Emergence of bimodality in noisy systems with single-well potential

We study the stationary probability density of a Brownian particle in a potential with a single-well subject to the purely additive thermal and dichotomous noise sources. We find situations where bimodality of stationary densities emerges due to presence of dichotomous noise. The solutions are constructed using stochastic dynamics (Langevin equation) or by discretization of the corresponding Fokker-Planck equations. We find that in models with both noises being additive the potential has to grow faster than |x| in order to obtain bimodality. For potentials ∝|x| stationary solutions are always of the double exponential form.     

Every Continuous Operator Has an Invariant Measure

We prove the existence of an invariant measure for a large class of random processes with discrete time without assuming their linearity. Our main examples are “processes with variable length”, in which components may appear and disappear in the course of functioning. One of these examples displays non-uniqueness of invariant measure in a 1-D process.     

Dynamics of a Tagged Particle in the Asymmetric Exclusion Process with the Step Initial Condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.     

Local Thermodynamic Equilibrium for some Stochastic Models of Hamiltonian Origin

We consider a class of 1-D stochastic models that are realizations of Hamiltonian models of heat conduction and prove that in the infinite volume limit local thermodynamic equilibrium is attained with linear energy profile.     

The Cluster Model: A Simulation of the Aerogel Structure as a Hierarchically-Ordered Arrangement of Randomly Packed Spheres

A new structural model based on the premises widely used for describing the structure of aerogels has been introduced. These structures have been described as an assemblage of randomly-packed spheres in several hierarchically-ordered levels. A new algorithm has been developed for constructing our models from these premises using computer simulation. Subsequently, several applications have been simulated to characterize real systems, obtaining textural parameters such as the specific surface area, specific porous volume or the apparent density of the systems, based on the Monte Carlo technique and on geometrical considerations. The object of these is to test the ability of the models to explain the structure of some real aerogels. This Cluster Model has also been applied as an initial approach to the study of the mechanical properties of aerogels. Results support the general conclusion that these models are useful for explaining the structure of aerogels.     

激光在雨中传输的分析与计算

本文通过分析雨滴其对激光的散射和吸收作用,研究激光在大气中传输时受雨滴作用的影响,计算不同雨滴对激光光强的影响,在不同降雨下,测试激光光强的变化,并通过软件仿真实时显示光斑的闪烁、漂移,为进一步优化激光通信系统性能设计、最终实现全天候超视距的大气激光通信做有意义的探索。     

A new method for modelling the space variability of significant wave height

Significant wave height, , is a measure of the variability of the ocean surface and is defined to be four times the standard deviation of the height of the ocean surface. In this paper, we present a methodology for modelling estimates of over space and time, using data obtained from satellite measurements. These estimates can be thought of as a random surface in space which develops over time. For each fixed time and over some limited region in space, the field consisting of the estimates may be considered stationary. Furthermore, it is reasonable to assume that the (natural) logarithms of the estimates are normally distributed. Under these assumptions and for each fixed time, the marginal distribution over space of the random field of the logarithms of the estimates is fitted by estimating its mean and covariance function, where the form of the covariance function is chosen to allow for correlation patterns at different spatial scales in the data. Both the mean and the covariance function of this model are allowed to be time dependent. A new methodology is developed for estimating the parameters of the chosen covariance structure. The proposed model is validated along the TOPEX-Poseidon satellite tracks by computing distributions of different quantities for the fitted model and comparing these to empirical estimates. Finally, the fitted model is used to compute the distribution of the global maximum over a certain region in the North Atlantic and to reconstruct the field.The research of Anastassia Baxevani is partially supported by the Gothenburg Stochastic Center.     

Exact Inference for Random Dirichlet Means

Two characterisations of a random mean from a Dirichlet process, as a limit of finite sums of a simple symmetric form and as a solution of a certain stochastic equation, are developed and investigated. These are used to reach results on and new insights into the distributions of such random means. In particular, identities involving functional transforms and recursive moment formulae are established. Furthermore, characterisations for several choices of the Dirichlet process parameter (leading to symmetric, unimodal, stable, and finite mixture distributions) are provided. Our methods lead to exact simulation recipes for prior and posterior random means, an approximation algorithm for the exact densities of these means, and limiting normality theorems for posterior distributions. The theory also extends to mixtures of Dirichlet processes and to the case of several random means simultaneously.     

A Crop Planning Problem with Fuzzy Random Profit Coefficients

The main purpose of this paper is to present a crop planning problem for agricultural management under uncertainty. It is significant that agricultural managers assign their limited farmlands to cultivation of which crops in a season. This planning is called the crop planning problem and influences their incomes for the season. Usually, the crop planning problem is formulated as a linear programming problem. But there are many uncertain factors in agricultural problems, so future profits for crops are not certain values. A linear programming model with constant profit coefficients may not reflect the environment of decision making properly. Therefore, we propose a model of crop planning with fuzzy profit coefficients, and an effective solution procedure for the model. Furthermore, we extend this fuzzy model, setting the profit coefficients as discrete randomized fuzzy numbers. We show concrete optimal solutions for each models.     

Algebraic polynomials with non-identical random coefficients

There are many known asymptotic estimates for the expected number of real zeros of a random algebraic polynomial The coefficients are mostly assumed to be independent identical normal random variables with mean zero and variance unity. In this case, for all sufficiently large, the above expected value is shown to be . Also, it is known that if the have non-identical variance , then the expected number of real zeros increases to . It is, therefore, natural to assume that for other classes of distributions of the coefficients in which the variance of the coefficients is picked at the middle term, we would also expect a greater number of zeros than . In this work for two different choices of variance for the coefficients we show that this is not the case. Although we show asymptotically that there is some increase in the number of real zeros, they still remain . In fact, so far the case of is the only case that can significantly increase the expected number of real zeros.