scholarly journals Action principle for numerical-relativity evolution systems

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
C. Bona ◽  
C. Bona-Casas ◽  
C. Palenzuela
Keyword(s):  
Numerical Relativity ◽  
Action Principle ◽  
Evolution Systems

NUMERICAL RELATIVITY: EVOLVING SPACETIME

1993 ◽  
Vol 04 (04) ◽  
pp. 883-907 ◽  
Author(s):  
C. BONA ◽  
J. MASSÓ
Keyword(s):  
Ad Hoc ◽  
Numerical Solutions ◽  
Numerical Relativity ◽  
Historical Review ◽  
Evolution System ◽  
Field Equations ◽  
Metric Tensor ◽  
New Family ◽  
Mandatory Use ◽  
Evolution Systems

The construction of numerical solutions of Einstein's General Relativity equations is formulated as an initial-value problem. The space-plus-time (3 + 1) decomposition of the spacetime metric tensor is used to discuss the structure of the field equations. The resulting evolution system is shown to depend in a crucial way on the coordinate gauge. The mandatory use of singularity avoiding coordinate conditions (like maximal slicing or similar gauges) is explained. A brief historical review of Numerical Relativity is included, showing the enormous effort in constructing codes based in these gauges, which lead to non-hyperbolic evolution systems, using "ad hoc" numerical techniques. A new family of first order hyperbolic evolution systems for the vacuum Einstein field equations in the harmonic slicing gauge is presented. This family depends on a symmetric 3 × 3 array of parameters which can be used to scale the dynamical variables in future numerical applications.

scholarly journals 3+1 covariant suite of numerical relativity evolution systems

2002 ◽  
Vol 66 (8) ◽  
Author(s):  
C. Bona ◽  
T. Ledvinka ◽  
C. Palenzuela
Keyword(s):  
Numerical Relativity ◽  
Evolution Systems

scholarly journals Non-Riemannian gravity actions from double field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
A. D. Gallegos ◽  
U. Gürsoy ◽  
S. Verma ◽  
N. Zinnato
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Technical Note ◽  
Action Principle ◽  
Relativistic Symmetry ◽  
Gravitational Theories ◽  
Double Field Theory

Abstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

scholarly journals Up-down instability of binary black holes in numerical relativity

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Vijay Varma ◽  
Matthew Mould ◽  
Davide Gerosa ◽  
Mark A. Scheel ◽  
Lawrence E. Kidder ◽  
...  
Keyword(s):  
Black Holes ◽  
Numerical Relativity ◽  
Binary Black Holes
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