Polydisperse lattice-gas model

Wilding, Nigel B.; Sollich, Peter; Buzzacchi, M.

doi:10.1103/physreve.77.011501

Cited by 24 publications

(30 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Fig. 3 we show similar results for other glass formers with A) purely repulsive potential [3] at d = 2, B) the Lennard-Jones system [4] at d = 3, C) the KobAndersen model [5] at d = 2 and D) the polydisperse model [6] at d = 2. The physical interpretation of these observations is discussed below, cf.…”

Section: The Arrhenius Regimesupporting

confidence: 75%

See 1 more Smart Citation

Relaxation mechanisms in glassy dynamics: The Arrhenius and fragile regimes

et al. 2012

View full text Add to dashboard Cite

Generic glass formers exhibit at least two characteristic changes in their relaxation behavior, first to an Arrhenius-type relaxation at some characteristic temperature, and then at a lower characteristic temperature to a super-Arrhenius (fragile) behavior. We address these transitions by studying the statistics of free energy barriers for different systems at different temperatures and space dimensions. We present a clear evidence for changes in the dynamical behavior at the transition to Arrhenius and then to a super-Arrhenius behavior. A simple model is presented, based on the idea of competition between single-particle and cooperative dynamics. We argue that Arrhenius behavior can take place as long as there is enough free volume for the completion of a simple T 1 relaxation process. Once free volume is absent one needs a cooperative mechanism to 'collect' enough free volume. We show that this model captures all the qualitative behavior observed in simulations throughout the considered temperature range.

show abstract

Section: The Arrhenius Regimesupporting

confidence: 75%

“…2 the contribution of the width σ 2 ≈ 2.5 × 10 −3 is of the order of 0.1% in Eq. (6). Obviously, for larger systems we expect σ to be even smaller, tending to zero for N → ∞.…”

Section: The Arrhenius Regimementioning

confidence: 89%

Relaxation mechanisms in glassy dynamics: The Arrhenius and fragile regimes

et al. 2012

View full text Add to dashboard Cite

show abstract

“…35 In Section 2 we present the model and its mean-field phase diagram. In Section 3 we endow the model with an appropriate dynamics and derive the mean-field evolution equations for this.…”

Section: Below)mentioning

confidence: 99%

“…One can also phrase the last step in the other direction, i.e. by writing (35) and checking that the site-dependent mobility M αγ i j is positive. This makes sense because a particle swap is driven by how the difference in α-chemical potential between sites i and j compares to the corresponding difference in γ-chemical potential.…”

Section: A Monotonic Decrease Of the Free Energymentioning

confidence: 99%

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Castro

Sollich

2017

Phys. Chem. Chem. Phys.

Self Cite

View full text Add to dashboard Cite

New insights into phase separation in colloidal suspensions are provided via a new dynamical theory based on the Polydisperse Lattice-Gas model. The model gives a simplified description of polydisperse colloids, incorporating a hard-core repulsion combined with polydispersity in the strength of the attraction between neighbouring particles. Our mean-field equations describe the local concentration evolution for each of an arbitrary number of species, and for an arbitrary overall composition of the system. We focus on the predictions for the dynamics of colloidal gas-liquid phase separation after a quench into the coexistence region. The critical point and the relevant spinodal curves are determined analytically, with the latter depending only on three moments of the overall composition. The results for the early-time spinodal dynamics show qualitative changes as one crosses a 'quenched' spinodal that excludes fractionation and so allows only density fluctuations at fixed composition. This effect occurs for dense systems, in agreement with a conjecture by Warren that, at high density, fractionation should be generically slow because it requires inter-diffusion of particles. We verify this conclusion by showing that the observed qualitative changes disappear when direct particle-particle swaps are allowed in the dynamics. Finally, the rich behaviour beyond the spinodal regime is examined, where we find that the evaporation of gas bubbles with strongly fractionated interfaces causes long-lived composition heterogeneities in the liquid phase; we introduce a two-dimensional density histogram method that allows such effects to be easily visualized for an arbitrary number of particle species.

show abstract

“…This simple picture is also known in the literature as "bit" gas model, in analogy to computational science [30,31]. Its use is usually adopted in different fields of physics, especially in order to model extended sites by numerical computations through Monte Carlo simulations, ranging from condensed matter to quantum computing and particle physics [32][33][34][35][36][37][38][39][40]. Under these hypotheses, the occupational variables σ i are actually analogous to spin variables in the well known Ising model [41,42].…”

Section: The Ising Fluid With Network Interactionsmentioning

confidence: 99%

Modeling Dark Energy Through an Ising Fluid With Network Interactions

Luongo

Tommasini

2014

Int. J. Mod. Phys. D

View full text Add to dashboard Cite

We show that the dark energy effects can be modeled by using an Ising perfect fluid with network interactions, whose low redshift equation of state, i.e. ω0, becomes ω0 = −1 as in the ΛCDM model. In our picture, dark energy is characterized by a barotropic fluid on a lattice in the equilibrium configuration. Thus, mimicking the spin interaction by replacing the spin variable with an occupational number, the pressure naturally becomes negative. We find that the corresponding equation of state mimics the effects of a variable dark energy term, whose limiting case reduces to the cosmological constant Λ. This permits us to avoid the introduction of a vacuum energy as dark energy source by hand, alleviating the coincidence and fine tuning problems. We find fairly good cosmological constraints, by performing three tests with supernovae Ia, baryonic acoustic oscillation and cosmic microwave background measurements. Finally, we perform the AIC and BIC selection criteria, showing that our model is statistically favored with respect to the CPL parametrization.PACS numbers: 98.80.Jk, 98.80.Es

show abstract

Polydisperse lattice-gas model

Cited by 24 publications

References 28 publications

Relaxation mechanisms in glassy dynamics: The Arrhenius and fragile regimes

Relaxation mechanisms in glassy dynamics: The Arrhenius and fragile regimes

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Modeling Dark Energy Through an Ising Fluid With Network Interactions

Contact Info

Product

Resources

About