The classical nucleation rate in two dimensions

Münster, Gernot; Rutkevich, S. B.

doi:10.1140/epjc/s2002-01091-4

Cited by 4 publications

(5 citation statements)

References 23 publications

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“…(16) is only the first order in the semiclassical approximation [3][4][5]. The next to leading order can be evaluated using quantum field theory methods and leads to a prefactor whose power can be predicted analitically and agrees very well with high precision Montecarlo simulations (see for instance [20]). We shall not further discuss this issue in the present paper since for our purposes the semiclassical result will be enough.…”

Section: Infinite Systemsmentioning

confidence: 87%

Nucleation dynamics in two-dimensional cylindrical Ising models and chemotaxis

2010

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The aim of our work is to study the effect of geometry variation on nucleation times and to address its role in the context of eukaryotic chemotaxis (i.e. the process which allows cells to identify and follow a gradient of chemical attractant). As a first step in this direction we study the nucleation dynamics of the 2d Ising model defined on a cylindrical lattice whose radius changes as a function of time. Geometry variation is obtained by changing the relative value of the couplings between spins in the compactified (vertical) direction with respect to the horizontal one. This allows us to keep the lattice size unchanged and study in a single simulation the values of the compactification radius which change in time. We show, both with theoretical arguments and numerical simulations, that squeezing the geometry allows the system to speed up nucleation times even in presence of a very small energy gap between the stable and the metastable states. We then address the implications of our analysis for directional chemotaxis. The initial steps of chemotaxis can be modelled as a nucleation process occurring on the cell membrane as a consequence of the external chemical gradient (which plays the role of energy gap between the stable and metastable phases). In nature most of the cells modify their geometry by extending quasi-onedimensional protrusions (filopodia) so as to enhance their sensitivity to chemoattractant. Our results show that this geometry variation has indeed the effect of greatly decreasing the timescale of the nucleation process even in presence of very small amounts of chemoattractants.2

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Section: Infinite Systemsmentioning

confidence: 87%

Nucleation dynamics in two-dimensional cylindrical Ising models and chemotaxis

2010

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“…Furthermore, the field theory of nucleation has been applied to the LG model. In fact, this was the first intended application of the original work [58], although later works [67][68][69][70] showed that the mathematical derivations can be further simplified. As a result, we can apply the nucleation rate formula derived for the LG model directly to the Arrow-Potts model.…”

Section: Field Theory Of Nucleationmentioning

confidence: 99%

“…[43], which follows closely the Refs. [71], the original work [58], and other past works [67][68][69][70]. To begin, we write the Langevin equation for the order parameter field φ(x, t) under non-conserving dynamics as a stochastic partial differential equation…”

Section: Field Theory Of Nucleationmentioning

confidence: 99%

“…A detailed derivation for φ(x) can be found in Ref. [69,70]. In the LG model, φ(x) physically represents a spherical cluster of the stable phase in a background of the metastable phase.…”

Section: Field Theory Of Nucleationmentioning

confidence: 99%

“…Regularization techniques must be used to simplify Eq. ( 30), some of which include cutoff regularization [43,67,68,71], analytic continuation [72], zeta-function regularization [69], and dimensional regularization [70].…”

Section: Field Theory Of Nucleationmentioning

confidence: 99%

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Theory of Crystallization versus Vitrification

Hasyim,

Mandadapu

2020

Preprint

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The competition between crystallization and vitrification in glass-forming materials manifests as a non-monotonic behavior in the time-temperature transformation (TTT) diagrams, which quantify the time scales for crystallization as a function of temperature. We develop a coarse-grained lattice model, the Arrow-Potts model, to explore the physics behind this competition. Using Monte Carlo simulations, the model showcases non-monotonic TTT diagrams resulting in polycrystalline structures, with two distinct regimes limited by either crystal nucleation or growth. At high temperatures, crystallization is limited by nucleation and results in the growth of compact crystal grains. At low temperatures, crystal growth is influenced by glassy dynamics, and proceeds through dynamically heterogeneous and hierarchical relaxation pathways producing fractal and ramified crystals.To explain these phenomena, we combine the Kolmogorov-Johnson-Mehl-Avrami theory with the field theory of nucleation, a random walk theory for crystal growth, and the dynamical facilitation theory for glassy dynamics. The unified theory yields an analytical formula relating crystallization timescale to the nucleation and growth rates through universal exponents governing glassy dynamics of the model. We show that the formula with the universal exponents yields excellent agreement with the Monte Carlo simulation data and thus, it also accounts for the non-monotonic TTT diagrams produced by the model. Both the model and theory can be used to understand structural ordering in various glassy systems including bulk metallic glass alloys, organic molecules, and colloidal suspensions.

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BubbleDet: a Python package to compute functional determinants for bubble nucleation

Ekstedt,

Gould,

Hirvonen

2023

J. High Energ. Phys.

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We present a Python package BubbleDet for computing one-loop functional determinants around spherically symmetric background fields. This gives the next-to-leading order correction to both the vacuum decay rate, at zero temperature, and to the bubble nucleation rate in first-order phase transitions at finite temperature. For predictions of gravitational wave signals from cosmological phase transitions, this is expected to remove one of the leading sources of theoretical uncertainty. BubbleDet is applicable to arbitrary scalar potentials and in any dimension up to seven. It has methods for fluctuations of scalar fields, including Goldstone bosons, and for gauge fields, but is limited to cases where the determinant factorises into a product of separate determinants, one for each field degree of freedom. To our knowledge, BubbleDet is the first package dedicated to calculating functional determinants in spherically symmetric backgrounds.

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The classical nucleation rate in two dimensions

Cited by 4 publications

References 23 publications

Nucleation dynamics in two-dimensional cylindrical Ising models and chemotaxis

Nucleation dynamics in two-dimensional cylindrical Ising models and chemotaxis

Theory of Crystallization versus Vitrification

BubbleDet: a Python package to compute functional determinants for bubble nucleation

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