Bayesian analysis of loss reserving using dynamic models with generalized beta distribution

A Bayesian approach is presented in order to model long tail loss reserving data using the generalized beta distribution of the second kind (GB2) with dynamic mean functions and mixture model representation. The proposed GB2 distribution provides a flexible probability density function, which nests various distributions with light and heavy tails, to facilitate accurate loss reserving in insurance applications. Extending the mean functions to include the state space and threshold models provides a dynamic approach to allow for irregular claims behaviors and legislative change which may occur during the claims settlement period. The mixture of GB2 distributions is proposed as a mean of modeling the unobserved heterogeneity which arises from the incidence of very large claims in the loss reserving data. It is shown through both simulation study and forecasting that model parameters are estimated with high accuracy.     

A standing wave model for acoustic pumping effect in microchannels

An acoustic impedance pump is comprised of a compressible section coupled at both ends to sections of different acoustic impedances. Liquid can be pumped from one end to another if the compressible section is actuated at certain locations. This paper presents an analytical model on the acoustic pumping effect in microchannels. A one-dimensional wave equation is developed for acoustic pressures in the compressible section, taking into account the actuations as acoustic source terms. The solution for the acoustic pressure is a set of standing waves established inside the compressible section, corresponding to the actuations. The pumping effect is attributed to the second-order terms of the acoustic pressures. Two control parameters are identified. One is the resonance frequency associated with the sound wave speed and length of the compressible section, and the other is the damping factor. The analytical results are compared with the experimental data, and a qualitative agreement is observed in terms of frequency characteristics of the pumping pressure.     

Why does shear banding behave like first-order phase transitions? Derivation of a potential from a mechanical constitutive model

Numerous numerical and experimental evidence suggest that shear banding behavior looks like first-order phase transitions. In this paper, we demonstrate that this correspondence is actually established in the so-called non-local diffusive Johnson-Segalman model (the DJS model), a typical mechanical constitutive model that has been widely used for describing shear banding phenomena. In the neighborhood of the critical point, we apply the reduction procedure based on the center manifold theory to the governing equations of the DJS model. As a result, we obtain a time evolution equation of the flow field that is equivalent to the time-dependent Ginzburg-Landau (TDGL) equations for modeling thermodynamic first-order phase transitions. This result, for the first time, provides a mathematical proof that there is an analogy between the mechanical instability and thermodynamic phase transition at least in the vicinity of the critical point of the shear banding of DJS model. Within this framework, we can clearly distinguish the metastable branch in the stress-strain rate curve around the shear banding region from the globally stable branch. A simple extension of this analysis to a class of more general constitutive models is also discussed. Numerical simulations for the original DJS model and the reduced TDGL equation is performed to confirm the range of validity of our reduction theory.     

GaN-nanowire-based dye-sensitized solar cells

GaN nanowires typically exhibit high electron mobility and excellent chemical stability. However, stability of GaN is detrimental for successful attachment of dye molecules and its application in dye-sensitized solar cells (DSSCs). Here we demonstrate DSSCs based on GaN/gallium oxide and GaN/TiO _x core–shell structures, and we show that coating of GaN nanowires with a TiO _x shell significantly increases dye adsorption and consequently photovoltaic performance. The best cells exhibited short circuit current density of 1.83 mA/cm² and power conversion efficiency of 0.44% under AM 1.5 simulated solar illumination.     

Memory effects in superparamagnetic La<Subscript>0.6</Subscript>Pb<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript> nanoparticles

Using different temperature and field protocols, the memory behaviors in the dc magnetization and magnetic relaxation are observed at temperature below blocking temperature T_B = 93 K in weakly interacting manganite La_0.6Pb_0.4MnO₃ nanoparticles. The results indicate that the magnetic dynamics of this nanoparticle system is strongly correlated with a wide distribution of particle relaxation times, which may arise from the particle weak interaction and distribution of the particle size.     

关联染料敏化太阳能电池薄膜厚度与光伏性能的漂移-扩散数值模拟

建立漂移-扩散模型来模拟敏化电池的电荷分离过程.该模型能够计算在稳态和非稳态条件下光生电子的多步受限扩散及其与电子受体的复合反应.通过对电池的电流-电压曲线的数值模拟,优化了电池的薄膜厚度并获得了最大的光电转换效率.发现膜厚的增加降低了电荷收集效率,但有利于提高电子注入流率,光电流的输出正是受控于这两个因素.复合速率常数严重影响了膜厚优化的结果.较厚的薄膜适合于电子复合被充分抑制的电池,而较薄的薄膜有利于降低快复合电池的电子复合损失.在开路条件下,膜厚的提高会减小电子浓度,在造成光电压的降低的同时会提高电子寿命.     

Design of diamond-shaped transient thermal cloaks with homogeneous isotropic materials

Transformation thermodynamics as a major extension of transformation optics has recently received considerable attention. In this paper, we present two-dimensional (2D) and three-dimensional (3D) diamond-shaped transient thermal cloaks with non-singular homogeneous material parameters. The absence of singularity in the parameters results from the fact that the linear coordinate transformation is performed by expanding a line segment rather than a point into a region, while the mechanism behind the homogeneity is the homogeneous stretching and compression along orthogonal directions during the transformation. Although the derived parameters remain anisotropic, we further show that this can be circumvented by considering a layered structure composed of only four types of isotropic materials based on the effective medium theory. Numerical simulation results confirm the good performance of the proposed cloaks.     

Effect of ZnAl2O4 coating on the compressive behaviors of aluminum borate whiskers-reinforced aluminum composites at elevated temperatures

Aluminum borate whiskers (ABOw) with or without ZnAl₂O₄ coating reinforced pure aluminum composites (ABOw/Al, ABOw/ZnAl₂O₄/Al) were fabricated by squeeze casting. The effects of ZnAl₂O₄ coating on the compressive behaviors, microstructures, and matrix textures of the composites were investigated at different temperatures and strain rates. The results indicate that the maximum compressive flow stress of the composites almost linearly decreases with the increase in temperature. The maximum compressive flow stress of ABOw/ZnAl₂O₄/Al composite is higher than that of ABOw/Al composite at the same temperature when the strain rate is larger, however, it is reversed when the strain rate is smaller. It is more serious for the fracture of whiskers in ABOw/ZnAl₂O₄/Al composite than that in ABOw/Al composite at the high compressive strain rate. However, the average length of whiskers in ABOw/ZnAl₂O₄/Al composite is larger than that in ABOw/Al composite at the low compressive strain rate. The strong matrix texture in ABOw/ZnAl₂O₄/Al composite appears at the high compressive strain rate, however, it is observed in ABOw/Al composite at the low compressive strain rate.     

Spectroscopic studies of sodium nitrate plasma produced by nanosecond laser ablation

We present the optical emission characteristics of the sodium plasma produced at the surface of sodium nitrate (NaNO₃) also known as Chile saltpeter. We used a Q-switched Nd:YAG (Quantel Brilliant) pulsed laser having a pulse duration of 5?ns and 10?Hz repetition rate which is capable of delivering 400?mJ at 1064?nm and 200?mJ at 532?nm. The target material was placed in front of laser beam in air (atmospheric pressure). The experimentally observed line profiles of neutral sodium have been used to extract the electron temperature using the Boltzmann plot method, whereas the electron number density has been determined from the Stark broadening. The electron temperature is calculated by varying the distance from the target surface along the line of propagation of the plasma plume and also by varying the laser irradiance. Besides, we have studied the variation of number density as a function of laser irradiance as well as its variation with the distance from the target surface. It is observed that electron temperature and electron number density increase as the laser irradiance is increased.     

Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming

This paper aims at showing that the class of augmented Lagrangian functions for nonlinear semidefinite programming problems can be derived, as a particular case, from a nonlinear separation scheme in the image space associated with the given problem. By means of the image space analysis, a global saddle point condition for the augmented Lagrangian function is investigated. It is shown that the existence of a saddle point is equivalent to a regular nonlinear separation of two suitable subsets of the image space. Without requiring the strict complementarity, it is proved that, under second order sufficiency conditions, the augmented Lagrangian function admits a local saddle point. The existence of global saddle points is then obtained under additional assumptions that do not require the compactness of the feasible set. Motivated by the result on global saddle points, we propose two modified primal-dual methods based on the augmented Lagrangian using different strategies and prove their convergence to a global solution and the optimal value of the original problem without requiring the boundedness condition of the multiplier sequence.