NONEXTENSIVE MICROSCOPIC BEHAVIOR OF LONG-RANGE INTERACTING PARTICLES IN PERIODIC MEDIA

2000 ◽  
Vol 11 (03) ◽  
pp. 629-634 ◽  
Author(s):  
SERGIO CURILEF
Keyword(s):  
Boundary Conditions ◽  
Long Range ◽  
Periodic Boundary ◽  
Present Model ◽  
Periodic Boundary Conditions ◽  
The Other ◽  
Attractive Potential ◽  
Periodic Media ◽  
Interacting Particles ◽  
Other Hand

This work presents a possible way to study the long-range interacting particles in finite-infinite (mesoscopic-macroscopic) systems with periodic boundary conditions. A symmetric lattice and their contributions over all space are used in the problem. In the present model, we assume that at long distances, the two-body attractive potential decays as a 1/rα law. We verified that the potential in any particle converges (diverges) when the interactions are short(long)-ranged. On the other hand, forces in any particle converge rapidly in all cases. However, we adopt a nonextensive scaling and we guarantee that the potential converges anywhere.

SUMMATION OF LOGARITHMIC INTERACTIONS IN PERIODIC MEDIA

1996 ◽  
Vol 07 (06) ◽  
pp. 873-881 ◽  
Author(s):  
NIELS GRØNBECH-JENSEN
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Monte Carlo Simulations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Dimensional System ◽  
Two Dimensional ◽  
Trigonometric Functions ◽  
Periodic Media ◽  
Two Dimensional System

We present a set of expressions for evaluating energies and forces between particles interacting logarithmically in a finite two-dimensional system with periodic boundary conditions. The formalism can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges. The expressions are shown to converge to usual computer accuracy (~10–16) by adding only few terms in a single sum of standard trigonometric functions.

Subsonic plane flow in an annulus or a channel with spacewise periodic boundary conditions

1955 ◽  
Vol 229 (1176) ◽  
pp. 63-85 ◽  
Keyword(s):  
Boundary Conditions ◽  
Mixed Problem ◽  
Direct Problem ◽  
Periodic Boundary ◽  
Subsonic Flow ◽  
Periodic Boundary Conditions ◽  
The Other ◽  
Closed Circuit ◽  
Inviscid Fluid ◽  
Plane Flow

Equations for the calculation of the subsonic flow of an inviscid fluid in channels with boundary conditions which are periodic in distance along the channel (for example flow in a closed circuit such as an annulus) are derived. Three types of boundary conditions are considered, namely, ( i ) shape of the walls given (‘direct’ problem), ( ii ) pressures or velocities on the walls given (‘indirect’ problem), and ( iii ) pressures on one wall and the shape of the other wall given (‘mixed’ problem). The theory, which is shown to have numerous aero-dynamic applications, is illustrated by several examples.

A numerical investigation of the Schaeffer homotopy in the problem of Taylor‒Couette flows

1989 ◽  
Vol 426 (1871) ◽  
pp. 331-342 ◽  
Keyword(s):  
Numerical Methods ◽  
Boundary Conditions ◽  
Numerical Investigation ◽  
Periodic Boundary ◽  
Exchange Process ◽  
Periodic Boundary Conditions ◽  
The Other ◽  
Taylor Vortex ◽  
Taylor Couette ◽  
Realistic Boundary Conditions

Numerical methods are used to study the 4, 6-cell exchange process in the Taylor vortex problem, with particular reference to the homotopy devised by Schaeffer. The homotopy describes a transformation between two models, one incorporating periodic boundary conditions and so referring to flows in an infinite annulus, the other with realistic boundary conditions. Our calculations indicate that the former model is more complicated than previously suspected and lead to a better under­standing of the consequences of Schaeffer’s device.

scholarly journals CONNECTION BETWEEN ζ AND CUTOFF REGULARIZATIONS OF CASIMIR ENERGIES

1996 ◽  
Vol 11 (16) ◽  
pp. 2871-2886 ◽  
Author(s):  
C.G. BENEVENTANO ◽  
E.M. SANTANGELO
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Scalar Fields ◽  
The Other ◽  
Massless Scalar ◽  
Finite Result

We study the connection between ζ- and cutoff-regularized Casimir energies for scalar fields. We show that, in general, both regularization schemes lead to divergent contributions, and to minimal finite parts which do not coincide. We determine the relationships among the various coefficients appearing in one approach and the other. We discuss the agreement with our predictions in the case of scalar fields in d-dimensional boxes under periodic boundary conditions. Finally, we apply our results to massless scalar fields in balls, an example where ambiguities remain under the physical prescriptions usually imposed to extract a finite result.

The necessity of periodic boundary conditions for the accurate calculation of crystalline terahertz spectra

2021 ◽  
Author(s):  
Peter A. Banks ◽  
Luke Burgess ◽  
Michael T Ruggiero
Keyword(s):  
Boundary Conditions ◽  
Long Range ◽  
Vibrational Spectroscopy ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Spectroscopic Technique ◽  
Accurate Calculation ◽  
Collective Dynamics ◽  
Long Range Interactions

Terahertz vibrational spectroscopy has emerged as a powerful spectroscopic technique, providing valuable information regarding long-range interactions - and associated collective dynamics - occurring in solids. However, the terahertz sciences are...

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