Modelling phase transitions via Young measures

Steffen Arnrich;

doi:10.3934/dcdss.2012.5.29

Young measures and the absence of fine microstructures in a class of phase transitions

European Journal of Applied Mathematics ◽

10.1017/s095679250000067x ◽

1992 ◽

Vol 3 (1) ◽

pp. 31-54 ◽

Cited By ~ 17

Author(s):

João Palhoto Matos

Keyword(s):

Phase Transitions ◽

Crystal Phase ◽

Young Measures ◽

Fine Structures

It is shown that for a class of pairs of energy wells the only Young measures having these wells as support must reduce to spatially constant Dirac masses. This implies the prediction that fine structures will be absent in certain crystal phase transitions.

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Oscillations in a dynamical model of phase transitions

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500000792 ◽

2001 ◽

Vol 131 (1) ◽

pp. 59-81 ◽

Cited By ~ 5

Author(s):

Deborah Brandon ◽

Irene Fonseca ◽

Pieter Swart

Keyword(s):

Fine Structure ◽

Phase Transitions ◽

Initial Data ◽

Initial Strain ◽

Dynamical Model ◽

Generalized Solutions ◽

Viscoelastic Damping ◽

Young Measures ◽

Image Position

The creation and propagation of oscillations in a model for the dynamics of fine structure under viscoelastic damping is studied. It is shown that oscillations in the velocity ut are lost immediately as time evolves, while oscillations in the initial strain ux cannot be created, and they persist for all time if initially present. Uniqueness of generalized solutions (Young measures) is obtained, and a characterization of these Young measures is provided in the case of periodic modulated initial data.

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Young measures in a nonlocal phase transition problem

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500029930 ◽

1997 ◽

Vol 127 (3) ◽

pp. 615-637 ◽

Cited By ~ 3

Author(s):

Xiaofeng Ren ◽

Matthias Winter

Keyword(s):

Phase Transition ◽

Phase Transitions ◽

Weak Convergence ◽

Variational Problem ◽

Convergence Result ◽

Young Measures ◽

Concentration Compactness ◽

Internal Layers ◽

Phase Transition Problem ◽

Infinite Tube

A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result for Young measures and the principle of concentration-compactness. The regularity of such global minimisers is discussed, and the nonlocal variational problem is also considered on asymptotic tubes.

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Electron Microscopy of Graphite Intercalation Compounds

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100055564 ◽

1982 ◽

Vol 40 ◽

pp. 544-545

Author(s):

G. Timp ◽

L. Salamanca-Riba ◽

L.W. Hobbs ◽

G. Dresselhaus ◽

M.S. Dresselhaus

Keyword(s):

Electron Microscopy ◽

Phase Transitions ◽

Domain Wall ◽

Intercalation Compounds ◽

Lattice Plane ◽

Wall Model ◽

Graphite Intercalation Compounds ◽

Fundamental Symmetry ◽

Graphite Intercalation

Electron microscopy can be used to study structures and phase transitions occurring in graphite intercalations compounds. The fundamental symmetry in graphite intercalation compounds is the staging periodicity whereby each intercalate layer is separated by n graphite layers, n denoting the stage index. The currently accepted model for intercalation proposed by Herold and Daumas assumes that the sample contains equal amounts of intercalant between any two graphite layers and staged regions are confined to domains. Specifically, in a stage 2 compound, the Herold-Daumas domain wall model predicts a pleated lattice plane structure.

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Multiple phase transitions investigated by high-speed TEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100175880 ◽

1990 ◽

Vol 48 (4) ◽

pp. 550-551

Author(s):

Oleg Bostanjoglo ◽

Peter Thomsen-Schmidt

Keyword(s):

Phase Transitions ◽

High Speed ◽

Short Exposure ◽

Semiconductor Film ◽

Time Resolved ◽

Short Exposure Time ◽

Multiple Phase ◽

Model Substance ◽

History Of ◽

Electron Image

Thin GexTe1-x (x = 0.15-0.8) were studied as a model substance of a composite semiconductor film, in addition being of interest for optical storage material. Two complementary modes of time-resolved TEM were used to trace the phase transitions, induced by an attached Q-switched (50 ns FWHM) and frequency doubled (532 nm) Nd:YAG laser. The laser radiation was focused onto the specimen within the TEM to a 20 μm spot (FWHM). Discrete intermediate states were visualized by short-exposure time doubleframe imaging /1,2/. The full history of a transformation was gained by tracking the electron image intensity with photomultiplier and storage oscilloscopes (space/time resolution 100 nm/3 ns) /3/. In order to avoid radiation damage by the probing electron beam to detector and specimen, the beam is pulsed in this continuous mode of time-resolved TEM,too.Short events ( <2 μs) are followed by illuminating with an extended single electron pulse (fig. 1c)

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