Related papers: Generalized gradient approximation for solids and …
One of the most popular approaches for solving total variation-regularized optimization problems in the space of measures are Particle Gradient Flows (PGFs). These restrict the problem to linear combinations of Dirac deltas and then perform…
This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss the Legendre structure with information geometry on the manifold of generalized…
Recovering unbiased kinetic and thermodynamic observables from the enhanced sampling simulations is a central challenge in rare-event sampling. Classical Girsanov Reweighting (GR) offers a principled solution by yielding exact pathwise…
Reformulation of the Dirac equation in terms of the real Spacetime Algebra (STA) reveals hidden geometric structure, including a geometric role for the unit imaginary as generator of rotations in a spacelike plane. The STA and the real…
We test Laplacian-level meta-generalized gradient approximation (meta-GGA) non-interacting kinetic energy functionals based on the fourth-order gradient expansion (GE4). We consider several well known Laplacian-level meta-GGAs from…
The Pauli kinetic energy enhancement factor $\alpha=(\tau-\tau^W)/\tau^{unif}$ is an important density ingredient, used to construct many meta-generalized gradient approximations (meta-GGA) exchange-correlation (XC) energy functionals,…
The strong-interaction functionals $W_\infty[n]$ and ${W'}_\infty[n]$ play an important role in the adiabatic-connection method of Density Functional Theory. The strictly-correlated electron approach can be used to exactly compute these…
We consider the variational formulation of the electric field integral equation on a Lipschitz polyhedral surface $\Gamma$. We study the Galerkin boundary element discretisations based on the lowest-order Raviart-Thomas surface elements on…
We prove global well-posedness for some molecular beam epitaxy models. This requires proving some bounds on the gradient of solutions. We also obtain some global bounds on the roughness of solutions.
Convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows to find the expressions for the diffusion coefficient for any value of the system's…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
The Pb/Si(111) thin films were simulated within the density functional theory (DFT). The well-known Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximation (GGA) and its recent nonempirical successor Wu-Cohen (WC)…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
Various types of parameter restart schemes have been proposed for accelerated gradient algorithms to facilitate their practical convergence in convex optimization. However, the convergence properties of accelerated gradient algorithms under…
Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for the storing and sampling of gradients and this work concerns the interactions between these two…
The generalized extreme value (GEV) distribution is commonly employed to help estimate the likelihood of extreme events in many geophysical and other application areas. The recently proposed blended generalized extreme value (bGEV)…
The electric field integral equation is a well known workhorse for obtaining fields scattered by a perfect electric conducting (PEC) object. As a result, the nuances and challenges of solving this equation have been examined for a while.…
In this contribution we assess the performance of two different exchange-correlation functionals in the first-principle prediction of the lattice thermal conductivity of bulk semiconductors, namely the local density approximation (LDA) and…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the…