Competitive nucleation in metastable systems

Metastability is observed when a physical system is close to a first order phase transition. In this paper the metastable behavior of a two state reversible probabilistic cellular automaton with self-interaction is discussed. Depending on the self-interaction, competing metastable states arise and a behavior very similar to that of the three state Blume-Capel spin model is found

Metastability for reversible probabilistic cellular automata with self--interaction

The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the existence of many fixed points and cyclic pairs of the zero temperature dynamics, in which the system can be trapped in its way to the stable phase. %The characterization of the metastable behavior %of a system in the context of parallel dynamics is a very difficult task, %since all the jumps in the configuration space are allowed. Our strategy is based on recent powerful approaches, not needing a complete description of the fixed points of the dynamics, but relying on few model dependent results. We compute the exit time, in the sense of logarithmic equivalence, and characterize the critical droplet that is necessarily visited by the system during its excursion from the metastable to the stable state. We need to supply two model dependent inputs: (1) the communication energy, that is the minimal energy barrier that the system must overcome to reach the stable state starting from the metastable one; (2) a recurrence property stating that for any configuration different from the metastable state there exists a path, starting from such a configuration and reaching a lower energy state, such that its maximal energy is lower than the communication energy

Basic Ideas to Approach Metastability in Probabilistic Cellular Automata

Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete time Markov chains on lattice with finite single--cell states whose distinguishing feature is the \textit{parallel} character of the updating rule. We review some of the results obtained about the metastable behavior of Probabilistic Cellular Automata and we try to point out difficulties and peculiarities with respect to standard Statistical Mechanics Lattice models.Comment: arXiv admin note: text overlap with arXiv:1307.823

A comparison between different cycle decompositions for Metropolis dynamics

In the last decades the problem of metastability has been attacked on rigorous grounds via many different approaches and techniques which are briefly reviewed in this paper. It is then useful to understand connections between different point of views. In view of this we consider irreducible, aperiodic and reversible Markov chains with exponentially small transition probabilities in the framework of Metropolis dynamics. We compare two different cycle decompositions and prove their equivalence

Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We introduce the notion of relaxation height in a general energy landscape and we prove sufficient conditions which are valid even in presence of multiple metastable states. We show how these results can be used to approach the problem of multiple metastable states via the use of the modern theories of metastability. We finally apply these general results to the Blume--Capel model for a particular choice of the parameters ensuring the existence of two multiple, and not degenerate in energy, metastable states

Competitive nucleation in reversible Probabilistic Cellular Automata

The problem of competitive nucleation in the framework of Probabilistic Cellular Automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self--interaction is discussed. An intermediate metastable phase, made of two flip--flopping chessboard configurations, shows up depending on the ratio between the magnetic field and the self--interaction. A behavior similar to the one of the stochastic Blume--Capel model with Glauber dynamics is found

Albumin nanoparticles for glutathione-responsive release of cisplatin: new opportunities for medulloblastoma treatment

Redox-responsive nanoparticles were synthesized by desolvation of bovine serum albumin followed by disulfide-bond crosslinking with N, Nʹ-Bis (acryloyl) cystamine. Dynamic light scattering and transmission electron microscopy studies revealed spherical nanoparticles (mean diameter: 83 nm, polydispersity index: 0.3) that were glutathione-responsive. Confocal microscopy revealed rapid, efficient internalization of the nanoparticles by Daoy medulloblastoma cells and healthy controls (HaCaT keratinocytes). Cisplatin-loaded nanoparticles with drug:carrier ratios of 5%, 10%, and 20% were tested in both cell lines. The formulation with the highest drug:carrier ratio reduced Daoy and HaCaT cell viability with IC50 values of 6.19 and 11.17 μg mL-1, respectively. The differential cytotoxicity reflects the cancer cells’ higher glutathione content, which triggers more extensive disruption of the disulfide bond-mediated intra-particle cross-links, decreasing particle stability and increasing their cisplatin release. These findings support continuing efforts to improve the safety and efficacy of antineoplastic drug therapy for pediatric brain tumors using selective nanoparticlebased drug delivery systems

Amyotrophic Lateral Sclerosis and Multiple Sclerosis Overlap: A Case Report

The concurrence of amyotrophic lateral sclerosis (ALS) and multiple sclerosis (MS) is extremely rare. We reported the case of a 33-year-old woman with a past history of paresthesias at the right hand, who developed progressive quadriparesis with muscular atrophy of limbs and, finally, bulbar signs and dyspnea. Clinical and neurophysiologic investigations revealed upper and lower motor neuron signs in the bulbar region and extremities, suggesting the diagnosis of ALS. Moreover, magnetic resonance imaging (MRI) and cerebrospinal fluid (CSF) analysis demonstrated 3 periventricular and juxtacortical lesions, hyperintense in T2 and FLAIR sequences, and 3 liquoral immunoglobulin G (IgG) oligoclonal bands, consistent with diagnosis of primary progressive MS (PPMS). This unusual overlap of ALS and MS leads to the discussion of a hypothetical common pathological process of immunological dysfunction in these two disorders, although the role of immune response in ALS remains ambivalent and unclear