Results 1 to 10 of about 2,852 (69)

Constraint and gauge shocks in one-dimensional numerical relativity [PDF]

, 2004
We study how different types of blow-ups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blow-ups can be expected ...
B. Gustafsson, Bernd Reimann, Darío Núñez, E. Hopf, F. John, F. John, F. John, F. John, H. Friedrich, H. O. Kreiss, J. York, José A. González, Miguel Alcubierre, P. Lax, R. Arnowitt, R. J. Leveque, S. Alinhac, S. Klainerman, T. Nakamura, W. Strauss, Y. Bruhat, Y. Choquet-Bruhat, Y. Choquet-Bruhat   +22 more
core   +3 more sources

Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks [PDF]

, 2002
I study the Bona-Masso family of hyperbolic slicing conditions, considering in particular its properties when approaching two different types of singularities: focusing singularities and gauge shocks.
Alcubierre M, Alcubierre M, Alcubierre M, Arnowitt R, Balakrishna J, Bernstein D, Bona C, Lax P D, Leveque R J, Miguel Alcubierre, Thornburg J, Thornburg J, Yo H-J, York J   +13 more
core   +2 more sources

The refined inviscid stability condition and cellular instability of viscous shock waves [PDF]

, 2009
Combining work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct the violation of the ...
Abouseif, Alexander, Alpert, Artola, Barker, Barmin, Benzoni-Gavage, Bourlioux, Bridges, Brin, Brin, Erpenbeck, Fickett, Fickett, Fickett, Fowles, Gardner, Henry, Humpherys, Kasimov, Kevin Zumbrun, Majda, Majda, Majda, Majda, Majda, Mascia, Mascia, Mascia, McVey, Métivier, Serre, Serre, Serre, Texier, Texier, Zumbrun, Zumbrun, Zumbrun, Zumbrun, Zumbrun, Zumbrun   +41 more
core   +1 more source

Gasdynamic wave interaction in two spatial dimensions [PDF]

, 2003
We examine the interaction of shock waves by studying solutions of the two-dimensional Euler equations about a point. The problem is reduced to linear form by considering local solutions that are constant along each ray and thereby exhibit no length ...
Sanderson, S. R.
core   +1 more source

Pathologies of hyperbolic gauges in general relativity and other field theories [PDF]

, 1998
We present a mathematical characterization of hyperbolic gauge pathologies in general relativity and electrodynamics. We show how non-linear gauge terms can produce a blow-up along characteristics and how this can be identified numerically by performing ...
Alcubierre, Miguel, Masso, Joan
core   +2 more sources

Nonclassical shallow water flows [PDF]

, 2007
This paper deals with violent discontinuities in shallow water flows with large Froude number $F$. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions ...
Edwards, C., Howison, S. D., Ockendon, H., Ockendon, J. R.   +3 more
core   +1 more source

Singular limiting induced from continuum solutions and the problem of dynamic cavitation [PDF]

, 2013
In the works of K.A. Pericak-Spector and S. Spector [Pericak-Spector, Spector 1988, 1997] a class of self-similar solutions are constructed for the equations of radial isotropic elastodynamics that describe cavitating solutions.
Giesselmann, Jan, Tzavaras, Athanasios E.   +1 more
core   +5 more sources

First order hyperbolic formalism for Numerical Relativity [PDF]

, 1997
The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift.
A. Abrahams, A. Abrahams, A. Harten, A. Lichnerowicz, C. Bona, C. Bona, C. Bona, C. Bona, C. Bona, D. Bernstein, E. Seidel, E. Seidel, F. Estabrook, G. A. Sod, H. Friedrich, J. Massó, J. Stela, J. W. York, Jr., M. Alcubierre, P. Anninos, P. Anninos, P. Anninos, P. D. Lax, R. D. Ritchmeyer, R. J. LeVeque, R. W. MacCormack, S. Frittelli, S. L. Shapiro, S. L. Shapiro, W. H. Press, Y. Choquet-Bruhat, Y. Choquet-Bruhat, Y. Choquet-Bruhat, Y. Foures-Bruhat   +33 more
core   +4 more sources

Formation and propagation of singularities in one-dimensional Chaplygin gas

, 2013
In this paper, we investigate the formation and propagation of singularities for the system for one-dimensional Chaplygin gas, which is described by a quasilinear hyperbolic system with linearly degenerate characteristic fields.
Kong, De-Xing, Wei, Changhua
core   +1 more source

The nature of spacetime singularities

, 2005
Present knowledge about the nature of spacetime singularities in the context of classical general relativity is surveyed. The status of the BKL picture of cosmological singularities and its relevance to the cosmic censorship hypothesis are discussed.
Rendall, Alan D.
core   +2 more sources