Theory of phase-ordering kinetics

Bray, A. J.

doi:10.1080/00018739400101505

Cited by 2,511 publications

(3,277 citation statements)

References 137 publications

(389 reference statements)

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“…This prevents reaching an asymptotic finite value of L(t), associated to a truly stationary distribution of the rod lengths and orientations. Well known examples of such coarsening dynamics are characterized, for instance, by a power-law or a logarithmic behavior of L with t [29]. In the latter case, the possibility to discuss the system properties in term of quasi-stationary solutions remains.…”

Section: A Spatial Organization: Domain Structurementioning

confidence: 99%

Collision induced spatial organization of microtubules

Baulin¹,

Marques²,

Thalmann³

2007

Biophysical Chemistry

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The dynamic behavior of microtubules in solution can be strongly modified by interactions with walls or other structures. We examine here a microtubule growth model where the increase in size of the plus-end is perturbed by collisions with other microtubules. We show that such a simple mechanism of constrained growth can induce ordered structures and patterns from an initially isotropic and homogeneous suspension. First, microtubules self-organize locally in randomly oriented domains that grow and compete with each other. By imposing even a weak orientation bias, external forces like gravity or cellular boundaries may bias the domain distribution eventually leading to a macroscopic sample orientation.

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Section: A Spatial Organization: Domain Structurementioning

confidence: 99%

Collision induced spatial organization of microtubules

Baulin¹,

Marques²,

Thalmann³

2007

Biophysical Chemistry

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“…We shall see later how important the third condition in (3) is. If the conditions (3) hold, one expects [2,4] …”

Section: Phenomenology Of Ageingmentioning

confidence: 99%

“…Our starting point is the rich evidence, accumulated through many decades and reviewed in [2], in favour of dynamical scale-invariance in ageing phenomena. The order parameter field φ = φ(t, r) scales…”

Section: Local Scale-invariancementioning

confidence: 99%

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Local Scale Invariance in Ageing Phenomena

Henkel¹

2004

Advances in Solid State Physics

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Abstract. Many materials quenched into their ordered phase undergo ageing and there show dynamical scaling. For any given dynamical exponent z, this can be extended to a new form of local scale-invariance which acts as a dynamical symmetry. The scaling functions of the two-time correlation and response functions of ferromagnets with a non-conserved order parameter are determined. These results are in agreement with analytical and numerical studies of various models, especially the kinetic Glauber-Ising model in 2 and 3 dimensions. : 05.70.Ln, 74.40.Gb, 64.60.Ht Ageing in its most general sense refers to the change of material properties as a function of time. In particular, physical ageing occurs when the underlying microscopic processes are reversible while on the other hand, biological systems age because of irreversible chemical reactions going on within them. Historically, ageing phenomena were first observed in glassy systems, see [1], but it is of interest to study them in systems without disorder. These should be conceptually simpler and therefore allow for a better understanding. Insights gained this way may become useful for a later study of glassy systems. PACS Phenomenology of ageingIn describing the phenomenology of ageing system, we shall refer throughout to simple ferromagnets, see [2,3,4,5] for reviews. We consider systems which undergo a second-order equilibrium phase transition at a critical temperature T c > 0 and we shall assume throughout that the dynamics admits no macroscopic conservation law. Initially, the system is prepared in some initial state (typically one considers an initial temperature T ini = ∞). The system is brought out of equilibrium by quenching it to a final temperature T ≤ T c . Then T is fixed and the system's temporal evolution is studied. It turns out that the relaxation back to global equilibrium is very slow (e.g. algebraic in time) with a formally infinite relaxation time for all T ≤ T c .Let φ(t, r) denote the time-and space-dependent order parameter and consider the two-time correlation and (linear) response functions C(t, s; r) = φ(t, r)φ(s, 0) , R(t, s; r) = δ φ(t, r) δh(s, 0) h=0 (1)

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“…The result is that C L (x) is a scaling function of argument x/L: (10) with intercept m o = 1 and α = 1/2. The argument of the scaling function indicates that it describes a phase-separated state [39]. The finite intercept m 2 o is a measure of long-range order.…”

Section: Bidirectional Disorder: Untiltedmentioning

confidence: 99%

Driven diffusive systems with disorder

Barma

2006

Physica A: Statistical Mechanics and its Applications

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We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial distribution of transition rates, both with a single easy direction and with random reversals of the easy direction; dynamical disorder, where particles move in a disordered landscape which itself evolves in time. In every case, the system exhibits phase separation; in some cases, it is of an unusual sort. The time-dependent properties of density fluctuations are in accord with the kinematic wave criterion that the dynamical universality class is unaffected by disorder if the kinematic wave velocity is nonzero.

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Theory of phase-ordering kinetics

Cited by 2,511 publications

References 137 publications

Collision induced spatial organization of microtubules

Collision induced spatial organization of microtubules

Local Scale Invariance in Ageing Phenomena

Driven diffusive systems with disorder

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