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268,751
The RungeKutta discontinuous Galerkin method for conservation laws V: multidimensional systems
, 1997
"... This is the fifth paper in a series in which we construct and study the socalled RungeKutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are describ ..."
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Cited by 508 (44 self)
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This is the fifth paper in a series in which we construct and study the socalled RungeKutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms
The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewiselinear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard programanalysis techniques can be adapted
Flocks, herds, and schools: a distributed behavior model,
 Proceedings of ACM SIGGRAPH
, 1987
"... Abstract The aggregate motion of a flock of birds, a herd of land animals, or a school of fish is a beautiful and familiar part of the natural world. But this type of complex motion is rarely seen in computer animation. This paper explores an approach based on simulation as an alternative to script ..."
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Cited by 1317 (5 self)
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their own course. Each simulated bird is implemented as an independent actor that navigates according to its local perception of the dynamic environment, the laws of simulated physics that rule its motion, and a set of behaviors programmed into it by the "animator." The aggregate motion
Unification of the state with the dynamical law
"... Abstract We address the question of why particular laws were selected for the universe, by proposing a mechanism for laws to evolve. Normally in physical theories, timeless laws act on timeevolving states. We propose that this is an approximation, good on time scales shorter than cosmological scal ..."
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Cited by 4 (3 self)
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Abstract We address the question of why particular laws were selected for the universe, by proposing a mechanism for laws to evolve. Normally in physical theories, timeless laws act on timeevolving states. We propose that this is an approximation, good on time scales shorter than cosmological
Control of Systems Integrating Logic, Dynamics, and Constraints
 Automatica
, 1998
"... This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and ..."
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Cited by 413 (50 self)
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This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real
Dynamical laws of superenergy in General Relativity
, 707
"... Abstract. Bel and BelRobinson tensors were introduced nearly fifty years ago in an attempt to generalize to gravitation the energymomentum tensor of electromagnetism. This generalization was successful from the mathematical point of view because these tensors share mathematical properties which ar ..."
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the dynamical laws of electromagnetism (Poynting theorem). The full orthogonal splitting of Bel and BelRobinson tensors is more complex but, as expected, similarities with electromagnetism are present. Also the covariant divergence of Bel tensor is analogous to the covariant divergence of the electromagnetic
Efficient Implementation of Weighted ENO Schemes
, 1995
"... In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially nonoscillatory) finite difference schemes of Liu, Osher and Chan [9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L¹ norm) ENO schemes are (r +1) th order accur ..."
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Cited by 412 (38 self)
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th order WENO scheme is as fast as the 4 th order WENO scheme of Liu et al. and, both schemes are about twice as fast as the 4th order ENO schemes on vector supercomputers and as fast on serial and parallel computers. For Euler systems of gas dynamics, we suggest to compute the weights from pressure
A DYNAMICAL LAW OF LARGE NUMBERS
, 2007
"... Let X1, X2,... denote i.i.d. random bits, each taking the values 1 and 0 with respective probabilities p and 1 − p. A wellknown theorem of Erdős and Rényi (1970) describes the length of the longest contiguous stretch, or “run, ” of ones in X1,..., Xn for large values of n. Benjamini, Häggström, Per ..."
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, Peres, and Steif (2003, Theorem 1.4) demonstrated the existence of unusual times, provided that the bits undergo equilibrium dynamics in time. The first of the two main results of this paper describes what happens if we allow for a fixed and finite number of “impurities ” [or zeros] in the longest run
Dynamical laws of superenergy in General Relativity
, 707
"... Abstract. The Bel and BelRobinson tensors were introduced nearly fifty years ..."
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Abstract. The Bel and BelRobinson tensors were introduced nearly fifty years
Some properties of Noether charge and a proposal for dynamical black hole entropy
 Phys. Rev
, 1994
"... We consider a general, classical theory of gravity with arbitrary matter fields in n dimensions, arising from a diffeomorphism invariant Lagrangian, L. We first show that L always can be written in a “manifestly covariant ” form. We then show that the symplectic potential current (n − 1)form, Θ, an ..."
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Cited by 326 (4 self)
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this formula for the Noether charge, we prove that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole. (For higher derivative theories, previous arguments had established this law only for stationary perturbations.) Finally, we propose a local, geometrical
Results 1  10
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268,751