Emilio N. M. Cirillo

Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbor two-dimensional lattice system with spin variables taking values in {−1,0, +1}. We consider large but finite volume, small fixed magnetic fieldh, and chemical potential λ in the limit of zero temperature; we analyze the first excursion from the metastable −1 configuration to the stable +1 configuration. We compute the asymptotic behavior of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the lineh=2λ is crossed.

Metastability for a stochastic dynamics with a parallel heat bath updating rule

We consider the problem of metastability for a stochastic dynamics with a parallel updating rule with single spin rates equal to those of the heat bath for the Ising nearest neighbors interaction. We study the exit from the metastable phase, we describe the typical exit path and evaluate the exit time. We prove that the phenomenology of metastability is different from the one observed in the case of the serial implementation of the heat bath dynamics. In particular we prove that an intermediate chessboard phase appears during the excursion from the minus metastable phase toward the plus stable phase.

Effect of metal clusters on the swelling of gold–fluorocarbon–polymer composite films

We have investigated the swelling of acetone in fluorocarbon polymer films doped with different gold concentrations below the percolation threshold. The presence of the gold clusters in the polymer improves the mixing between the polymer and the acetone, which is not a good solvent for this kind of polymer. To explain our results, the stoichiometry and the morphology of the polymer–metal system have been studied and a modified Flory–Huggins model has been developed.

Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T → 0, h → 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.

Phase coexistence in consolidating porous media

The appearance of the fluid-rich phase in saturated porous media under the effect of an external pressure is investigated. For this purpose we introduce a two field second gradient model allowing the complete description of the phenomenon. We study the coexistence profile between poor and rich fluid phases and we show that for a suitable choice of the parameters nonmonotonic interfaces show up at coexistence.

Renormalization group at criticality and complete analyticity of constrained models: A numerical study

We study the majority rule transformation applied to the Gibbs measure for the 2D Ising model at the critical point. The aim is to show that the renormalized Hamiltonian is well defined in the sense that the renormalized measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman uniqueness (DSU) finite-size condition for the “constrained models” corresponding to different configurations of the “image” system. It is known that DSU implies, in our 2D case, complete analyticity from which, as recently shown by Haller and Kennedy. Gibbsianness follows. We introduce a Monte Carlo algorithm to compute an upper bound to Vasserstein distance (appearing in DSU) between finite-volume Gibbs measures with different boundary conditions. We get strong numerical evidence that indeed the DSU condition is verified for a large enough volumeV for all constrained models.

Allen-Cahn and Cahn-Hilliard-like equations for dissipative dynamics of saturated porous media

Abstract We consider a saturated porous medium in the solid–fluid segregation regime under the effect of an external pressure applied on the solid constituent. We prove that, depending on the dissipation mechanism, the dynamics is described either by a Cahn–Hilliard or by an Allen–Cahn-like equation. More precisely, when the dissipation is modeled via the Darcy law we find that, provided the solid deformation and the fluid density variations are small, the evolution equation is very similar to the Cahn–Hilliard one. On the other hand, when only the Stokes dissipation term is considered, we find that the evolution is governed by an Allen–Cahn-like equation. We use this theory to describe the formation of interfaces inside porous media. We consider a recently developed model proposed to study the solid–liquid segregation in consolidation and we give a complete description of the formation of an interface between the fluid-rich and the fluid-poor phase.

Monte Carlo study of gating and selection in potassium channels.

The study of selection and gating in potassium channels is a very important issue in modern biology. Indeed, such structures are known in essentially all types of cells in all organisms where they play many important functional roles. The mechanism of gating and selection of ionic species is not clearly understood. In this paper we study a model in which gating is obtained via an affinity-switching selectivity filter. We discuss the dependence of selectivity and efficiency on the cytosolic ionic concentration and on the typical pore open state duration. We demonstrate that a simple modification in the way in which the selectivity filter is modeled yields larger channel efficiency.

Graded cluster expansion for lattice systems

In this paper we develop a general theory which provides a unified treatment of two apparently different problems. The weak Gibbs property of measures arising from the application of Renormalization Group maps and the mixing properties of disordered lattice systems in the Griffiths’ phase. We suppose that the system satisfies a mixing condition in a subset of the lattice whose complement is sparse enough namely, large regions are widely separated. We then show how it is possible to construct a convergent multi-scale cluster expansion.

The Phase Diagram of the Gonihedric 3d Ising Model via CVM

Abstract We use the cluster variation method (CVM) to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The geometrical spin cluster boundaries in these systems serve as models for the string worldsheets of the gonihedric string embedded in Z 3 . The models are interesting from the statistical mechanical point of view because they have a vanishing bare surface tension. As a result the action depends only on the angles of the discrete surface and not on the area, which is the antithesis of the standard 3d Ising model. The results obtained with the CVM are in good agreement with Monte Carlo simulations for the critical temperatures and the order of the transition as the self-avoidance coupling κ is varied. The value of the magnetization critical exponent β = 0.062±0.003, calculated with the cluster variation-Pade approximant method, is also close to the simulation results.