On the geometric autocorrelation function of polycrystalline materials

Herein we derive an expression for direct determination of the geometric autocorrelation function W of a polycrystalline material from images of its grain boundary network (e.g., those delivered by orientation imaging microscopy). We also obtain an identity that relates the mean linear intercept function to a directional derivative of the geometric autocorrelation function. These formulae were applied to examine whether a widely-used formula for W, particularly in theoretical studies of attenuation of elastic waves in polycrystalline media, would be valid for the grain boundary structure of a commercial aluminum alloy. The conclusion was negative.     

A generalized geometric-programming solution to “An economic production quantity model with flexibility and reliability considerations”

The classical economic production quantity (EPQ) model assumes that items are produced by a perfectly reliable production process with a fixed set-up cost. While the reliability of the production process cannot be perfected cost-free, the set-up cost can be reduced by investment in flexibility improvement. In this paper, we propose an EPQ model with a flexible and imperfect production process. We formulate this inventory decision problem using geometric programming (GP), establish more general results using the arithmetic-geometric mean inequality, and solve the problem to obtain a closed-form optimal solution. Following the theoretical treatment, we provide a numerical example to demonstrate that GP has potential as a valuable analytical tool for studying a certain class of inventory control problems. Finally we discuss some aspects of sensitivity analysis of the optimal solution based on the GP approach.     

Geometric phases and coherent states

A cyclic evolution of a pure quantum state is characterized by a closed curve γ in the projective Hilbert space , equipped with the Fubini-Study geometry. It is known that the geometric phase for this evolution is given by the integral of the symplectic form of the Fubini-Study geometry over an arbitrary surface spanning γ. This result extends to an infinite-dimensional Hilbert space for a bosonic quantum field. We prove that is bounded above by the infimum area over all surfaces spanning γ, and that the bound is attained if γ can be spanned by a holomorphic curve. Using an earlier result concerning the intrinsic Euclidean geometry of the coherent state submanifold , we derive an expression for the geometric phase for a cyclic evolution amongst coherent states. We indicate how the intensity of a classical configuration can be inferred from the winding number of the exponential geometric phase about the origin in the complex plane. In the case of photon states we present group theoretic and 2-component spinor representations of . We derive an expression for in the case of a sequence of measurements such that the resulting states are coherent at each step, in terms of a sequence of projection operators. The situation in relation to some earlier experiments of Pancharatnam and Tomita–Chiao is explained.     

High Order Optimized Geometric Integrators for Linear Differential Equations

In this paper new integration algorithms based on the Magnus expansion for linear differential equations up to eighth order are obtained. These methods are optimal with respect to the number of commutators required. Starting from Magnus series, integration schemes based on the Cayley transform an the Fer factorization are also built in terms of univariate integrals. The structure of the exact solution is retained while the computational cost is reduced compared to similar methods. Their relative performance is tested on some illustrative examples.     

保险联结风险投资模型的赤字问题

保险公司被允许将部分资金投入风险市场,这样保险公司经营的风险来自于未来实际发生索赔的不确定性和投资收益的不确定性。研究了由经典的Cramer-Lundberg模型与按照几何布朗运动股票价格变动的一个风险模型,获得了三种资产分配情况下股票价格波动对赤字发生概率下界的影响。     

The dynamics of coupled planar rigid bodies. II. Bifurcations,periodic solutions,and chaos

We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.     

Numerical Analysis of Structural Systems Subjected to Non-Gaussian Random Fields

This paper deals with the stochastic response of structures loaded by non-Gaussian random fields. A finite element model is used to describe a cantilever beam assuming both linear and non-linear behavior. The cross-correlated stochastic field is generated by a numerical procedure based on the translation processes theory. The marginal distribution of the load is assumed to be lognormal and the correlation structure is based on the second-order Markov process. The statistical analysis of the results highlights the effects of the involved non-linearity and non-Gaussianity properties on the structures response.     

Stabilization of transmission coupled wave and Euler–Bernoulli equations on Riemannian manifolds by nonlinear feedbacks

We consider the transmission system of coupling wave equations with Euler–Bernoulli equations on Riemannian manifolds. By introducing nonlinear boundary feedback controls, we establish the exponential and rational energy decay rate for the problem. Our proofs rely on the geometric multiplier method.     

Comparison of Planar and 3‐D Interdigitated Electrodes as Electrochemical Impedance Biosensors

It has been reported that the introduction of a dielectric barrier between adjacent digits of an interdigitated electrode array can improve the sensitivity of the array as an electrochemical impedance biosensor. Here we present an in‐depth analysis of the impedance in planar interdigitated electrodes and 3‐D interdigitated electrodes (with dielectric barriers). The analysis indicates that the planar geometry not only provides lower impedance but also a higher change impedance as a result of molecular immobilization on the electrode array surface.