Comparison of closure approximations for continuous dislocation dynamics

2014 ◽  
Vol 1651 ◽  
Author(s):  
Mehran Monavari ◽  
Michael Zaiser ◽  
Stefan Sandfeld
Keyword(s):  
Maximum Entropy ◽  
Orientation Distribution ◽  
Dislocation Dynamics ◽  
Optimal Estimate ◽  
Benchmark Problem ◽  
Closed Set ◽  
Closure Approximations ◽  
Maximum Entropy Formalism ◽  
Continuous Field

ABSTRACTWe discuss methods to describe the evolution of dislocation systems in terms of a limited number of continuous field variables while correctly representing the kinematics of systems of flexible and connected lines. We show that a satisfactory continuum representation may be obtained in terms of only four variables. We discuss the consequences of different approximations needed to formulate a closed set of equations for these variables and propose a benchmark problem to assess the performance of the resulting models. We demonstrate that best results are obtained by using the maximum entropy formalism to arrive at an optimal estimate for the dislocation orientation distribution based on its lowest-order angular moments.

BRAGG-PEAK LOCATION EMPLOYING A MAXIMUM-ENTROPY FORMALISM

1986 ◽  
Vol 47 (C5) ◽  
pp. C5-55-C5-62
Author(s):  
M. S. LEHMANN ◽  
T. E. ROBINSON ◽  
S. W. WILKINS
Keyword(s):  
Maximum Entropy ◽  
Bragg Peak ◽  
Peak Location ◽  
Maximum Entropy Formalism

Continuum Dislocation Dynamics Based on the Second Order Alignment Tensor

2014 ◽  
Vol 1651 ◽  
Author(s):  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Evolution Equations ◽  
Continuum Theory ◽  
Orientation Distribution ◽  
Line Length ◽  
Second Order ◽  
Dislocation Dynamics ◽  
Alignment Tensor ◽  
Length Changes ◽  
Edge Dislocations

ABSTRACTIn the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.

Application of the Maximum Entropy Formalism on Sprays Produced by Ultrasonic Atomizers

2003 ◽  
Vol 20 (2) ◽  
pp. 150-161 ◽  
Author(s):  
Christophe Dumouchel ◽  
Daniel Sindayihebura ◽  
Léon Bolle
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Formalism

A new computational method for the solution of flow problems of microstructured fluids. Part 2. Inhomogeneous shear flow of a suspension

1994 ◽  
Vol 262 ◽  
pp. 171-204 ◽  
Author(s):  
Andrew J. Szeri ◽  
L. Gary Leal
Keyword(s):  
Planck Equation ◽  
Orientation Distribution ◽  
Companion Paper ◽  
Computational Method ◽  
Flat Plates ◽  
New Approach ◽  
Flow Problems ◽  
Closure Approximations ◽  
Rigid Rod ◽  
Microstructured Fluids

A numerical investigation is conducted into the flow of a dilute suspension of rigid rod-like particles between parallel flat plates, driven by a uniform pressure gradient. The particles are assumed to be small relative to lengthscales of the flow with the effect that particle orientations evolve according to the local velocity gradient; the particles are also assumed to be small in an absolute sense, with the consequence that Brownian motions are of consequence. The calculations are performed using a novel approach, with a theoretical basis that has been developed previously in a companion paper (Szeri & Leal 1992). The new approach permits one to solve flow problems of microstructured fluids (such as suspensions, liquid crystals, polymer solutions and melts) without ‘pre-averaging’ or closure approximations. In the present work, the new approach is used to expose previously unknown pathological, non-physical predictions in various constitutive models derived using closure approximations. This appears to have passed unnoticed in prior work. In addition, the new approach is shown to possess several computational advantages. The determination of the orientation distribution of particles is self-adaptive; this leads, in effect, to a very efficient solution of the associated Smoluchowski (or Fokker–Planck) equation. Moreover, the new approach is highly suited to parallel (and vector) implementation on modern computers. These issues are explored in detail in the context of the example flow.

scholarly journals The maximum entropy formalism and the idiosyncratic theory of biodiversity

2007 ◽  
Vol 10 (11) ◽  
pp. 1017-1028 ◽  
Author(s):  
Salvador Pueyo ◽  
Fangliang He ◽  
Tommaso Zillio
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Formalism
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