ON THE SCALAR CASIMIR ENERGIES IN SPACE-TIMES WITH Md × Tq STRUCTURE

1991 ◽  
Vol 06 (20) ◽  
pp. 1855-1861 ◽  
Author(s):  
F. CARUSO ◽  
N. P. NETO ◽  
B. F. SVAITER ◽  
N. F. SVAITER
Keyword(s):  
Scalar Field ◽  
Energy Density ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Casimir Energy ◽  
Space Time ◽  
Time Dimension

The Casimir energy density of a scalar field quantized in a Md × Tq space-time is calculated. The field is supposed to satisfy Dirichlet and periodic boundary conditions in the (d − 1)- and q-dimensional submanifolds respectively. On account of this non-trivial topology, the sign of the Casimir energy is shown to have the same peculiar and entangled dependence on the number of finite sides of the hyperparallelopipedal cavity and on the space-time dimension, with only one exception which is discussed.

scholarly journals RADIUS DESTABILIZATION IN FIVE-DIMENSIONAL ORBIFOLDS DUE TO AN ENHANCED CASIMIR EFFECT

2009 ◽  
Vol 24 (19) ◽  
pp. 1495-1506 ◽  
Author(s):  
R. OBOUSY ◽  
G. CLEAVER
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Periodic Boundary ◽  
Casimir Force ◽  
Casimir Effect ◽  
Periodic Boundary Conditions ◽  
Casimir Energy ◽  
Higher Dimensional ◽  
The One

One of the challenges in connecting higher dimensional theories to cosmology is stabilization of the moduli fields. We investigate the role of a Lorentz violating vector field in the context of stabilization. Specifically, we compute the one-loop Casimir energy in Randall–Sundrum five-dimensional (non-supersymmetric) S1/ Z2 orbifolds resulting from the interaction of a real scalar field with periodic boundary conditions with a Lorentz violating vector field. We find that the result is an enhanced attractive Casimir force. Hence, for stability, positive contributions to the Casimir force from branes and additional fields would be required to counter the destabilizing, attractive effect of Lorentz violating fields.

scholarly journals CASIMIR ENERGY DENSITY IN CLOSED HYPERBOLIC UNIVERSES

2002 ◽  
Vol 17 (29) ◽  
pp. 4385-4392 ◽  
Author(s):  
DANIEL MÜLLER ◽  
HELIO V. FAGUNDES
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Energy Density ◽  
Boundary Conditions ◽  
Negative Curvature ◽  
Casimir Effect ◽  
Casimir Energy ◽  
The Difference

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with closed spatial sections of negative curvature.

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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