Criticality of Parasitic Disease Transmission in a Diffusive Population

Through using the methods of finite-size effect and short time dynamic scaling, we study the critical behavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment. Through comprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. We determine the critical population density, above which the system reaches an epidemic spreading stationary state. We also perform a scaling analysis to determine the order parameter and critical relaxation exponents. The results show that the model does not belong to the usual directed percolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields.     

Critical behavior of a two-species reaction-diffusion problem in 2D

In this work we study the critical behavior of a model that simulates the propagation of an epidemic process over a population. We simulate the model on two-dimensional finite lattices to determine the critical density of the diffusive population. A finite size scaling analysis is employed to determine the order parameter and correlation length critical exponents.     

A parity conserving dimer model with infinitely many absorbing states

We propose and study a model where two aspects are present: parity conservation and infinitely many absorbing states. Whereas steady-state simulations show that the static critical behaviour is not affected by the presence of multiple absorbing configurations, the influence of the initial state associated with the presence of slowly decaying memory effects is clearly displayed in time dependent simulations. We report results of a detailed investigation of the dependence of critical spreading exponents on the initial particle density. Received 13 January 1999 and Received in final form 7 April 1999     

Diffusive and dynamical radiating stars with realistic equations of state

We model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.     

Microscopic noise,adaptation and survival in hostile environments

The survival of autocatalytic agents in hostile environments depends on their ability to adapt their spatial configuration to local fluctuations. A model of diffusive reactants that extract the advantage of spatio-temporal fluctuations associated with the stochastic wandering of diffusive catalysts is discussed. Two arguments are presented for the basic processes behind this extraordinary behavior. In the first, the local colonies that evolve around any spatially advantageous region overlap in space-time and an infinite directed percolation cluster emerges. The second argument is based on the return probability of a diffusive agent that is shown to yield finite density of active “oases" with an exponentially large contribution to the reactant population. The different range of applicability of these survival lower bounds to small systems is discussed.     

The influence of short-range order on electronic properties of transition metals: II. Amorphous metals

Local electronic properties have been calculated for the amorphous transition metals Nb, Mo, and Tc using a cluster model which accounts for the topology of the local structure. Trends in the density of states observed in metallic glasses are reproduced, and the behaviour of the averaged electron-phonon coupling strength correlates well with the behaviour of the superconducting transition temperature. The ratios of the critical temperatures in the amorphous and the crystalline state are reproduced correctly. The results show that the change in the critical temperature on going from the crystalline to the amorphous state can be explained by the change in short-range order.     

The influence of short-range order on electronic properties of transition metals: II. Amorphous metals

Local electronic properties have been calculated for the amorphous transition metals Nb, Mo, and Tc using a cluster model which accounts for the topology of the local structure. Trends in the density of states observed in metallic glasses are reproduced, and the behaviour of the averaged electron-phonon coupling strength correlates well with the behaviour of the superconducting transition temperature. The ratios of the critical temperatures in the amorphous and the crystalline state are reproduced correctly. The results show that the change in the critical temperature on going from the crystalline to the amorphous state can be explained by the change in short-range order.     

Field theory of critical behaviour in driven diffusive systems

We present a field theoretic renormalisation group study for the critical behaviour of a diffusive system with a single conserved density subjected to an external driving force. The anisotropies induced by the external field require the introduction of two critical parameters associated with transverse and longitudinal order. The transition to transverse order is governed by a fixed point which is infrared stable below five dimensions. With the help of Ward-Takahashi identities based on Galilei invariance, we derive scaling forms for density correlation functions, critical exponents to all orders in =5–d, and the equation of state, taking care of a dangerous irrelevant composite operator. The transition is continuous and of mean-field type, with anomalous long-wavelength and long-time correlations in the longitudinal direction only. For the transition to longitudinal order, no infrared stable fixed point is found. An analysis of the mean-field equations indicates that the transition is discontinuous.     

Spatiotemporal Characteristic of Epidemic Spreading in Mobile Individuals

We numerical simulate the propagation behaviour and people distribution trait of epidemic spreading in mobile individuals by using cellular automaton method. The simulation results show that there exists a critical value of infected rate fluctuating amplitude, above which the epidemic can spread in whole population. Moreover, with the value of infected rate fluctuating amplitude increasing, the spatial distribution of infected population exhibits the spontaneous formation of irregular spiral waves and convergence phenomena, at the same time, the density of different populations will oscillate automatically with time. What is more, the traits of dynamic grow clearly and stably when the time and the value of infected rate fluctuating amplitude increasing. It is also found that the maximal proportion of infected individuals is independent of the value of fluctuating amplitude rate, but increases linearly with the population density.     

Gate Tunable Supercurrent in Josephson Junctions Based on Bi_2Te_3 Topological Insulator Thin Films

We report transport measurements on Josephson junctions consisting of Bi_2Te_3 topological insulator(TI) thin films contacted by superconducting Nb electrodes.For a device with junction length L=134 nm,the critical supercurrent I_c can be modulated by an electrical gate which tunes the carrier type and density of the TI film.I_c can reach a minimum when the TI is near the charge neutrality regime with the Fermi energy lying close to the Dirac point of the surface state.In the p-type regime the Josephson current can be well described by a short ballistic junction model.In the n-type regime the junction is ballistic at 0.7 K T 3.8 K while for T 0.7 K the diffusive bulk modes emerge and contribute a larger I_c than the ballistic model.We attribute the lack of diffusive bulk modes in the p-type regime to the formation of p-n junctions.Our work provides new clues for search of Majorana zero mode in TI-based superconducting devices.     

Dislocation density-based constitutive model for the mechanical behaviour of irradiated Cu

Performance degradation of structural steels in nuclear environments results from the formation of a high number density of nanometre-scale defects. The defects observed in copper-based alloys are composed of vacancy clusters in the form of stacking fault tetrahedra and/or prismatic dislocation loops that impede the motion of dislocations. The mechanical behaviour of irradiated copper alloys exhibits increased yield strength, decreased total strain to failure and decreased work hardening as compared to their unirradiated behaviour. Above certain critical defect concentrations (neutron doses), the mechanical behaviour exhibits distinct upper yield points. In this paper, we describe the formulation of an internal state variable model for the mechanical behaviour of such materials subject to these (irradiation) environments. This model has been developed within a multiscale materials-modelling framework, in which molecular dynamics simulations of dislocation–radiation defect interactions inform the final coarse-grained continuum model. The plasticity model includes mechanisms for dislocation density growth and multiplication and for irradiation defect density evolution with dislocation interaction. The general behaviour of the constitutive (homogeneous material point) model shows that as the defect density increases, the initial yield point increases and the initial strain hardening decreases. The final coarse-grained model is implemented into a finite element framework and used to simulate the behaviour of tensile specimens with varying levels of irradiation-induced material damage. The simulation results compare favourably with the experimentally observed mechanical behaviour of irradiated materials.     

Short-range order in spin density wave antiferromagnets

The model of the short-range order state for itinerant antiferromagnets with SDW is developed. The thermodynamic transverse spin density fluctuation are shown to influence essentially on the formation of the long-range magnetic order. In the wide temperature range these occurs the shortprange, magnetic order regim. The properties of the low-frequency transverse excitations of the spin density are analized. The existence of a fully diffusive mode at small wave vectors is predicted.     

第二类超导体输运临界电流密度的一个临界态模型计算

给出了第二类超导体临界电流密度随样品尺寸及外加磁场变化的一个临界态模型计算。计算中考虑了样品中混合态与迈斯纳态共存的情况。用该模型对Tl2Ba2Ca2Cu3O10样品的实验测量结果进行了模拟计算,并讨论了有关问题。     

Spatio-temporal patterns in a square-lattice Hodgkin-Huxley neural network

The collective behaviour of a square-lattice Hodgkin-Huxley neural network model with white noise is investigated by numerical methods. It is found that for an intermediate value of noise the Hodgkin-Huxley neurons in the square lattice exhibit an ordered circular structure. However, as the noise level increases, the ordered circular structures are distorted, and eventually totally destroyed. Thereby, the constructive role of appropriately pronounced random perturbations in the studied network is revealed. Furthermore, it is shown that as the diffusive coefficient increases, the typical width of the spatial waves also increases accordingly, which results in a decrease of the number of cycles by a given size of the spatial grid. More interestingly, it is observed that the spatio-temporal coherence resonance is enhanced as the diffusive coefficient is increased. Finally, the dependence of the typical width and the average period of the firing rate function on the diffusive coefficient is studied. Results presented in this paper should prove valuable for the understanding of information processing of neural systems in the presence of noise.     

Axialisation, cooling and quenching of ions in a Penning trap

On the basis of a macroscopic ground state population it was argued recently that Bose-Einstein condensation should occur in a one-dimensional harmonic potential. We examine this situation by drawing analogies to bosons in a two-dimensional box, where the thermodynamic limit is well-defined. We show that in both systems although the ground state populations show sharp onsets at the critical temperature, the behaviour of the specific heat is analytic, which proves the absence of a phase transition in these systems. Received: 17 February 1997 / Revised: 3 September 1997 / Accepted: 13 October 1997     

Freezing transition in the mean-field approximation model of pedestrian counter flow

We study the freezing transition in the counter flow of pedestrians within the channel numerically and analytically. We present the mean-field approximation (MFA) model for the pedestrian counter flow. The model is described in terms of a couple of nonlinear difference equations. The excluded-volume effect and bi-directionality are taken into account. The fundamental diagrams (current-density diagrams) are derived. When pedestrian density is higher than a critical value, the dynamical phase transition occurs from the free flow to the freezing (stopping) state. The critical density is derived by using the linear stability analysis. Also, the velocity and current (flow) at the steady state are derived analytically. The analytical result is consistent with that obtained by the numerical simulation.     

Configurations and observables in an Ising model with heat flow

We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The relevance of such complex states on thermodynamic or geometrical observables is investigated. In particular, we study energy, magnetization and metric properties of interfaces and clusters which, in principle, are sensitive to local features of configurations. With respect to equilibrium states, the presence of the heat flow amplifies the fluctuations of both thermodynamic and geometrical observables in a domain around the critical energy. The dependence of this phenomenon on various parameters (size, thermal gradient, interaction) is discussed also with reference to other possible diffusive models.     

A model for anomalous directed percolation

We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for long-range infections which decays in d spatial dimensions as . Extensive numerical simulations are performed in order to determine the density exponent and the correlation length exponents and for various values of . We observe that these exponents vary continuously with , in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions. Received: 4 September 1998 / Accepted: 22 September 1998