Related papers: A sensible estimate for the stability constant of …
We provide a lower bound for the convergence radius of the Mayer series of the Lennard-Jones gas which strongly improves on the classical bound obtained by Penrose and Ruelle 1963. To obtain this result we use an alternative estimate…
The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of $N$ atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form $f(x) = 4\sum_{i=1}^N \sum_{j=1,j<i}^N…
We revisit two old and apparently little known papers by Basuev [2] [3] and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle…
In this note we revisit the recent developments concerning rigorous results on the virial series of a continuous system of classical particles interacting via a stable and tempered pair potential and we provide new lower bounds for its…
Good a-priori bounds on the smallest pairwise distance $r_{\rm{{min}}}(\mbox{LJ}_N^{\rm{gmin}})$ for a three-dimensional (3D) Lennard-Jones $N$-body cluster of globally minimal energy can significantly reduce the computational search space…
The Lennard-Jones 12-6 potential (LJ) is arguably the most widely used pair potential in Molecular Simulations. In fact, it is so popular that the question is rarely asked whether it is fit for purpose. In this paper, we argue that, whilst…
It is well-known that any Lennard-Jones type potential energy must have a periodic ground state given by a triangular lattice in dimension 2. In this paper, we describe a computer-assisted method that rigorously shows such global minimality…
We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power…
The aim of this paper is to present an analytical calculation of the chemical potential of a Lennard Jones fluid. The integration range is divided into two regions. In the small distance region,which is $r\leq\sigma$ in the usual…
We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination…
The stability of the Standard Model is determined by the true minimum of the effective Higgs potential. We show that the potential at its minimum when computed by the traditional method is strongly dependent on the gauge parameter. It…
There is a family of potentials that minimize the lowest eigenvalue of a Schr\"odinger eigenvalue under the constraint of a given L^p norm of the potential. We give effective estimates for the amount by which the eigenvalue increases when…
We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem
We analyse the stability lower bounds on the Standard Model Higgs mass by carefully controlling the scale independence of the effective potential. We include resummed leading and next-to-leading-log corrections, and physical pole masses for…
We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness…
Extending results of Linial (1984) and Aigner (1985), we prove a uniform lower bound on the balance constant of a poset $P$ of width $2$. This constant is defined as $\delta(P) = \max_{(x, y)\in P^2}\min\{\mathbb{P}(x\prec y),…
The simplified Lennard-Jones (LJ) potential minimization problem is minimize f(x)=4\sum_{i=1}^N \sum_{j=1,j<i}^N (\tau_{ij}^{-6} -\tau_{ij}^{-3}) subject to x\in \mathbb{R}^n, where $\tau_{ij}=(x_{3i-2}-x_{3j-2})^2…
We apply the effective potential method to study the vacuum stability of the bounded from above $(-\phi^{6})$ (unstable) quantum field potential. The stability ($\partial E/\partial b=0)$ and the mass renormalization ($\partial^{2}…
We study the stationary phi^6 model given by the equation -phi''(x) + 2 phi(x) - 8 phi(x)^3 + 6 phi(x)^5 = 0 for x in R, and establish sharp quantitative stability estimates for configurations close to two weakly interacting kinks. More…
This paper investigates the stability of the least squares approximation $P_m^n$ within the univariate polynomial space of degree $m$, denoted by ${\mathbb P}_m$. The approximation $P_m^n$ entails identifying a polynomial in ${\mathbb P}_m$…