Related papers: Interatomic Potential Models for Nanostructures
The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of author's version of the non-Abelian Stokes theorem in the framework of path-integral formalism.
We provide a methodology for generating interatomic potentials for use in classical molecular dynamics simulations of atomistic phenomena occurring at energy scales ranging from lattice vibrations to crystal defects to high energy…
Large-scale atomistic computer simulations of materials rely on interatomic potentials providing computationally efficient predictions of energy and Newtonian forces. Traditional potentials have served in this capacity for over three…
This is an expository and introductory note on some results obtained in "Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some original material is contained in the last two sections, where we consider linear Poisson…
PREAMBLE, BRIEF HISTORY AND PRELIMINARIES, QUICK REVIEW OF BASIC NEUTRINO PROPERTIES, CHARGED CURRENT NEUTRINO PROCESSES, NEUTRAL CURRENT NEUTRINO PROCESSES, VERY HEAVY NEUTRINOS, CONCLUDING SUMMARY
A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpotentials of dimension $3\times3$ are given…
The aim of these lectures is to give a self-contained introduction to nonrelativistic potential models, to their formulation as well as to their possible applications. At the price of some lack of (in a mathematical sense) rigorous…
We develop a structure theory for nilpotent symplectic alternating algebras.
Nanoparticles with "sticky patches" have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they…
This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
A Neutrino Unbound gem (http://www.to.infn.it/~giunti/NU). Essential information (formulas, figures, tables, references, etc.) on solar neutrinos.
The Atomic Cluster Expansion (ACE) [R. Drautz, Phys. Rev. B, 99:014104 (2019)] provides a systematically improvable, universal descriptor for the environment of an atom that is invariant to permutation, translation and rotation. ACE is…
This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2
An overview on various results concerning the Dirac-Fock model, the various variational characterization of its solutions and its nonrelativistic limit. A notion of ground state for this totally unbounded is also defined.
In this paper, we construct isospectral Hamiltonians without shape invariant potentials for the relativistic quantum mechanical potentials such as the Dirac Oscillator and Hydrogen-like atom.
We present an elementary introduction to the construction of integrable models on hyper-elliptic surfaces for non specialists; also, we present some of the details of the paper `solv-int/9504002' for the more interested readers. (Based on a…
Understanding the interactions of a solute with its environment is of fundamental importance in chemistry and biology. In this work, we propose a deep neural network architecture for atom type embeddings in its molecular context and…
This is a preliminary version of the Chapter 1 of a book "Computable Integrability"
Editorial for the Special Issue of "Zeitschrift fuer Physikalische Chemie" on "Hierarchical Colloidal Nanostructures"