5,501 research outputs found
Remarks on the formation and decay of multidimensional shock waves
In this paper, we present a formula describing the formation and decay of
shock wave type solutions in some special cases.Comment: Latex, 7
Weak asymptotics method
We present a new method for constructing solutions to nonlinear evolutionary
equations describing the propagation and interaction of nonlinear waves.Comment: 15 pages, 2 figure
Global in Time Asymptotic Solutions to Kolmogorov--Feller-Type Parabolic Pseudodifferential Equations with a Small Parameter. Forward and Backward in Time Motion
The goal of the present paper is to present a new approach to the
construction of asymptotic (approximating) solutions to parabolic PDE by using
the characteristics.Comment: Latex, 19 p.,9 fig
A simple proof of associativity and commutativity of LR-coefficients (or the hive ring)
We give a simple bijective proof of associativity and commutativity of the
Littlewood-Richardson coefficients or the hive ring. Specifically, we establish
existence a polarized polymatroidal discretely concave functions on the
tetrahedron with given boundary values at two adjoint faces.Comment: 18 pages, 9 figure
Arrays and the octahedron recurrence
Recently, in papers by Knutson, Tao and Woodward, Henriques and Kamnitzer,
Pak and Vallejo have been constructed several interesting bijections of
associativity and commutativity. In the first two papers bijections relate
special sets of discretely concave functions (hives) on triangular grids and
the octahedron recurrence plays the key role for these bijections. Pak and
Vallejo related special sets of Young tableaux and constructions of these
bijections based on standard algorithms in this theory, jeu de taquen,
Schutzenberger involution, tableaux switching, etc. In this paper we
investigate these constructions from the third point of view, combinatorics of
arrays, theory worked out recently by the authors. Arrays naturally related as
well to functions on the lattice of integers as to Young tableaux. In the
tensor category of arrays, the bijections of associativity and commutativity
arise naturally. We establish coincidence of our bijections with that defined
in the first two papers and in the integer-valued set-up with the bijection in
the third paper (that is, in particular, a solution of Conjecture 1 by Pak and
Vallejo). In order to relate different approaches and to reveal combinatorics
of the octahedron recurrence, we, first, show that the octahedron recurrence
agrees with discrete convexity and, second, we construct another bijection
using the octahedron recurrence, the functional form of the RSK correspondence.Comment: 34 pages, 11 figure
Numerical and analytical investigation of the free boundary confluence for the phase field system
In this paper we numerically research the solutions of the phase field system
for the spherically symmetric Stefan-Gibbs-Thomson problem in the case of
interaction of the free boundaries. We analyze the effect of the soliton type
disturbance of the temperature in the point of the contact of the free
boundaries.Comment: Latex, 15p., 14 fig
On the Origin of the Multiplicity Fluctuations in High Energy Heavy Ion Collisions
Multiplicity fluctuations in heavy ion collisions obtain comparable
contributions both from initial stage of the collisions, and from final stage
interaction. We calculate the former component, using the ``wounded nucleon''
model and standard assumptions about nuclei and NN cross section. Combining it
with the second one, calculated previously by Stephanov,Rajagopal and Shuryak,
ref.2, we obtain good quantitative description of experimental data (ref.3)
from NA49 collaboration at CERN on central PbPb collisions.Comment: 3 pages, 2 figure
Confluence of the nonlinear waves in the Stefan problem with undercooling
We assume that the Stefan problem with undercooling has a classical solution
until the moment of contact of free boundaries and the free boundaries have
continuous velocities until the moment of contact. Under these assumptions, we
construct a smooth approximation of the global solution of the Stefan problem
with undercooling, which, until the contact, gives the classical solution
mentioned above and, after the contact, gives a solution which is the solution
of the heat equation.Comment: 36 pages, Late
Global in Time Madelung Transformation for Kolmogorov-Feller Pseudodifferential Equations
Using an idea going back to Madelung we construct global in time solutions to
the transport equation corresponding to the asymptotic solution of the
Kolmogorov-Feller equation describing a system with diffusion, potential and
jump terms. To do that we use the construction of a generalized delta -shock
solution of the continuity equation for a discontinuous velocity field. We also
discuss corresponding problem of asymptotic solution construction (Maslov
tunnel asymptotics).Comment: Latex, 21
Delta shock wave formation in the case of triangular hyperbolic system of conservation laws
We describe shock wave arising from continuous initial data in the
case of triangular conservation law system arising from "generalized
pressureless gas dynamics model". We use the weak asymptotic method.Comment: 22 pages, Late
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