Unstable and Stable Galaxy Models

To determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the Vlasov theory for galaxy dynamics. In this article, we study the stability of isotropic spherical symmetric galaxy models f ₀(E), for which the distribution function f ₀ depends on the particle energy E only. In the first part of the article, we derive the first sufficient criterion for linear instability of f ₀(E) : f ₀(E) is linearly unstable if the second-order operator

Statistical Geometry and Lattices

Statistical geometry furnishes the tool that allows the transfer of results from a lattice with finite lattice parameter to the continuum. Since lattice simulations are simpler than continuum ones, this suggests that larger scale simulations for the continuum might be more effectively carried out on a lattice with finite lattice parameter followed by the indicated transfer. We also show that a statistical geometry, peculiar to hard particles on a lattice, can be developed. Among other things, this opens the possibility that a scaled particle theory on a lattice might be derived.     

Noncommutative Geometry and Integrable Models

A construction of conservation laws for -models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing theordinary calculus of differential forms with other differentialcalculi and introducing an analogue of the Hodge operator on thelatter. The general method is illustrated with several examples.     

Magnetic Resonance Spectra and Statistical Geometry

Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints which introduce curvature into parameter space and discuss the appropriate mathematical tools for treating curvature effects. Channel capacity, a term from communication theory, is suggested as a useful figure of merit for estimating the information content of spectra in the presence of noise. The tools introduced here are applied to the case of a model nitroxide system as a concrete example, but we stress that the methods described here are of general utility.     

Local Statistics of Realizable Vertex Models

We study planar “vertex” models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including the dimer model, and 1-2 model, which we will define. We express the local statistics of a large class of vertex models on a finite hexagonal lattice as a linear combination of the local statistics of dimers on the corresponding Fisher graph, with the help of a generalized holographic algorithm. Using an n × n torus to approximate the periodic infinite graph, we give an explicit integral formula for the free energy and local statistics for configurations of the vertex model on an infinite bi-periodic graph. As an example, we simulate the 1-2 model by the technique of Glauber dynamics.     

Scaling Limits for Multi-species Statistical Mechanics Mean-Field Models

We study the limiting thermodynamic behavior of the normalized sums of spins in multi-species Curie-Weiss models. We find sufficient conditions for the limiting random vector to be Gaussian (or to have an exponential distribution of higher order) and compute the covariance matrix in terms of model parameters.     

Spatial Statistics of Stochastic Fiber Networks

From the known statistics of fiber-fiber contacts in random fiber networks, an analytic estimate is obtained for the variance of local porosity in random fiber suspensions and evolving filtrate networks. The variance of local porosity, and hence the distribution of projected areal density, seem to depend on fiber geometry only through the cube of mean diameter. Also, the coefficient of variation of local flow rate perpendicular to the plane of the pad is, to a first approximation, independent of the mode of flow. Analytic estimates are obtained also for the effect of fiber clumping on the variance of local porosity of pads for small inspection zones.     

One-Way Information Deficit and Geometry for a Class of Two-Qubit States

The work deficit, as introduced by Jonathan Oppenheim et al. [Phys. Rev. Lett. 89 (2002) 180402] is a good measure of the quantum correlations in a state and provides a new standpoint for understanding quantum non-locality. In this paper, we analytically evaluate the one-way information deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and further give the geometry picture for OWID. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID of some classes of X states is more robust against the decoherence than the entanglement.     

Statistical Dynamics of Clustering in the Genome Structure

Clustering and long-range correlations in the nucleotide sequences of different categories of organisms are studied. As a result of clustering, the size distribution of coding and non-coding DNA regions is estimated analytically using the Generalised Central Limit Theorem.The alternation of coding regions (which follow a short range size distribution) with non-coding regions (which follow a long range size distribution in higher organisms) leads to DNA structures which have a striking resemblance to random Cantor Fractals. For lower organisms (such as viruses, procaryotes etc.) long-range correlations are sporadically observed and the DNA structures do not present fractality.Statistical models are proposed based on biologically motivated dynamical mechanisms (such as aggregation of oligonucleotides, influx and DNA length reduction), which can account for the above statistical features.     

Statistical Dynamics of Clustering in the Genome Structure

Clustering and long-range correlations in the nucleotide sequences of different categories of organisms are discussed. Clustering, mostly observed in higher eucaryotes, can be found at different length scales in DNA and Central Limit Theorems are used as links between these length scales. Several dynamical, statistical, mean-field models are proposed based on biologically motivated dynamical mechanisms and they successfully reproduce both the short range behavior observed in coding DNA and the long range, out-of-equilibrium features of non-coding DNA. Such dynamical mechanisms include aggregation of oligonucleotides, influx and DNA length reduction schemes, transpositions, and fusions of large DNA macromolecules. Fractality can be inferred from the short and long range correlations observed in the sequence structure of higher eucaryotes, where the non-coding part is relatively extended. In these organisms the DNA coding/non-coding alternation has the characteristics of finite size, fractal, random sets.     

Comparison of Quantum Statistical Models: Equivalent Conditions for Sufficiency

A family of probability distributions (i.e. a statistical model) is said to be sufficient for another, if there exists a transition matrix transforming the probability distributions in the former to the probability distributions in the latter. The Blackwell-Sherman-Stein (BSS) Theorem provides necessary and sufficient conditions for one statistical model to be sufficient for another, by comparing their information values in statistical decision problems. In this paper we extend the BSS Theorem to quantum statistical decision theory, where statistical models are replaced by families of density matrices defined on finite-dimensional Hilbert spaces, and transition matrices are replaced by completely positive, trace-preserving maps (i.e. coarse-grainings). The framework we propose is suitable for unifying results that previously were independent, like the BSS theorem for classical statistical models and its analogue for pairs of bipartite quantum states, recently proved by Shmaya. An important role in this paper is played by statistical morphisms, namely, affine maps whose definition generalizes that of coarse-grainings given by Petz and induces a corresponding criterion for statistical sufficiency that is weaker, and hence easier to be characterized, than Petz’s.     

Statistical Models in Theory of Polarization Bremsstrahlung

Universal relations have been derived to describe the spectral-angular dependence of the polarization bremsstrahlung of a fast charged particle, based on a statistical model for the electron skeleton of the target. Three statistical atomic models are considered in terms of which the target characteristics that determine the cross section for polarization bremsstrahlung are calculated and analyzed.     

Statistical Interaction Term of One-Dimensional Anyon Models

A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.     

Lattice Statistical Models for the Nematic Transitions in Liquid-Crystalline Systems

We investigate the connections between some simple Maier-Saupe lattice models, with a discrete choice of orientations of the microscopic directors, and a recent proposal of a two-tensor formalism to describe the phase diagrams of nematic liquid-crystalline systems. This two-tensor proposal is used to formulate the statistical problem in terms of fully connected lattice Hamiltonians, with the local nematic directors restricted to the Cartesian axes. Depending on the choice of interaction parameters, we regain all of the main features of the original mean-field two-tensor calculations. With a standard choice of parameters, we obtain the well-known sequence of isotropic, uniaxial, and biaxial nematic structures, with a Landau multicritical point. With another suitably chosen set of parameters, we obtain two tricritical points, according to some recent predictions of the two-tensor calculations. The simple statistical lattice models are quite easy to work with, for all values of parameters, and the present calculations can be carried out beyond the mean-field level.     

Optical Parametric Amplification of Single Photon: Statistical Properties and Quantum Interference

By using phase space method, we theoretically investigate the quantum statistical properties and quantum interference of optical parametric amplification of single photon. The statistical properties, such as the Wigner function (WF), average photon number, photon number distribution and parity, are derived analytically for the fields of the two output ports. The results indicate that the fields in the output ports are multiphoton states rather than single photon state due to the amplification of the optical parametric amplifiers (OPA). In addition, the phase sensitivity is also examined by using the detection scheme of parity measurement.     

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.     

基于几何标记模型参数反演的作物株形敏感性分析

传统的利用冠层反射光谱和光谱指数进行叶面积指数反演时,株形(利用平均叶倾角ALA等指标来表征)对叶面积指数的反演精度存在较大的影响,使得利用遥感手段进行作物长势监测和肥水调控决策时,株形因素不容忽略,以免造成遥感监测精度不高。研究首先利用模拟作物冠层反射光谱的PROSAIL模型将影响作物冠层光谱的叶面积指数等其他参数保持不变的情况下,分析了ALA对作物冠层反射光谱的影响;并基于半经验的几何光学模型对作物株形对冠层光谱影响的不同波段受到ALA变化的敏感性进行了定量分析,对于研究如何消除株形影响,提高遥感反演作物长势和叶面积指数的精度和提高作物大面积、快速遥感肥水调控决策水平具有重要意义。     

基于核驱动模型参数反演的作物株型遥感识别

传统的单一方向遥感只能得到地面目标一个方向的辐射量,缺乏足够信息来同时推断像元的波谱和空间结构。多角度的反射光谱对于植被结构特征的估算及类型鉴别比垂直光谱具有明显的优越性。将多角度观测数据和核驱动模型结合,构建了基于核参数各向同性核所占比例(f_iso),几何光学核所占比例(f_geo)和体散射核所占比例(f_vol)的植被结构参数敏感指数(SPEI)来进行作物株型的遥感识别,并将SPEI与结构散射指数(SSI)和归一化差异参数指数(NDFI)等对紧凑型品种京411和披散型品种中优9507的实测多角度冠层方向反射率数据进行了核参数的反演,不同指数对作物株型结构表现出的敏感性依次为：SPEI＞SSI＞NDFI。SPEI较以往学者构建的指数对不同株型品种遥感识别具有更好的敏感性,该方法可以在其他作物上拓展应用,具有很好的理论基础和应用前景。