Potts Model on Maple Leaf Lattice with Pure Three-Site Interaction

We use Monte Carlo method to study three-state Potts model on maple leaf lattice with pure three-site interaction. The critical behavior of both ferromagnetic and antiferromagnetic cases is studied. Our results confirm that the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. For the antiferromagnetic case the transition is of the first order. We have calculated the energy jump and critical temperature in this area. We find there is a tricritical point separating the first order and second order phases for this system.

An Analytical Study of Three-State Potts Model on Lattice

We investigate the phase structure of the three-state Ports model by the variational cumulant expansion approach, it is shown that there is a weak first-order phase transition in three and four dimensions. The critical coupling given by this method is in good agreement with MC data.

Comparison of Ising Model and Potts Model on Non-Local Directed Small-World Networks

Further to the investigation of the critical properties of the Potts model with q = 3 and 8 states in one dimension (1D) on directed small-world networks reported by Aquino and Lima, which presents, in fact, a second-order phase transition with a new set of critical exponents, in addition to what was reported in Sumour and Lima in studying Ising model on non-local directed small-world for several values of probability 0 < P < 1. In this paper the behavior of two models discussed previously, will be re-examined to study differences between their behavior on directed small-world networks for networks of different values of probability P = 0.1, 0.2, 0.3, 0.4 and 0.5 with different lattice sizes L = 10, 20, 30, 40, and 50 to compare between the important physical variables between Ising and Potts models on the directed small-world networks. We found in our paper that is a phase transitions in both Ising and Potts models depending essentially on the probability P.

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric（disorder） and broken（order） phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.

Short—Time Dynamics of Random—Bond Potts Ferromagnet with Continuous Self—Dual Quenched Disorders

We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson–Young self-dual distribution of quenched disorders in two dimensions. By exploring the short-time scaling dynamics, we find the universal power-law critical behavior of the magnetization and Binder cumulant at the critical point, and thus obtain estimates of the dynamic exponent and magnetic exponent , as well as the exponent . Our special attention is paid to the dynamic process for the Potts model.

Geometric regulation of collective cell tangential ordering migration

Collective cell migration is a coordinated movement of multi-cell systems essential for various processes throughout life.The collective motions often occur under spatial restrictions,hallmarked by the collective rotation of epithelial cells confined in circular substrates.Here,we aim to explore how geometric shapes of confinement regulate this collective cell movement.We develop quantitative methods for cell velocity orientation analysis,and find that boundary cells exhibit stronger tangential ordering migration than inner cells in circular pattern.Furthermore,decreased tangential ordering movement capability of collective cells in triangular and square patterns are observed,due to the disturbance of cell motion at unsmooth corners of these patterns.On the other hand,the collective cell rotation is slightly affected by a convex defect of the circular pattern,while almost hindered with a concave defect,also resulting from different smoothness features of their boundaries.Numerical simulations employing cell Potts model well reproduce and extend experimental observations.Together,our results highlight the importance of boundary smoothness in the regulation of collective cell tangential ordering migration.

A Stochastic Study on the Wicking Phenomena

A stochastic approach based on a 3D 3-state Potts model combined with Monte Carlo simulation was used to study the equilibrium wicking height of liquids in vertical cylindrical capillaries. The Lifshitz-van der Waals and Lewis acid-base theories were adopted to characterize the apolar and polar interactions in the spin system. The evolution of the spin system was driven by the difference in total energy for two successive states. To verify the model, equilibrium wicking height of water, formamide, heptane, and octane in capillaries of different radii were examined and the corresponding computer simulations were implemented. Good agreement was obtained between the simulation and experimental results. It shows the potential of the proposed approach to be applied in this area.

Monte Carlo Simulations of Topological Properties in Two-Phase Polycrystalline Materials for Several Diffusion Mechanism

Numerical simulations by means of the Monte Carlo Potts model have been provided to simulate grain structures in two-phase polycrystalline materials. The topological features in the simulated microstructure analyzed for different diffusion mechanisms over a broad range of volume fractions for both phases. The topological properties include the average number of sides, grain topology distribution and the topological size relation function. It is found that the average number of sides depends proportionally on the volume fraction. It increases as the volumes fraction increases and vice versa. Moreover, it is shown that the grain topology distribution in the self-similar growth regime can be described by time unchanged function of the relative grain size. Additionally, topological size function in the simulated microstructure can be evaluated by a quadratic function.

Bubble coalescence in interacting system of DNA molecules

We consider two models of interacting DNA molecules:First is(four parametric)bubble coalescence model in interacting DNAs(shortly:BCI-DNA).Second is(three parametric)bubble coalescence model in a condensed DNA molecules(shortly BCC-DNA).To study bubble coalescence thermodynamics of BCI-DNA and BCC-DNA models we use methods of statistical physics.Namely,we define Hamiltonian of each model and give their translation-invariant Gibbs measures(TIGMs).For the first model,we find parameters such that corresponding Hamiltonian has up to three TIGMs(three phases of system)biologically meaning existence of three states:“No bubble coalescence”,“Dominated soft zone”,“Bubble coalescence”.For the second model,we show that for any(admissible)parameters,this model has unique TIGM.This is a state where“No bubble coalescence”phasedominates.

A Survey on Parallel Computing and its Applications in Data-Parallel Problems Using GPU Architectures

Parallel computing has become an important subject in the field of computer science and has proven to be critical when researching high performance solutions.The evolution of computer architectures(multi-core and many-core)towards a higher number of cores can only confirm that parallelism is the method of choice for speeding up an algorithm.In the last decade,the graphics processing unit,or GPU,has gained an important place in the field of high performance computing(HPC)because of its low cost and massive parallel processing power.Super-computing has become,for the first time,available to anyone at the price of a desktop computer.In this paper,we survey the concept of parallel computing and especially GPU computing.Achieving efficient parallel algorithms for the GPU is not a trivial task,there are several technical restrictions that must be satisfied in order to achieve the expected performance.Some of these limitations are consequences of the underlying architecture of the GPU and the theoretical models behind it.Our goal is to present a set of theoretical and technical concepts that are often required to understand the GPU and its massive parallelism model.In particular,we show how this new technology can help the field of computational physics,especially when the problem is data-parallel.We present four examples of computational physics problems;n-body,collision detection,Potts model and cellular automata simulations.These examples well represent the kind of problems that are suitable for GPU computing.By understanding the GPU architecture and its massive parallelism programming model,one can overcome many of the technical limitations found along the way,design better GPU-based algorithms for computational physics problems and achieve speedups that can reach up to two orders of magnitude when compared to sequential implementations.

Scalably Revealing the Dynamics of Soft Community Structure in Complex Networks

Revealing the dynamics of community structure is of great concern for scientists from many fields. Specifically, how to quantify the dynamic details of soft community structure is a very interesting topic. In this paper, the authors propose a novel framework to study the scalable dynamic behavior of the soft community structure. First, the authors model the Potts dynamics to detect community structure using a "soft" Markov process. Then the soft stability of in a multiscale view is proposed to naturally uncover the local uniform behavior of spin values across multiple hierarchical levels. Finally, a new partition index is developed to detect fuzzy communities based on the stability and the dynamical information. Experiments on the both synthetically generated and real-world networks verify that the framework can be used to uncover hierarchical community structures effectively and efficiently.

Topological rearrangements and flow simulation of dry ordered foams

Flow through a narrow bent channel may induce topological rearrangements in a twodimensional monodispersed dry liquid foam.We use the Cellular Potts Model to simulate a foam under a variable driving force in order to investigate the strain-rate response from these rearrangements.We observe a set of foams’behaviors ranging from elastic,viscoelastic to fluid regime.Bubble’s topological rearrangements are localized and their cumulative rearrangements change linearly with time,thus nonavalanches critical behavior is found.The strain-rate affects the rate of topological rearrangements,its dependence on the drag force is nonlinear,obeying a Herschel–Bulkley-like relationship below the foam’s flow point.

Connections between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation

Deep neural network is a powerful tool for many tasks.Understanding why it is so successful and providing a mathematical explanation is an important problem and has been one popular research direction in past years.In the literature of mathematical analysis of deep neural networks,a lot of works is dedicated to establishing representation theories.How to make connections between deep neural networks and mathematical algorithms is still under development.In this paper,we give an algorithmic explanation for deep neural networks,especially in their connections with operator splitting.We show that with certain splitting strategies,operator-splitting methods have the same structure as networks.Utilizing this connection and the Potts model for image segmentation,two networks inspired by operator-splitting methods are proposed.The two networks are essentially two operator-splitting algorithms solving the Potts model.Numerical experiments are presented to demonstrate the effectiveness of the proposed networks.