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Entropy evaluation sheds light on ecosystem complexity

Physical Review E 2018年第4期98卷 042402-042402页

作者： Mattia Miotto Lorenzo Monacelli Univ Sapienza Dept Phys Piazzale Aldo Moro 5 I-00185 Rome Italy

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy of a minimal ecosystem on a lattice in which two species struggle for survival. The method quantitatively reproduces the scale-free law of the prey shoals size, where the simpler mean-field approach fails: the direct near-neighbor correlations are found to be the fundamental ingredient describing the system self-organized behavior. Furthermore, entropy allows the measurement of structural ordering we found to be a key ingredient in characterizing two different coexistence behaviors, one where predators form localized patches in a sea of preys and another where species display more complex patterns. The general nature of the introduced method paves the way for its application in many other systems of interest.

关键词： Animal behavior Biological complexity Clustering Ecological population dynamics Ecology & evolution Entropy Entropy production Optimization problems Population dynamics Cellular automata Information theory Ising model metropolis algorithm Monte Carlo methods

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Impact of the Injection Protocol on an Impurity’s Stationary State

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Physical Review Letters 2018年第22期120卷 220605-220605页

作者： Oleksandr Gamayun Oleg Lychkovskiy Evgeni Burovski Matthew Malcomson Vadim V. Cheianov Mikhail B. Zvonarev Instituut-Lorentz Universiteit Leiden P.O. Box 9506 Leiden 2300 RA Netherlands Bogolyubov Institute for Theoretical Physics 14-b Metrolohichna street Kyiv 03680 Ukraine Skolkovo Institute of Science and Technology Skolkovo Innovation Center 3 Moscow 143026 Russia Steklov Mathematical Institute of Russian Academy of Sciences Gubkina street 8 Moscow 119991 Russia Russian Quantum Center Novaya Street 100A Skolkovo Moscow Region 143025 Russia National Research University Higher School of Economics Moscow 101000 Russia Science Center in Chernogolovka Chernogolovka 142432 Russia Physics Department Lancaster University Lancaster LA1 4YB United Kingdom LPTMS CNRS Univ. Paris-Sud Université Paris-Saclay Orsay 91405 France

We examine stationary-state properties of an impurity particle injected into a one-dimensional quantum gas. We show that the value of the impurity’s end velocity lies between zero and the speed of sound in the gas and is determined by the injection protocol. This way, the impurity’s constant motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of the Landau approach to superfluidity. We provide exact analytic results in the thermodynamic limit and perform finite-size numerical simulations to demonstrate that the predicted phenomena are within the reach of the ultracold gas experiments.

关键词： Mixtures of atomic and/or molecular quantum gases Quantum field theory (low energy) 1-dimensional systems Bethe ansatz metropolis algorithm

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A Bayesian approach to determine the composition of heterogeneous cancer tissue

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BMC BIOINFORMATICS 2018年第3-Sup期19卷 90-90页

作者： Katiyar, Ashish Mohanty, Anwoy Hua, Jianping Chao, Sima Lopes, Rosana Datta, Aniruddha Bittner, Michael L. Texas A&M Univ Dept Elect & Comp Engn College Stn TX 77843 USA Brigham & Womens Hosp Div Genet Dept Med POB 1212 Boston MA 02115 USA Harvard Med Sch POB 1212 Boston MA 02115 USA Texas A&M Univ Ctr Bioinformat & Genom Syst Engn TEES College Stn TX 77843 USA Translat Genom Res Inst Phoenix AZ USA

Background: Cancer Tissue Heterogeneity is an important consideration in cancer research as it can give insights into the causes and progression of cancer. It is known to play a significant role in cancer cell survival, growth and metastasis. Determining the compositional breakup of a heterogeneous cancer tissue can also help address the therapeutic challenges posed by heterogeneity. This necessitates a low cost, scalable algorithm to address the challenge of accurate estimation of the composition of a heterogeneous cancer tissue. Methods: In this paper, we propose an algorithm to tackle this problem by utilizing the data of accurate, but high cost, single cell line cell-by-cell observation methods in low cost aggregate observation method for heterogeneous cancer cell mixtures to obtain their composition in a Bayesian framework. Results: The algorithm is analyzed and validated using synthetic data and experimental data. The experimental data is obtained from mixtures of three separate human cancer cell lines, HCT116 (Colorectal carcinoma), A2058 (Melanoma) and SW480 (Colorectal carcinoma). Conclusion: The algorithm provides a low cost framework to determine the composition of heterogeneous cancer tissue which is a crucial aspect in cancer research.

关键词： Cancer tissue heterogeneity Bayesian modeling metropolis algorithm Kernel density estimation

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Fluctuations of conformational mobility of macromolecules around the glass transition

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Physical Review E 2018年第6期97卷 062605-062605页

作者： C. Torregrosa Cabanilles J. Molina-Mateo R. Sabater i Serra J. M. Meseguer-Dueñas J. L. Gómez Ribelles Center for Biomaterials and Tissue Engineering Universitat Politècnica de València València Spain

The heterogeneity of local dynamics in disordered systems is behind some key features of glass transition. In order to improve our understanding of the molecular dynamics in disordered systems in the vicinity of the glass transition, different parameters have been proposed to quantitatively describe dynamical heterogeneity. In the case of polymers, free volume models relate the macromolecular mobility to the free or accessible volume. The relationship between dynamic heterogeneity and fluctuations of accessible volume seems straightforward. In the present work, the heterogeneity of local dynamics in polymeric systems is analyzed by computer simulation with the bond fluctuation model. The value of the accessible volume around each polymer chain is evaluated from a snapshot or static structure at each system state, resulting in a distribution of accessible volume that reflects system heterogeneity. The relationship between the average value and the standard deviation of free volume distributions at different temperatures fits a master curve for different systems, regardless of the specific inter- and intramolecular interaction potentials that define each material. The dynamic slowdown around the glass transition is accompanied by a clear evolution of the mean value and shape of the accessible free volume distribution. The relative fluctuation of the dynamically accessible volume has been used as a parameter to quantitatively describe heterogeneity. The fluctuation varies with temperature with remarkable differences between the liquid and glassy states of the systems studied, presenting a peak at the glass transition temperature, which can be interpreted as a reflection of the distribution of local glass transition temperatures.

关键词： Glass transition Polymer behavior Glassy systems Macromolecules Coarse graining metropolis algorithm

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Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature

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Physical Review E 2018年第1期98卷 012124-012124页

作者： Wei Zhong Debabrata Panja Gerard T. Barkema Robin C. Ball Department of Information and Computing Sciences Utrecht University Princetonplein 5 3584 CC Utrecht The Netherlands Department of Physics University of Warwick Coventry CV4 7AL United Kingdom

We consider the two- (2D) and three-dimensional (3D) Ising models on a square lattice at the critical temperature Tc, under Monte Carlo spin flip dynamics. The bulk magnetization and the magnetization of a tagged line in the 2D Ising model, and the bulk magnetization and the magnetization of a tagged plane in the 3D Ising model, exhibit anomalous diffusion. Specifically, their mean-square displacements increase as power laws in time, collectively denoted as ∼tc, where c is the anomalous exponent. We argue that the anomalous diffusion in all these quantities for the Ising model stems from time-dependent restoring forces, decaying as power laws in time—also with exponent c —in striking similarity to anomalous diffusion in polymeric systems. Prompted by our previous work that has established a memory-kernel based generalized Langevin equation (GLE) formulation for polymeric systems, we show that a closely analogous GLE formulation holds for the Ising model as well. We obtain the memory kernels from spin-spin correlation functions, and the formulation allows us to consistently explain anomalous diffusion as well as anomalous response of the Ising model to an externally applied magnetic field in a consistent manner.

关键词： Anomalous diffusion Critical phenomena Equilibrium lattice models Ising model Langevin equation metropolis algorithm

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Diffusion dynamics and steady states of systems of hard rods on a square lattice

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Physical Review E 2018年第2期97卷 022108-022108页

作者： Saugata Patra Dibyendu Das R. Rajesh Mithun K. Mitra Department of Physics Indian Institute of Technology Bombay Powai Mumbai-400076 India The Institute of Mathematical Sciences CIT Campus Taramani Chennai-600113 India Homi Bhabha National Institute Training School Complex Anushakti Nagar Mumbai 400094 India

It is known from grand canonical simulations of a system of hard rods on two-dimensional lattices that an orientationally ordered nematic phase exists only when the length of the rods is at least seven. However, a recent microcanonical simulation with diffusion kinetics, conserving both total density and zero nematic order, reported the existence of a nematically phase-segregated steady state with interfaces in the diagonal direction for rods of length six [Phys. Rev. E 95, 052130 (2017)], violating the equivalence of different ensembles for systems in equilibrium. We resolve this inconsistency by demonstrating that the kinetics violate detailed balance condition and drives the system to a nonequilibrium steady state. By implementing diffusion kinetics that drive the system to equilibrium, even within this constrained ensemble, we recover earlier results showing phase segregation only for rods of length greater than or equal to seven. Furthermore, in contrast to the nonequilibrium steady state, the interface has no preferred orientational direction. In addition, by implementing different nonequilibrium kinetics, we show that the interface between the phase segregated states can lie in different directions depending on the choice of kinetics.

关键词： Nonequilibrium statistical mechanics Phase separation Phase transitions Equilibrium lattice models Lattice models in statistical physics Nonequilibrium lattice models metropolis algorithm

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Statistical mechanics of a coevolving spin system

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Physical Review E 2018年第3期98卷 030301(R)-030301(R)页

作者： Tomasz Raducha Mateusz Wilinski Tomasz Gubiec H. Eugene Stanley Institute of Experimental Physics Faculty of Physics University of Warsaw Pasteura 5 02-093 Warsaw Poland Instituto de Fisica Interdisciplinary Sistemas Complejos IFISC (CSIC-UIB) 07122 Palma de Mallorca Spain Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa Italy Center for Polymer Studies and Department of Physics Boston University Boston Massachusetts 02215 USA

We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a Hamiltonian that merges the classical Ising model and the statistical theory of correlated random networks. As a result, we obtain rich phase diagrams with different phase transitions both in the state of nodes and in the graph topology. We argue that the coupling between the spin dynamics and the structure of the network is crucial in understanding the complex behavior of real-world systems and omitting one of the approaches renders the description incomplete.

关键词： Magnetic phase transitions Network phase transitions Network structure Phase transitions Structural properties Topological phase transition Spin glasses Ising model metropolis algorithm Monte Carlo methods Network Models

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Two Phase Transitions in the Two-Dimensional Nematic Three-Vector Model with No Quasi-Long-Range Order: Monte Carlo Simulation of the Density of States

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Physical Review Letters 2018年第21期121卷 217801-217801页

作者： B. Kamala Latha V. S. S. Sastry School of Physics University of Hyderabad Hyderabad 500046 India Centre for Modelling Simulation and Design University of Hyderabad Hyderabad 500046 India

The presence of stable topological defects in a two-dimensional (d=2) liquid crystal model allowing molecular reorientations in three dimensions (n=3) was largely believed to induce a defect-mediated Berzenskii-Kosterlitz-Thouless-type transition to a low temperature phase with quasi-long-range order. However, earlier Monte Carlo (MC) simulations could not establish certain essential signatures of the transition, suggesting further investigations. We study this model by computing its equilibrium properties through MC simulations, based on the determination of the density of states of the system. Our results show that, on cooling, the high temperature disordered phase deviates from its initial progression towards the topological transition, crossing over to a new fixed point, condensing into a nematic phase with exponential correlations of its director fluctuations. The thermally induced topological kinetic processes continue, however, limited to the length scales set by the nematic director fluctuations, and lead to a second topological transition at a lower temperature. It is argued that in the (d=2, n=3) system with an attractive biquadratic Hamiltonian, the presence of additional molecular degrees of freedom and local Z2 symmetry associated with lattice sites together promote the onset of an additional relevant scaling field at matching length scales in the high temperature region, leading to a crossover.

关键词： Critical phenomena Exotic phases of matter Phase transitions Nematic liquid crystals Entropic sampling methods metropolis algorithm

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Formation and morphological evolution of self-similar 3D nanostructures on weakly interacting substrates

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Physical Review Materials 2018年第6期2卷 063401-063401页

作者： B. Lü G. A. Almyras V. Gervilla J. E. Greene K. Sarakinos Nanoscale Engineering Division Department of Physics Chemistry and Biology Linköping University SE 581 83 Linköping Sweden Thin Film Physics Division Department of Physics Chemistry and Biology Linköping University SE-581 83 Linköping Sweden Materials Science and Physics Departments University of Illinois Urbana Illinois 61801 USA

Vapor condensation on weakly interacting substrates leads to the formation of three-dimensional (3D) nanoscale islands (i.e., nanostructures). While it is widely accepted that this process is driven by minimization of the total film/substrate surface and interface energy, current film-growth theory cannot fully explain the atomic-scale mechanisms and pathways by which 3D island formation and morphological evolution occurs. Here, we use kinetic Monte Carlo simulations to describe the dynamic evolution of single-island shapes during deposition of Ag on weakly interacting substrates. The results show that 3D island shapes evolve in a self-similar manner, exhibiting a constant height-to-radius aspect ratio, which is a function of the growth temperature. Furthermore, our results reveal the following chain of atomic-scale events that lead to compact 3D island shapes: 3D nuclei are first formed due to facile adatom ascent at single-layer island steps, followed by the development of sidewall facets bounding the islands, which in turn facilitates upward diffusion from the base to the top of the islands. The limiting atomic process which determines the island height, for a given number of deposited atoms, is the temperature-dependent rate at which adatoms cross from sidewall facets to the island top. The overall findings of this study provide insights into the directed growth of metal nanostructures with controlled shapes on weakly interacting substrates, including two-dimensional crystals, for use in catalytic and nanoelectronic applications.

关键词： Growth Island Nucleation on surfaces Surface diffusion Nanoparticles Thin films metropolis algorithm Molecular dynamics

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Structural properties of the Jagla fluid

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Physical Review E 2018年第1期98卷 012138-012138页

作者： Mariano López de Haro Álvaro Rodríguez-Rivas Santos B. Yuste Andrés Santos Instituto de Energías Renovables Universidad Nacional Autónoma de México (U.N.A.M.) Temixco Morelos 62580 Mexico Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx) Universidad de Extremadura Badajoz E-06006 Spain

The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, g(r), from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of g(r) in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher-Widom and Widom lines of the Jagla fluid are obtained.

关键词： Classical statistical mechanics Colloids Soft colloids metropolis algorithm Monte Carlo methods

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