Almost Sure Relative Stability of the Overshoot of Power Law Boundaries

We give necessary and sufficient conditions for the almost sure relative stability of the overshoot of a random walk when it exits from a two-sided symmetric region with curved boundaries. The boundaries are of power-law type, ±rn ^b , r > 0, n = 1, 2,..., where 0 ≤ b < 1, b≠ 1/2. In these cases, the a.s. stability occurs if and only if the mean step length of the random walk is finite and non-zero, or the step length has a finite variance and mean zero.      

Influence of the Grain Boundaries on the Heat Transfer in Laser Ceramics

Grain boundaries play a key role in determining several key properties of polycrystalline laser ceramics. Heat transfer measurements at low temperature constitute a good tool to probe grain boundaries. We review the results of heat transfer measurements in polycrystalline Y₃Al₅O₁₂ garnets as well as Y₂O₃ and Lu₂O₃ sesquioxide materials obtained by self-energy-driven sintering of nano-particles. The average phonon mean free path in Y₃Al₅O₁₂ was found to be significantly larger than the average grain size and to scale with temperature as T ⁻² at low temperature. Existing models describing the interaction between phonons and grain boundaries are reviewed. Correct temperature dependence of the mean free path and order of magnitude of scattering rates were found by assuming the existence of a grain boundary layer having acoustic properties different from those of the bulk. A different temperature dependence of phonon mean free path was found for the sesquioxides and was ascribed to the stronger elastic anisotropy of these materials. The thermal resistance associated to the grain boundaries of laser ceramics was found to be lower than in other dense polycrystalline ceramic materials reported in the literature.     

Structure of Artificial Grain Boundaries in Sapphire Bicrystals with Intermediate Layers

The structure of the artificial grain boundaries in Al₂O₃ bicrystals withY₃Al₅O₁₂ and Y-stabilizedZrO₂ (Y-ZrO₂) intermediate layers was studiedwith high resolution electron microscopy, electron diffraction and energydispersive X-ray analysis. TheY₃Al₅O₁₂ intermediate layer wasfound to be polycrystalline with three different orientation relationshipsbetween the ₂O₃ and theY₃Al₅O₁₂. The structure of theY₃Al₅O₁₂/₂O₃ interfaces is described.Also₂O₃ bicrystals with an Y-ZrO₂/₂O₃/Y-ZrO₂/₂O₃/Y-ZrO₂intermediate layer, prepared at two different temperatures, werestudied.Recry stallization of the intermediate layers occurred during thesolid phase intergrowth of the ₂O₃ bicrystalsparts and only an Y-ZrO₂ layer was found as intermediatelayer. The misorientation between the consecutive Y-ZrO₂grains was less than 1.5°. Misfit dislocations and atomic height stepsdecorate the Y-ZrO₂/₂O₃interface.     

Stokes flow solutions in infinite and semi-infinite porous channels

We derive a class of exact solutions for Stokes flow in infinite and semi-infinite channel geometries with permeable walls. These simple, explicit, series expressions for both pressure and Stokes flow are valid for all permeability values. At the channel walls, we impose a no-slip condition for the tangential fluid velocity and a condition based on Darcy's law for the normal fluid velocity. Fluid flow across the channel boundaries is driven by the pressure drop between the channel interior and exterior; we assume the exterior pressure to be constant. We show how the ground state is an exact solution in the infinite channel case. For the semi-infinite channel domain, the ground-state solutions approximate well the full exact solution in the bulk and we derive a method to improve their accuracy at the transverse wall. This study is motivated by the need to quantitatively understand the detailed fluid dynamics applicable in a variety of engineering applications including membrane-based water purification, heat and mass transfer, and fuel cells.     

Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation

Nanoindentation experiments have shown that microstructural inhomogeneities across the surface of gold thin films lead to position-dependent nanoindentation behavior [Phys. Rev. B (2002), to be submitted]. The rationale for such behavior was based on the availability of dislocation sources at the grain boundary for initiating plasticity. In order to verify or refute this theory, a computational approach has been pursued. Here, a simulation study of the initial stages of indentation using the embedded atom method (EAM) is presented. First, the principles of the EAM are given, and a comparison is made between atomistic simulations and continuum models for elastic deformation. Then, the mechanism of dislocation nucleation in single crystalline gold is analyzed, and the effects of elastic anisotropy are considered. Finally, a systematic study of the indentation response in the proximity of a high angle, high sigma (low symmetry) grain boundary is presented; indentation behavior is simulated for varying indenter positions relative to the boundary. The results indicate that high angle grain boundaries are a ready source of dislocations in indentation-induced deformation.     

Effects of Multi Global Bifurcations on Basin Organization,Catastrophes and Final Outcomes in a Driven Nonlinear Oscillator at the 2T-Subharmonic Resonance

The behavior of the escape driven oscillator at the 2T-periodic subharmonic resonance is considered, and the mechanism of generating different fractal patterns of the basins of attraction of coexisting attractors, as well as its effects on the unpredictable asymptotic system behaviors, are the main points of interest. The analysis is based on the numerical study of the sudden qualitative changes of the structure of basin-phase portraits, the changes implied by multi global bifurcations. Attention is focused on two qualitatively different regions of control space: the region prior to the subcritical flip bifurcation, where all three attractors (2T-periodic, T-periodic and the attractor at infinity) coexist, and the region after the bifurcation, where only two attractors (2T-periodic and the attractor at infinity) coexist. In particular, the concept of the global (homoclinic and heteroclinic) bifurcations is extended to the latter region, where the arising flip saddle (instead of the direct saddle) is involved in the events. The possible forms of unpredictable outcomes, which arise in both regions of control parameters, are pointed out.     

Imaging the domain structure of organic semiconductor films

State‐of‐the‐art solution‐processed organic field‐effect transistors typically use polycrystalline organic semiconductor thin films as the active layer. Although it is widely regarded that boundaries between polycrystalline domains are a likely source of charge trapping limiting charge carrier mobility, little is known about the detailed domain structure of such films. Furthermore, variations in local order particularly in conjugated polymer films are likely to further impede charge transport. In recent years a number of techniques have been exploited that are able to provide information regarding local domain orientation and molecular order in polycrystalline organic thin films. These techniques have provided new information regarding the nature of domain structure providing an opportunity to directly evaluate the influence of domain structure on device operation. This article aims to provide a timely review of the experimental approaches used to date and provide a perspective for future work. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Numerical methods for a fixed domain formulation of the glacier profile problem with alternative boundary conditions

In this paper we develop a set of numerical techniques for the simulation of the profile evolution of a valley glacier in the framework of isothermal shallow ice approximation models. The different mathematical formulations are given in terms of a highly nonlinear parabolic equation. A first nonlinearity comes from the free boundary problem associated with the unknown basal extension of the glacier region. This feature is treated using a fixed domain complementarity formulation which is solved numerically by a duality method. The nonlinear diffusive term is explicitly treated in the time marching scheme. A convection dominated problem arises, so a characteristic scheme is proposed for the time discretization, while piecewise linear finite elements are used for the spatial discretization. The presence of infinite slopes in polar regimes motivates an alternative formulation based on a prescribed flux boundary condition at the head of the glacier instead a homogeneous Dirichlet one. Finally, several numerical examples illustrate the performance of the proposed methods.     

Non-equilibrium grain boundary structure and inelastic deformation using atomistic simulations

Grain boundary influence on material properties becomes increasingly significant as grain size is reduced to the nanoscale. Nanostructured materials produced by severe plastic deformation techniques often contain a higher percentage of high-angle grain boundaries in a non-equilibrium or energetically metastable state. Differences in the mechanical behavior and observed deformation mechanisms are common due to deviations in grain boundary structure. Fundamental interfacial attributes such as atomic mobility and energy are affected due to a higher non-equilibrium state, which in turn affects deformation response. In this research, atomistic simulations employing a biased Monte Carlo method are used to approximate representative non-equilibrium bicrystalline grain boundaries based on an embedded atom method potential, leveraging the concept of excess free volume. An advantage of this approach is that non-equilibrium boundaries can be instantiated without the need of simulating numerous defect/grain boundary interactions. Differences in grain boundary structure and deformation response are investigated as a function of non-equilibrium state using Molecular Dynamics. A detailed comparison between copper and aluminum bicrystals is provided with regard to boundary strength, observed deformation mechanisms, and stress-assisted free volume evolution during both tensile and shear simulations.     

Jordan-Wigner approach to the frustrated spin one-half XXZ chain

The Jordan-Wigner transformation is applied to study the ground state properties and dimerization transition in the J₁-J₂ XXZ chain. We consider different solutions of the mean-field approximation for the transformed Hamiltonian. Ground state energy and the static structure factor are compared with complementary exact diagonalization and good agreement is found near the limit of the Majumdar-Ghosh model. Furthermore, the ground state phase diagram is discussed within the mean-field theory. In particular, we show that an incommensurate ground state is absent for large J₂ in a fully self-consistent mean-field analysis.