Pattern formation induced by cross-diffusion in a predator--prey system

This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator-prey system.     

Sexually Transmitted Diseases on Bipartite Graph

We study the susceptible infected-susceptible （SIS） epidemic model on bipartite graph. According to the difference of sex conception in western and oriental nations, we construct the Barabasi Albert Barabasi Albert （BA-BA） model and Barabasi-Albert Homogeneity （BA-HO） model for sexually transmitted diseases （STDs）. Applying the rate equation approach, the positive equilibria of both models are given analytically. We find that the ratio between infected females and infected males is distinctly different in both models and the infected density in the BA-HO model is much less than that in the BA-BA model. These results explain that the countries with small ratio have less infected density than those with large ratio. Our numerical simulations verify these theoretical results.     

Spatial Games Based on Pursuing the Highest Average Payoff

We propose a strategy updating mechanism based on pursuing the highest average payoff to investigate the prisoner＇s dilemma game and the snowdrift game. We apply the new rule to investigate cooperative behaviours on regular, small-world, scale-free networks, and find spatial structure can maintain cooperation for the prisoner＇s dilemma game. fn the snowdrift game, spatial structure can inhibit or promote cooperative behaviour which depends on payoff parameter. We further study cooperative behaviour on scale-free network in detail. Interestingly, non-monotonous behaviours observed on scale-free network with middle-degree individuals have the lowest cooperation level. We also find that large-degree individuals change their strategies more frequently for both games.     

An Efficient Control Strategy of Epidemic Spreading on Scale-Free Networks

We present a novel and effective method for controlling epidemic spreading on complex networks, especially on scale-free networks. The proposed strategy is performed by deleting edges according to their significances （the significance of an edge is defined as the product of the degrees of two nodes of this edge）. In contrast to other methods, e.g., random immunization, proportional immunization, targeted immunization, acquaintance immunization and so on, which mainly focus on how to delete nodes to realize the control of epidemic spreading on complex networks, our method is more effective in realizing the control of epidemic spreading on complex networks, moreover, such a method can better retain the integrity of complex networks.     

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.     

Comparison of immunization strategies in geographical networks

The epidemic spread and immunizations in geographically embedded scale-free (SF) and Watts-Strogatz (WS) networks are numerically investigated. We make a realistic assumption that it takes time which we call the detection time, for a vertex to be identified as infected, and implement two different immunization strategies: one is based on connection neighbors (CN) of the infected vertex with the exact information of the network structure utilized and the other is based on spatial neighbors (SN) with only geographical distances taken into account. We find that the decrease of the detection time is crucial for a successful immunization in general. Simulation results show that for both SF networks and WS networks, the SN strategy always performs better than the CN strategy, especially for more heterogeneous SF networks at long detection time. The observation is verified by checking the number of the infected nodes being immunized. We found that in geographical space, the distance preferences in the network construction process and the geographically decaying infection rate are key factors that make the SN immunization strategy outperforms the CN strategy. It indicates that even in the absence of the full knowledge of network connectivity we can still stop the epidemic spread efficiently only by using geographical information as in the SN strategy, which may have potential applications for preventing the real epidemic spread.     

Pattern formation in a predator–prey model with spatial effect

In this paper, spatial dynamics in the Beddington–DeAngelis predator–prey model with self-diffusion and cross-diffusion is investigated. We analyze the linear stability and obtain the condition of Turing instability of this model. Moreover, we deduce the amplitude equations and determine the stability of different patterns. Numerical simulations show that this system exhibits complex dynamical behaviors. In the Turing space, we find three types of typical patterns. One is the coexistence of hexagon patterns and stripe patterns. The other two are hexagon patterns of different types. The obtained results well enrich the finding in predator–prey models with Beddington–DeAngelis functional response.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.     

Complex turing patterns in non-linearly coupled systems

Recently pattern formation in layered structures, showing complicated superimposed patterns, has been modeled by coupling two Turing systems linearly, i.e., passively, such that the characteristic length scales of the independent systems are well separated. Here we propose a model of two non-linearly coupled Turing systems to study pattern formation in layered membrane-like structures, where the coupling plays an active role and changes the kinetics of the uncoupled systems. Extensive numerical simulations show that non-linear coupling generates a number of new regular patterns different from the ones observed earlier with linearly coupled systems. Some of them turn out to be superimposed patterns with different length scales, but many are not. Also, contrary to the linear coupling case, the strength of the non-linear coupling is found to play an important role in the formation and selection of patterns.     

Pattern dynamics of network-organized system with cross-diffusion

Cross-diffusion is a ubiquitous phenomenon in complex networks, but it is often neglected in the study of reaction–diffusion networks. In fact, network connections are often random. In this paper, we investigate pattern dynamics of random networks with cross-diffusion by using the method of network analysis and obtain a condition under which the network loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation for the network and prove the stability of the amplitude equation which is also an effective tool to investigate pattern dynamics of the random network with cross diffusion. In the meantime, the pattern formation consistently matches the stability of the system and the amplitude equation is verified by simulations. A novel approach to the investigation of specific real systems was presented in this paper. Finally, the example and simulation used in this paper validate our theoretical results.     

Information Filtering via Improved Similarity Definition

Based on a new definition of user similarity, we introduce an improved collaborative filtering （ICF） algorithm, which couM improve the algorithmic accuracy and diversity simultaneously. In the ICF, instead of the standard Pearson coefficient, the user-user similarities are obtained by integrating the heat conduction and mass diffusion processes. The simulation results on a benchmark data set indicate that the corresponding algorithmic accuracy, measured by the ranking score, is improved by 6. 7% in the optimal case compared to the standard collaborative filtering （CF） algorithm. More importantly, the diversity of the recommendation lists is also improved by 63.6%. Since the user similarity is crucial for the CF algorithm, this work may shed some light on how to improve the algorithmic performance by giving accurate similarity measurement.     

Theoretical Studies on Defects of Kaolinite in Clays

Using the first-principles methods, we study the formation energeties and charge doping properties of the extrinsic substitutional defects in kaolinite. Especially, we choose Be, Mg, Ca, Fe, Cr, Mn, Cu, Zn as extrinsic defects to substitute for Al atoms. By systematically calculating the impurity formation energies and transition energy levels, we find that all group-Ⅱ defects introduce the relative shallow transition energy levels in kaolinite. Among them, MgAl has the shallowest transition energy level at 0.08 eV above the valence band maximum. The transition- elemental defects FeAl, CrAl, and MnAl are found to have relative low formation energies, suggesting their easy formation in kaolinite under natural surrounding conditions. Our calculations show that the defects CuAl and ZnAl have the high formation energies and deep transition energy levels, which exclude the possibility of their formation in natural kaolinite.     

Temperature-Controllable Preparation of ZnS Nanosaws on Si Substrate

A large number of ZnS nanosaws are synthesized on Si substrates in the presence of Au catalyst by thermally evaporating ZnS powder. Morphologies and structures of thus-grown ZnS nanosaws are characterized by a field emission scanning electron microscopy （FE-SEM） and a transmission electron microscopy （TEM）. The results show that temperature of the Si substrates used for collection of the products is a critical experimental parameter for the formation of ZnS nanostruetures with different morphologies. The growth mechanism of the ZnS nanosaws is discussed on the basis of the experimental findings.     

Evolutionary Prisoner＇s Dilemma on a Weighted Scale-Free Network

We investigate the evolutionary prisoner＇s dilemma on a weighted scale-free network where the diversity of teaching ability is introduced to the network in the form of weight. Though the diversity of teaching ability is not a sufficient condition for the enhancement of cooperation, we find that the degree-dependent teaching ability plays an active role in the evolution of cooperation. A new phenomenon is found when the degree-dependent teaching ability is used： the distribution of the cooperator frequency displays a two-peak structure for a certain parameter range. We also investigate the effects of the degree-degree correlation of the network on the evolution of cooperation in the presence of the diversity of the teaching ability.     

Effects of Helium and Oxygen Common Implantation in Silicon Wafer

Defect engineering for SiO2 precipitation is investigated using He-ion implantation as the first stage of separation by implanted oxygen （SIMOX）. Cavities axe created in Si by implantation with helium ions. After thermal annealing at different temperatures, the sample is implanted with 120 keV 8.0 ×1016 cm 2 0 ions. The Q ion energy is chosen such that the peak of the concentration distribution is centred at the cavity band. For comparison, another sample is implanted with O ions alone. Cross-sectionM transmission electron microscopy （XTEM）, Fourier transform infrared absorbance spectrometry （FTIR） and atomic force microscopy （AFM） measurements are used to investigate the samples. The results show that a narrow nano-cavity layer is found to be excellent nucleation sites that effectively assisted SiO2 formation and released crystal lattice strain associated with silicon oxidation.     

Generation of Anti-Stokes Line in Fundamental Mode of Photonic Crystal Fibre

A photonic crystal fibre （PCF） with zero-dispersion wavelength around 800 nm is designed and fabricated. Simulated results show that the zero-dispersion wavelength of fundamental mode for this PCF is at 826nm, and phase-matched four-wave mixing can be achieved in fundamental mode. Using 20ors Ti：sapphire laser with central wavelength at 810nm as pump, the anti-Stokes line around 610hm ＆ generated efficiently. The output signal has a Gaussian-like profile, which indicates that the anti-Stokes signal is in the fundamental mode of the PCF. The energy of anti-Stokes signal is higher than that of residual pump laser and the maximum ratio of the anti-Stokes signal to the pump component in the output spectrum is estimated to be 1.2.     

Effect of Correlated Noises in a Genetic Model

The Stratonovich stochastic differential equation is used to analyze genotype selection in the presence ot correlatecl Gaussian white noises. We study the steady state properties of the genotype selection and discuss the effects of the correlated noises. It is found that the degree of correlation of the noises can be used to select one type of genes from another type of mixing genes. The strong selection of genes caused by a large value of multiplicative noise intensity can be weakened by the intensive negative correlation.     

Finite Space Complete Basis Method: Precision Computation of High-Resolution Spectrum near Ionization Threshold

A new method is proposed to describe quantum dynamical processes in finite space by using of a set of discretized complete bases. In this method, the finite space complete basis is obtained by solving the self-consistent field equation with reflecting boundary conditions. Hence, both negative and positive orbital energies can be obtained. Such method can be used in systems which involve dynamics only in the reaction zone, i.e., in a finite space. To illustrate the validity of the method, we present two examples: theoretical calculation of the high excited states spectra including the continuum of sodium and barium.     

Stochastic Simulation of Turing Patterns

We investigate the effects of intrinsic noise on Turing pattern formation near the onset of bifurcation from the homogeneous state to Turing pattern in the reaction-diffusion Brusselator. By performing stochastic simulations of the master equation and using Gillespie＇s algorithm, we check the spatiotemporal behaviour influenced by internal noises. We demonstrate that the patterns of occurrence frequency for the reaction and diffusion pro- cesses are also spatially ordered and temporally stable. Turing patterns are found to be robust against intrinsic fluctuations. Sfochastic simulations also reveal that under the influence of intrinsic noises, the onset of Turing instability is advanced in comparison to that predicted deterministically.     

Susceptible-infected-recovered epidemics in populations with heterogeneous contact rates

Heterogeneity of contact patterns is recognized as an important feature for realistic modeling of many epidemics. During an outbreak, the frequency of contacts can vary a great deal from person to person and period to period. Contact heterogeneity has been shown to have a large impact on epidemic thresholds and the final size of epidemics. We develop and apply a model which incorporates an arbitrary distribution of contact rates. The model consists of a low-dimensional system of ordinary differential equations which incorporates arbitrary heterogeneity by making use of generating functions of the contact rate distribution. We show further how this model can be applied to the study of simple intervention strategies, such as quarantine of public venues with probability proportional to size. The dynamic model allows us to investigate the effects of gradually implementing such strategies in response to an ongoing epidemic, and we investigate these strategies using data on the contact patterns within a large US city.