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The accuracy of applying density functional theory to noncovalent interactions is hindered by errors arising from low-density regions of interaction-induced change in the density gradient, error compensation between correlation and exchange…

Chemical Physics · Physics 2014-10-22 Marcin Modrzejewski , Grzegorz Chałasiński , Małgorzata M. Szczęśniak

We study an evolution equation that is the gradient flow in the $2$-Wasserstien metric of a non-convex functional for densities in $\mathbb{R}^n$ with $n \geq 3$. Like the Patlack-Keller-Segel system on $\mathbb{R}^2$, this evolution…

Analysis of PDEs · Mathematics 2021-02-17 Eric A. Carlen , Suleyman Ulusoy

Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…

Chaotic Dynamics · Physics 2025-06-02 Preet Mishra , Shyam Kumar , Sapna Ratan Shah , R. K. Brojen Singh

We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…

Analysis of PDEs · Mathematics 2017-05-12 Young-Pil Choi , Samir Salem

Recently, Tao and Mo proposed an accurate meta-generalized gradient approximation for the exchange-correlation energy. The exchange part is derived from the density matrix expansion, while the correlation part is obtained by improving the…

Chemical Physics · Physics 2017-10-11 Yuxiang Mo , Guocai Tian , Jianmin Tao

We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the…

High Energy Physics - Theory · Physics 2008-11-26 M. Bordag , D. Vassilevich , H. Falomir , E. M. Santangelo

We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…

Statistical Mechanics · Physics 2014-06-30 Babak Fotouhi , Michael G. Rabbat

In this work we investigate the multivariate statistical description of the matter distribution in the nonlinear regime. We introduce the multivariate Edgeworth expansion of the lognormal distribution to model the cosmological matter field.…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-20 F. S. Kitaura

An approximation for the exchange-correlation energy of reduced-density-matrix-functional theory was recently derived from a study of the homogeneous electron gas (N.N. Lathiotakis, N. Helbig, E.K.U. Gross, Phys. Rev. B 75, 195120 (2007)).…

Strongly Correlated Electrons · Physics 2009-11-13 N. N. Lathiotakis , N. Helbig , A. Zacarias , E. K. U. Gross

The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate technique to design semilocal exchange energy functionals in two-dimensional density…

Materials Science · Physics 2018-05-09 Abhilash Patra , Subrata Jana , Prasanjit Samal

We examine the leading order semiclassical gradient corrections to the non-interacting kinetic energy density functional of a two dimensional Fermi gas by applying the extended Thomas-Fermi theory at finite temperature. We find a non-zero…

Quantum Gases · Physics 2015-05-20 Brandon P. van Zyl , K. Berkane , K Bencheikh , A. Farrell

We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…

Analysis of PDEs · Mathematics 2017-09-13 Katy Craig , Inwon Kim , Yao Yao

Starting from the recently proposed dynamical exchange-correlation field framework, the equation of motion of the diagonal part of the many-electron Green function is derived, from which the spectral function can be obtained. The resulting…

Strongly Correlated Electrons · Physics 2023-03-02 F. Aryasetiawan

The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral…

Mathematical Physics · Physics 2008-06-12 Gianni Pagnini , Francesco Mainardi

We present a practical and accurate density functional for the exchange-correlation energy of electrons in two dimensions. The exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the…

Strongly Correlated Electrons · Physics 2010-06-30 E. Rasanen , S. Pittalis , J. G. Vilhena , M. A. L. Marques

We investigate the non-equilibrium large deviations function of the particle densities in two steady-state driven systems exchanging particles at a vanishing rate. We first derive through a systematic multi-scale analysis the coarse-grained…

Statistical Mechanics · Physics 2020-08-26 Jules Guioth , Éric Bertin

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation…

Materials Science · Physics 2009-02-20 Jianmin Tao , John P. Perdew , Viktor N. Staroverov , Gustavo E. Scuseria

The exact universal functional of integer charge leads to an extension to fractional charge asymptotically when it is applied to a system made of asymptotically separated densities. The extended functional is asymptotically local and is…

Chemical Physics · Physics 2024-12-17 Jing Kong

The exchange-correlation hole and potential of the homogeneous electron gas have been investigated within the random-phase approximation, employing the plasmon-pole approximation for the linear density response function. The angular…

Strongly Correlated Electrons · Physics 2023-04-12 K. Karlsson , F. Aryasetiawan

A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg, et al., Phys. Rev. Lett. 91, 126402…

Materials Science · Physics 2009-11-10 M. Dion , H. Rydberg , E. Schroder , D. C. Langreth , B. I. Lundqvist