Performance limitations of flat-histogram methods

We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based upon the exact density of states of 2D Ising models. The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the +/-J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Fréchet extremal value distribution that obeys exponential scaling. Furthermore, the shape parameters of these distributions indicate that statistical sample means become ill defined already for moderate system sizes within these complex energy landscapes.     

Vibrational spectroscopic investigation of poly(p‐phenylene sulfide)

Poly(p‐phenylene sulfide) (PPS) is an important polymer of engineering interest particularly useful in the electronics and automotive industries. Normal mode analysis including phonon dispersion has been performed to understand completely the vibrational spectra of this polymer. Various characteristic features of the dispersion curves have been reported. Crossing/Repulsion between various pairs of modes at certain phase values have been explained as arising due to internal symmetry in the energy momentum space. The heat capacity is calculated as a function of temperature via density‐of‐states in the range 220–360 K. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2353–2367, 2009     

A completely iterative method for the infinite domain electrostatic problem with nonlinear dielectric media

We present an iterative method for the solution of the exterior all-space electrostatic problem for nonlinear dielectric media. The electric potential is specified on interior boundaries and the electric field decays at infinity. Our approach uses a natural variational formulation based on the total energy of the nonlinear dielectric medium subject to boundary conditions. The problem is decomposed into an exterior calculation and an interior calculation with the boundary-specified electric potentials imposed as constraints between them. Together, these enable an iterative method that is based on the variational formulation. In contrast to direct solution of the electrostatic problems, we avoid the construction, storage and solution of dense and large linear systems. This provides important advantages for multiphysics problems that couple the linear electrostatic Poisson problem to nonlinear physics: the latter necessarily involves iterative approaches, and our approach replaces a large number of direct solves for the electrostatics with an iterative algorithm that can be coupled to the iterations of the nonlinear problem. We present examples applying the method to inhomogeneous, anisotropic nonlinear dielectrics. A key advantage of our variational formulation is that we require only the free-space, isotropic, homogeneous Greens function for all these settings.     

Kinetics of phase transformations in the peridynamic formulation of continuum mechanics

We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces.We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classical continuum theory, the peridynamic formulation does not require any extraneous constitutive laws such as the kinetic relation (the relation between the velocity of the interface and the thermodynamic driving force acting across it) or the nucleation criterion (the criterion that determines whether a new phase arises from a single phase). Instead this information is obtained from inside the theory simply by specifying the inter-particle interaction. We derive a nucleation criterion by examining nucleation as a dynamic instability. We find the induced kinetic relation by analyzing the solutions of impact and release problems, and also directly by viewing phase boundaries as traveling waves.We also study the interaction of a phase boundary with an elastic non-transforming inclusion in two dimensions. We find that phase boundaries remain essentially planar with little bowing. Further, we find a new mechanism whereby acoustic waves ahead of the phase boundary nucleate new phase boundaries at the edges of the inclusion while the original phase boundary slows down or stops. Transformation proceeds as the freshly nucleated phase boundaries propagate leaving behind some untransformed martensite around the inclusion.     

Onset of Surface Damage in Modular Orthopedic Implants: Influence of Normal Contact Loading and Stress-assisted Dissolution

Surface damage at interfaces of modular implants results from repeated fretting contacts between metallic surfaces in a corrosive environment. As a first step in understanding this complex process, multi-asperity contact experiments were conducted to characterize roughness evolution due to action of contact loads and exposure to a reactive environment. Cobalt–chromium specimens with surface roughness similar to modular implant were first subjected to only contact loading and subsequently, to alternating contact loads and exposure to reactive environment. During repeated normal contact loading, amplitude of surface roughness reached a steady value after decreasing during the first few cycles. However during the second phase surface roughness amplitude continuously evolved—decreasing during contact loading and increasing on exposure to corrosive environment. The increase in roughness amplitude during surface reaction depended on the magnitude of applied contact loads. A damage mechanism that incorporates contact-induced residual stress development and stress-assisted dissolution is proposed to elucidate the measured surface roughness evolution.