Monte Carlo studies of the square Ising model with next-nearest-neighbor interactions

We apply a new entropic scheme to study the critical behavior of the square-lattice Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions. Estimates of the present scheme are compared with those of the Metropolis algorithm. We consider interactions in the range where superantiferromagnetic (SAF) order appears at low temperatures. A recent prediction of a first-order transition along a certain range (0.5–1.2) of the interaction ratio (R=J_nnn/J_nn) is examined by generating accurate data for large lattices at a particular value of the ratio (R=1). Our study does not support a first-order transition and a convincing finite-size scaling analysis of the model is presented, yielding accurate estimates for all critical exponents for R=1. The magnetic exponents are found to obey “weak universality” in accordance with a previous conjecture.     

基于光子数目比较的激光测距法

提出了一种新颖的激光测距方法。该方法避开了传统激光测距法中使用复杂辅助电子设备对脉冲计时或比较相位差的过程,而主要通过光学手段分析和提取待测距离信息,最终通过比较大量光子数目的方法求得待测距离。并利用单轴晶体的双折射和全内双反射性质,用特殊结构的单块LiNbO3晶体设计了实施该方法的主体装置。结果表明,该激光测距法同目前普遍使用的激光测距法相比,不但简化了结构,而且有很高的测距精度,从而为激光测距开拓了一种新的思路。     

Exploring inequality violations by classical hidden variables numerically

There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser–Horne–Shimony–Holt (CHSH) inequality is very robust. However, we argue that with the Einstein–Podolsky–Rosen setup, the CHSH is inferior to the Bell inequality, although and because the latter must assume anti-correlation of entangled photon singlet states. We simulate how often quantum behavior violates both inequalities, depending on the number of photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We present hidden variables that violate the Bell and CHSH inequalities with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. We discuss how to present the quantum correlations to a wide audience and conclude that, when defending against claims of hidden classicality, one should demand numerical simulations and insist on anti-correlation and the full amount of Bell violation.     

On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

Generic axiomatic-nonextensive statistics introduces two asymptotic properties,to each of which a scaling function is assigned.The first and second scaling properties are characterized by the exponents c and d,respectively.In the thermodynamic limit,a grand-canonical ensemble can be formulated.The thermodynamic properties of a relativistic ideal gas of hadron resonances are studied,analytically.It is found that this generic statistics satisfies the requirements of the equilibrium thermodynamics.Essential aspects of the thermodynamic self-consistency are clarified.Analytical expressions are proposed for the statistical fits of various transverse momentum distributions measured in most-central collisions at different collision energies and colliding systems.Estimations for the freezeout temperature(T_(ch)) and the baryon chemical potential(μ_b) and the exponents c and d are determined.The earlier are found compatible with the parameters deduced from Boltzmann-Gibbs(BG) statistics(extensive),while the latter refer to generic nonextensivities.The resulting equivalence class(c,d) is associated with stretched exponentials,where Lambert function reaches its asymptotic stability.In some measurements,the resulting nonextensive entropy is linearly composed on extensive entropies.Apart from power-scaling,the particle ratios and yields are excellent quantities to highlighting whether the particle production takes place(non)extensively.Various particle ratios and yields measured by the STAR experiment in central collisions at 200,62.4 and 7.7 GeV are fitted with this novel approach.We found that both c and d 1,i.e.referring to neither BG-nor Tsallis-type statistics,but to(c,d)-entropy,where Lambert functions exponentially rise.The freezeout temperature and baryon chemical potential are found comparable with the ones deduced from BG statistics(extensive).We conclude that the particle production at STAR energies is likely a nonextensive process but not necessarily BG or Tsallis type.     

A probability distribution for precipitation data analysis

Hydrologic design is often based on assessments of large return interval measures; it is vital to be able to conclude them as precisely as possible. Henceforth, the selection of a probability distribution is very crucial for such cases. In view of this scenario, we propose and study a pliant probability distribution for precipitation data analysis. Some mathematical and statistical properties are analyzed. In order to make stronger predictions and judge the realistic return period, we have also characterized the model via Laplace transformation. We have estimated its parameters via the maximum likelihood estimation and constructed its information matrix for developing the confidence belt of population parameters. Moreover, a real-life setup is also considered by applying the model over precipitation data of diverse regions, including Jacksonville, Florida (USA), Barkhan (Pakistan), British Columbia (Canada), and Alexandria (Egypt). This investigated study is based on various statistical parametric and nonparametric tests, which indicates that the proposed model is one of the better strategies for precipitation data analysis when compared with the famous three-parameter Kappa model.     

Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem

We investigate the statistics of the numberN(R, S) of lattice pointsnZ ², in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c ₁ T,c ₂,T],c ₂>c ₁>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area.     

Segregation effect in symmetric cellular automata model for two-lane mixed traffic

Segregation effects commonly exist in granular mixtures with difference in size, shape or density. In mixed traffic flow, slow vehicle and fast vehicle, as two types of particles, have different desired speed. We investigate the segregation along the road in mixed traffic flow by using a symmetric two-lane cellular automata model. A parameter D, which quantifies the degree of segregation, is defined. We study the density dependency of the parameter at different randomization probability. Simulation results show that segregation is more obviously in free flow region. We argue that the overtaking maneuvers have similar effect as percolation in granular flow.     

Two long-standing problems in Tsallis’ statistics

On the basis of Tsallis’ entropy and the joint probability factorization condition, two controversial problems existing in Tsallis’ statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained show clearly that like entropy, energy is also nonextensive in Tsallis’ statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis’ statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in Tsallis’ statistics, because its corollary is in contradiction with the zeroth law of thermodynamics.     

An alternative approach to calculate the density of states in nonextensive statistical mechanics

A relation between the generalized partition function (Tsallis) and density of states is established by using the method of integral transform which enables reducing some integral equations into the algebraic equations. Inverse Mellin transformation of this equation gives the density of states. Similar relation is also hold the for standard partition function (Boltzmann-Gibbs) and the density of states. Using these relations, we recover the density of states for the classical ideal gas within both statistics.