Search results for "Boundary Condition"
showing 10 items of 235 documents
Anisotropic interfacial tension, contact angles, and line tensions: A graphics-processing-unit-based Monte Carlo study of the Ising model
2014
As a generic example for crystals where the crystal-fluid interface tension depends on the orientation of the interface relative to the crystal lattice axes, the nearest neighbor Ising model on the simple cubic lattice is studied over a wide temperature range, both above and below the roughening transition temperature. Using a thin film geometry $L_x \times L_y \times L_z$ with periodic boundary conditions along the z-axis and two free $L_x \times L_y$ surfaces at which opposing surface fields $\pm H_{1}$ act, under conditions of partial wetting, a single planar interface inclined under a contact angle $\theta < \pi/2$ relative to the yz-plane is stabilized. In the y-direction, a generaliza…
Unconstrained periodic boundary conditions for solid state elasticity
2004
We introduce a method to implement dynamics on an elastic lattice without imposing constraints via boundary or loading conditions. Using this method we are able to examine fracture processes in two-dimensional systems previously inaccessible for reliable computer simulations. We show the validity of the method by benchmarking and report a few preliminary results.
Simple absorbing layer conditions for shallow wave simulations with Smoothed Particle Hydrodynamics
2013
Abstract We study and implement a simple method, based on the Perfectly Matched Layer approach, to treat non reflecting boundary conditions with the Smoothed Particles Hydrodynamics numerical algorithm. The method is based on the concept of physical damping operating on a fictitious layer added to the computational domain. The method works for both 1D and 2D cases, but here we illustrate it in the case of 1D and 2D time dependent shallow waves propagating in a finite domain.
Casimir-Polder interaction between an accelerated two-level system and an infinite plate
2007
We investigate the Casimir-Polder interaction energy between a uniformly accelerated two-level system and an infinite plate with Dirichlet boundary conditions. Our model is a two-level atom interacting with a massless scalar field, with a uniform acceleration in a direction parallel to the plate. We consider the contributions of vacuum fluctuations and of the radiation reaction field to the atom-wall Casimir-Polder interaction, and we discuss their dependence on the acceleration of the atom. We show that, as a consequence of the noninertial motion of the two-level atom, a thermal term is present in the vacuum fluctuation contribution to the Casimir-Polder interaction. Finally we discuss the…
Perturbative results for two and three particle threshold energies in finite volume
2015
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The calculation is performed in relativistic quantum field theory with particles coupled via a $\lambda \phi^4$ interaction, and we work through order $\lambda^3$. The energy shifts begin at ${\cal O}(1/L^3)$, and we keep subleading terms proportional to $1/L^4$, $1/L^5$ and $1/L^6$. These terms allow a non-trivial check of the results obtained from quantization conditions that hold for arbitrary interactions, namely that of L\"uscher for two particles and our re…
The Fučík spectrum for nonlocal BVP with Sturm–Liouville boundary condition
2014
Boundary value problem of the form x''=-μx++λx-, αx(0)+(1-α)x'(0)=0, ∫01 x(s)ds=0 is considered, where μ,λ∈ R and α∈ [0,1]. The explicit formulas for the spectrum of this problem are given and the spectra for some α values are constructed. Special attention is paid to the spectrum behavior at the points close to the coordinate origin.
Classical thermodynamics of the Heisenberg chain in a field by generalized Bethe ansatz method
1990
Abstract Using the classical action-angle variables for the continuous model, we study the thermodynamics of the classical Heisenberg chain in an applied field by a generalized Bethe ansatz approach. The crucial point consists in the derivation of a phase-shifted density of states for the excitations of the model, obtained by imposing periodic boundary conditions. In the thermodynamic limit, the free energy can be expressed in terms of the solution of a non-linear integral equation, showing the universal dependece of the variable x=(JH) 1 2 /T .
The Poisson Bracket Structure of the SL(2, R)/U(1) Gauged WZNW Model with Periodic Boundary Conditions
2000
The gauged SL(2, R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. A second-order differential equation of the Gelfand-Dikii type defines the Poisson bracket structure of the theory. For periodic boundary conditions zero modes imply non-local Poisson brackets which, nevertheless, can be represented by canonical free fields.
High-precision studies of domain-wall properties in the 2D Gaussian Ising spin glass
2019
In two dimensions, short-range spin glasses order only at zero temperature, where efficient combinatorial optimization techniques can be used to study these systems with high precision. The use of large system sizes and high statistics in disorder averages allows for reliable finite-size extrapolations to the thermodynamic limit. Here, we use a recently introduced mapping of the Ising spin-glass ground-state problem to a minimum-weight perfect matching problem on a sparse auxiliary graph to study square-lattice samples of up to 10 000 × 10 000 spins. We propose a windowing technique that allows to extend this method, that is formally restricted to planar graphs, to the case of systems with …
Effective coefficients of thermoconductivity on some symmetric periodically perforated plane structures
1996
In this article we discuss an auxiliary problem which arises in the homogenization theory for the Laplacian on the plane with periodic array of square holes and homogeneous Neumann boundary conditions on those. Independently, this problem describes the process of thermoconductivity. We find the explicit formulas for effective coefficients of thermoconductivity (homogenized modula). We make also the asymptotic analysis of these formulas in the cases of big and small holes.