相关论文: Simple CVM-based approximations for the configurat…

A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…

Many enhanced sampling methods, such as Umbrella Sampling, Metadynamics or Variationally Enhanced Sampling, rely on the identification of appropriate collective variables. For proteins, even small ones, finding appropriate collective…

We demonstrate an intuitive relation between conditional entropy and conditional expectation that is useful when one want to compare them as measurement tools to evaluate secrecy systems. In particular, we give a Security Property…

Cardy-Verlinde (CV) formula relates the entropy of a conformal field theory (CFT) in arbitrary dimensions to its total energy (with an appropriate insertion of additional internal energy for charged systems) and Casimir energy. While…

We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…

Lattice models parameterized using first-principles calculations constitute an effective framework to simulate the thermodynamic behavior of physical systems. The cluster expansion method is a flexible lattice-based method used extensively…

In the framework of the computational determination of highly-accurate vertical excitation energies in small organic compounds, we explore the possibilities offered by the equation-of-motion formalism relying on the approximate fourth-order…

We study tagged particle diffusion at large packing fractions, for a model of particles interacting with a generalized Lennard-Jones 2n-n potential, with large n. The resulting short-range potential mimics interactions in colloidal systems.…

We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…

We consider the symmetric simple exclusion process evolving on the interval of length $n-1$ in contact with reservoirs of density $\rho \in (0,1)$ at the boundary. We use Yau's relative entropy method to show that if the initial measure is…

We present a computationally efficient method to calculate the configurational entropy of network-forming materials. The method requires only the atomic coordinates and bonds of a single well-relaxed configuration. This is in contrast to…

We consider configurations of $N$ charged particles on the interval with nearest neighbour Coulomb interaction and constant external force. For different values of external force we find 4 different phases of the asymptotic particle density…

Finding optimal (or low energy) centroidal Voronoi tessellations (CVTs) on a 2D domain is a challenging problem. One must navigate an energy landscape whose desirable critical points have sufficiently small basins of attractions that they…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

We discuss the low-energy behavior of the virtual Compton scattering amplitude off a spin-zero target. We first compare various methods of obtaining a low-energy expression based either on the soft-photon approximation or the use of…

The so-called configurational entropy (CE) framework has proved to be an efficient instrument to study nonlinear scalar field models featuring solutions with spatially-localized energy, since its proposal by Gleiser and Stamapoulos.…

Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce {\it tomographic} entropic sampling, a scheme which uses multiple…

Solid solutions occur when multiple chemical species share sites of a common crystal lattice. Although the single site occupation is random, chemical interaction preferences bias the occupation probabilities of neighboring sites, and this…

We compute the structure factor of the $J_1$-$J_2$ Ising model in an external field on the square lattice within the Cluster Variation Method. We use a four point plaquette approximation, which is the minimal one able to capture phases with…

This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error equation. The geometric assumptions, which are necessary…