
A description of the motion equation of a single two-dimensional finite element used to model a multi-body system with elastic elements is made in the article. To establish them, the Lagrange’s equations are used. Obtaining the dynamic response...
The Feynman–Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrödinger equation in quantum mechanics. Specifically, the formula provides a solution to the part...
Fractional–stochastic Drinfel’d–Sokolov–Wilson equations (FSDSWEs) forced by multiplicative Brownian motion are assumed. This equation is employed in mathematical physics, plasma physics, surface physics, applied sciences, and...
Generally, new and renewable energy systems generate electricity by installing and operating multiple modules simultaneously. In the Republic of Korea, recent studies and developments have focused on asymmetric wave energy converters (hereafter refer...
The solution of the motion equation for a structural system under prescribed loading and the prediction of the induced accelerations, velocities, and displacements is of special importance in structural engineering applications. In most cases, howeve...
A disc-type underwater glider (DTUG) has a highly symmetrical shape and is characterized by omnidirectional characteristics and high maneuverability in small bodies of water. To further explore the disc shape’s advantages and characteristics in...
The fluid-structure interaction of solid objects freely falling in a Newtonian fluid was investigated numerically by direct-forcing immersed boundary (DFIB) method. The Navier–Stokes equations are coupled with equations of motion through virtua...
An approach combining frequency and time domain analysis is introduced in this study for ship motions assessment. The open-source NEMOH code is utilized to compute the excitation forces and the hydrodynamic coefficients, while heave and pitch motions...
The paper briefly presents the dynamic synthesis of mechanisms with superior couplings, force, and speed distribution, efficiency, loss coefficient, dynamic coefficient or motion transmission function, determination of variable angular input speed fr...
In the present study, an effort to propose and adopt appropriate Ground Motion Prediction Equations (GMPEs) for the Rapid Earthquake Damage Assessment System (REDAS) in the Black Sea basin is attempted. Emphasis of GMPE harmonization in the cross-bor...
A partial Lagrangian method is proposed as an inverse dynamics analysis method for multi-link systems. This method, combined with automatic differentiation, allows for the derivation of equations of motion and analytical extraction of motion-induced...
This article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagran...
A quantum model of a free-electron laser (FEL) is considered. Two different approaches for the exploration of the the FEL system are considered. In the first case, the Heisenberg equations of motion are mapped on the basis of the initial wave functio...
In this study, we present a new approach with semi-analytical and numerical findings for solving equations of motion of small orbiter m, which is moving under the combined gravitational attraction of three primaries,
The frequency content of strong ground motion significantly affects the response of engineered systems under seismic excitation. Among some scalar parameters which exist in the literature, the mean period Tm has proved to be the most efficient. Groun...
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