716 research outputs found
Open Boundaries for the Nonlinear Schrodinger Equation
We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF)
which is used to solve time dependent Nonlinear Schrodinger Equations (NLS).
The algorithm consists of solving the NLS on a box with periodic boundary
conditions (by any algorithm). Periodically in time we decompose the solution
into a family of coherent states. Coherent states which are outgoing are
deleted, while those which are not are kept, reducing the problem of reflected
(wrapped) waves. Numerical results are given, and rigorous error estimates are
described.
The TDPSF is compatible with spectral methods for solving the interior
problem. The TDPSF also fails gracefully, in the sense that the algorithm
notifies the user when the result is incorrect. We are aware of no other method
with this capability.Comment: 21 pages, 4 figure
Uniformly high order accurate essentially non-oscillatory schemes 3
In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear
Numerical Methods for Multilattices
Among the efficient numerical methods based on atomistic models, the
quasicontinuum (QC) method has attracted growing interest in recent years. The
QC method was first developed for crystalline materials with Bravais lattice
and was later extended to multilattices (Tadmor et al, 1999). Another existing
numerical approach to modeling multilattices is homogenization. In the present
paper we review the existing numerical methods for multilattices and propose
another concurrent macro-to-micro method in the numerical homogenization
framework. We give a unified mathematical formulation of the new and the
existing methods and show their equivalence. We then consider extensions of the
proposed method to time-dependent problems and to random materials.Comment: 31 page
Pulsating Strings in Deformed Backgrounds
This is a brief summary on pulsating strings in beta deformed backgrounds
found recently.Comment: 8 pages. Talk presented at Quantum Theory and Symmetries 7, Prague,
August 7-13, 201
The SU(3) spin chain sigma model and string theory
The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous
dimension of single trace operators involving the three complex scalars of N=4
supersymmetric Yang-Mills. We construct the non-linear sigma model describing
the continuum limit of the SU(3) spin chain. We find that this sigma model
corresponds to a string moving with large angular momentum in the five-sphere
in AdS_5xS^5. The energy and spectrum of fluctuations for rotating circular
strings with angular momenta along three orthogonal directions of the
five-sphere is reproduced as a particular case from the spin chain sigma model.Comment: 14 pages. Latex.v2: Misprints corrected. v3: Minor changes and
improved details from journal versio
Anomalous dimension and local charges
AdS space is the universal covering of a hyperboloid. We consider the action
of the deck transformations on a classical string worldsheet in . We argue that these transformations are generated by an infinite linear
combination of the local conserved charges. We conjecture that a similar
relation holds for the corresponding operators on the field theory side. This
would be a generalization of the recent field theory results showing that the
one loop anomalous dimension is proportional to the Casimir operator in the
representation of the Yangian algebra.Comment: 10 pages, LaTeX; v2: added explanations, reference
Evaluating the AdS dual of the critical O(N) vector model
We argue that the AdS dual of the three dimensional critical O(N) vector
model can be evaluated using the Legendre transform that relates the generating
functionals of the free UV and the interacting IR fixed points of the boundary
theory. As an example, we use our proposal to evaluate the minimal bulk action
of the scalar field that it is dual to the spin-zero ``current'' of the O(N)
vector model. We find that the cubic bulk self interaction coupling vanishes.
We briefly discuss the implications of our results for higher spin theories and
comment on the bulk-boundary duality for subleading N.Comment: 17 pages, 1 figure, v2 references added, JHEP versio
Numerical Modeling of Transient Wave Propagation for High Frequency NDT
Electromagnetic nondestructive testing (NDT) methods use frequencies ranging from low (dc) to high (microwave) frequencies [1]. Applications of numerical methods to model two- and three-dimensional low-frequency (dc or eddy current) nondestructive testing phenomena, where displacement currents can be omitted, were extensively examined, [2,3]. These are all interior boundary value problems. Finite element study of ultrasonic wave propagation and scattering in metals, which is again an interior boundary value problem, was recently reported in [4]. However, modeling of wave propagation for high-frequency NDT problems have not yet been attempted. Recently, finite difference methods in time domain have been successfully applied to solve transient electromagnetic wave propagation problems over the atmosphere and the ground [5], and time-dependent eddy current problems [6]. The method used here is a generalization of this work and is designed for numerical modeling of high-frequency electromagnetic wave propagation arising from nondestructive testing applications. The physical situation includes examination of the scattering effects by cracks inside a piece of material (especially dielectrics) or due to surface variations when the material is illuminated by a TM plane wave. This leads to an interface type problem
Field theory simulation of Abelian-Higgs cosmic string cusps
We have performed a lattice field theory simulation of cusps in Abelian-Higgs
cosmic strings. The results are in accord with the theory that the portion of
the strings which overlaps near the cusp is released as radiation. The radius
of the string cores which must touch to produce the evaporation is
approximately in natural units. In general, the modifications to the
string shape due to the cusp may produce many cusps later in the evolution of a
string loop, but these later cusps will be much smaller in magnitude and more
closely resemble kinks.Comment: 9 pages, RevTeX, 13 figures with eps
Geometry and dynamics of higher-spin frame fields
We give a systematic account of unconstrained free bosonic higher-spin fields
on D-dimensional Minkowski and (Anti-)de Sitter spaces in the frame formalism.
The generalized spin connections are determined by solving a chain of
torsion-like constraints. Via a generalization of the vielbein postulate these
allow to determine higher-spin Christoffel symbols, whose relation to the de
Wit--Freedman connections is discussed. We prove that the generalized Einstein
equations, despite being of higher-derivative order, give rise to the AdS
Fronsdal equations in the compensator formulation. To this end we derive
Damour-Deser identities for arbitrary spin on AdS. Finally we discuss the
possibility of a geometrical and local action principle, which is manifestly
invariant under unconstrained higher-spin symmetries.Comment: 30 pages, uses youngtab.sty, v2: minor changes, references adde
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