An efficient numerical approach utilizing a variational weak form, grounded in 2D elastic theory and variational principles, is proposed for analyzing the in-plane vibrational behavior of rectangular plates resting on elastically restrained boundarie...
A plasma photonic crystal (PPC) was formed using an array of discharge plasma tubes. The transmission spectra and bandstructure of PPCs with different lattice types under different polarization modes were studied through simulation and measurement. T...
Solids can be cooled by driving impurity ions with lasers, allowing them to transfer heat from the lattice phonons to the electromagnetic surroundings. This exemplifies a quantum thermal machine, which uses a quantum system as a working medium to tra...
A Schrödinger equation with a time-fractional derivative, posed in (0,∞)×I, where I=]a,b], is investigated in this paper. The equation involves a singular Hardy potential of the form λ(x−a)2, where the parameter λ...
We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, d...
We derive new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form compared to the four-wave turbulence kinetic equation in the wave turbulence theory....
In this paper, we mainly establish Liouville-type theorems for the elliptic semi-linear equations involving the fractional Laplacian on the upper half of Euclidean space. We employ a direct approach by studying an equivalent integral equation instead...
In this paper, we study a class of non-linear fractional hybrid differential equations involving three mixed fractional orders with boundary conditions. Under weak assumptions, a formula of solutions is constructed and the existence results of the so...
This paper is devoted to the fundamental problem of investigating the solvability of initial-boundary value problems for a quasi-linear pseudo-parabolic equation of fractional order with a sufficiently smooth boundary. The difference between the stud...
In this article, we study the form of the deviation of geodesics (tidal forces) and the Raychaudhuri equation in a Schwarzschild–Finsler–Randers (SFR) spacetime which has been investigated in previous papers. This model is obtained by con...
The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is the unification of solutions of considered matrix equations with co...
The production performance of waterflood reservoirs with years of production is severely challenged by high water cuts and extensive water channels. Among IOR/EOR methods, weak gel injection is particularly effective in improving the water displaceme...
This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix; and the Laplace tra...
A generally nonlocal problem is investigated for a class of second order differential equations with weak singularities. New adjoint problem and Green functional concepts are introduced for completely nonhomogeneous problem. The solvability condition...
Analytical mechanics provides methods for analyzing multibody systems with mathematically equivalent elastic elements. The paper analyzes several of these models, highlighting the advantages and disadvantages offered by each of these methods. The mai...
The paper considers the analysis of a traveling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be...
In this article, we introduce the concept of weak Fℜm,η-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where η is a control function and ℜ is a relation. Then, we detail some fixed poi...
This paper proposes a three–dimensional (3D) local boundary element model based on meshless moving least squares (MLS) method for ultrasonic wave propagation fractional order boundary value problems of functionally graded anisotropic (FGA) fibe...
A semiclassical approach based on the WKB–Maslov method is developed for the kinetic ionization equation in dense plasma with approximations characteristic of metal vapor active media excited by a contracted discharge. We develop the technique...
We consider asset price processes Xt which are weak solutions of one-dimensional stochastic differential equations of the form (equation (2)) Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownia...
We compare the finite sample performance of a number of Bayesian and classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider Bayesian approaches developed by Chao and Philli...
We examined the composition and molecular weight dependence of the glass transition temperature in detail for two types of hydrogen bonding miscible blends: poly (2-vinyl pyridine)/poly (vinyl phenol) (2VPy/VPh) and poly (4-vinyl pyridine)/poly (viny...
The meshless local Petrov–Galerkin (MLPG) method was developed to analyze 2D problems for flexoelectricity and higher-grade thermoelectricity. Both problems were multiphysical and scale-dependent. The size effect was considered by the strain an...
The main purpose of engineering applications for fluid with natural and mixed convection is to control or enhance the flow motion and the heat transfer. In this paper, we use mathematical tools based on optimal control theory to show the possibility...
The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforc...
The kinetics of diffusion-dependent phase transformations (including austenitisation of ferrite in dual steels or ferritic nodular cast irons) is very often described by the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation. This description is not comp...
The reproducing kernel particle method (RKPM) is one of the most universal meshless methods. However, when solving three-dimensional (3D) problems, the computational efficiency is relatively low because of the complexity of the shape function. To ove...
The present study aimed to develop and investigate the local discontinuous Galerkin method for the numerical solution of the fractional logistic differential equation, occurring in many biological and social science phenomena. The fractional derivati...
Using the Laplace transform technique, we investigate the generalized solutions of the third-order Cauchy-Euler equation of the form t 3 y ′ ′ ′ ( t ) + a t 2 y ′ ′ ( t ) + b y ′ ( t ) + c y...
We investigate the thermodynamic compatibility of weakly nonlocal materials with constitutive equations depending on the third spatial gradient of the deformation and the heat flux ruled by an independent balance law. In such materials, the molecules...
The purpose of this paper is to investigate a class of initial value problems of fuzzy fractional coupled partial differential equations with Caputo gH-type derivatives. Firstly, using Banach fixed point theorem and the mathematical inductive method,...
We study the finite-sample properties of tests for overidentifying restrictions in linear regression models with a single endogenous regressor and weak instruments. Under the assumption of Gaussian disturbances, we derive expressions for a variety of...
In this paper, we propose a new notion, which we name S-contractive mapping, in a framework of vector-valued white noise functionals Wω⊗N⊂Γ(H)⊗K⊂(Wω⊗N)*. And we give concrete definitions of S-contractive...
The prospects of extracting new physics signals in coherent elastic neutrino–nucleus scattering (CEνNS) processes are limited by the precision with which the underlying nuclear structure physics, embedded in the weak nuclear form factor, is...
This paper presents an efficient numerical manifold method for solving the Burgers’ equation. To improve accuracy and streamline the solution process, we apply a nonlinear function transformation technique that reformulates the original problem...
We show that by treating the weak probe field as a perturbation to the strong coupling fields in the atomic system and using the perturbative method in a master equation, the features of linear response of phenomena of electromagnetically induced tra...
To improve the accuracy of solving the Poisson equation and the efficiency of handling complex boundary shapes in the particle method, this paper proposes a Local Regular-distributed Background Particles (LRBP) as an alternative to traditional bounda...
In this work, a mode parabolic equation method with interacting modes accounting for the weak elasticity at the bottom is developed. An important feature of the proposed method is that computations of elastic modes are avoided and that the solution i...
In this paper, we are interested in studying a mixed formulation of weak Galerkin type to approach the electric field and a Lagrange multiplier, which are solutions of a problem deriving from Maxwell’s equations. Our numerical scheme is formed...
In this contribution, the variational problem for the Kirchhoff plate based on the modified strain gradient theory (MSGT) is derived, and the Euler-Lagrange equations governing the equation of motion are obtained. The Galerkin-type weak form, upon wh...
In this study, a novel arbitrary order Virtual Element Method (p-VEM) for free torsional vibration analysis of beams with negligible warping is presented. This method can serve as an equivalent beam model for slender aerospace structural components....
We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w|<1), carrying a circular electric current in the angular direction. Thi...
A novel three-equation turbulence model has been proposed as a potential solution to overcome some of the issues related to the k–ε models of turbulence. A number of turbulence models found in the literature designed for compressed turb...
This article examines the application of the theory of critical strain energy levels to the determination of the limiting states of rod systems. A redundant truss is chosen to illustrate the peculiarities of changes in the self-stressing states of th...
The rough Heston model is a form of a stochastic Volterra equation, which was proposed to model stock price volatility. It captures some important qualities that can be observed in the financial market—highly endogenous, statistical arbitrages...
In order to obtain the numerical results of 3D convection-diffusion-reaction problems with variable coefficients efficiently, we select the improved element-free Galerkin (IEFG) method instead of the traditional element-free Galerkin (EFG) method by...
In this paper, we comprehensively review the five-dimensional (5D) fully-covariant theory of gravitation developed by Zhang two decades ago and its recent applications in astrophysics and cosmology. This 5D gravity describes not only the fields, but...
Besides the closed-form expansion coefficients of a weak-form numerical differentiator (WFND), we introduce a cubic boundary shape function with the aid of two parameters for reducing the boundary errors of fourth-order numerical derivatives to zero....
A new closed-form analytical solution to the radial transport of tracers in porous media under the influence of linear drift is presented. Specifically, the transport of tracers under convection–diffusion-dominated flow is considered. First, th...
Foam metal/epoxy interpenetrating phase composite is a new type of composite material with interpenetrating continuity in composition, which exhibits different intrinsic relationships under different stress states in tension and compression, and it i...
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