Related papers: Discrete knot energies
We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions,…
This paper presents a family of spatial discretisations of the nonlinear rotating shallow-water equations that conserve both energy and potential enstrophy. These are based on two-dimensional mixed finite element methods and hence, unlike…
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling…
A short review of recent results on the global performance of covariant energy density functionals is presented. It is focused on the analysis of the accuracy of the description of physical observables of ground and excited states as well…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that…
This work aims to enable persistent, event-driven sensing and decision capabilities for energy-harvesting (EH)-powered devices by deploying lightweight DNNs onto EH-powered devices. However, harvested energy is usually weak and…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
The quasilocal energy associated with a constant stationary time slice of the Kerr spacetime is presented. The calculations are based on a recent proposal \cite{by} in which quasilocal energy is derived from the Hamiltonian of spatially…
Scalar fields are among the possible candidates for dark energy. This paper is devoted to the scalar fields from the inert doublet model, where instead of one as in the standard model, two SU(2) Higgs doublets are used. The component fields…
We summarize several semi-phenomenological approaches to estimate the internal energy of one-component-plasma (OCP) in two (2D) and three (3D) dimensions. Particular attention is given to a hybrid approach, which reproduces the…
The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…
The discrete spectrum solutions corresponding to dually-charged mesoatom on the space of constant negative curvature are obtained. The discrete spectrum of energies is finite and vanishes, when the magnetic charge of the nucleus exceeds the…
In this paper, we develop a discretization for the non-linear coupled model of classical Darcy-Forchheimer flow in deformable porous media, an extension of the quasi-static Biot equations. The continuous model exhibits a generalized…
The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and…
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…
We present a methodology for computing model independent perturbations in dark energy and modified gravity. This is done from the Lagrangian for perturbations, by showing how field content, symmetries, and physical principles are often…
We propose a dark energy density based on the Gauss-Bonnet 4-dimensional invariant and its modification. This model avoids the necessity of introducing the black hole limit to define the holographic density, since it can be considered as a…
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…
We examine computer experiments that can be performed to understand the dynamics of knots under self-repulsion. In the course of specific computer exploration we use the knot theory of rational knots and rational tangles to produce classes…