Related papers: On assessing the accuracy of defect free energy co…
We study the ground--state shell correction energy of a fermionic gas in a mean--field approximation. Considering the particular case of 3D harmonic trapping potentials, we show the rich variety of different behaviors (erratic, regular,…
We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach…
In this paper, the geometric properties of the conformal metric are studied and its exact solution of the geodesic deviation equation is presented. We also find out the stress-energy tensor of this geometry and compare it with the usual…
This paper introduces a method for computing the Helmholtz free energy using the flow matching technique. Unlike previous work that utilized flow-based models for variational free energy calculations, this method provides bounds for free…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
We propose accurate computable error bounds for quantities of interest in plane-wave electronic structure calculations, in particular ground-state density matrices and energies, and interatomic forces. These bounds are based on an…
Free energy calculations based on atomistic Hamiltonians and sampling are key to a first principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the Free Energy Perturbation…
We develop a second order correction to commonly used density functional approximations (DFA) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact…
An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based…
Accurate free-energy calculations are essential for predicting thermodynamic properties and phase stability, but existing methods are limited: phonon-based approaches neglect anharmonicity and liquids, while molecular dynamics (MD) is…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation.…
A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach…
We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy…
Damage gradient models approximate fracture mechanics using a modulation of the material stiffness. To this aim a single scalar field, the damage, is used to degrade as a whole the elastic energy. If applied to the structural models of…
This thesis is concerned with the theory and the phenomenology of rapidity gap processes. We perform perturbative calculations of energy flow observables in jet-gap-jet processes, which consist of resummed primary emission calculations…
Since the seminal paper of Graham and Zworski (Invent. Math. 2003), conformal geometric problems are studied in the fractional setting. We consider the convergence of fractional Yamabe flow, which is previously known under small initial…
Approximate circuits trading the power consumption for the quality of results play a key role in the development of energy-aware systems. Designing complex approximate circuits is, however, a very difficult and computationally demanding…