Exact solutions of some singular integro-differential equations related to adhesive contact problems of elasticity theoryThe problem of constructing an exact solution of singular integro-differential equations related to problems of adhesive interaction between elastic thin semi-infinite homogeneous patch and elastic…N. Shavlakadze, N. Odishelidze, F. Criado-Aldeanueva·May 26, 2024SaveLearn
Well Posed Origin Anywhere Consistent Systems in Celestial MechanicsCertain measurements in celestial mechanics necessitate having the origin O of a Cartesian coordinate system (CCS) coincide with a point mass. For the two and three body problems we show mathematical…Harry Gingold, Jocelyn Quaintance·May 24, 2024SaveLearn
2D discrete Yang-Mills equations on the torusIn this paper, we introduce a discretization scheme for the Yang-Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define…Volodymyr Sushch·May 24, 2024SaveLearn
Two-center problem with harmonic-like interactions: periodic orbits and non-integrabilityWe study the classical planar two-center problem of a particle m subjected to harmonic-like interactions with two fixed centers. For convenient values of the dimensionless parameter of this problem…A. M. Escobar Ruiz, L. Jiménez-Lara, J. Llibre et al.·May 23, 2024SaveLearn
Layers of planar hexagonal heterostructure modeled by quantum graphsThe work presents a study on the quantum theory of periodic graphs applied to mono- and bilayer hexagonal materials. Different parameters associated with the atoms present at the vertices of these…Osmar N. Souza·May 23, 2024SaveLearn
Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimensionWe prove a logarithmically enhanced area law for all R\'enyi entanglement entropies of the ground state of a free gas of relativistic Dirac fermions. Such asymptotics occur in any dimension if the…Leon Bollmann, Peter Müller·May 23, 2024SaveLearn
Traveling Wave Solutions For Newton's Equations of Celestial Mechanics: Kepler's ProblemThis article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in…Harry Gingold, Jocelyn Quaintance·May 22, 2024SaveLearn
Lagrangian Multiform for Cyclotomic Gaudin ModelsWe construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the…Vincent Caudrelier, Anup Anand Singh, Benoît Vicedo·May 21, 2024SaveLearn
Sachs equations and plane waves II: Isometries and conformal isometriesThis article describes the symmetries of plane wave spacetimes in dimension four and greater. It begins with a description of the isometric automorphisms, and in particular the homogeneous plane…Jonathan Holland, George Sparling·May 21, 2024SaveLearn
Quantum-classical motion of charged particles interacting with scalar fieldsThe goal of this article is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution is the derivation of…Shahnaz Farhat·May 21, 2024SaveLearn
The Schwarzian Approach in Sturm-Liouville ProblemsA novel method for finding the eigenvalues of a Sturm-Liouville problem is developed. Following the minimalist approach the problem is transformed to a single first-order differential equation with…Nektarios Vlahakis·May 21, 2024SaveLearn
Formal languages, spin systems, and quasicrystalsWe present a categorical formalism for context-free languages with morphisms given by correspondences obtained from rational transductions. We show that D0L-systems are a special case of the…Francesca Fernandes, Matilde Marcolli·May 21, 2024SaveLearn
Method of Filtration in first passage time problemsStatistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one…Yuta Sakamoto, Takahiro Sakaue·May 20, 2024SaveLearn
Cluster transformations, the tetrahedron equation and three-dimensional gauge theoriesWe define three families of quivers in which the braid relations of the symmetric group Sn are realized by mutations and automorphisms. A sequence of eight braid moves on a reduced word for the…Xiaoyue Sun, Junya Yagi·May 20, 2024SaveLearn
Limiting absorption principle for contractionsWe establish limiting absorption principles for contractions on a Hilbert space. Our sufficient conditions are based on positive commutator estimates. We discuss the dynamical implications of this…Joachim Asch, Olivier Bourget·May 19, 2024SaveLearn
The boundary value contact problem of electroelasticity for piecewise-homogeneous piezo-electric plate with elastic inclusion and cutA contact problem of the theory of electroelasticity for piecewise-homogeneous plate of piezo-electric material with infinite cut and elastic finite inclusion of variable bending rigidity is…Nugzar Shavlakadze, Nana Odishelidze, Francisco Criado-Aldeanueva·May 19, 2024SaveLearn
Modes, Bounds, and Synthesis of Optimal Electromagnetic ScatterersThis paper presents an optimal synthesis of material distributions in obstacles for maximal extinction, scattering, or absorption. The material synthesis is based on an explicit construction…Mats Gustafsson·May 19, 2024SaveLearn
Model of the effective separable potential in the problem of three one-dimensional quantum particlesThe goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range)…Sergey B. Levin, Alexandr S. Bagmutov, Victor O. Toropov·May 19, 2024SaveLearn
Distribution of points on the real line under a class of repulsive potentialsIn a 1979 paper, Ventevogel and Nijboer showed that classical point particles interacting via the pair potential φ(x)=(1+x4)-1 are not equally spaced in their ground states in one…Roni Edwin·May 19, 2024SaveLearn
Symplectic duality via log topological recursionWe review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of x-y…Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski et al.·May 17, 2024SaveLearn
On pressureless Euler equation with external forceHodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form…B. G. Konopelchenko, G. Ortenzi·May 17, 2024SaveLearn
Localization and unique continuation for non-stationary Schr\"odinger operators on the 2D latticeWe extend methods of Ding and Smart from their breakthrough paper in 2020 which showed Anderson localization for certain random Schr\"odinger operators on 2(Z2) via a quantitative…Omar Hurtado·May 17, 2024SaveLearn
Spectral analysis of Dirac operators for fermion scattering on topological solitons in the nonlinear O(3) σ-modelWe investigate the existence of discrete positive or negative energy ground states of the Dirac operator H which describe the fermion scattering on topological solitons in the nonlinear O(3)…Daiju Funakawa, Satoshi Okumura, Yuki Ueda·May 17, 2024SaveLearn
Segre surfaces and geometry of the Painlev\'e equationsIn this paper, we consider a six parameter family of affine Segre surfaces embedded in C6. For generic values of the parameters, this family is associated to the q-difference sixth…Nalini Joshi, Marta Mazzocco, Pieter Roffelsen·May 17, 2024SaveLearn
A systematic path to non-Markovian dynamics II: Probabilistic response of nonlinear multidimensional systems to Gaussian colored noise excitationThe probabilistic characterization of non-Markovian responses to nonlinear dynamical systems under colored excitation is an important issue, arising in many applications. Extending the…Gerassimos A. Athanassoulis, Nikolaos P. Nikoletatos-Kekatos, Konstantinos Mamis·May 16, 2024SaveLearn