711 research outputs found
Fusion Rules for Extended Current Algebras
The initial classification of fusion rules have shown that rational conformal
field theory is very limited. In this paper we study the fusion rules of extend
ed current algebras. Explicit formulas are given for the S matrix and the
fusion rules, based on the full splitting of the fixed point fields. We find
that in s ome cases sensible fusion rules are obtained, while in others this
procedure lea ds to fractional fusion constants.Comment: 19 pages, Latex, few references and figures are adde
Finite Volume Method for the Relativistic Burgers Model on a (1+1)-Dimensional de Sitter Spacetime
Several generalizations of the relativistic models of Burgers equations have
recently been established and developed on different spacetime geometries. In
this work, we take into account the de Sitter spacetime geometry, introduce our
relativistic model by a technique based on the vanishing pressure Euler
equations of relativistic compressible fluids on a (1+1)-dimensional background
and construct a second order Godunov type finite volume scheme to examine
numerical experiments within an analysis of the cosmological constant.
Numerical results demonstrate the efficiency of the method for solutions
containing shock and rarefaction waves
Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms
We consider nonlinear hyperbolic conservation laws, posed on a differential
(n+1)-manifold with boundary referred to as a spacetime, and in which the
"flux" is defined as a flux field of n-forms depending on a parameter (the
unknown variable). We introduce a formulation of the initial and boundary value
problem which is geometric in nature and is more natural than the vector field
approach recently developed for Riemannian manifolds. Our main assumption on
the manifold and the flux field is a global hyperbolicity condition, which
provides a global time-orientation as is standard in Lorentzian geometry and
general relativity. Assuming that the manifold admits a foliation by compact
slices, we establish the existence of a semi-group of entropy solutions.
Moreover, given any two hypersurfaces with one lying in the future of the
other, we establish a "contraction" property which compares two entropy
solutions, in a (geometrically natural) distance equivalent to the L1 distance.
To carry out the proofs, we rely on a new version of the finite volume method,
which only requires the knowledge of the given n-volume form structure on the
(n+1)-manifold and involves the {\sl total flux} across faces of the elements
of the triangulations, only, rather than the product of a numerical flux times
the measure of that face.Comment: 26 page
Realizations of pseudo bosonic theories with non-diagonal automorphisms
Pseudo conformal field theories are theories with the same fusion rules, but
with different modular matrix as some conventional field theory. One of the
authors defined these and conjectured that, for bosonic systems, they can all
be realized by some actual RCFT, which is of free bosons. We complete the proof
here by treating the non diagonal automorphism case. It is shown that for
characteristics they are all equivalent to a diagonal case, fully
classified in our previous publication. For we realize the non diagonal
case, establishing this theorem.Comment: 12 pages, no figure
Relativistic Burgers equations on curved spacetimes. Derivation and finite volume approximation
Within the class of nonlinear hyperbolic balance laws posed on a curved
spacetime (endowed with a volume form), we identify a hyperbolic balance law
that enjoys the same Lorentz invariance property as the one satisfied by the
Euler equations of relativistic compressible fluids. This model is unique up to
normalization and converges to the standard inviscid Burgers equation in the
limit of infinite light speed. Furthermore, from the Euler system of
relativistic compressible flows on a curved background, we derive, both, the
standard inviscid Burgers equation and our relativistic generalizations. The
proposed models are referred to as relativistic Burgers equations on curved
spacetimes and provide us with simple models on which numerical methods can be
developed and analyzed. Next, we introduce a finite volume scheme for the
approximation of discontinuous solutions to these relativistic Burgers
equations. Our scheme is formulated geometrically and is consistent with the
natural divergence form of the balance laws under consideration. It applies to
weak solutions containing shock waves and, most importantly, is well-balanced
in the sense that it preserves steady solutions. Numerical experiments are
presented which demonstrate the convergence of the proposed finite volume
scheme and its relevance for computing entropy solutions on a curved
background.Comment: 19 page
New Solvable Lattice Models from Conformal Field Theory
We build the trigonometric solutions of the Yang-Baxter equation that can not
be obtained from quantum groups in any direct way. The solution is obtained
using the construction suggested recently from the rational conformal field
theory corresponding to the WZW model on . We
also discuss the full elliptic solution to the Yang-Baxter equation whose
critical limit corresponds to the trigonometric solution found below.Comment: 15 pages, latex, 1 figur
Scalar Conservation Laws
We present a theoretical aspect of conservation laws by using simplest scalar
models with essential properties. We start by rewriting the general scalar conserva-
tion law as a quasilinear partial differential equation and solve it by method of
characteristics. Here we come across with the notion of strong and weak solutions
depending on the initial value of the problem. Taking into account a special initial
data for the left and right side of a discontinuity point, we get the related Riemann
problem. An illustration of this problem is provided by some examples. In the
remaining part of the chapter, we extend this analysis to the gas dynamics given in
the Euler system of equations in one dimension. The transformations of this system
into the Lagrangian coordinates follow by applying a suitable change of coordinates
which is one of the main issues of this section. We next introduce a first-order
Godunov finite volume scheme for scalar conservation laws which leads us to write
Godunov schemes in both Eulerian and Lagrangian coordinates in one dimension
where, in particular, the Lagrangian scheme is reformulated as a finite volume
method. Finally, we end up the chapter by providing a comparison of Eulerian and
Lagrangian approaches
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