8,522 research outputs found
Shock wave interaction with an abrupt area change
The wave patterns that occur when a shock wave interacts with an abrupt area changed are analyzed in terms of the incident shock wave Mach number and area-jump ratio. The solutions predicted by a semi-similar models are in good agreement with those obtained numerically from the quasi-one-dimensional time-dependent Euler equations. The entropy production for the wave system is defined and the principle of minimum entropy production is used to resolve a nonuniqueness problem of the self-similar model
Local stability analysis for a planar shock wave
A procedure to study the local stability of planar shock waves is presented. The procedure is applied to a Rankine-Hugoniot shock in a divergent/convergent nozzle, to an isentropic shock in a divergent/convergent nozzle, and to Rankine-Hugoniot shocks attached to wedges and cones. It is shown that for each case, the equation governing the shock motion is equivalent to the damped harmonic oscillator equation
Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
We analyze the scaling and finite-size-scaling behavior of the
two-dimensional 4-state Potts model. We find new multiplicative logarithmic
corrections for the susceptibility, in addition to the already known ones for
the specific heat. We also find additive logarithmic corrections to scaling,
some of which are universal. We have checked the theoretical predictions at
criticality and off criticality by means of high-precision Monte Carlo data.Comment: 46 pages including 8 figures. Self-unpacking file containing the tex
file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 8 ps file
B\"acklund transformations in 2D dilaton gravity
We give a B\"acklund transformation connecting a generic 2D dilaton gravity
theory to a generally covariant free field theory. This transformation provides
an explicit canonical transformation relating both theories.Comment: LaTeX file, 7 page
Three-dimensional simulation of vortex breakdown
The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state
Multiple steady states for characteristic initial value problems
The time dependent, isentropic, quasi-one-dimensional equations of gas dynamics and other model equations are considered under the constraint of characteristic boundary conditions. Analysis of the time evolution shows how different initial data may lead to different steady states and how seemingly anamolous behavior of the solution may be resolved. Numerical experimentation using time consistent explicit algorithms verifies the conclusions of the analysis. The use of implicit schemes with very large time steps leads to erroneous results
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