Collective beliefs versus individual inflexibility: The unavoidable biases of a public debate

The combined effects of collective beliefs and individual inflexibility in the dynamics of a public debate are investigated using the Galam sequential probabilistic model of opinion dynamics. The study is focused on pair interactions for which the bias produced by collective beliefs is the decisive factor to win the debate. The current value of that bias is a fixed external parameter. It is a constant of the problem not given to change. In contrast, inflexibility is an individual property. It results from external ingredients, which are susceptible to be modified during the debate. More precisely, giving some beliefs we determine the required inflexibility to oppose its associated bias in the debate outcome. The results shed a new and counter intuitive light on paradoxical outcomes of sensitive issues, which are discussed in the public. The cases of global warming issue and debate over evolution are discussed.     

Statistical physics of hard combinatorial optimization:Vertex cover problem

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics,and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity.In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial(NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.     

Pseudo-Hermiticity and electromagnetic wave propagation: The case of anisotropic and lossy media

Pseudo-Hermitian operators can be used in modeling electromagnetic wave propagation in stationary lossless media. We extend this method to a class of non-dispersive anisotropic media that may display loss or gain. We explore three concrete models to demonstrate the utility of our general results and reveal the physical meaning of pseudo-Hermiticity and quasi-Hermiticity of the relevant wave operator. In particular, we consider a uniaxial model where this operator is not diagonalizable. This implies left-handedness of the medium in the sense that only clockwise circularly polarized plane-wave solutions are bounded functions of time.     

零折射率材料的物理与应用

零折射率材料因其异常的电磁/光学特性在电磁波操控、新型天线和波导器件、非线性光学、光学吸收、电光调制等领域有着广泛的应用前景。文章首先介绍了零折射率材料的分类和实现方法,然后总结了零折射率材料的基本概念和电磁/光学特性,包括电磁波在零折射率材料中的折射、反射特性和“隧穿”效应,掺杂杂质对二维和三维体系的零折射率材料的影响,各向异性零折射率的电磁特性,零折射率材料内外的电场分布特性;最后介绍了零折射率材料的部分典型应用,并对零折射率材料的研究进行了展望。     

厄米-高斯光束在热非局域介质中传输的数值模拟研究

基于非线性薛定谔方程和热扩散的泊松方程,采用分步傅里叶算法以及多重网格法对厄米-高斯光束在不同形状的热非局域介质铅玻璃中的传输进行了数值模拟研究. 结果表明,低阶厄米-高斯光束可以较为稳定地在铅玻璃中传输. 高阶厄米-高斯光束在铅玻璃中传输变得不稳定,并且阶数越高,稳定性越差. 样品的形状对于厄米-高斯光束的影响很大. 在正方形样品中,厄米-高斯光束的传输与Snyder-Mitchell模型符合得相对较好. 在矩形样品中厄米-高斯光束在传输过程中的强度分布将发生较大的变化. 关键词： 非局域非线性介质 厄米-高斯光束 光束传输     

Statistical physics of inference: thresholds and algorithms

Many questions of fundamental interest in today's science can be formulated as inference problems: some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. The connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which, formulated as an inference problem, we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic.     

Rotation of elliptic optical beams in anisotropic media

We investigate the linear propagation of a paraxial optical beam in anisotropic media. We start from the eigenmode solution of the plane wave in the media, then subsequently derive the wave equation for the beam propagating along a general direction except the optic axes. The wave equation contains a second-order mixed derivative term originating from the anisotropy, and this term can result in the rotation of the beam-spot. The rotation effect is investigated by solving analytically the wave equation with an initial elliptical Gaussian beam for both uniaxial and biaxial media. For both media, it is found that there exists a specific direction, which is dependent on anisotropy of the media, on the cross-section perpendicular to propagation direction to determine the rotation of the beam-spot. When the major axes of the elliptical beam-spot of the input beam are parallel to the specific direction, the beam-spot will not rotate during propagation, otherwise, it will rotate with the direction and the velocity determined by input parameters of the beam.     

Enhanced localization of waves in one-dimensional random media due to nonlinearity: Fixed input case

We study the influence of nonlinearity on wave localization in one-dimensional random media. Using a discrete nonlinear Schrödinger equation with a random on-site energy term, we calculate the localization length in a numerically exact manner. Unlike in many previous works, we fix the intensity of the incident wave and calculate quantities as a function of other parameters. We find that localization is enhanced due to nonlinearity for the focusing and defocusing nonlinearities. For small nonlinearity, the localization length is a decreasing function of nonlinearity. For sufficiently large nonlinearity, however, the localization length is found to approach a saturation value.     

Propagation of partially polarized Gaussian Schell-model beams in anomalously dispersive media

By use of a tensor method, analytical transform formulae for isotropic partially polarized GSM beams propagating in anomalously dispersive media are derived. Based on the derived formula, the propagation properties of isotropic partially polarized GSM beams in anomalously dispersive media are studied in detail. The results show that the polarization and the irradiance distribution and the coherence degree properties are influenced by the anomalously dispersive media and beam's initial coherence. In addition, the evolution of the spectrum shows that spectrum splitting and spectral shift occur during propagation in anomalously dispersive media.     

Statistical physics of crime: A review

Containing the spread of crime in urban societies remains a major challenge. Empirical evidence suggests that, if left unchecked, crimes may be recurrent and proliferate. On the other hand, eradicating a culture of crime may be difficult, especially under extreme social circumstances that impair the creation of a shared sense of social responsibility. Although our understanding of the mechanisms that drive the emergence and diffusion of crime is still incomplete, recent research highlights applied mathematics and methods of statistical physics as valuable theoretical resources that may help us better understand criminal activity. We review different approaches aimed at modeling and improving our understanding of crime, focusing on the nucleation of crime hotspots using partial differential equations, self-exciting point process and agent-based modeling, adversarial evolutionary games, and the network science behind the formation of gangs and large-scale organized crime. We emphasize that statistical physics of crime can relevantly inform the design of successful crime prevention strategies, as well as improve the accuracy of expectations about how different policing interventions should impact malicious human activity that deviates from social norms. We also outline possible directions for future research, related to the effects of social and coevolving networks and to the hierarchical growth of criminal structures due to self-organization.     

Public debates driven by incomplete scientific data: The cases of evolution theory, global warming and H1N1 pandemic influenza

Public debates driven by incomplete scientific data where nobody can claim absolute certainty, due to the current state of scientific knowledge, are studied. The cases of evolution theory, global warming and H1N1 pandemic influenza are investigated. The first two are of controversial impact while the third is more neutral and resolved. To adopt a cautious balanced attitude based on clear but inconclusive data appears to be a lose-out strategy. In contrast overstating arguments with incorrect claims which cannot be scientifically refuted appears to be necessary but not sufficient to eventually win a public debate. The underlying key mechanisms of these puzzling and unfortunate conclusions are identified using the Galam sequential probabilistic model of opinion dynamics (Galam, 2002 [4], Galam, 2005 [18], Galam and Jacobs, 2007 [19]). It reveals that the existence of inflexible agents and their respective proportions are the instrumental parameters to determine the faith of incomplete scientific data in public debates. Acting on one’s own inflexible proportion modifies the topology of the flow diagram, which in turn can make irrelevant initial supports. On the contrary focusing on open-minded agents may be useless given some topologies. When the evidence is not as strong as claimed, the inflexibles rather than the data are found to drive the opinion of the population. The results shed a new but disturbing light on designing adequate strategies to win a public debate.     

Bulk heterogeneous plane waves propagation through viscoelastic plates and stratified media with large values of frequency domain

This paper introduces the bulk heterogeneous waves concept into the well known Thomson-Haskell method for computing transmission/reflection coefficients through stratified media. If one of the layers is absorbing, bulk heterogeneous waves are generated at interfaces with other layers and the generalized Snell's laws for heterogeneous modes have to be used. This method was reported to be unstable for large values of frequency domain (FD), the product of the frequency and the medium thickness. The new expression for the matrix transfer between interfaces given in this paper is tested with large values of FD, without showing instability. Large values of FD imply significant effects of attenuation, which is frequency dependent. One particular effect is the interface transmission of modes beyond the limit angle if it is defined with the homogeneous waves concept. This is shown with acquired and simulated waveforms, after transmission through an epoxy layer. Waveforms transmitted by adhesive joints are also presented.     

强非局域非线性介质中拉盖尔-高斯型光孤子相互作用

利用强非局域非线性介质中傍轴光束传输的线性模型(修正的Snyder-Mitchell模型)讨论了两束共线(即光束中心和传输方向都相同)拉盖尔-高斯型光孤子的传输过程. 改变双光束的相对阶数和相对强度比,叠加光场在传输截面上的光强分布呈现出多样性,通过叠加的方法在该介质中产生了多环形光孤子. 一定条件下传输光束在传输过程中会出现旋转现象,叠加光场成为旋转光场,给出了旋转光束的旋转条件以及旋转速度. 进一步利用拉盖尔-高斯光束在传输过程中特有的螺旋相位特点分析了光场截面强度多样性产生的物理机理. 关键词： 强非局域非线性介质 拉盖尔-高斯型光孤子 共线传输 涡旋相位     

A new empirical model for the acoustic properties of loose granular media

This paper examines physical parameters of loose granular mixes and their empirical relations to the acoustic performance of these mixes. In this work a new classification of granular media has been proposed which is related to the characteristic particle dimension and the specific density of the grain base. It has been shown that this classification is a useful characteristic for rapid evaluation of the acoustic performance of loose granular mixes. The characteristic impedance and propagation constant have been measured for a representative selection of grain mixes and used to develop a new empirical model. This model relates the above acoustic characteristics to the characteristic particle dimension, porosity, tortuosity and specific density of the grain base, which are routinely measurable parameters. A very good agreement with the experimental data is illustrated in the frequency range of 250-4000 Hz for materials with the grain base of 0.4-3.5 mm and specific densities between 200 and 1200 kg/m³. Unlike many theoretical models for the prediction of the acoustic properties of porous media, the proposed expressions do not involve any special functions of complex argument, empirical shape factors or sophisticated characteristics of porous structure. These are practical enough to be of interest to acoustic and noise control engineers and material manufacturers.     

Statistical physics of shear flow: a non-equilibrium problem

Complex fluids are easily and reproducibly driven into non-equilibrium steady states by the action of shear flow. The statistics of the microstructure of non-equilibrium fluids is important to the material properties of every complex fluid that flows, e.g. axle grease on a rotating bearing; blood circulating in capillaries; molten plastic flowing into a mould; the non-equilibrium onion phase of amphiphiles used for drug delivery; the list is endless. Such states are as diverse and interesting as equilibrium states, but are not governed by the same statistics as equilibrium materials. I review some recently discovered principles governing the probabilities of various types of molecular re-arrangements taking place within a sheared fluid. As well as providing new foundations for the study of non-equilibrium matter, the principles are applied to some simple models of particles interacting under flow, showing that the theory exhibits physically convincing behaviour.     

Temporal broadening of pulsed waves propagating through turbulent media

Pulse signals, propagating through a turbulent medium such as the ionosphere, can be distorted by dispersion and scattering from both the background medium and irregularities embedded in. Thus, the mean square pulse width is changed, and temporal broadening is introduced. We carry out a study on the temporal broadening with theoretical analyses and numerical simulations by using an analytical solution of two-frequency mutual coherence function obtained recently by iteration. As a case of study, pulse broadening is investigated in detail in trans-ionospheric propagation. Results show that most contributions are mainly from the dispersion of the background ionosphere and scattering effects of electron density irregularities in most cases.     

Statistical physics of human beings in games:Controlled experiments

It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings;making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system,thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems.     

平顶高斯光束在梯度折射率介质中的传输特性

利用广义惠更斯-菲涅耳衍射积分法,推导出平顶高斯光束在梯度折射率介质中传输时的解析表达式,对平顶高斯光束在梯度折射率介质中的传输特性进行了分析,讨论了介质梯度折射率系数和光束阶数对传输特性的影响。研究表明,平顶高斯光束在梯度折射率介质中传输时轴上光强分布呈现周期性变化,其周期决定于介质梯度折射率系数,而与光束的阶数无关;轴上峰值处的横向光强分布受梯度折射率系数和光束阶数的影响较大,横向光强的最大值随着梯度折射率系数的增大而增大。     

Beam propagation factor of partially coherent beams in gain or absorbing media

The definition of second-order intensity moments in the spatial domain and spatial frequency domain has been generalized for the case that the linear gain or absorbing media are included, where the wave number is generally complex. The formula for beam propagation M²-factor of partially coherent beams in linear gain or absorbing media has been given. The partially coherent flat-topped Schell-model beam is taken as an example. The closed-form expression for the beam propagation M²-factor of partially coherent flat-topped beam in gain or absorbing media has been derived. The changes of the M²-factor in media have been discussed with numerical examples. It can be shown that the M²-factor of flat-topped Schell-model beams in gain or absorbing media depends on the coherent parameter β, the coherent length σ₀, the beam order M, the propagation distance B, the imaginary part of the wave number K_i, as well as the real part of the wave number K_r.