scholarly journals Mathematical analysis of a phase-field model of brain cancers with chemotherapy and antiangiogenic therapy effects

2021 ◽  
Vol 7 (1) ◽  
pp. 1536-1561
Author(s):  
Monica Conti ◽  
◽  
Stefania Gatti ◽  
Alain Miranville ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Phase Field ◽  
Mathematical Analysis ◽  
Existence And Uniqueness ◽  
Field Model ◽  
Antiangiogenic Therapy ◽  
Phase Field Model ◽  
Optimal Treatment ◽  
Biologically Relevant ◽  
Nonnegative Solutions

<abstract><p>Our aim in this paper is to study a mathematical model for brain cancers with chemotherapy and antiangiogenic therapy effects. We prove the existence and uniqueness of biologically relevant (nonnegative) solutions. We then address the important question of optimal treatment. More precisely, we study the problem of finding the controls that provide the optimal cytotoxic and antiangiogenic effects to treat the cancer.</p></abstract>

A Simulation of Ferroelastic Phase Formation by Using Phase Field Model

2016 ◽  
Vol 725 ◽  
pp. 208-213
Author(s):  
Mayu Muramatsu ◽  
Tatsuya Kawada ◽  
K. Terada
Keyword(s):  
Mathematical Model ◽  
Fuel Cell ◽  
Phase Field ◽  
Elastic Energy ◽  
Field Model ◽  
Phase Field Model ◽  
Nucleation And Growth ◽  
Solid Oxide ◽  
Oxide Fuel ◽  
Numerical Examples

In order to incorporate the mechanical behavior of ferroelastic phase into the stress analysis of solid oxide fuel cell in consideration of elastic, creep, thermal and reduction strains, we propose a mathematical model to predict the formation of ferroelastic phases in crystal grains of La0.6Sr0.4Co0.2Fe0.8O3-δ. The phase field model equipped with the elastic energy is introduced to realize the morphology formation of ferroelastic phases in a crystal grain. By the use of the developed mathematical model, some numerical examples are performed to reproduce the deformation-induced nucleation and growth of ferroelastic phases of La0.6Sr0.4Co0.2Fe0.8O3-δ.

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

scholarly journals Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Min Yang ◽  
Lu Wang ◽  
Wentao Yan
Keyword(s):  
Additive Manufacturing ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Nucleation Theory ◽  
Experimental Result ◽  
Classical Nucleation Theory ◽  
Validation Experiment ◽  
Powder Particles

AbstractA three-dimensional phase-field model is developed to simulate grain evolutions during powder-bed-fusion (PBF) additive manufacturing, while the physically-informed temperature profile is implemented from a thermal-fluid flow model. The phase-field model incorporates a nucleation model based on classical nucleation theory, as well as the initial grain structures of powder particles and substrate. The grain evolutions during the three-layer three-track PBF process are comprehensively reproduced, including grain nucleation and growth in molten pools, epitaxial growth from powder particles, substrate and previous tracks, grain re-melting and re-growth in overlapping zones, and grain coarsening in heat-affected zones. A validation experiment has been carried out, showing that the simulation results are consistent with the experimental results in the molten pool and grain morphologies. Furthermore, the grain refinement by adding nanoparticles is preliminarily reproduced and compared against the experimental result in literature.

A two-scale iterative scheme for a phase-field model for precipitation and dissolution in porous media

2021 ◽  
Vol 396 ◽  
pp. 125933
Author(s):  
Manuela Bastidas Olivares ◽  
Carina Bringedal ◽  
Iuliu Sorin Pop
Keyword(s):  
Porous Media ◽  
Phase Field ◽  
Field Model ◽  
Iterative Scheme ◽  
Phase Field Model
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