Theory of phase-ordering kinetics

Bray, A. J.

doi:10.1080/00018730110117433

Cited by 752 publications

(1,280 citation statements)

References 173 publications

(508 reference statements)

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“…When the system approaches the critical state, clusters of the new phase are formed by enhanced fluctuations and their size increases as does the correlation length. But this happens not instantly, because long range correlations develop gradually leading to the so-called dynamic phase transition (critical transition) (Bray 1994;Stanley 1999;Sicilia et al 2007;Varotsos et al 2011b, c). Thus, the time series emitted in such a nonequilibrium process will be nonstationary and p k , or the corresponding probability density function p(v) will no longer be independent of v.…”

Section: Discussionmentioning

confidence: 99%

Identifying the occurrence time of an impending major earthquake: a review

2017

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Section: Discussionmentioning

confidence: 99%

Identifying the occurrence time of an impending major earthquake: a review

2017

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“…Topological defects [26,77] abound systems with broken symmetries: in ordered media like magnetic materials, crystalline materials -both solids and liquids, in superfluid helium, and in quantum Hall fluids [45,[78][79][80][81][82][83][84]. Owing to the similarities in nature of the scaling laws characterizing such systems, liquid crystals provide an easily accessible platform for investigations.…”

Section: Topological Defectsmentioning

confidence: 99%

Nematic Liquid Crystals and Nematic Colloids in Microfluidic Environment

Sengupta

Herminghaus

Bahr

2011

Molecular Crystals and Liquid Crystals

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Where the mind is without fear and the head is held high;Where knowledge is free;Where the world has not been broken up into fragments by narrow domestic walls;Where words come out from the depth of truth;Where tireless striving stretches its arms towards perfection;Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit;Where the mind is led forward by thee into ever-widening thought and actionInto that heaven of freedom, my Father, let my country awake.Rabindranath Tagore (1861Tagore ( -1941 To my parents, my brother, and all the sacrifices they made for me AbstractThe doctoral thesis presented here is one of the first systematic attempts to unravel the wonderful world of liquid crystals within microfluidic confinements, typically channels with dimensions of tens of micrometers. The present work is based on experiments with a roomtemperature nematic liquid crystal, 5CB, and its colloidal dispersions within microfluidic devices of rectangular cross-section, fabricated using standard techniques of soft lithography. To begin with, a combination of physical and chemical methods was employed to create well defined boundary conditions for investigating the flow experiments. The walls of the microchannels were functionalized to induce different kinds of surface anchoring of the 5CB molecules: degenerate planar, uniform planar, and homeotropic surface anchoring. Channels possessing composite anchoring conditions (hybrid) were additionally fabricated, e. g. homeotropic and uniform planar anchoring within the same channel. On filling the microchannels with 5CB in the isotropic phase, different equilibrium configurations of the nematic director resulted, as the sample cooled down to nematic phase. For a given surface anchoring, the equilibrium director configuration varied also with the channel aspect ratio. The static director field within the channel registered the initial conditions for the flow experiments. The static and i ii dynamic experiments have been analyzed using a combination of polarization, and confocal fluorescence microscopy techniques, along with particle tracking method for measuring the flow speeds. Additionally, dual-focus fluorescence correlation spectroscopy is introduced as a generic velocimetry tool for liquid crystal flows.The flow of nematic liquid crystals is inherently complex due to the coupling between the flow and the nematic director. The presence of the four confining walls and the nature of surface anchoring on them complicate the flow-director interactions further. In microchannels possessing degenerate planar anchoring, four different flow-induced defect textures were identified with increasing Ericksen number: π-walls, disclination lines pinned to the channel walls, disclination lines with one pinned and one freely suspended end, and disclination loops freely flowing in a chaotic manner. However, such textures and sequence of defects were not observed for flows within channels with homogeneous anchoring.Using experiments and numerical modeling...

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“…The spectral gap c gap (µ) and the logarithmic Sobolev constant c sob (µ) of µ are then defined by 6) where the infimum in each case is over non-constant functions f . The spectral gap c gap (µ) measures the rate of exponential decay as t → ∞ of the variance w.r.t.…”

Section: 2mentioning

confidence: 99%

“…ii) If so, how fast does the law of σ η t approach µ + ? The above questions, with G some regular lattice, have their origin in the theory of "phase ordering kinetics" [6] -that is growth of order through a dynamical domain coarsening -and clearly represent basic problems in the theory of interacting particle systems. Unfortunately, a rigorous approach to these problems is still largely missing.…”

Section: Introductionmentioning

confidence: 99%

Phase ordering after a deep quench: the stochastic Ising and hard core gas models on a tree

Caputo

Martinelli

2005

Probab. Theory Relat. Fields

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ABSTRACT. Consider a low temperature stochastic Ising model in the phase coexistence regime with Markov semigroup Pt. A fundamental and still largely open problem is the understanding of the long time behavior of δηPt when the initial configuration η is sampled from a highly disordered state ν (e.g. a product Bernoulli measure or a high temperature Gibbs measure). Exploiting recent progresses in the analysis of the mixing time of Monte Carlo Markov chains for discrete spin models on a regular b-ary tree T b , we study the above problem for the Ising and hard core gas (independent sets) models on T b . If ν is a biased product Bernoulli law then, under various assumptions on the bias and on the thermodynamic parameters, we prove ν-almost sure weak convergence of δηPt to an extremal Gibbs measure (pure phase) and show that the limit is approached at least as fast as a stretched exponential of the time t. In the context of randomized algorithms and if one considers the Glauber dynamics on a large, finite tree, our results prove fast local relaxation to equilibrium on time scales much smaller than the true mixing time, provided that the starting point of the chain is not taken as the worst one but it is rather sampled from a suitable distribution.

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Theory of phase-ordering kinetics

Cited by 752 publications

References 173 publications

Identifying the occurrence time of an impending major earthquake: a review

Identifying the occurrence time of an impending major earthquake: a review

Nematic Liquid Crystals and Nematic Colloids in Microfluidic Environment

Phase ordering after a deep quench: the stochastic Ising and hard core gas models on a tree

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