Related papers: Ewald Sums for One Dimension
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
We discuss the application of Widom insertion method for calculation of the chemical potential of individual ions in computer simulations with Ewald summation. Two approaches are considered. In the first approach, an individual ion is…
In this note, we prove analytic bounds on the equation of state of a cosmological fluid composed of an arbitrary number of canonical scalars evolving in a negative multi-exponential potential. Because of the negative energy, the universe is…
The electrostatic potential and energy of point charges in a real crystal, in the presence of thermal vibrations, is obtained as a special case of the Fourier method. Incorporating the role of thermal vibrations in electrostatic energy…
The traditional ambiguity about the bulk electrostatic potentials in crystals is due to the conditional convergence of Coulomb series. The classical Ewald approach turns out to be the first one resolving this task as consistent with a…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…
The late time accelerated expansion of the universe can be realized using scalar fields with given self-interacting potentials. Here we consider a straightforward approach where a three cosmic fluid mixture is assumed. The fluids are…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
In this work, simple exact results are presented for summations in two-particle potential with long-range interactions. Polygamma function is used to evaluate summations. Results are found when a periodic media is consider. Periodic…
We study the most general cosmological model with real scalar field which is minimally coupled to gravity. Our calculations are based on Friedmann-Lemaitre-Robertson-Walker (FLRW) background metric. Field equations consist of three…
A family of cosmological solutions with $(n+1)$ Ricci-flat spaces in the theory with several scalar fields and multiple exponential potential is obtained when coupling vectors in exponents obey certain relations. Two subclasses of solutions…
The evolution of multiple scalar fields in cosmology has been much studied, particularly when the potential is formed from a series of exponentials. For a certain subclass of such systems it is possible to get `assisted` behaviour, where…
We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial. The method we use is a blend of techniques coming from…
I propose a method to calculate logarithmic interaction in two dimensions and coulomb interaction in three dimensions under periodic boundary conditions. This paper considers the case of a rectangular cell in two dimensions and an…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
Starting from pure multidimensional gravity with curvature-nonlinear terms but no matter fields in the initial action, we obtain a cosmological model with two effective scalar fields related to the size of two extra factor spaces. The model…
In this work, we propose a convenient framework for infinite-dimensional analysis (including both real and complex analysis in infinite dimensions), in which differentiation (in some weak sense) and integration operations can be easily…
One dimensional versions of cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. They can resolve a large range of time and length scales, and admit exact numerical…