Search results for "Boundary Conditions"
showing 10 items of 97 documents
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.
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…
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 …
Ising systems with pairwise competing surface fields
2005
The magnetization distribution and phase behaviour of large but finite Ising simple cubic L × L × L lattices in d = 3 dimensions and square L × L lattices in d = 2 dimensions are studied for the case where four free boundaries are present, at which surface fields +Hs act on one pair of opposite boundaries while surface fields −Hs act on the other pair (in d = 3, periodic boundary conditions are used for the remaining pair). Both the distribution PL(m) of the global magnetization and also the distribution of the local magnetization m(x,z) are obtained by Monte Carlo simulations, where x and z denote the coordinates when the boundaries are oriented along the x-axis and z-axis (in d = 2); or a…
Critical properties and finite-size effects of the five-dimensional Ising model
1985
Monte Carlo calculations of the thermodynamic properties (energy, specific heat, magnetization suceptibility, renormalized coupling) of the nearest-neighbour Ising ferromagnet on a five-dimensional hypercubic lattice are presented and analyzed. Lattices of linear dimensionsL=3, 4, 5, 6, 7 with periodic boundary conditions are studied, and a finite size scaling analysis is performed, further confirming the recent suggestion thatL does not scale with the correlation length ξ (the temperature variation of which near the critical temperatureT c is ξ∝|1-T/T c |−1/2), but rather with a “thermodynamic length”l (withl∝|1-T/T c |−2/d ,d=5 here). The susceptibility (extrapolated to the thermodynamic …
A finite difference time domain model for the Titan ionosphere Schumann resonances
2007
[1] This paper presents a numerical approach to model the electrical properties of Titan's atmosphere. The finite difference time domain technique is applied to model the atmosphere of Saturn's satellite in order to determine Schumann resonant frequencies and electromagnetic field distributions at the extremely low frequency range. Spherical coordinates are employed, and periodic boundary conditions are implemented in order to exploit the symmetry in rotation of the celestial body. Results are compared with a previous model using the transmission line matrix method up to 180 km altitude. For the first time a numerical FDTD model up to 800 km altitude is carried out, and we report lower freq…
Multiscale Computer Simulations in Physics, Chemistry, and Biology: The Example Of Silica
2002
We show to what extent molecular dynamics simulations (MD) can explore struc-tural and dynamic properties of atomic systems whereby the system under consideration is amorphous silica (SiO2). Two studies are presented: (i) a large scale simulation of the dynam-ics of a SiO2 melt and (ii) the investigation of free silica surfaces where a mixture of a classical MD and a Car-Parrinello molecular dynamics is used.
Interface Localization-Delocalization in a Double Wedge: A New Universality Class with Strong Fluctuations and Anisotropic Scaling
2002
Using Monte Carlo simulations and finite-size scaling methods we study ``wetting'' in Ising systems in a $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ pore with quadratic cross section. Antisymmetric surface fields ${H}_{s}$ act on the free $L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ surfaces of the opposing wedges, and periodic boundary conditions are applied along the $y$ direction. In the limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$, ${L}_{y}/{L}^{3}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$, the system exhibits a new type of phase transition, which is the analog of the ``filling transition'' that occurs in a single wedge. It is charac…