相关论文: Competitive nucleation and the Ostwald rule in a g…

Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…

We present a brief analysis of the crossover phase diagram for the decay of a metastable phase in a simple dynamic lattice-gas model of a two-phase system. We illustrate the nucleation-theoretical analysis with dynamic Monte Carlo…

We review some aspects of current knowledge regarding the decay of metastable phases in many-particle systems. In particular we emphasize recent theoretical and computational developments and numerical results regarding homogeneous…

We analyze the dynamics of competitions with a large number of players. In our model, n players compete against each other and the winner is decided based on the standings: in each competition, the mth ranked player wins. We solve for the…

Pemantle and Steif provided a sharp threshold for the existence of a RPT (robust phase transition) for the continuous rotator model and the Potts model in terms of the branching number and the second eigenvalue of the transfer operator,…

We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…

When a system is brought to a metastable state, nuclei of the equilibrium phase form and grow. This is the well-known nucleation and growth of first-order phase transitions. Near a critical point of a continuous phase transition, critical…

Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…

For most organisms with viscous population structure, spatially localized growth drives the invasive advance of a favorable mutation. We model a two-allele competition where recurrent mutation introduces a genotype with a rate of local…

The stochastic spectral expansion method offers a simple framework for calculations in de Sitter spacetimes. We show how to extend its reach to metastable vacuum states, both in the case when the potential is bounded from below, and when it…

In 1897 Ostwald formulated his step rule for formation of the most stable crystal state for a system with crystal polymorphism. The rule describes the irreversible way a system converts to the crystal with lowest free energy. But in fact…

Monte Carlo simulations are performed to study the two-dimensional Potts models with q=3 and 4 states on directed Small-World network. The disordered system is simulated applying the Heat bath Monte Carlo update algorithm. A first-order and…

Recent years have witnessed a growing interest in using machine learning to predict and identify phase transitions in various systems. Here we adopt convolutional neural networks (CNNs) to study the phase transitions of Vicsek model,…

The interplay between densification and positional ordering during the process of crystal nucleation is a greatly investigated topic. Even for the simplest colloidal model -- hard spheres -- there has been much debate regarding the…

Epigenetic histone modifications play an important role in the maintenance of different cell phenotypes. The exact molecular mechanism for inheritance of the modification patterns over cell generations remains elusive. We construct a…

We propose an iterative proposal to estimate critical points for statistical models based on configurations by combing machine-learning tools. Firstly, phase scenarios and preliminary boundaries of phases are obtained by…

We extend a recently introduced class of exactly solvable models for recurrent neural networks with competition between 1D nearest neighbour and infinite range information processing. We increase the potential for further frustration and…

As cancer advances, cells often spread from the primary tumor to other parts of the body and form metastases. This is the main cause of cancer related mortality. Here we investigate a conceptually simple model of metastasis formation where…

We consider the problem of metastability for stochastic reversible dynamics with exponentially small transition probabilities. We generalize previous results in several directions. We give an estimate of the spectral gap of the transition…

Tumor development is an evolutionary process in which a heterogeneous population of cells with differential growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to…