scholarly journals Nonclassical Symmetry Solutions for Fourth-Order Phase Field Reaction–Diffusion

Symmetry ◽  
2018 ◽  
Vol 10 (3) ◽  
pp. 72 ◽  
Author(s):  
Philip Broadbridge ◽  
Dimetre Triadis ◽  
Dilruk Gallage ◽  
Pierluigi Cesana
Keyword(s):  
Fourth Order ◽  
Phase Field ◽  
Reaction Diffusion ◽  
Nonclassical Symmetry ◽  
Field Reaction

scholarly journals Nonclassical Symmetry Solutions for 4th Order Phase Field Reaction-Diffusion

2018 ◽  
Author(s):  
Philip Broadbridge ◽  
Dimetre Triadis ◽  
Dilruk Gallage ◽  
Pierluigi Cesana
Keyword(s):  
Phase Field ◽  
Spherical Inclusion ◽  
Reaction Diffusion ◽  
Physical Structure ◽  
Reaction Diffusion Equations ◽  
Phase System ◽  
Two Phase ◽  
Nonclassical Symmetry ◽  
Field Reaction ◽  
Cahn Hilliard Equation

Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

Fourth-order hybrid phase field analysis with non-equal order elements and dual meshes for simulating crack propagation

2022 ◽  
Vol 142 ◽  
pp. 104587
Author(s):  
Feng Zhu ◽  
Hongxiang Tang ◽  
Xue Zhang ◽  
George Papazafeiropoulos
Keyword(s):  
Crack Propagation ◽  
Fourth Order ◽  
Phase Field ◽  
Field Analysis

scholarly journals Optimal control of stochastic phase-field models related to tumor growth

2020 ◽  
Vol 26 ◽  
pp. 104
Author(s):  
Carlo Orrieri ◽  
Elisabetta Rocca ◽  
Luca Scarpa
Keyword(s):  
Optimal Control ◽  
Tumor Growth ◽  
Phase Field ◽  
Phase Field Model ◽  
Growth Dynamics ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Adjoint System ◽  
Reaction Diffusion Equation ◽  
Cahn Hilliard Equation

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong well-posedness of the system in a general framework through monotonicity and stochastic compactness arguments. We introduce then suitable controls representing the concentration of cytotoxic drugs administered in medical treatment and we analyze a related optimal control problem. We derive existence of an optimal strategy and deduce first-order necessary optimality conditions by studying the corresponding linearized system and the backward adjoint system.

Analytic solutions for calcium ion fertilisation waves on the surface of eggs

2019 ◽  
Vol 36 (4) ◽  
pp. 549-562 ◽  
Author(s):  
Bronwyn H Bradshaw-Hajek ◽  
Philip Broadbridge
Keyword(s):  
Calcium Ion ◽  
Calcium Concentration ◽  
Analytic Solution ◽  
Reaction Diffusion ◽  
Approximate Equation ◽  
Analytic Solutions ◽  
Nonlinear Reaction ◽  
Nonclassical Symmetry ◽  
Sperm Entry ◽  
Insight Into

Abstract The evolution of calcium fertilisation waves on the cortex of amphibian eggs can be described by a nonlinear reaction-diffusion process on the surface of a sphere. Here, we use the nonclassical symmetry technique to find an exact analytic solution that describes the evolution of the calcium concentration. The solutions presented compare well with published experimental results. The analytic solution can be used to give insight into the processes governing the fertilisation wave, such as the flow of calcium ions from the sperm entry point. By finding a spiral solution to an approximate equation linearised near saturation, we also demonstrate how solutions with other properties may be constructed using this technique.

Transient Mean-Field Reaction-Diffusion Model Applied to Hydrogen Evolution From Hydrogenated Amorphous Silicon

1995 ◽  
Vol 377 ◽  
Author(s):  
A. J. Franzi ◽  
M. Mavrikakis ◽  
J. W. Schwank ◽  
J. L. Gland
Keyword(s):  
Amorphous Silicon ◽  
Hydrogen Evolution ◽  
Diffusion Model ◽  
Mean Field ◽  
Hydrogenated Amorphous Silicon ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Wide Range ◽  
Field Reaction ◽  
Hydrogenated Amorphous

ABSTRACTHydrogen bulk mobility plays an important role in determining a wide range of materials and electronic properties of hydrogenated amorphous silicon (a-Si:H). The existence of two types of hydrogen traps plays an important role in controlling hydrogen mobility in, and evolution of hydrogen from a-Si:H, however, theoretical and experimental literature values for the trap energetics vary considerably. We have developed a mean-field reaction-diffusion model which explicitly includes two trap states and realistic surface processes to model hydrogen evolution from a-Si:H. Modern numerical techniques were required to solve this challenging problem over the wide range of temperatures and concentrations encountered in typical hydrogen evolution experiments. The model is based on a number of experimentally established parameters. Comparison of our rigorous model with temperature programmed hydrogen evolution experiments provides a powerful method for characterizing the energetics, trap concentrations and diffusivity of hydrogen in a-Si:H.

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