A variational perturbation approximation method in Tsallis non-extensive statistical physics

For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order in variational perturbation expansion. The approximation up to the first order amounts to a variational approach which covers the variational method developed by E.K. Lenzi, L.C. Malacarne, R.S. Mendes [Phys. Rev. Lett. 80 (1998) 218] and the approximations up to higher orders can systematically improve variational results. As an illustrated example, the generalized free energy for a classical harmonic oscillator (considered in the Lenzi's joint work) are calculated up to the third order, and the resultant approximations up to the first, second, and third orders are numerically compared with the exact result.     

Statistical analysis of geomagnetic field reversals and their consequences

In this paper we focus on the statistical distribution of time intervals between geomagnetic reversals. Recently the Tsallis distribution was pointed out as a possible alternative to previous proposals. We have performed statistical tests to further prove this and find the parameters of the Tsallis distribution that better fit the data. Additionally we have analyzed the correlation of time intervals between consecutive reversals to show the presence of memory effects on the mechanism that generates them, as could be expected for some Tsallis systems.     

Comparing emerging and mature markets during times of crises: A non-extensive statistical approach

One of the important issues in finance and economics for both scholars and practitioners is to describe the behavior of markets, especially during times of crises. In this paper, we analyze the behavior of some mature and emerging markets with a Tsallis entropy framework that is a non-extensive statistical approach based on non-linear dynamics. During the past decade, this technique has been successfully applied to a considerable number of complex systems such as stock markets in order to describe the non-Gaussian behavior of these systems. In this approach, there is a parameter q$q$, which is a measure of deviation from Gaussianity, that has proved to be a good index for detecting crises. We investigate the behavior of this parameter in different time scales for the market indices. It could be seen that the specified pattern for q$q$ differs for mature markets with regard to emerging markets. The findings show the robustness of the stated approach in order to follow the market conditions over time. It is obvious that, in times of crises, q$q$ is much greater than in other times. In addition, the response of emerging markets to global events is delayed compared to that of mature markets, and tends to a Gaussian profile on increasing the scale. This approach could be very useful in application to risk and portfolio management in order to detect crises by following the parameter q$q$ in different time scales.     

Clustering of polarity reversals of the geomagnetic field

Often in nature the temporal distribution of inhomogeneous stochastic point processes can be modeled as a realization of renewal Poisson processes with a variable rate. Here we investigate one of the classical examples, namely, the temporal distribution of polarity reversals of the geomagnetic field. In spite of the commonly used underlying hypothesis, we show that this process strongly departs from a Poisson statistics, the origin of this failure stemming from the presence of temporal clustering. We find that a Lévy statistics is able to reproduce paleomagnetic data, thus suggesting the presence of long-range correlations in the underlying dynamo process.     

一种预测材料蠕变速率的新模型

长期以来,由于对材料蠕变过程缺乏清晰的微观物理描述,人们均使用经验公式预测稳态蠕变速率,这导致预测结果的不可靠.将单原子统计模型拓展到该领域,在原子扩散水平上建立了一个预测材料稳态蠕变速率的模型.为了检验该模型的可靠性,实验测量了42CrMoA,2Cr12Ni,1Cr12Mo三种材料的稳态蠕变速率.所获得的实验结果以及其他文献的实验测试结果均与新模型的计算结果相符合.     

A modified Euler–Maclaurin formula in 1D and 2D with applications in statistical physics

The Euler–Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler–Maclaurin summation formula and the Poisson summation formula as special cases. By making use of the modified formula, a possible numerical summation method is obtained and the remainder can be controlled. The modified formula is also generalized from one dimension to two dimensions. Approximate expressions of partition functions of a classical particle in square well in 1D and 2D and that of a quantum rotator are obtained with error estimation.     

Adsorption of hydrogen in defective carbon nanotube: modelling and consequent investigations using statistical physics formalism

ABSTRACT

Experimental adsorption isotherms of hydrogen in CNT samples (CNT-A, activated CNT-A CNT-B and activated CNT-B) at T?=?77, 87 and 90?K have been fitted using some theoretical model expressions treated by statistical physics through the grand canonical ensemble. The monolayer model with single energy is selected to fit and interpret the experimental data obtained with CNTs. The physico-chemical parameters, interfering in the adsorption process and implicated in the model expressions, could be directly determined from the experimental data through numerical simulation. Three parameters of the model are fitted, namely the number of hydrogen molecule per site n, the interstitial site density N_m and the energetic parameter P_1/2. The evolution of these parameters as function of temperature is plotted and interpreted in relation to adsorption process. Finally, the thermo-dynamic potential functions, which involve in the adsorption mechanism like free enthalpy of Gibbs G_a, internal energy E_int and entropy S_a, are derived by statistical physics calculations from the selected model.     

The quartic oscillator in an external field and the statistical physics of highly anisotropic solids

The statistical mechanics of one- and two-dimensional Ginzburg–Landau systems is evaluated analytically, via the transfer matrix method, using an expression of the ground state energy of the quartic anharmonic oscillator in an external field. In the two-dimensional case, the critical temperature of the order–disorder phase transition is expressed as a Lambert function of the inverse inter-chain coupling constant.     

A non-extensive statistical mechanical approach to define the equilibrium value function in the kinetics of voltage-gated ion channels

We present a model for the steady-state (or equilibrium) behaviors of the voltage-gated ion channels in cell membranes using the non-extensive or generalized statistical mechanics. The equilibrium value function in the gating kinetics of batrachotoxin-modified sodium channels from a squid optic nerve in planar bilayers are calculated for different values of entropic index (q) which characterizes the degree of non-extensivity of Tsallis’ entropy and the fractal structure of the channels. It is found that in the limit q→1, the results of calculation reduce to the results described by the well-known Boltzmann statistics or the extensive physics. For the non-extensive case (q≠1), a small deviation with respect to the Boltzmann curve which was observed in a great variety of physical systems occurred.     

A new universality class in corpus of texts; A statistical physics study

Text can be regarded as a complex system. There are some methods in statistical physics which can be used to study this system. In this work, by means of statistical physics methods, we reveal new universal behaviors of texts associating with the fractality values of words in a text. The fractality measure indicates the importance of words in a text by considering distribution pattern of words throughout the text. We observed a power law relation between fractality of text and vocabulary size for texts and corpora. We also observed this behavior in studying biological data.     

Studies of magnetization reversals about two kinds of MR curves observed in the spin valve using the (110) magnetite pinning layer

In the spin valves composed of Co/Cu/Co on the epitaxial (110) Fe₃O₄ as the pinning layer, we found out that shapes of magnetoresistance (MR) curves depended on thickness of the cobalt pinned layer (PL) with the field applied in the 〈110〉 direction of Fe₃O₄: (1) the flat-shaped MR curve showed low MR ratio under 2 nm thickness of cobalt pinned layer (PL): (2) the unusually shaped MR curve showed high MR ratio over 5 nm thickness of PL in spite of the hard direction of Co layers. We assumed that the synchronous magnetization reversal (SR) of PL and Fe₃O₄ would occur at the MR switching field due to 90° coupling between PL and Fe₃O₄ layers. Then, only occurrence of SR of PL cause the drastic change of the magnetization relative angle between FL and PL, indicating the observation of the unusually shaped MR curve having high MR ratio. On the other hand, the SR of cobalt free layer (FL) together with the PL flip also occur due to the large contribution of Néel-type ferromagnetic coupling between FL and PL, which lead to less changing the relative angle of FL and PL during magnetization processes, indicating the observation of a flat-shaped MR curve having low MR ratio. This dependence of PL thickness on MR curves might come from the balance of Néel (ferromagnetic) and stray field (antiferromagnetic) coupling due to magnetic free pole at edge of PL.     

Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field

This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of micro-crack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field.     

Divergence structure of the statistical entropy of the Dirac field in a plane symmetry black hole geometry

The divergences at all levels for the statistical entropy of a plane symmetry black hole arising from the massless Dirac field are considered using the brick-wall model. It is shown that if we ignore the usual contribution from the vacuum surrounding the system, then the statistical entropy consists of two parts: one is the linearly divergent term which has the geometric character, the other consists of two logarithmically divergent terms which are not proportional to the surface area of the horizon. The entropy of the Dirac field on extremal plane symmetry spacetime background has higher divergence than usual.     

量子统计权重对原子场电离效率的影响

原子能级的量子统计权重(G)是原子的重要光谱参数,但在研究原子的电离过程中通常却为了简化问题而被忽略.本文在锂原子的三步光激发(PE)+电场电离(EFI)过程中计入了其影响,并发现其对原子EFI效率的影响显著.本文精心设计了一套锂原子的PE+EFI方案:首先,采用三台不同波长的脉冲激光器分三步将原子从基态激发到某一Rydberg态上,经过一段时间延迟后再施加脉冲电场将其电离.针对原子所经历的PE、零场和EFI这三个物理过程,本文对其物理机制进行了分析并建立了服从粒子数守恒的物理模型进而导出了显含G参数的普适的速率方程组.其次,通过Matlab编程,分别针对精心选定的两条激发路径2S_(1/2)→2P_(1/2)→3S_(1/2)→25P_(1/2,3/2)和2S_(1/2)→2P_(3/2)→3D_(5/2)→25F_(5/2,7/2)开展了数值计算.研究发现:PE+EFI过程的总体效率的上限既与激光参数无关,也不依赖于G参数的绝对值,而是决定于Rydberg态的G参数的分支比.总之,通过精选激发路径可以调控PE过程各相关态的布居率,并能适当提高PE+EFI过程的总电离效率,但却因受到Rydberg态布居率的限制而很难进一步提高.     

A discrete approach to topological quantum field theories

First, we describe a rather general scheme for constructing three-dimensional euclidean topological quantum field theories, whose basic building blocks are provided by the representation theory of a certain class of (bi-)algebras. Secondly, we discuss in some detail examples, where the algebra is either the function algebra of a finite group, the group algebra of a finite group or a deformation of the enveloping algebra of a classical simple Lie group.     

博雅理念在大学物理实验教学中的实践

博雅教育是对大学本科生实施的一种教育,它更关注个人的发展而不是为具体职业做准备,作为理科和工科大学所共有的基础课程——大学物理实验,是最能体现博雅教育理念的课程之一.但是教师如果缺乏理念和意识,博雅的哲学教育以及教育的目标就无法得到很好的贯彻.本文以具体的大学物理实验教学为例,从微观层面进行分析和阐述,研究如何结合博雅教育思想来实践教学.     

A field theory approach to cosmological density perturbations

Adiabatic perturbations propagate in the expanding universe like scalar massless fields in some effective Robertson–Walker space–time.     

Effect of a force-free end on the mechanical property of a biopolymer——A path integral approach

We study the effect of a force-free end on the mechanical property of a stretched biopolymer.The system can be divided into two parts.The first part consists of the segment counted from the fixed point(i.e.,the origin) to the forced point in the biopolymer,with arclength L_f.The second part consists of the segment counted from the forced point to the force-free end with arclength △L.We apply the path integral technique to find the relationship between these two parts.At finite temperature and without any constraint at the end,we show exactly that if we focus on the quantities related to the first part,then we can ignore the second part completely.Monte Carlo simulation confirms this conclusion.In contrast,the effect for the quantities related to the second part is dependent on what we want to observe.A force-free end has little effect on the relative extension,but it affects seriously the value of the end-to-end distance if △L is comparable to L_f.     

A feasible approach to field concentrators of arbitrary shapes

We propose a simple method to design field concentrators of arbitrary shapes based on Fabry–Pérot resonances. The material parameters are feasible in terms of metallic layered structures and gradient index dielectrics. The functionalities are well confirmed by numerical simulations.     

A new approach for the justification of ensembles in quantum statistical mechanics — II

The results of the first paper in this series are generalized to include spin, permutation symmetry, and time dependence. In particular, the question of time invariance of localness in the Heisenberg picture is discussed and it is conjectured that an operator that is initially local will remain local over time. In order to treat macroscopic systems, it is shown that the ensemble decomposition of the previous paper can be used to coarsegrain configuration space. Finally, a physical interpretation of the ensemble decomposition in terms of redundant macroscopic information is used to give a derivation of the generalized microcanonical average.This work was supported in part by research grants from the National Science Foundation and the U.S. Public Health Service. Some of the material in this paper is contained in a doctoral dissertation submitted by the author to the University of Oregon (1969).