Clustering data by melting

We derive a new clustering algorithm based on information theory and statistical mechanics, which is the only algorithm that incorporates scale. It also introduces a new concept into clustering: cluster independence. The cluster centers correspond to the local minima of a thermodynamic free energy, which are identified as the fixed points of a one-parameter nonlinear map. The algorithm works by melting the system to produce a tree of clusters in the scale space. Melting is also insensitive to variability in cluster densities, cluster sizes, and ellipsoidal shapes and orientations. We tested the algorithm successfully on both simulated data and a Synthetic Aperture Radar image of an agricultural site with 12 attributes for crop identification

Identifying structural changes with unsupervised machine learning methods

Unsupervised machine learning methods are used to identify structural changes using the melting point transition in classical molecular dynamics simulations as an example application of the approach. Dimensionality reduction and clustering methods are applied to instantaneous radial distributions of atomic configurations from classical molecular dynamics simulations of metallic systems over a large temperature range. Principal component analysis is used to dramatically reduce the dimensionality of the feature space across the samples using an orthogonal linear transformation that preserves the statistical variance of the data under the condition that the new feature space is linearly independent. From there, k-means clustering is used to partition the samples into solid and liquid phases through a criterion motivated by the geometry of the reduced feature space of the samples, allowing for an estimation of the melting point transition. This pattern criterion is conceptually similar to how humans interpret the data but with far greater throughput, as the shapes of the radial distributions are different for each phase and easily distinguishable by humans. The transition temperature estimates derived from this machine learning approach produce comparable results to other methods on similarly small system sizes. These results show that machine learning approaches can be applied to structural changes in physical systems

Study of theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids

Theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids are investigated. Mean-field models are considered first but shown to be inadequate. An alternate approach is then studied in which each statistical configuration of the material is treated as inhomogeneous, with the energy of each ion being determined by its local environment. Nonadditive interactions, due to valence electron delocalization, are a crucial feature of the model. This alternate approach is implemented within a lattice-gas approximation which takes into account the observed mode of expansion in the materials of interest and which is able to treat the equilibrium density fluctuations. We have carried out grand canonical Monte Carlo simulations, for this model, which allow a unified, self-consistent, study of the structural, thermodynamic, and electronic properties of alkali fluids. Applications to Cs, Rb, K, and Na yield results in good agreement with observations.Comment: 13 pages, REVTEX, 10 ps figures available by e-mail

Clustering and melting in a wet granular monolayer

We investigate experimentally the collective behavior of a wet granular monolayer under vertical vibrations. The spherical particles are partially wet such that there are short-ranged attractive interactions between adjacent particles. As the vibration strength increases, clustering, reorganizing and melting regimes are identified subsequently through a characterization with the bond-orientational order parameters and the mean kinetic energy of the particles. The melting transition is found to be a continuous process starting from the defects inside the crystal.Comment: 4 pages, 3 figures, accepted by Powders and Grains 201

Cluster and reentrant anomalies of nearly Gaussian core particles

We study through integral equation theory and numerical simulations the structure and dynamics of fluids composed of ultrasoft, nearly Gaussian particles. Namely, we explore the fluid phase diagram of a model in which particles interact via the generalized exponential potential u(r)=\epsilon exp[-(r/\sigma)^n], with a softness exponent n slightly larger than 2. In addition to the well-known anomaly associated to reentrant melting, the structure and dynamics of the fluid display two additional anomalies, which are visible in the isothermal variation of the structure factor and diffusivity. These features are correlated to the appearance of dimers in the fluid phase and to the subsequent modification of the cluster structure upon compression. We corroborate these results through an analysis of the local minima of the potential energy surface, in which clusters appear as much tighter conglomerates of particles. We find that reentrant melting and clustering coexist for softness exponents ranging from 2^+ up to values relevant for the description of amphiphilic dendrimers, i.e., n=3.Comment: 10 pages, 8 figure

Anomalous dynamics of interstitial dopants in soft crystals

The dynamics of interstitial dopants governs the properties of a wide variety of doped crystalline materials. To describe the hopping dynamics of such interstitial impurities, classical approaches often assume that dopant particles do not interact and travel through a static potential energy landscape. Here we show, using computer simulations, how these assumptions and the resulting predictions from classical Eyring-type theories break down in entropically-stabilised BCC crystals due to the thermal excitations of the crystalline matrix. Deviations are particularly severe close to melting where the lattice becomes weak and dopant dynamics exhibit strongly localised and heterogeneous dynamics. We attribute these anomalies to the failure of both assumptions underlying the classical description: i) the instantaneous potential field experienced by dopants becomes largely disordered due to thermal fluctuations and ii) elastic interactions cause strong dopant-dopant interactions even at low doping fractions. These results illustrate how describing non-classical dopant dynamics requires taking the effective disordered potential energy landscape of strongly excited crystals and dopant-dopant interactions into account.Comment: 16 pages, 14 figures. Includes Supplementary Informatio

Crystallization and melting of bacteria colonies and Brownian Bugs

Motivated by the existence of remarkably ordered cluster arrays of bacteria colonies growing in Petri dishes and related problems, we study the spontaneous emergence of clustering and patterns in a simple nonequilibrium system: the individual-based interacting Brownian bug model. We map this discrete model into a continuous Langevin equation which is the starting point for our extensive numerical analyses. For the two-dimensional case we report on the spontaneous generation of localized clusters of activity as well as a melting/freezing transition from a disordered or isotropic phase to an ordered one characterized by hexagonal patterns. We study in detail the analogies and differences with the well-established Kosterlitz-Thouless-Halperin-Nelson-Young theory of equilibrium melting, as well as with another competing theory. For that, we study translational and orientational correlations and perform a careful defect analysis. We find a non standard one-stage, defect-mediated, transition whose nature is only partially elucidated.Comment: 13 Figures. 14 pages. Submitted to Phys. Rev.