Critical Behaviors in a Stochastic One-Dimensional Sand-Pile Model

A one-dimensional sand-pile model （Manna model）, which has a stochastic redistribution process, is studied both in discrete and continuous manners. The system evolves into a critical state after a transient period. A detailed analysis of the probability distribution of the avalanche size and duration is numerically investigated. Interestingly,contrary to the deterministic one-dimensional sand-pile model, where multifractal analysis works well, the analysis based on simple finite-size scaling is suited to fitting the data on the distribution of the avalanche size and duration. The exponents characterizing these probability distributions are measured. Scaling relations of these scaling exponents and their universality class are discussed.     

Block Entanglement in the Single-Hole Hubbard Model

We investigate the distribution of the entanglement of the one-dimensional single-hole Hubbard model （HM） and study the relationship between the entanglement and quantum phase transition in the model. The von Neumann entropy of a block with neighbouring spins L for a single-hole HM is calculated using the densitymatrix renormalization group. The distributions of the entanglement entropy in the ground state, as a function of block length, show a dramatic effect, i.e. effectively decoupling with the centres, no matter how the Coulomb interaction u 〉0 or u 〈0. Contrarily, for the Coulomb interaction u = 0 or close to zero, the entanglement entropy in the single-hole model reaches a saturation value for a certain block size. For a fixed size L = 40, the ground state entanglement entropy measure, as a function of u1 shows a peak corresponding to the critical quantum phase transition.     

DEMAGNETIZATION EFFECT IN CRITICAL STATE IN CYLINDRICAL SUPERCONDUCTORS

This paper presents the results of field and current distribution in the critical state in a superconducting cylinder using Bean critical state model and isotropic critical current density Jc. We introduced an equivalent effective field and demagnetization factor Dc, and showed that Dc, from extremely long cylinder to very thin disks, is equal to Meissner demagnetization factor of the inscribed spheroid of the cylinder. The application of these parameters is discussed at the end of paper.     

Numerical simulation and experimental validation of a direct current air corona discharge under atmospheric pressure

Air corona discharge is one of the critical problems associated with high-voltage equipment. Investigating the corona mechanism plays a key role in enhancing the electrical insulation performance. An improved self-consistent multi-component two-dimensional plasma hybrid model is presented for the simulation of a direct current atmospheric pressure corona discharge in air. The model is based on plasma hydrodynamic and chemical models, and includes 12 species and 26 reactions. In addition, the photoionization effect is introduced into the model. The simulation on a bar-plate electrode configuration with an inter-electrode gap of 5.0 mm is carried out. The discharge voltage-current characteristics and the current density distribution predicted by the hybrid model agree with the experimental measurements. In addition, the dynamics of volume charged species generation, discharge current waveform, current density distribution at an electrode, charge density, electron temperature, and electric field variations are investigated in detail based on the model. The results indicate that the model can contribute valuable insights into the physics of an air plasma discharge.     

Sandpile Dynamics Driven by Degree on Scale-Free Networks

We introduce a sandpile model driven by degree on scale-free networks, where the perturbation is triggered at nodes with the same degree. We numerically investigate the avalanche behaviour of sandpile driven by different degrees on scale-free networks. It is observed that the avalanche area has the same behaviour with avalanche size. When the sandpile is driven at nodes with the minimal degree, the avalanches of our model behave similarly to those of the original Bak-Tang-Wiesenfeld （BTW） model on scale-free networks. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually changes from a clean power law, then a mixture of Poissonian and power laws, finally to a Poisson-like distribution. The average avalanche area is found to increase with the degree of driven nodes so that perturbation triggered on higher-degree nodes will result in broader spreading of avalanche propagation.     

Numerical simulation and experimental validation of direct current air corona discharge under atmospheric pressure

Air corona discharge is one of the critical problems associated with high-voltage equipment. Investigating the corona mechanism plays a key role in enhancing the electrical insulation performance. An improved self-consistent multi-component two-dimensional plasma hybrid model is presented for the simulation of a direct current atmospheric pressure corona discharge in air. The model is based on plasma hydrodynamic and chemical models, and includes 12 species and 26 reactions. In addition, the photoionization effect is introduced into the model. The simulation on a bar-plate electrode configuration with an inter-electrode gap of 5.0 mm is carried out. The discharge voltage– current characteristics and the current density distribution predicted by the hybrid model agree with the experimental measurements. In addition, the dynamics of volume charged species generation, discharge current waveform, current density distribution at an electrode, charge density, electron temperature, and electric field variations are investigated in detail based on the model. The results indicate that the model can contribute valuable insights into the physics of an air plasma discharge.     

Effects of Vertex Activity and Self-organized Criticality Behavior on a Weighted Evolving Network

Effects of vertex activity have been analyzed on a weighted evolving network. The network is characterized by the probability distribution of vertex strength, each edge weight and evolution of the strength of vertices with different vertex activities. The model exhibits self-organized criticality behavior. The probability distribution of avalanche size for different network sizes is also shown. In addition, there is a power law relation between the size and the duration of an avalanche and the average of avalanche size has been studied for different vertex activities.     

Short—Time Critical Behavior Affected by Weakly Long—Range Interactions

The theoretic renormalization group approach is applied to the study of short-time critical behavior of the Ginzburg-Landau model with weakly long-range interactions pσsps-p,The system initially at a high temperature is firstly quenched to the critical temperature Tc and then released to an evolution with a model A dynamics,A double expansion in ε=2σ-d and α=1-σ/2 with α of order ε of order ε is employed,where d is the spatial dimension.The asymptotic scaling laws and the initial slip exponents θ′and θ for the order parameter and the response function respectively are calculated to the second order in ε for σ close to 2.     

Critical volume fraction and size for a colloidal cluster to nucleate

With the aid of the critical size of colloidal cluster,the critical volume fraction of phase transition of colloidal system is determined by the principle of entropy maximum and Carnahan-Starling(CS) state equation in this paper.In our discussion,no parameter is introduced externally,and our results are in good agreement with the experimental results.     

Criticality in Two-Variable Earthquake Model on a Random Graph

A two-variable earthquake model on a quenched random graph is established here. It can be seen as a generalization of the OFC models. We numerically study the critical behavior of the model when the system is nonconservative： the result indicates that the model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. We compare our mode/with the mode/ introduced by Stefano Lise and Maya Paczuski [Phys. Rev. Lett. 88 （2002） 228301], it is proved that they are not in the same universality class.     

Self-organized Criticality in Hierarchical Brain Network

It is shown that the cortical brain network of the macaque displays a hierarchically clustered organization and the neuron network shows small-world properties. Now the two factors will be considered in our model and the dynamical behavior of the model will be studied. We study the characters of the model and find that the distribution of avalanche size of the model follows power-law behavior.     

Dynamics of quintessential inflation

In this paper, we study a realistic model of quintessential inflation with radiation and matter. By the analysis of the dynamical system and numerical work about the evolution of the equation of state and cosmic density parameter, we show that this model is a good match for the current astronomical observation. The conclusion we obtain is in favour of the model where the modular part of the complex field plays the role of the inflaton whereas the argument part is the quintessence field. Numerical calculation shows that a heteroclinic orbit (solution of the dynamical system) is interpolated between early-time de Sitter phase (an unstable critical point) and a late-time de Sitter attractor.     

Switching effects in superconductor/ferromagnet/superconductor graphene junctions

The Josephson effect in the superconductor/ferromagnet/superconductor （SFS） graphene Josephson junction is studied using the Dirac Bogoliubov-de Gennes （DBdG） formalism. It is shown that the SFS graphene junction drives 0–π transition with the increasing of p=h0L/vF？, which captures the effects of both the exchange field and the length of the junction; the spin-down current is dominant. The 0 state is stable for p 〈 pc （critical value pc ≈ 0.80） and the π state is stable for p 〉 pc, where the free energy minima are at φg=0 and φg=π, respectively. The coexistence of the 0 and π states appears in the vicinity of pc.     

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|~(-(d-2+η))and a finite-size scaling function of the variables r/L and tL~(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.     

Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model

We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.     

A Conjecture on the Origin of Dark Energy

A conjecture on the origin of the dark energy in our universe is proposed. The analysis indicates that the dark energy may originate from the quantum fluctuations of space-time limited in our universe. Applying both the uncertainty principle and the holographic principle, the author finds that the density of such quantum fluctuation energy is pv = 3c^4/32GL^2H, where LH is the size of the event horizon of our universe and G is the gravitational constant. Using this dark energy model which contains no adjustable parameters, we obtain the current fraction ΩA ≡ ρv/ρc ≈ π/4 and the corresponding equation of state w(z) ≈ -1 (1 - π/4)z with ρc being the critical energy density. These theoretical results are perfectly consistent with the recent cosmological observations. The striking coincidence implies that the quantum fluctuation energy of space-time may be the only source of dark energy. In addition, the analysis shows that the vacuum fluctuation energy does exist, but it comes from spacetime rather than matter. This may have some deep implications for discrete space-time and quantum gravity.     

Cosmological Constant or Variable Dark Energy？

Selection statics of the Akaike information criterion （AIC） model and the Bayesian information criterion （BIC） model are applied to the A-cold dark matter （ACDM） cosmological model, the constant equation of state of dark energy, w =constant, and the parametrized equation of state of dark energy, w（z） = wo ＋ wlz/（1 ＋ z）, to determine which one is the better cosmological model to describe the evolution of the universe by combining the recent cosmic observational data including She Ia, the size of baryonic acoustic oscillation （BAO） peak from SDSS, the three-year WMAP CMB shift parameter. The results show that AIC, BIC and current datasets are not powerful enough to discriminate one model from the others, though odds suggest differences between them.     

Pattern Structure of Deterministic Displacement in Random Porous Media with Dispersion Effect

A new model-model of random porous mediz degradation via several fluid displacing,freezing,and thawing cycles is introduced and investigated in this paper.The fluid transport is based on the deterministic method with dispersion effect.The result shows that the topology and the geometry of the porous media have a strong effect on displacement processes.The cluster size of viscous fingering (VF) pattern in percolation cluster increases with the increase of iteration parameter n.When iteration parameter n≥10,VF pattern does not change with n.We find that the displacement fluid forms trapping regions in random porous media with dispersion effect.And the trapping regions will expand with the increasing of the iteration parameter n.When r (throat size)→1 and n≥5,the peak value of the distribution Nmat(r) increases as n increases,where Nmat(r) is the normalized distribution of throat sizes after different displacement-damages but before freezing.The peak value of the distribution Ninv(r) reaches a maximum when n≥10 and r=1,where Ninv(r) is the normalized distribution of the size of invaded throat.This result is different from invasion percolation.It is found that the sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L,and E has a minimum as L increases to the maximum size of lattice.The VF pattern in percolation cluster has one frozen zone and one active zone.     

Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of α-decay is extended to the regions around doubly magic spherical nucleus 208pb and around deformed shell closure 270Hs, respectively. The effects of spherical shell closures (N = 126 and Z = 82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical α-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus 208 Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of a-decays from the ground state of a parent nucleus to the ground state (0 ) of its deformed daughter nucleus and to the first excited state (2 ) are .calculated in the framework of the cluster model. The results indicate that a measurement of c spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus 270 Hs.     

Different Avalanche Behaviors in Different Specific Areas of a System Based on Neural Networks

Based on the standard self-organizing map (SOM) neural network model and an integrate-and-fire mecha-nism, we introduce a kind of coupled map lattice system to investigate scale-invariance behavior in the activity of model neural populations. We find power-law distribution behavior of avalanche size in our model. But more importantly, we find there are different avalanche distribution behaviors in different specific areas of our system, which are formed by the topological learning process of the SOM net.