A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements, the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.     

Diffusion-Ordered Spectroscopy (DOSY) as a Powerful NMR Method to Investigate Molecular Mobilities and Intermolecular Interactions in Complex Oil Mixtures

Studying the characteristics and molecular mechanisms of liquid self-diffusion coefficient and viscosity changes is of great significance for, e. g., chemical and petroleum processing. As examples of highly complex liquid,an asphaltene-free high-acid and high-viscosity crude oil and its extracted fractions were studied by comparing their ¹H DOSY diffusion maps. The crude oil exhibited a polydisperse diffusion distribution, including multiple diffusion portions with diffusion coefficients much smaller than that of any single fraction in independent diffusion. The main mechanism that leads to the decreases in the diffusion coefficients of crude oil is attributed to diffusion resistance enhanced by Dynamical Molecular-Interaction Networks (DMINs), rather than by enlargement of the diffusion species caused by molecular aggregation. Constructed through the synergistic interactions of various polar molecules in crude oil, DMINs dynamically bind polar molecules, trap polarizable molecules, and spatially hinder the free motion of non-polar molecules. Overall, this reduces the mobility of all molecular species, as illustrated by the decreased diffusion coefficients. This study demonstrates that DOSY is a powerful NMR method to investigate molecular motion abilities also in complex mixtures. In addition, the insights in the influence of the interaction matrix on the molecular mobility also help to understand the contribution of “structural viscosity” to the viscosity of heavy oil.     

利用动态反射法对手性液晶Bragg反射的分析

利用动态反射法对手性液晶材料的选择性反射特性进行了分析。根据理论分析结果，利用MATLAB程序计算了手性液晶膜层的反射光谱，得到了反射光谱随手性液晶的螺距和折射率变化的关系；利用动态反射法可以较为方便、快速地对手性液晶膜的Bragg反射特性进行数值求解分析，分析和计算结果可以为反射式液晶显示的设计和计算提供理论参考。由于在数值求解中引入了简化条件，因此该计算方法只能应用于△n值较小的情况，当Δn值较大时，应该用其他求解方法来完成计算分析工作。     

Moment equations for a spatially extended system of two competing species

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns.     

Quantifying coherence with dynamical discord

Quantum coherence and discord are two kinds of manifestations of nonclassicality. By calculating the coherence and discord in the specific bipartite quantum systems, we show quantitative connections between the coherence and the discord in the bipartite quantum systems created from local systems with the help of incoherent operations. We show that the coherence bounds the dynamical discord, and under particular conditions of the initial quantum states, the coherence of single systems is equal to the dynamical discord. We extend these results to the multipartite quantum systems.     

Removing of vortices in incompressible flows by distributed controls

We consider an optimal control problem of fluids flow. The fluid motion is governed by the incompressible time-dependent Navier-Stokes equations. A new optimal control formulation for the reduction and possibly extinction of vortices is proposed. A cost functional based on a local dynamical systems characterization of vortices is investigated. The resulting functional is a non-convex function of the velocity gradient tensor. The optimality system describing first order necessary optimality conditions is derived. The gradient and the second derivative of the cost functional with respect to the distributed control are established.     

DYNAMICAL CHARACTER FOR A PERTURBED COUPLED NONLINEAR SCHRODINGER SYSTEM

The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument.     

EAPPROXIMATE INERTIAL MANIFOLDS FOR THE SYSTEM OF THE J-J EQUATIONS

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SOME DYNAMICAL PROPERTIES OF THE UNIVERSAL UNFOLDING OF PITCHFORK

From the point of view of dynamics,the phenomenon of mode jumpingin the imperfect pitchfork problem is discussed.The dynamical mechanism of modeljumping of structures,such as plate and shell,that is brought about by the extremurninstability,is explained.Finally,we give numerical simulation to show the validity ofour results.     

从具体例子看惯性流形概念的推广

惯性流形的概念要求所有轨道指数收敛于唯一吸引子[5],这对于很多物理问题,例如sine-Gordon方程是很难满足的[4],本文中给出的人工例子建议了惯性流形的推广形式,这个推广形式去掉了整体吸引子是唯一的预先要求,该推广概念使用于sine-Gordon方程。