Thresholds and Universality of the Site Percolation on the Sierpinski Carpets

Following the methods proposed by Yonezawa, Sakamoto and Hori, we have calculated the percolation thresholds P_c, their error bars ΔP_c, and the correlation length exponents v of a family of the Sierpinski carpets for the site percolation problems by making use of MonteCarlo simulations and finite size scaling. We have found the dependence of P_c and v on the fractal dimensionality D_f and the lacunarity. We ascertain that the site percolation problems on a family of Sierpinski carpets with central cutouts and different D belong to different universal classes, and those on Sierpinski carpets with same D_f but of different lacunarities belong to different universal classes.     

Fractal Aggregation with Next-Nearest Neighbor Interactions in External Fields

In this paper, we present a particle-cluster model for a two-dimensional fractal aggregation with the nearest neighbor and next-nearest neighbor interactions in external fields. The external field is described by the probability P. Our computer simulation results show that the threshold concentration is P_c^a = 0.59 ± 0.02 and the fractal dimension is D_c = 1.67 ± 0.03 at this concentration. In comparison with previous results with nearest neighbor interaction only, we find that D_c is the same, but P_c^a is smaller, which is reasonable, since the connectivity has been changed significantly.     

Fractal Aggregation Near the Threshold

In this papel, we present two fractal aggregation models, line pattern seed model (model 1) and point pattern seed model (model 2), which are particle-cluster models. Using the current models, we investigate the critical transition in fractal aggregation processes in two dimensions, and suggest a method for finding the critical transition point. The computer simulation results show that the critical concentration is P_ca=0.69±0.02 for model 1 and P_ca=0.72±0.01 for model 2, critical fractal dimension. D_c= 1.71±0.06 for model 1 and D_c=1.66±0.07 for model 2, which are in good agreement with those of DLA model (D=5/3) and experimental data. The results also show that the critical transition point in two dimensions seems to be inilependent of the size of lattices and the initial seed patterns. The results seem to belong to the same universality class.     

Critical Behavior of Nonlinear Properties in Percolating Superconductor/Nonlinear-Normal Conductor Networks

The critical behavior of nonlinear response in random networks of superconductor/nonlinear-normal conductors below the percolation threshold is investigated. Two cases are examined: (i) The nonlinear normal conductor has weakly nonlinear current (i)-voltage (ν) response of the form ν = ri + bi^α (bi^α-1《t and α > 1). Both the crossover current density and the crossover electric field are introduced to mark the transition between the linear and nonlinear responses of the network and are found to have power-law dependencies ～(f_c - f)^H and ～(f_c - f)^M as the percolation threshold f_c of the superconductor is approached from below, where H = ν_d - s_d > 0, M = ν_d > 0, ν_d and s_d are the correlation length exponent and the critical exponent of linear conductivity in percolating S/N system respectively; (ii) The nonlinear-normal conductor has strongly nonlinear ν-i response, i.e., i = X^να The effective nonlinear response X_e, behaves as X_e ～(f_c - f)^-W(α), where W ( α ) is the critical exponent of the nonlinear response x_e(α) and is α-dependent in general. The results are compared with recently published data, reasonable agreement is found.     

热阴极电离真空计的线性理论

从繁流放电理论可直接导出热阴极电离真空计的特性方程,证明通常的概念即在热计的电子流i_e一定时其离子流i₊与压强P成正比的关系,只在离子流甚小于电子流时才能成立。在被测气体的压强较高时,离子流和压强之间呈现下列指数关系: i₊/i_e=1-e^{(-(K₁P-K₂P2))}(K₁及K₂为常数),且随着压强的增长而逐步趋于饱和。进一步的推导则得出,当容许测量误差为1％时,热计的线性上限(临界压强)为P_c=0.22/Г,此处Г为热计的灵敏度。这种理论可以容易地解释近年来一些实验工作者例如Nottingham,Schultz,Goto,Hinzpeter等的实验结果。此外我们还使用了特殊设计的“封闭式”电离计作实验,得到的结果和理论预计十分符合。这种电离计本身则可用作10^-7～0.6托的宽程量具。 关键词：     

Combined site and bond percolation with nearest- and next-nearest-neighbour bonds

Percolation on a square lattice, in which there exist different occupation probabilities for sites, nearest-neighbour bonds and next-nearest-neighbour bonds, is studied by a real-space renormalization technique. The critical surface is controlled by a single fixed point, in accordance with universality. The critical probability for site percolation on the square lattice with diagonal bonds present, is estimated to be $\text{p}\text{?}{}_{\mathrm{<mtext>c</mtext>}}\text{=0.41}$, in agreement with series estimates.     

Experimental study of relativistic self-focusing andself-channeling of an intense laser pulse in an underdense plasma

This paper reports on experimental investigations on relativistic self-focusing and self-channeling of a terawatt laser pulse (0.7 TW⩽P⩽15 TW) in an underdense plasma. We present results obtained with picosecond (τ=1 ps) and subpicosecond (τ=0.4 ps) pulses. In the “long pulse” regime, modifications in the laser propagation are observed for Pc, the critical power for self-focusing. By contrast, self-guiding of subpicosecond pulses is observed for P≈P_c. Using a paraxial envelope model describing the laser propagation and taking into account the plasma response to the ponderomotive force, it is shown that a maximum laser intensity of 5-15 times that reached in vacuum may be achieved when P is in the (1.25-4)×P_c range. It is also demonstrated that ion motion may significantly reduce the effective P_c     

Efficient Monte Carlo algorithm and high-precision results for percolation

We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at p(c) = 0.592 746 21(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.     

Multi-Type Directed Scale-Free Percolation

In this paper,we study a long-range percolation model on the lattice Z d with multi-type vertices and directed edges.Each vertex x ∈ Z d is independently assigned a non-negative weight Wx and a type ψx,where(Wx) x∈Z d are i.i.d.random variables,and(ψx) x∈Z d are also i.i.d.Conditionally on weights and types,and given λ,α 0,the edges are independent and the probability that there is a directed edge from x to y is given by pxy = 1 exp(λφψ x ψ y WxWy /| x-y | α),where φij 's are entries from a type matrix Φ.We show that,when the tail of the distribution of Wx is regularly varying with exponent τ-1,the tails of the out/in-degree distributions are both regularly varying with exponent γ = α(τ-1) /d.We formulate conditions under which there exist critical values λ WCC c ∈(0,∞) and λ SCC c ∈(0,∞) such that an infinite weak component and an infinite strong component emerge,respectively,when λ exceeds them.A phase transition is established for the shortest path lengths of directed and undirected edges in the infinite component at the point γ = 2,where the out/in-degrees switch from having finite to infinite variances.The random graph model studied here features some structures of multi-type vertices and directed edges which appear naturally in many real-world networks,such as the SNS networks and computer communication networks.     

Effects of ramification and connectivity degree on site percolation threshold on regular lattices and fractal networks

This Letter is focused on the impact of network topology on the site percolation. Specifically, we study how the site percolation threshold depends on the network dimensions (topological d and fractal D), degree of connectivity (quantified by the mean coordination number $Z_{\infty }$), and arrangement of bonds (characterized by the connectivity index Q also called the ramification exponent). Using the Fisher's containment principle, we established exact inequalities between percolation thresholds on fractal networks contained in the square lattice. The values of site percolation thresholds on some fractal lattices were found by numerical simulations. Our findings suggest that the most relevant parameters to describe properly the values of site percolation thresholds on fractal networks contained in square lattice (Sierpiński carpets and Cantor tartans) and based on the square lattice (weighted planar stochastic fractal and Cantor lattices) are the mean coordination number and ramification exponent, but not the fractal dimension. Accordingly, we propose an empirical formula providing a good approximation for the site percolation thresholds on these networks. We also put forward an empirical formula for the site percolation thresholds on d-dimensional simple hypercubic lattices.     

Spontaneous magnetization of randomly dilute ferromagnets

We consider Ising ferromagnets on random subgraphs of the square lattice. These are obtained by independent random selections either of sites or of bonds. We assume that for each site (or, respectively, bond) the probability of being selected exceeds the critical percolation probability. Then, at sufficiently low temperatures and zero external field, spontaneous magnetization occurs. Some further related results are obtained.     

The Nucleon Axial Isoscalar Coupling and First Moments of p,n, d Spin Structure Functions

The nucleon coupling constant to the axial isoscalar current, g_A^s, is calculated in the framework of QCD sum rules by including the effects of the three-gluon condensates. The contribution from the polarized strange sea quarks to g_A^s is extracted in a constituent quark model with a QCD modification. The combined resultant theoretical value, g_A^s = 0.60±0.20, agrees with the experimental estimate. The first moments of the proton, neutron and deuteron spin structure functions are evaluated and compared with the experimental data.     

New universality classes in “Percolative” dynamics

We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of the parameter space, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice.     

Matter Effects on Neutrino Oscillations in Different Supernova Models

In recent years,with the development of simulations about supernova explosion,we have a better understanding about the density profiles and the shock waves in supernovae than before.There might be a reverse shock wave,another sudden change of density except the forward shock wave,or even no shock wave,emerging in the supernova.Instead of using the expression of the crossing probability at the high resonance,PH,we have studied the matter effects on neutrino oscillations in different supernova models.In detail,we have calculated the survival probability of νe(P_s)and the conversion probability of ν_x(P_c) in the Schrodinger equation within a simplified two-flavor framework for a certain case,in which the neutrino transfers through the supernova matter from an initial flavor eigenstate located at the core of the supernova.Our calculations was based on the data of density in three different supernova models obtained from simulations.In our work,we do not steepen the density gradient around the border of the shock wave,which differs to what was done in most of the other simulations.It is found that the mass and the density distribution of the supernova do make a difference on the behavior of P_s and P_c.With the results of P_s and P_c,we can estimate the number of νe(and ν_x) remained in the beam after they go through the matter in the supernova.     

Cellular automata approach to site percolation on ℤ2. A numerical study

We present a cellular automata model as a new approach to Bernoulli site percolation on the square lattice. A new macroscopic quantity is defined and numerically computed at each level step of the automata dynamics. Its limit manifests a critical behavior at a value of the site occupancy probability quite close to those obtained for site percolation on ² with the best-known numerical methods.     

Probability of a ductile fracture

The present paper studies ductile fracture by a random fractal and calculates the fracture probability q of a ductile fracture. The fracture probability q is sensitive to the number n (microvoid size) and the probability p of forming microvoids. There are two critical probabilities p_c1 and p_c2. When pp_c2 = 1-1/n², the fracture probability q is 100%, the ductile fracture occurs with probability 1; when p_c2 > p>p_c1, there is a positive probability q (1>q>0), the fracture probability q increases with increasing probability p and/or decreasing number n; when p<p_c1, the fracture probability q is zero (in fact less than 0.00001), the fracture does not occur. The critical probabilities p_c1 and p_c2 increase with increasing n. When 1-1/n²>p>1-1/n, though a ductile fracture does not occur, there is at least a macrovoid which passes through the transverse plane of the specimen.     

Shot noises of spin and charge currents in a ferromagnet-quantum-dot-ferromagnet system

We have investigated the shot noises of charge and spin current by considering the spin polarized electron tunneling through a ferromagnet-quantum-dot-ferromagnet system. We have derived the spin polarized current noise matrix, from which we can derive general expressions of shot noises associated with charge and spin currents. The spin and charge currents are intimately related to the polarization angles, and they behave quite differently from each other. The shot noise of charge current is symmetric about the gate voltage whose structure is modified by the Zeeman field considerably. There exists oscillations in spin current shot noise in the absence of source-drain bias at zero temperature, and it is asymmetric in the positive and negative regimes of sourcedrain voltage. The shot noise of spin current behaves quite differently from the shot noise of charge current, since the spin current components I_x^s, I_y^s oscillate sinusoidally with the frequency ?_? in the ?th lead, while the I_z^s component of spin current is independent of time.     

Critical behavior of a random diode network

We study the percolation properties of a random diode network (RDN) which contains two kinds of directed bonds on a square lattice. This network is a special case of the random insulation-resistor-diode network. Both Monte Carlo simulations and series expansion for the percolation probability show that an estimated critical exponent, beta=0.1794+/-0.008, is different from known values for a conventional insulation-resistor-diode network. RDN belongs to neither the isotropic percolation universality class nor to the directed percolation universality, which we attribute to a difference of symmetry breakdown around the critical point.     

Sr2SiO4:Ce3+,Li+蓝紫色荧光粉发光性能的研究

以MCM-41为硅源,采用共沉淀法制备Sr_2-xSiO₄:xCe³⁺(x=0.01~0.09,步长为0.01)和Sr_1.95-ySiO₄: 0.05Ce³⁺,yLi⁺(y= 0.01~0.07,步长为0.02)蓝紫色荧光粉。Sr_2-xSiO₄:xCe³⁺的发射光谱是一个不对称的宽带,最大峰值在410 nm左右。Ce³⁺的最佳掺杂量为5%。Ce³⁺离子倾向于占据九配位的Sr(Ⅱ)格位。共掺电荷补偿剂Li⁺可以有效地提高Sr_1.95SiO₄: 0.05Ce³⁺的发光强度,其中Li⁺离子对1 100 ℃煅烧样品的发光强度的提高程度比1 000 ℃的更高,Li⁺的最佳掺杂量为y=0.05。     

Mott glass in site-diluted S=1 antiferromagnets with single-ion anisotropy

The interplay between site dilution and quantum fluctuations in S=1 Heisenberg antiferromagnets on the square lattice is investigated using quantum Monte Carlo simulations. Quantum fluctuations are tuned by a single-ion anisotropy D. In the clean limit, a sufficiently large D>Dc=5.65(2)J forces each spin into its mS=0 state, and thus destabilizes antiferromagnetic order. In the presence of site dilution, quantum fluctuations are found to destroy Néel order before the percolation threshold of the lattice is reached, if D exceeds a critical value D*=2.3(2)J. This mechanism opens up an extended quantum-disordered Mott-glass phase on the percolated lattice, characterized by a gapless spectrum and vanishing uniform susceptibility.