Statistical Mechanics of Liquids and Fluids in Curved Space

Tarjus, Gilles; Sausset, François; Viot, Pascal

doi:10.1002/9781118158715.ch4

Cited by 26 publications

(31 citation statements)

References 122 publications

(333 reference statements)

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“…The coarsening dynamics can also be elucidated by tracking the motion and distribution of topological defects. At early times, the disorder in the lattice screens out the local curvature, producing a roughly random distribution of defects throughout the system [38]. At this early stage the dynamics are relatively unaffected by the curvature and thus the process of defect annihilation can be expected to follow "line-tension-driven"Allen-Cahn dynamics [32,39].…”

Section: ) When Comparing G(r)mentioning

confidence: 99%

Crystallization dynamics on curved surfaces

García

Vega

et al. 2013

Phys. Rev. E

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We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is rapidly relaxed through isolated defects. Further relaxation involves a mechanism of crystal growth and defect annihilation where regions with high curvature act as sinks for the diffusion of domain walls. The pinning of grain boundaries at regions of low curvature leads to the formation of a metastable structure of defects, characterized by asymptotically slow dynamics of ordering and activation energies dictated by the largest curvatures of the system. These glassylike ordering dynamics may completely inhibit the appearance of the ground-state structures.

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Section: ) When Comparing G(r)mentioning

confidence: 99%

Crystallization dynamics on curved surfaces

García

Vega

et al. 2013

Phys. Rev. E

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“…A relevant feature of such low dimensional exactly solvable fluids is that they often play an important role as exact standards and guides to test approximate solutions and numerical experiments for (higher dimensional) fluid's models. In a more general context, the few exact analytical results have helped form new qualitative insights given by sum rules and in clarifying the nature of the long distance asymptotic decay of the truncated two (or more) particle distribution functions (Martin, 1988;Tarjus et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Plasma living in a curved surface at some special temperature

Fantoni

2019

Physica A: Statistical Mechanics and its Applications

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The simplest statistical mechanics model of a Coulomb plasma in two spatial dimensions admits an exact analytic solution at some special temperature in several (curved) surfaces. We present in a unifying perspective these solutions for the (non-quantum) plasma, made of point particles carrying an absolute charge e, in thermal equilibrium at a temperature T = e 2 /2k B , with k B Boltzmann's constant, discussing the importance of having an exact solution, the role of the curvature of the surface, and the densities of the plasma.

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“…The statistical mechanics of fluids in manifolds has been recently discussed and reviewed by Tarjus et al 22 In soft condensed matter, rather than the exception, dynamical phea) Electronic mail: pcastrov@unach.mx b) Electronic mail: avillada@fis.cinvestav.mx c) Electronic mail: jmendez@fis.cinvestav.mx d) Electronic mail: ramoncp@fisica.ugto.mx e) Electronic mail: sestrada@unach.mx nomena take place commonly in curved manifolds. A few particular examples, among others, are the diffusion of adsorbed particles on a curved substrate, 23,24 the dynamics of confined polymer chains, [25][26][27] the single-file diffusion in narrow cavities, 28 and the dynamics of colloidal halos.…”

Section: Introductionmentioning

confidence: 99%

A Brownian dynamics algorithm for colloids in curved manifolds

Castro-Villarreal

Villada-Balbuena

Méndez‐Alcaraz

et al. 2014

The Journal of Chemical Physics

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The many-particle Langevin equation, written in local coordinates, is used to derive a Brownian dynamics simulation algorithm to study the dynamics of colloids moving on curved manifolds. The predictions of the resulting algorithm for the particular case of free particles diffusing along a circle and on a sphere are tested against analytical results, as well as with simulation data obtained by means of the standard Brownian dynamics algorithm developed by Ermak and McCammon [J. Chem. Phys. 69, 1352 (1978)] using explicitly a confining external field. The latter method allows constraining the particles to move in regions very tightly, emulating the diffusion on the manifold. Additionally, the proposed algorithm is applied to strong correlated systems, namely, paramagnetic colloids along a circle and soft colloids on a sphere, to illustrate its applicability to systems made up of interacting particles.

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Statistical Mechanics of Liquids and Fluids in Curved Space

Cited by 26 publications

References 122 publications

Crystallization dynamics on curved surfaces

Crystallization dynamics on curved surfaces

Plasma living in a curved surface at some special temperature

A Brownian dynamics algorithm for colloids in curved manifolds

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