565 research outputs found
Numerical solution of the unsteady Navier-Stokes equation
The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear 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
Superspace Formulation of 4D Higher Spin Gauge Theory
Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so
far have been formulated as constrained systems of differential forms living in
a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory
in superspace, leaving the internal twistor space intact. Remarkably, the
superspace constraints have the same form as those defining the theory in
ordinary spacetime. This construction generalizes straightforwardly to higher
spin gauge theories N>1 supersymmetry.Comment: 24 p
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
Triangle based TVD schemes for hyperbolic conservation laws
A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented
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
Rotating strings and D2-branes in type IIA reduction of M-theory on G2 manifold and their semiclassical limits
We consider rotating strings and D2-branes on type IIA background, which
arises as dimensional reduction of M-theory on manifold of G2 holonomy, dual to
N=1 gauge theory in four dimensions. We obtain exact solutions and explicit
expressions for the conserved charges. By taking the semiclassical limit, we
show that the rotating strings can reproduce only one type of semiclassical
behavior, exhibited by rotating M2-branes on G2 manifolds. Our further
investigation leads to the conclusion that the rotating D2-branes reproduce two
types of the semiclassical energy-charge relations known for membranes in
eleven dimensions.Comment: LaTeX, 29 pages, no figures; V2:comments added; V3:no changes, to
appear in JHE
Absorbing boundary conditions for the Westervelt equation
The focus of this work is on the construction of a family of nonlinear
absorbing boundary conditions for the Westervelt equation in one and two space
dimensions. The principal ingredient used in the design of such conditions is
pseudo-differential calculus. This approach enables to develop high order
boundary conditions in a consistent way which are typically more accurate than
their low order analogs. Under the hypothesis of small initial data, we
establish local well-posedness for the Westervelt equation with the absorbing
boundary conditions. The performed numerical experiments illustrate the
efficiency of the proposed boundary conditions for different regimes of wave
propagation
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
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