scholarly journals Numerical Analysis of a Nonconvex Variational Problem Related to Solid-Solid Phase Transitions

1994 ◽  
Vol 31 (1) ◽  
pp. 111-127 ◽  
Author(s):  
Pierre-Alain Gremaud
Keyword(s):  
Phase Transitions ◽  
Numerical Analysis ◽  
Variational Problem ◽  
Solid Phase ◽  
Nonconvex Variational Problem

scholarly journals On the minimization of some nonconvex double obstacle problems

2003 ◽  
Vol 2003 (10) ◽  
pp. 535-551
Author(s):  
A. Elfanni
Keyword(s):  
Numerical Analysis ◽  
Variational Problem ◽  
Minimization Problem ◽  
Lipschitz Functions ◽  
Discrete Space ◽  
Obstacle Problems ◽  
Minimizing Sequences ◽  
Nonconvex Variational Problem ◽  
Admissible Functions

We consider a nonconvex variational problem for which the set of admissible functions consists of all Lipschitz functions located between two fixed obstacles. It turns out that the value of the minimization problem at hand is equal to zero when the obstacles do not touch each other; otherwise, it might be positive. The results are obtained through the construction of suitable minimizing sequences. Interpolating these minimizing sequences in some discrete space, a numerical analysis is then carried out.

scholarly journals Prion-Like Proteins in Phase Separation and Their Link to Disease

Biomolecules ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1014
Author(s):  
Macy L. Sprunger ◽  
Meredith E. Jackrel
Keyword(s):  
Protein Folding ◽  
Phase Transitions ◽  
Phase Separation ◽  
Liquid Phase ◽  
Protein Misfolding ◽  
Solid Phase ◽  
Liquid Phase Separation ◽  
Therapeutic Approaches ◽  
Important Physiological Process ◽  
Liquid Liquid Phase Separation

Aberrant protein folding underpins many neurodegenerative diseases as well as certain myopathies and cancers. Protein misfolding can be driven by the presence of distinctive prion and prion-like regions within certain proteins. These prion and prion-like regions have also been found to drive liquid-liquid phase separation. Liquid-liquid phase separation is thought to be an important physiological process, but one that is prone to malfunction. Thus, aberrant liquid-to-solid phase transitions may drive protein aggregation and fibrillization, which could give rise to pathological inclusions. Here, we review prions and prion-like proteins, their roles in phase separation and disease, as well as potential therapeutic approaches to counter aberrant phase transitions.

The dynamics of solid-solid phase transitions 2. Incoherent interfaces

1994 ◽  
Vol 127 (1) ◽  
pp. 41-99 ◽  
Author(s):  
Paolo Cermelli ◽  
Morton E. Gurtin
Keyword(s):  
Phase Transitions ◽  
Solid Phase

scholarly journals Study of the kinetics of solid-solid phase transitions in HMX

2018 ◽  
Author(s):  
P. Bowlan ◽  
L. Smilowitz ◽  
B. F. Henson ◽  
N. Suvorova ◽  
D. Oschwald
Keyword(s):  
Phase Transitions ◽  
Solid Phase ◽  
Kinetics Of
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