Related papers: Ewald Sums for One Dimension
An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made of a uniformly charged background, positive particles, and negative particles, on the surface of a…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
We discuss the unitarity of the quantum evolution between arbitrary Cauchy surfaces of a 1+1 dimensional free scalar field defined on a bounded spatial region and subject to several types of boundary conditions including Dirichlet, Neumann…
We present a new approach to efficiently simulate electrolytes confined between infinite charged walls using a 3d Ewald summation method. The optimal performance is achieved by separating the electrostatic potential produced by the charged…
We discuss a coupled-cluster formalism for carrying out imaginary-time evolution from an arbitrary reference, and study the properties of the resulting evolution trajectories. The evolution converges to a solution of the standard…
We propose a new approach for multiverse analysis based on computational complexity, which leads to a new family of "computational" measure factors. By defining a cosmology as a space-time containing a vacuum with specified properties (for…
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions.…
Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern…
We study the dynamics of a non-minimally coupled scalar field cosmology with a potential function. We use the framework of dynamical systems theory to investigate all evolutional paths admissible for all initial conditions. Additionally, we…
Social evolutionary theory seeks to explain increases in the scale and complexity of human societies, from origins to present. Over the course of the twentieth century, social evolutionary theory largely fell out of favor as a way of…
We investigate whether an accelerating universe can be realized as an asymptotic late-time solution of FLRW-cosmology with multi-field multi-exponential potentials. Late-time cosmological solutions exhibit a universal behavior which enables…
We investigate the influence of the chimney topology $T\times T\times R$ of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One…
We consider a periodic evolution inclusion defined on an evolution triple of spaces. The inclusion involves also a subdifferential term. We prove existence theorems for both the convex and the nonconvex problem, and we also produce extremal…
We show that the late-time acceleration of the universe can be understood as a codimension-one bifurcation of the Friedmann dynamical system in the variables $(H,\Omega)$. At a critical value of the density-parameter combination, a…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
Self-gravitating systems have acquired growing interest in statistical mechanics, due to the peculiarities of the 1/r potential. Indeed, the usual approach of statistical mechanics cannot be applied to a system of many point particles…
A novel approach to quantization is shown to allow for superpositions of the cosmological constant in isotropic and homogeneous mini-superspace models. Generic solutions featuring such superpositions display unitary evolution and resolution…
We show that the properties of the lower part of the spectrum of the Helmholtz equation for an heterogeneous system in a finite region in $d$ dimensions, where the solutions to the homogeneous problems are known, can be systematically…
This paper examines the issues involved with concretely implementing a sum over conifolds in the formulation of Euclidean sums over histories for gravity. The first step in precisely formulating any sum over topological spaces is that one…
In this paper we study the set of rational solutions of equations defined by power sums symmetric polynomials with coefficients in a finite field. We do this by means of applying a methodology which relies on the study of the geometry of…