ON THE SPACE-TIME MAPPING OF WHILE-LOOPS

1994 ◽  
Vol 04 (03) ◽  
pp. 221-232 ◽  
Author(s):  
MARTIN GRIEBL ◽  
CHRISTIAN LENGAUER
Keyword(s):  
Computational Model ◽  
Upper Bound ◽  
Automatic Parallelization ◽  
Space Time

A WHILE-loop can be viewed as a FOR-loop with a dynamic upper bound. The computational model of polytopes is useful for the automatic parallelization of FOR-loops. We investigate its potential for the parallelization of WHILE-loops.

A Tight Upper Bound on the PEP of a Space-Time Coded System

2007 ◽  
Vol 6 (9) ◽  
pp. 3238-3247 ◽  
Author(s):  
Ranjan Mallik ◽  
Q. Zhang
Keyword(s):  
Upper Bound ◽  
Space Time

scholarly journals A REVIEW OF THE N-BOUND AND THE MAXIMAL MASS CONJECTURES USING NUT-CHARGED dS SPACE–TIMES

2004 ◽  
Vol 19 (24) ◽  
pp. 3987-4035 ◽  
Author(s):  
RICHARD CLARKSON ◽  
A. M. GHEZELBASH ◽  
ROBERT B. MANN
Keyword(s):  
Upper Bound ◽  
De Sitter Space ◽  
Space Time ◽  
Conserved Quantities ◽  
De Sitter ◽  
Cosmological Singularity ◽  
Gravitational Entropy ◽  
The Status ◽  
Maximal Mass ◽  
Gravitational Thermodynamics

The proposed dS/CFT correspondence remains an intriguing paradigm in the context of string theory. Recently it has motivated two interesting conjectures: the entropic N-bound and the maximal mass conjecture. The former states that there is an upper bound to the entropy in asymptotically de Sitter space–times, given by the entropy of pure de Sitter space. The latter states that any asymptotically de Sitter space–time cannot have a mass larger than the pure de Sitter case without inducing a cosmological singularity. Here we review the status of these conjectures and demonstrate their limitation. We first describe a generalization of gravitational thermodynamics to asymptotically de Sitter space–times, and show how to compute conserved quantities and gravitational entropy using this formalism. From this we proceed to a discussion of the N-bound and maximal mass conjectures. We then illustrate that these conjectures are not satisfied for certain asymptotically de Sitter space–times with NUT charge. We close with a presentation of explicit examples in various space–time dimensionalities.

An efficient space-time operator-splitting method for high-dimensional vector-valued Allen–Cahn equations

2019 ◽  
Vol 29 (9) ◽  
pp. 3437-3453 ◽  
Author(s):  
Yunxia Sun ◽  
Xufeng Xiao ◽  
Zhiming Gao ◽  
Xinlong Feng
Keyword(s):  
Upper Bound ◽  
Operator Splitting ◽  
Splitting Method ◽  
Mass Conservation ◽  
Space Time ◽  
Time Operator ◽  
High Dimensional ◽  
Heat Equations ◽  
Content Type ◽  
Operator Splitting Method

Purpose The purpose of this paper is to propose an efficient space-time operator-splitting method for the high-dimensional vector-valued Allen–Cahn (AC) equations. The key of the space-time operator-splitting is to devide the complex partial differential equations into simple heat equations and nolinear ordinary differential equations. Design/methodology/approach Each component of high-dimensional heat equations is split into a series of one-dimensional heat equations in different spatial directions. The nonlinear ordinary differential equations are solved by a stabilized semi-implicit scheme to preserve the upper bound of the solution. The algorithm greatly reduces the computational complexity and storage requirement. Findings The theoretical analyses of stability in terms of upper bound preservation and mass conservation are shown. The numerical results of phase separation, evolution of the total free energy and total mass conservation show the effectiveness and accuracy of the space-time operator-splitting method. Practical implications Extensive 2D/3D numerical tests demonstrated the efficacy and accuracy of the proposed method. Originality/value The space-time operator-splitting method reduces the complexity of the problem and reduces the storage space by turning the high-dimensional problem into a series of 1D problems. We give the theoretical analyses of upper bound preservation and mass conservation for the proposed method.

scholarly journals ON SIGNATURE TRANSITION IN ROBERTSON–WALKER COSMOLOGIES

2000 ◽  
Vol 15 (10) ◽  
pp. 1521-1531 ◽  
Author(s):  
K. GHAFOORI-TABRIZI ◽  
S. S. GOUSHEH ◽  
H. R. SEPANGI
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Upper Bound ◽  
Classical Model ◽  
Space Time ◽  
Scale Factor ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Lorentzian Space ◽  
Einstein's Field Equations

We analyze a classical model of gravitation coupled to a self-interacting scalar field. We show that, within the context of this model for Robertson–Walker cosmologies, there exist solutions in the spatially non-flat cases exhibiting transitions from a Euclidean to a Lorentzian space–time. We then discuss the conditions under which these signature changing solutions to Einstein's field equations exist. In particular, we find that an upper bound for the cosmological constant exists and that close to the signature changing hypersurface, both the scale factor and the scalar field have to be constant. Moreover we find that the signature changing solutions do not exist when the scalar field is massless.

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