scholarly journals Periodic boundary conditions for three dimensional dislocation dynamics

1997 ◽  
Author(s):  
H., Diaz de la Rubia, T. Huang
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
Periodic Boundary Conditions ◽  
Dislocation Dynamics

scholarly journals Periodic Boundary Conditions for Dislocation Dynamics Simulations in Three Dimensions

2000 ◽  
Vol 653 ◽  
Author(s):  
Vasily V. Bulatov ◽  
Moon Rhee ◽  
Wei Cai
Keyword(s):  
Boundary Conditions ◽  
Large Scale ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Dislocation Dynamics ◽  
Three Dimensions ◽  
Translational Invariance ◽  
Timing Data ◽  
Dynamics Simulations ◽  
Consistent Treatment

AbstractThis article presents an implementation of periodic boundary conditions (PBC) for Dislocation Dynamics (DD) simulations in three dimensions (3D). We discuss fundamental aspects of PBC development, including preservation of translational invariance and line connectivity, the choice of initial configurations compatible with PBC and a consistent treatment of image stress. On the practical side, our approach reduces to manageable proportions the computational burden of updating the long-range elastic interactions among dislocation segments. The timing data confirms feasibility and practicality of PBC for large-scale DD simulations in 3D.

Optimal feedback control problem for Bingham media motion with periodic boundary conditions

2019 ◽  
Vol 485 (2) ◽  
pp. 139-141
Author(s):  
V. G. Zvyagin ◽  
M. V. Turbin
Keyword(s):  
Feedback Control ◽  
Boundary Conditions ◽  
Control Problem ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
Degree Theory ◽  
Periodic Boundary Conditions ◽  
Optimal Feedback Control ◽  
Operator Inclusion ◽  
Optimal Feedback

We study the optimal feedback control problem for the motion of Bingham media with periodic boundary conditions in two- and three-dimensional cases. First, the considered problem is interpreted as an operator inclusion with a multivalued right-hand side. Then, the approximation-topological approach to hydrodynamic problems and the degree theory for a class of multivalued maps are used to prove the existence of solutions of this inclusion. Finally, we prove that, among the solutions of the considered problem, there exists one minimizing the given cost functional.

scholarly journals Thermodynamic limit for a system with dipole-dipole interactions

1975 ◽  
Vol 19 (1) ◽  
pp. 116-128 ◽  
Author(s):  
E. R. Smith ◽  
J. W. Perram
Keyword(s):  
Free Energy ◽  
Variational Principle ◽  
Boundary Conditions ◽  
Thermodynamic Limit ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
Periodic Boundary Conditions ◽  
Free Energies ◽  
Dipole Interactions ◽  
Simple Boundary

AbstractIt is shown that for the three dimensional Ising model with dipole-dipole interactions, the thermodynamic limit of the free energy with simple boundary conditions is not the same as the thermodynamic limit of the free energy with periodic boundary conditions. A variational principle is developed to connect the two free energies.

A Simplified CFD Model With Multi-Periodic Boundary Conditions for Cross Wavy Channels

2011 ◽  
Author(s):  
L. X. Du ◽  
M. Zeng ◽  
Q. W. Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Flow Direction ◽  
Wave Length ◽  
Three Dimensional ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
The Cross ◽  
Wavy Channels

The compact and efficient primary surface heat exchangers are often used as recuperators in microturbine regenerative cycle systems. In the present study, the flow and the heat transfer performance of the cross wavy (CW) ducts have been simulated by three-dimensional models. The hydrodynamic diameters of the models are 1.689mm. Navier-Stokes and energy equations are solved by COMSOL3.5. Because one single wavy cell will overlap more than one adjacent channel, multi-periodic boundary conditions are especially adopted to simplify the calculations. Multi-periodic boundary conditions have been proved to have more reasonable flow field and heat transfer coefficient compared with the literature results. A dimensionless parameter L/A (wave length L, internal height of the corrugation in flow direction A) is defined as the optimization target. The numerical results indicated that when L/A = 6, the CW channel has the best comprehensive performance in all the cases. The comprehensive performances of the CW ducts are evaluated by the j/f (heat transfer factor j and friction factor f). The flow and heat transfer characteristics are much more complex in the cross wavy channels, especially when L/A is small.

The Harmonic Solid

2019 ◽  
pp. 331-349
Author(s):  
Robert H. Swendsen
Keyword(s):  
Boundary Conditions ◽  
Specific Heat ◽  
Periodic Boundary ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Normal Modes ◽  
Periodic Boundary Conditions ◽  
One Dimension ◽  
Debye Approximation

In Chapter 26 we return to calculating the contributions to the specific heat of a crystal from the vibrations of the atoms. The vibrations of a model of a solid, for which the interactions are quadratic in form, is investigated. Calculations are restricted to one dimension for simplicity in the derivations of the Fourier modes and the equations of motion. Both pinned and periodic boundary conditions are discussed. The representation of the Hamiltonian in terms of normal modes and the solution in terms of the equations of motion are derived. The Debye approximation is then introduced for three-dimensional systems.

Phase Transitions in Three Dimensional Ising Systems under Free and Periodic Boundary Conditions

2004 ◽  
Vol 301 (1) ◽  
pp. 91-95
Author(s):  
M FELISA MARTÍNEZ RUIZ ◽  
FRANCISCA PAJUELO ◽  
JORGE GARCÍA ◽  
CARMEN ARAGÓ ◽  
JULIO. A. GONZALO
Keyword(s):  
Phase Transitions ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Three Dimensional ◽  
Periodic Boundary Conditions ◽  
Ising Systems
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