scholarly journals Variational principle and one-point functions in three-dimensional flat space Einstein gravity

2014 ◽  
Vol 89 (8) ◽  
Author(s):  
Stephane Detournay ◽  
Daniel Grumiller ◽  
Friedrich Schöller ◽  
Joan Simón
Keyword(s):  
Variational Principle ◽  
Three Dimensional ◽  
Flat Space ◽  
Einstein Gravity

scholarly journals Three-dimensional Einstein gravity: Dynamics of flat space

1984 ◽  
Vol 152 (1) ◽  
pp. 220-235 ◽  
Author(s):  
S Deser ◽  
R Jackiw ◽  
G 't Hooft
Keyword(s):  
Three Dimensional ◽  
Flat Space ◽  
Einstein Gravity

Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution

1992 ◽  
Vol 59 (3) ◽  
pp. 587-595 ◽  
Author(s):  
Charles R. Steele ◽  
Yoon Young Kim
Keyword(s):  
Variational Principle ◽  
Equations Of State ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Shells Of Revolution ◽  
Elastic Bodies ◽  
Mixed Variational Principle ◽  
Stress Components ◽  
Independent Variable ◽  
Nonsymmetric Deformation

A modified mixed variational principle is established for a class of problems with one spatial variable as the independent variable. The specific applications are on the three-dimensional deformation of elastic bodies and the nonsymmetric deformation of shells of revolution. The possibly novel feature is the elimination in the variational formulation of the stress components which cannot be prescribed on the boundaries. The result is a form exactly analogous to classical mechanics of a dynamic system, with the equations of state exactly in the form of the canonical equations of Hamilton. With the present approach, the correct scale factors of the field variables to make the system self-adjoint are readily identified, and anisotropic materials including composites can be handled effectively. The analysis for shells of revolution is given with and without the transverse shear deformation considered.

THE VILKOVISKY EFFECTIVE ACTION IN THE EVEN-DIMENSIONAL QUANTUM GRAVITY

1989 ◽  
Vol 04 (07) ◽  
pp. 633-644 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA ◽  
S. D. ODINTSOV
Keyword(s):  
Numerical Calculation ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Einstein Gravity ◽  
Quantum Field ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
The One

The one-loop Vilkovisky effective potential which is not dependent on a gauge and a parametrization of quantum field, is investigated. We have considered Einstein gravity on a background manifold of (flat space) × (d−4- sphere) or × (d−4- dimensional torus ), d is even, and of R3 × (1- sphere ), where R3 is flat space. The numerical calculation for the cases R4 × Td−4 (d = 6,8,10) and R3 × S1 is done. The solution to the one-loop corrected equations of motion is found, although the spontaneous compactification is not stable in these cases.

A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle

1996 ◽  
Vol 118 (1) ◽  
pp. 33-42 ◽  
Author(s):  
Xuefeng Tian ◽  
Bharat Bhushan
Keyword(s):  
Variational Principle ◽  
Contact Problem ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Computation Time ◽  
Inversion Method ◽  
Three Dimensional Model ◽  
Perfectly Plastic ◽  
Contact Points ◽  
Uniqueness Of The Solution

A new numerical method for the analysis of elastic and elastic-plastic contacts of two rough surfaces has been developed. The method is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. The present variational approach guarantees the uniqueness of the solution of the contact problem and significantly reduces the computation time as compared with the conventional matrix inversion method, and thus, makes it feasible to solve 3-D contact problem with large number of contact points. The model is extended to elastic-perfectly plastic contacts. The model is used to predict contact statistics for computer generated surfaces.

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