Crack propagation in viscoelastic materials has been understood with the use of Barenblatt cohesive models by many authors since 1970’s. In polymers and metal creep, it is customary to assume that relaxed modulus zero, so we have typically a crack speed which depends on some power stress intensity factor. Generally, when there finite modulus, shown “apparent” toughness semi-infinite increases b...

The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potential...

Lipid-protein interactions in membranes are dynamic, and consequently are well studied by magnetic resonance spectroscopy. More recently, lipids associated with integral membrane proteins have been resolved in crystals by X-ray diffraction, mostly at cryogenic temperatures. The conformation and chain ordering of lipids in crystals of integral proteins are reviewed here and are compared and cont...

This paper gives a regular vector boundary integral equation for solving the problem of viscous scattering of a pressure wave by a rigid body. Firstly, single-layer viscous potentials and a generalized stress tensor are introduced. Correspondingly, generalized viscous double-layer potentials are defined. By representing the scattered field as a combination of a single-layer viscous potential an...

This paper addresses an integral sliding mode control approach for automatic generation control (AGC) of a single area power system. Genetic algorithm (GA) is employed to search the parameters of the sliding surface. The proposed design is investigated for AGC of a single area power system, made up of reheated thermal and gas power generations. Compared with the GA-based proportion-integral (PI...

A new single surface integral equation is derived for light scattering by circular dielectric cylinders. Without adopting the concept of equivalent electric or magnetic surface currents, our formulation is directly derived from coupled-surface integral equations by the property of commutative matrices of Green functions. Further development by such matrix equations leads to only one unknown fun...

In earlier work, the authors Tracy, C. A. and Widom, H., “Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815 2008 obtained integral formulas for probabilities for a single particle in the asymmetric simple exclusion process. Here, formulas are obtained for joint probabilities for several particles. In the case of a single particle, the derivation here i...

in this paper, we give a generalization of the integral dependence from rings to modules. we study the stability of the integral closure with respect to various module theoretic constructions. moreover, we introduce the notion of integral extension of a module and prove the lying over, going up and going down theorems for modules.