Dynamic crystal plasticity: An Eulerian approach

In this paper an Eulerian rate-dependent single crystal model that accounts for high-strain rates, large strains and rotations is developed. The viscoplastic law as well as the evolution equations for the lattice are written in terms of vectorial and tensorial quantities associated with the current configuration. The viscoplastic law is obtained from Schmid law using an overstress approach. Such an expression for the viscoplastic law is motivated by the microdynamics of crystal defects. A general analysis of the plane-strain response of the proposed rigid-viscoplastic single crystal model is presented. It is shown that only one differential equation, involving the orientation of one composite in-plane slip system, is necessary to describe the lattice evolution. Several two-dimensional boundary value problems, such as equal-channel die extrusion and channel die compression are selected to illustrate the predictive capabilities of the model. The results show that even at relatively low strain rates the viscosity plays an important role in the development of localized deformation modes. At high crosshead velocity, the plastic properties and crystal anisotropy are less important while inertia effects are dominant. Finally, the grains interaction is investigated by analyzing the compression of a grains multicrystal.     

Mixed Convection Boundary-Layer Flow Along a Vertical Cylinder Embedded in a Porous Medium Filled by a Nanofluid

The steady mixed convection boundary-layer flow on a vertical circular cylinder embedded in a porous medium filled by a nanofluid is studied for both cases of a heated and a cooled cylinder. The governing system of partial differential equations is reduced to ordinary differential equations by assuming that the surface temperature of the cylinder and the velocity of the external (inviscid) flow vary linearly with the axial distance x measured from the leading edge. Solutions of the resulting ordinary differential equations for the flow and heat transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle volume fraction ${\phi}$ , the mixed convection or buoyancy parameter ?? and the curvature parameter ??. Results are presented for the specific case of copper nanoparticles. A critical value ?? _c of ?? with ?? _c <?0 is found, with the values of | ?? _c| increasing as the curvature parameter ?? or nanoparticle volume fraction ${\phi}$ is increased. Dual solutions are seen for all values of ?? >??? _c for both aiding, ?? >?0 and opposing, ?? <?0, flows. Asymptotic solutions are also determined for both the free convection limit ${(\lambda \gg 1)}$ and for large curvature parameter ${(\gamma \gg 1)}$ .     

Free Convection in a Square Cavity Filled with a Tridisperse Porous Medium

This work is dealing with the natural convection heat transfer in a square filled with porous medium that has been extended according to the Nield and Kuznetsov model to tridisperse porous medium. Considering impermeable walls which the horizontal ones are insulated and vertical ones are assumed to be isothermal, the governing equations are set as the three equations for momentum and three equations for energy for three phases of porosity and are numerically solved utilizing finite element method. In this study isothermal contours, streamlines and Nusselt number values are foremost criteria which are presented for three levels of porosity. The influence of various governing parameters on the heat transfer is investigated.     

Error bound results for convex inequality systems via conjugate duality

The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. First of all, we deal with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of a general vector function. We also propose a second approach for guaranteeing the existence of global error bounds of the latter, which meanwhile sharpens the classical result of Robinson.     

Existence for nonlinear evolution inclusions with nonlocal retarded initial conditions

In this paper, we prove a sufficient condition for the global existence of bounded C⁰-solutions for a class of nonlinear functional differential evolution equation of the form where X is a real Banach space, A is the infinitesimal generator of a nonlinear compact semigroup, is a nonempty, convex, weakly compact valued, and almost strongly–weakly u.s.c. multi-function, and is nonexpansive.     

Earth surface effects on active faults: An eigenvalue asymptotic analysis

We study in this paper an eigenvalue problem (of Steklov type), modeling slow slip events (such as silent earthquakes, or earthquake nucleation phases) occurring on geological faults. We focus here on a half space formulation with traction free boundary condition: this simulates the earth surface where displacements take place and can be picked up by GPS measurements. We construct an appropriate functional framework attached to a formulation suitable for the half space setting. We perform an asymptotic analysis of the solution with respect to the depth of the fault. Starting from an integral representation for the displacement field, we prove that the differences between the eigenvalues and eigenfunctions attached to the half space problem and those attached to the free space problem, is of the order of d^-2, where d is a depth parameter: intuitively, this was expected as this is also the order of decay of the derivative of the Green's function for our problem. We actually prove faster decay in case of symmetric faults. For all faults, we rigorously obtain a very useful asymptotic formula for the surface displacement, whose dominant part involves a so called seismic moment. We also provide results pertaining to the analysis of the multiplicity of the first eigenvalue in the line segment fault case. Finally we explain how we derived our numerical method for solving for dislocations on faults in the half plane. It involves integral equations combining regular and Hadamard's hypersingular integration kernels.     

Duality for location problems with unbounded unit balls

Given an optimization problem with a composite of a convex and componentwise increasing function with a convex vector function as objective function, by means of the conjugacy approach based on the perturbation theory, we determine a dual to it. Necessary and sufficient optimality conditions are derived using strong duality. Furthermore, as special case of this problem, we consider a location problem, where the “distances” are measured by gauges of closed convex sets. We prove that the geometric characterization of the set of optimal solutions for this location problem given by Hinojosa and Puerto in a recently published paper can be obtained via the presented dual problem. Finally, the Weber and the minmax location problems with gauges are given as applications.