Parallel Computation of Nearly Recurrent Components of Piecewise Constant Vector Fields

2014 ◽  
pp. 119-132
Author(s):  
Nicholas Brunhart-Lupo ◽  
Andrzej Szymczak
Keyword(s):  
Parallel Computation ◽  
Vector Fields ◽  
Constant Vector ◽  
Piecewise Constant

Boundary-aware hodge decompositions for piecewise constant vector fields

2016 ◽  
Vol 78 ◽  
pp. 126-136 ◽  
Author(s):  
Konstantin Poelke ◽  
Konrad Polthier
Keyword(s):  
Vector Fields ◽  
Constant Vector ◽  
Piecewise Constant

scholarly journals Some minisuperspace model for the Faddeev formulation of gravity

2014 ◽  
Vol 29 (27) ◽  
pp. 1450141 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Distinctive Feature ◽  
Vector Fields ◽  
Measure Zero ◽  
Equations Of Motion ◽  
Zero Set ◽  
Constant Vector ◽  
Field Equations ◽  
Piecewise Constant ◽  
The Continuum

We consider Faddeev formulation of General Relativity (GR) in which the metric is composed of ten vector fields or a 4 ×10 tetrad. This formulation reduces to the usual GR upon partial use of the field equations. A distinctive feature of the Faddeev action is its finiteness on the discontinuous fields. This allows to introduce its minisuperspace formulation where the vector fields are constant everywhere on ℝ4 with exception of a measure zero set (the piecewise constant fields). The fields are parametrized by their constant values independently chosen in, e.g. the 4-simplices or, say, parallelepipeds into which ℝ4 can be decomposed. The form of the action for the vector fields of this type is found. We also consider the piecewise constant vector fields approximating the fixed smooth ones. We check that if the regions in which the vector fields are constant are made arbitrarily small, the minisuperspace action and equations of motion tend to the continuum Faddeev ones.

Nearly Recurrent Components in 3D Piecewise Constant Vector Fields

2012 ◽  
Vol 31 (3pt3) ◽  
pp. 1115-1124 ◽  
Author(s):  
Andrzej Szymczak ◽  
Nicholas Brunhart-Lupo
Keyword(s):  
Vector Fields ◽  
Constant Vector ◽  
Piecewise Constant

Parallel Computation of Complex Antennas around the Coated Object Using Iterative Vector Fields Technique

2014 ◽  
Vol E97.C (7) ◽  
pp. 661-669
Author(s):  
Ying YAN ◽  
Xunwang ZHAO ◽  
Yu ZHANG ◽  
Changhong LIANG ◽  
Zhewang MA
Keyword(s):  
Parallel Computation ◽  
Vector Fields

The Divergence Equation

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Vector Fields ◽  
Classical Mechanics ◽  
Main Lemma ◽  
Constant Vector ◽  
Smooth Vector ◽  
Continuous Solutions ◽  
All Solutions ◽  
Divergence Equation ◽  
Conservation Of Momentum ◽  
Special Solutions

This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a smooth function and a smooth vector field on ³, plus an unknown, symmetric (2, 0) tensor. The chapter presents a proposition that takes into account a condition relating to the conservation of momentum as well as a condition that reflects Newton's law, which states that every action must have an equal and opposite reaction. This axiom, in turn, implies the conservation of momentum in classical mechanics. In view of Noether's theorem, the constant vector fields which act as Galilean symmetries of the Euler equation are responsible for the conservation of momentum. The chapter shows proof that all solutions to the Euler-Reynolds equations conserve momentum.

scholarly journals First-order minisuperspace model for the Faddeev formulation of gravity

2015 ◽  
Vol 30 (32) ◽  
pp. 1550174 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Field Equations ◽  
Piecewise Constant ◽  
First Order ◽  
Weyl Connection ◽  
Type Form ◽  
Connection Type ◽  
Discrete Theory

Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual GR. Earlier we have proposed some minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like 4-simplices or, say, cuboids into which [Formula: see text] can be decomposed. Now we study some representation of this (discrete) theory, an analogue of the Cartan–Weyl connection-type form of the Hilbert–Einstein action in the usual continuum GR.

scholarly journals Spectrum of area in the Faddeev formulation of gravity

2016 ◽  
Vol 31 (19) ◽  
pp. 1650114 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Hamiltonian Formalism ◽  
Black Hole Entropy ◽  
Field Equations ◽  
Piecewise Constant ◽  
First Order ◽  
Connection Matrices ◽  
Order Representation ◽  
Connection Type

Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual general relativity (GR). Earlier, we have proposed first-order representation of the minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like four-simplices or, say, cuboids into which [Formula: see text] can be decomposed, an analogue of the Cartan–Weyl connection-type form of the Hilbert–Einstein action in the usual continuum GR. In the Hamiltonian formalism, the tetrad bilinears are canonically conjugate to the orthogonal connection matrices. We evaluate the spectrum of the elementary areas, functions of the tetrad bilinears. The spectrum is discrete and proportional to the Faddeev analog [Formula: see text] of the Barbero–Immirzi parameter [Formula: see text]. The possibility of the tetrad and metric discontinuities in the Faddeev gravity allows to consider any surface as consisting of a set of virtually independent elementary areas and its spectrum being the sum of the elementary spectra. Requiring consistency of the black hole entropy calculations known in the literature we are able to estimate [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document