Mathematical Physics
The dynamic fracture behaviour of two moving collinear Griffith cracks in an initially stressed dry sandy medium subjected to concentrated crack-face loading and moving punch pressure is investigated. A moving coordinate system transforms…
We show that scalar discrete-series unitary irreducible representations (UIRs) $\Pi_{p,0}$ ($p=1,2,\cdots$) of the de Sitter (dS) group $\mathrm{SO}_0(1,4)$ admit a dS-covariant Krein realization on the dS hyperboloid, endowed with a…
The boundary correction to the free energy of a disordered Ising model depends on the boundary condition, the normalization, and the finite-volume sequence. We give a one-dimensional i.i.d. counterexample showing that the surface…
We investigate the stochastic stability of master--slave synchronization for a class of nonlinear dissipative evolution equations with a Burgers-type convective nonlinearity and a polynomial linear differential operator. The family includes…
The Lee-Yang theory is based on the theorem concerning a property of the ferromagnetic Ising model partition function proved by T. D. Lee and C. N. Yang in 1952. It provides powerful tools for understanding the very nature of phase…
We consider the nearest-neighbor Edwards--Anderson Ising model on cubic boxes with random perturbations supported at the boundary. We prove that any perturbation admitting an energy envelope that is negligible compared with the volume, both…
We introduce approximate expressions for the thermodynamics of the two-dimensional Ising model in an external magnetic field. The external field breaks the system's symmetry, which complicates the exact calculation of the free energy. To…
We introduce a novel discretization of the incompressible Euler equations based on their interpretation as geodesic equations on the Lie group of volume-preserving diffeomorphisms. It is well known that encoding diffeomorphisms and their…
We investigate the geometric content of the first-order part of the Laplace--Beltrami operator on an oriented Riemannian manifold. Relative to an arbitrary local orthonormal frame, the first-order part of the Laplace--Beltrami operator…
We study the inertial motion of incompressible continua within a geometric and variational framework, extending the classical Arnold-Ebin-Marsden theory from the group of volume-preserving diffeomorphisms of a fixed domain to configuration…
This study aims to develop a numerical homogenization method that can be applied to a heterogeneous stratified medium. Traditional scale transition methods are inadequate in capturing the essential gradient properties of some materials.…
We develop a GNS-based construction of geometric tensors on smooth parametric statistical models over $C^*$-algebras. Since the state space of a $C^*$-algebra is generally not a smooth manifold, the construction does not rely on pulling…
The ``goldfish'' equations, so named because of their striking beauty, are a system of $N$ nonlinear ODE's, where $N$ is an arbitrary integer. They can be solved exactly in a very simple manner, by transforming them to free motion using a…
The undamped Duffing oscillator is a nonlinear dynamical system with broad applications in physics, engineering and biological system. We present a comprehensive analysis of this system using the Lindstedt Poincare method (LPM) and its…
In this paper, we introduce a mathematical structure called the quasiPfaffian. The quasiPfaffian is analogous to the quasideterminant, a structure used instead of a determinant in noncommutative settings. Building on the Sylvester identity…
The G-Scheme is an explicit, adaptive integration framework for stiff systems of ordinary differential equations that exploits a local time-scale decomposition provided by the eigensystem of the Jacobian (the kernel set). Its computational…
We express in polar form the Dirac operator as left-multiplication by an assigned matrix: we use this technique to find its right-resolvent for low-dimensional spaces.
Given only the probability distribution of an aggregate counting variable, what independent latent counting processes are compatible with the observation? Equivalently, when does a probability-generating function admit a factorization into…
We study a mixed quantum Ising-$XY$ model on the semi-infinite rooted Cayley tree of order two. For every vertex $u$, the edge $\langle u,(u,1)\rangle$ carries an $XY$ interaction and the edge $\langle u,(u,2)\rangle$ carries an Ising…
From the perspective of continuum thermodynamics, we revisit the pressure oscillation problem in finite-volume methods for real fluids and clarify the physical counterpart of the Real Fluid Quasi-Conservative (RFQC) method. The RFQC method…