scholarly journals A Non-local Phase Field Model of Bohm’s Quantum Potential

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Roberto Mauri
Keyword(s):  
Body Force ◽  
Field Model ◽  
Mass Density ◽  
Phase Field Model ◽  
Equation Of Motion ◽  
Quantum Potential ◽  
The Body ◽  
Local Phase ◽  
Non Local ◽  
Non Locality

AbstractAssuming that the free energy of a gas depends non-locally on the logarithm of its mass density, the body force in the resulting equation of motion consists of the sum of density gradient terms. Truncating this series after the second term, Bohm’s quantum potential and the Madelung equation are identically obtained, showing explicitly that some of the hypotheses that led to the formulation of quantum mechanics admit a classical interpretation based on non-locality.

Initial-Value Problem for the Non-local Generalization of the Lorentz-Dirac Equation

1976 ◽  
Vol 31 (12) ◽  
pp. 1457-1464
Author(s):  
M. Sorg
Keyword(s):  
Proper Time ◽  
Perturbation Expansion ◽  
Equation Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Dirac Theory ◽  
Initial Value ◽  
Local Character ◽  
Non Local ◽  
Non Locality

AbstractAlthough the equation of motion, recently proposed for the classical radiating electron, is of non-local character in proper time, the Newtonian initial data (position and velocity) are sufficient to guarantee existence and uniqueness of the solutions. The corresponding existence proof is accomplished by the Picard-Lindelöf method of successive approximations. This method indicates the possibility of a perturbation expansion of the exact solution in terms of the non-locality parameter. Such a perturbation expansion does not seem to be possible in the Lorentz-Dirac theory.

A phase field model with non-local and anisotropic potential

2011 ◽  
Vol 19 (4) ◽  
pp. 045006 ◽  
Author(s):  
Xinfu Chen ◽  
Gunduz Caginalp ◽  
Emre Esenturk
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Non Local

scholarly journals Phase-field modelling and computing for a large number of phases

2019 ◽  
Vol 53 (3) ◽  
pp. 805-832
Author(s):  
Élie Bretin ◽  
Roland Denis ◽  
Jacques-Olivier Lachaud ◽  
Édouard Oudet
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Representation ◽  
High Resolution Data ◽  
Phase Field Models ◽  
Efficient Storage ◽  
Non Local ◽  
Discretization Point ◽  
Field Approaches

We propose a framework to represent a partition that evolves under mean curvature flows and volume constraints. Its principle follows a phase-field representation for each region of the partition, as well as classical Allen–Cahn equations for its evolution. We focus on the evolution and on the optimization of problems involving high resolution data with many regions in the partition. In this context, standard phase-field approaches require a lot of memory (one image per region) and computation timings increase at least as fast as the number of regions. We propose a more efficient storage strategy with a dedicated multi-image representation that retains only significant phase field values at each discretization point. We show that this strategy alone is unfortunately inefficient with classical phase field models. This is due to non local terms and low convergence rate. We therefore introduce and analyze an improved phase field model that localizes each phase field around its associated region, and which fully benefits of our storage strategy. To demonstrate the efficiency of the new multiphase field framework, we apply it to the famous 3D honeycomb problem and the conjecture of Weaire–Phelan’s tiling.

MARMOT Phase-Field Model for the U-Si System

2016 ◽  
Author(s):  
Larry Kenneth Aagesen ◽  
Daniel Schwen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

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