Mixed mode fracture of a piezoelectric–piezomagnetic bi-layer structure with two un-coaxial cracks parallel to the interface and each in a layer

The purpose of the present work is to study the mixed mode fracture of a piezoelectric–piezomagnetic composite with two un-coaxial cracks parallel to the interface and each in a layer. Methods of generalized dislocation simulation, Green’s function, Cauchy singular integral equation and Lobatto–Chebyshev collocation are combined together to get the numerical results of mechanical strain energy release rate (MSERR). Three kinds of effects are revealed by parametric studies, i.e., the free-surface effect, the shielding effect and the interference effect, and they are used to interpret the characteristics of COD and MSERR curves. In addition, the effects of shear loading, magnetic loading and electric loading on MSERR are also disclosed, respectively, by varying the corresponding loading factor.     

Sloshing waves in a heated viscoelastic fluid layer in an excited rectangular tank

In this paper, we have investigated the motion of a heated viscoelastic fluid layer in a rectangular tank that is subjected to a horizontal periodic oscillation. The mathematical model of the current problem is communicated with the linearized Navier–Stokes equation of the viscoelastic fluid and heat equation together with the boundary conditions that are solved by means of Laplace transform. Time domain solutions are consequently computed by using Durbin's numerical inverse Laplace transform scheme. Various numerical results are provided and thereby illustrated graphically to show the effects of the physical parameters on the free-surface elevation time histories and heat distribution. The numerical applications revealed that increasing the Reynolds number as well as the relaxation time parameter leads to a wider range of variation of the free-surface elevation, especially for the short time history.     

Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis.     

一类非光滑Chua’s电路的同步控制

本文研究两个带x|x|非线性项的Chua’s电路的全局指数同步和全局同步的控制问题.证明这两个系统在未加控制时不可能同步,但设计不同的控制器可以实现这两个系统的全局指数同步和全局同步.     

Poisson’s equation for discrete-time single-birth processes

We consider Poisson’s equation for discrete-time single-birth processes, and we derive its solutions by solving a linear system of infinitely many equations. We apply the solution of Poisson’s equation to obtain the asymptotic variance. The results are further applied to birth–death processes and the scalar-valued GI/M/1-type Markov chains.     

On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times

The structural properties of the moments of the time to ruin are studied in dependent Sparre Andersen models. The moments of the time to ruin may be viewed as generalized versions of the Gerber–Shiu function. It is shown that structural properties of the Gerber–Shiu function hold also for the moments of the time to ruin. In particular, the moments continue to satisfy defective renewal equations. These properties are discussed in detail in the model of Willmot and Woo (2012), which has Coxian interclaim times and arbitrary time-dependent claim sizes. Structural quantities needed to determine the moments of the time to ruin are specified under this model. Numerical examples illustrating the methodology are presented.     

Calix[4]pyrrolato Aluminates: The Effect of Ligand Modification on the Reactivity of Square-Planar Aluminum Anions

Structural constraint represents an attractive tool to modify p-block element properties without the need for unusual oxidation or valence states. The recently reported methyl-calix[4]pyrrolato aluminate established the effect of forcing a tetrahedral aluminum anion into a square-planar coordination mode. However, the generality of this structural motif and any consequence of ligand modification remained open. Herein, a systematic ligand screening was launched, and the class of square-planar aluminum anions was extended by two derivatives that differ in the meso-substitution at the calix[4]pyrrolato ligand. Strikingly, this modification provoked opposing trends in the preference for a Lewis acidic binding mode with σ-donors versus the aluminum-ligand cooperative binding mode with carbonyls. Insights into the origin of these counterintuitive experimental observations were provided by computation and bond analysis. Importantly, this rationale might allow to exploit mode-selective binding for catalytic rate control.     

The initial stage of structural transformation of Aβ42 peptides from the human and mole rat in the presence of Fe2+ and Fe3+: Related to Alzheimer's disease

The early stage of secondary structural conversion of amyloid beta (Aβ) to misfolded aggregations is a key feature of Alzheimer's disease (AD). Under normal physiological conditions, Aβ peptides can protect neurons from the toxicity of highly concentrated metals. However, they become toxic under certain conditions. Under conditions of excess iron, amyloid precursor proteins (APP) become overexpressed. This subsequently increases Aβ production. Experimental studies suggest that Aβ fibrillation (main-pathway) and amorphous (off-pathway) aggregate formations are two competitive pathways driven by factors such as metal binding, pH and temperature. In this study, we performed molecular dynamic (MD) simulations to examine the initial stage of conformational transformations of human Aβ (hAβ) and rat Aβ (rAβ) peptides in the presence of Fe²⁺ and Fe³⁺ ions. Our results demonstrated that Fe²⁺ and Fe³⁺ play key roles in Aβs folding and aggregation. Fe³⁺ had a greater effect than Fe²⁺on Aβs’ folding during intermolecular interactions and subsequently, had a greater effect in decreasing structural diversity. Fe²⁺ was observed to be more likely than Fe³⁺ to interact with nitrogen atoms from the residues of imidazole rings of His. rAβ peptides are more energetically favorable than hAβ for intermolecular interactions and amorphous aggregations. We concluded that most hAβ structures were energetically unfavorable. However, hAβs with intermolecular β-sheet formations in the C-terminal were energetically favorable. It is notable that Fe²⁺ can change the surface charge of hAβ. Furthermore, Fe³⁺ can promote C-terminal folding by binding to Glu22 and Ala42, and by forming stable β-sheet formations on the C-terminal. Fe³⁺ can also pause the main-pathway by inducing random aggregations.     

Disjoining pressure and the film-height-dependent surface tension of thin liquid films: New insight from capillary wave fluctuations

In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications.