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A new approach was recently introduced by the authors for constructing analytic solutions of the linear PDEs describing elastodynamics. Here, this approach is applied to the case of a homogeneous isotropic half-space body satisfying…

Analysis of PDEs · Mathematics 2010-10-15 A. S. Fokas , D. Yang

Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum…

Chemical Physics · Physics 2023-01-26 Edit Mátyus , Dávid Ferenc , Péter Jeszenszki , Ádám Margócsy

The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In…

Chemical Physics · Physics 2020-08-26 Xavier Blase , Ivan Duchemin , Denis Jacquemin , Pierre-François Loos

Recently, a variant of the Bohr Hamiltonian was proposed where the mass term is allowed to depend on the beta variable of nuclear deformation. Analytic solutions of this modified Hamiltonian have been obtained using the Davidson and the…

Nuclear Theory · Physics 2019-12-25 D. Petrellis , Dennis Bonatsos , N. Minkov

The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…

Numerical Analysis · Mathematics 2023-01-03 Alexander Schlüter , Henning Müller , Sikang Yan , Erik Faust , Ralf Müller

We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the…

General Mathematics · Mathematics 2017-04-11 Omer Acan , Dumitru Baleanu

The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic…

Mathematical Physics · Physics 2021-09-01 Laurent Bétermin , Manuel Friedrich , Ulisse Stefanelli

Many physical problems can be modelled by partial differential equations on unknown domains. Several examples can easily be found in the dynamics of free interfaces in fluid dynamics, solid mechanics or in fluid-solid interactions. To solve…

Numerical Analysis · Mathematics 2018-10-25 Javier Rivero-Rodriguez , Miguel Perez-Saborid , Benoit Scheid

Some results obtained by a new method for solving the Bethe-Salpeter equation are presented. The method is valid for any kernel given by irreducible Feynman graphs. The Bethe-Salpeter amplitude, both in Minkowski and in Euclidean spaces,…

High Energy Physics - Theory · Physics 2009-11-11 V. A. Karmanov , J. Carbonell , M. Mangin-Brinet

The Lippmann-Schwinger equation for the nucleon-nucleon $t$-matrix as well as the corresponding Bethe-Goldstone equation to determine the Brueckner reaction matrix in nuclear matter are reformulated in terms of the resolvents for the total…

Nuclear Theory · Physics 2016-09-21 H. Müther , O. A. Rubtsova , V. I. Kukulin , V. N. Pomerantsev

Adomian decomposition method is used for solving the seventh order boundary value problems. The approximate solutions of the problems are calculated in the form of a rapid convergent series and not at grid points. Two numerical examples…

Numerical Analysis · Mathematics 2013-01-17 Shahid S. Siddiqi , Muzammal Iftikhar

Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P(x_1, ...…

Statistical Mechanics · Physics 2009-10-30 Gunter M. Schütz

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…

High Energy Physics - Theory · Physics 2009-10-22 H. J. de Vega , A. González--Ruiz

The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary…

Mathematical Physics · Physics 2021-02-24 G. B. Mainland

In this paper, we solve Laplace equation analytically by using differential transform method. For this purpose, we consider four models with two Dirichlet and two Neumann boundary conditions and obtain the corresponding exact solutions. The…

Analysis of PDEs · Mathematics 2013-12-30 M. Jamil Amir , M. Yaseen , Rabia Iqbal

We report on a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisenberg chain we derive, for arbitrary values of the anysotropy, a single non-linear…

High Energy Physics - Theory · Physics 2007-05-23 H. J. de Vega

We present a numerical approach which allows the solving of Bethe equations whose solutions define the eigenstates of Gaudin models. By focusing on a new set of variables, the canceling divergences which occur for certain values of the…

Mesoscale and Nanoscale Physics · Physics 2011-06-15 Alexandre Faribault , Omar El Araby , Christoph Sträter , Vladimir Gritsev

This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian…

Classical Analysis and ODEs · Mathematics 2017-06-08 Mostafa Akrami , Taher Lotfi , Farajollah Mohammadi Yaghoobi

An equation-by-equation (EBE) method is proposed to solve a system of nonlinear equations arising from the moment constrained maximum entropy problem of multidimensional variables. The design of the EBE method combines ideas from homotopy…

Numerical Analysis · Mathematics 2018-07-04 Wenrui Hao , John Harlim

A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor…

Analysis of PDEs · Mathematics 2017-10-20 Ryan M. Evans , Arvind Balijepalli , Anthony J. Kearsley