Related papers: The Integral Equation Method for a Steady Kinemati…
In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work…
Understanding event-by-event correlations and fluctuations is crucial for the comprehension of the dynamics of heavy ion collisions. Relativistic hydrodynamics is an elegant tool for modeling these phenomena; however, such simulations are…
This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the…
Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue problems for differential operators on unbounded domains. In this paper we propose to detect and approximate the point spectra of such operators…
In ideal MHD, shear Alfv\'{e}n eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfv\'{e}n continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of…
The incompressible 2D Euler equations on a sphere constitute a fundamental model in hydrodynamics. The long-time behaviour of solutions is largely unknown; statistical mechanics predicts a steady vorticity configuration, but detailed…
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which…
Applying the method of integral estimates to the analysis of three-wave processes we derive the sufficient criteria for the hard loss of stability of the charged plane surface of liquids with different physical properties. The influence of…
We investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime $|\Delta|< 1$, initially prepared in a product state with two domain walls i.e,…
A new computationally efficient method has been introduced to treat self-gravity in mesh based hydrodynamical simulations. It is applied simply by slightly modifying the Poisson equation into an inhomogeneous wave equation. This roughly…
The spheroidal wave functions are investigated in the case m=1. The integral equation is obtained for them. For the two kinds of eigenvalues in the differential and corresponding integral equations, the relation between them are given…
Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mapped to a multiply-connected region in the complex plane via a…
The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of…
The direct-forcing immersed boundary method (DF-IBM) algorithm previously developed by the authors is extended by coupling the Navier-Stokes equations with the Newton-Euler equations for rigid body dynamics within the DF-IBM framework. This…
In many applications, the information about the number of eigenvalues inside a given region is required. In this paper, we propose a contour-integral based method for this purpose. The new method is motivated by two findings. There exist…
In order better to understand how dynamo systems saturate, we study the kinematic dynamo properties of velocity fields that arise from nonlinearly saturated dynamos. The technique is implemented by solving concurrently, in addition to the…
Complete discrimination system for polynomial and direct integral method were discussed systematically. In particularly, we pointed out some mistaken viewpoints. Combining with complete discrimination system for polynomial, direct integral…
We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…
We consider frequency-weighted damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the…
To help reveal the complete picture of linear kinetic drift modes, four independent numerical approaches, based on integral equation, Euler initial value simulation, Euler matrix eigenvalue solution and Lagrangian particle simulation,…