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This work is concerned with analysis and refinement for a class of island dynamics models for epitaxial growth of crystalline thin films. An island dynamics model consists of evolution equations for step edges (or island boundaries), coupled with a diffusion equation for the adatom density, on an epitaxial surface. The island dynamics model with irreversible aggregation is confirmed to be mathematically ill-posed, with a growth rate that is approximately linear for large wavenumbers. By including a kinetic model for the structure and evolution of step edges, the island dynamics model is made mathematically well-posed. In the limit of small edge Peclet number, the edge kinetics model reduces to a set of boundary conditions, involving line tension and one-dimensional surface diffusion, for the adatom density. Finally, in the infinitely fast terrace diffusion limit, a simplified model of one-dimensional surface diffusion and kink convection is derived and found to be linearly stable.

Signal fragmentation is the (approximate) representation of a signal as a sum of signal fragments, each of which has compact support. It has been proposed as a method for transmitting a low frequency signal over an array of small antennas. We present a mathematical analysis of signal fragmentation for an idealized model of antenna transmission. In the simplest form of signal fragmentation, each fragment has the same waveform, but the nth fragment has an amplitude an and is shifted in time by an amount tn = nΔ. We analyze the spectral leakage (i.e., the error in the Fourier representation) and energy efficiency of signal fragmentation. For a special choice of wavelet the spectral leakage can be eliminated for sinusoidal signals. We also formulate a measure of energy efficiency and perform a scaling analysis of the efficiency with a large number of fragments. Although the efficiency is poor for the original wavelet expansion, an alternative form of fragmentation has efficiency that scales well with the number of fragments. We then find the fragment waveform that optimizes the energy efficiency for a given choice of support size, and we generalize some of these results to AM signals. [ABSTRACT FROM AUTHOR]

Compressed modes are solutions of the Laplace equation with a potential and a subgradient term. The subgradient term comes from addition of an L¹ penalty in the corresponding variational principle. This paper presents an analysis of compressed modes, finding the minimizer of the variational principle, showing the spatial localization property of compressed modes, and establishing an upper bound on the volume of their support. [ABSTRACT FROM AUTHOR]

A numerical method for investigating singularities in solutions to non-linear evolution equations is presented. The method is based on a complex analytical approach to singularities introduced by Sulem, Sulem and Frisch, which uses analytic continuation of an independent variable and numerical detection of the width of the analyticity strip, defined as the distance δ from the real domain to the nearest complex singularity. Their method, originally formulated for functions of a single variable, is here generalized to problems and functions of several variables. We first analyse the asymptotic behaviour of the multidimensional Fourier transform of an analytic function, and use this to numerically detect the complex singularity surface. The approach allows us to determine the parameters that characterize the singularity surface in a neighbourhood of its closest point to the real domain. [ABSTRACT FROM PUBLISHER]

We explore the potential of parallel tempering as a combinatorial optimization method, applying it to the traveling salesman problem. We compare simulation results of parallel tempering with a benchmark implementation of simulated annealing, and study how different choices of parameters affect the relative performance of the two methods. We find that a straightforward implementation of parallel tempering can outperform simulated annealing in several crucial respects. When parameters are chosen appropriately, both methods yield close approximation to the actual minimum distance for an instance with 200 nodes. However, parallel tempering yields more consistently accurate results when a series of independent simulations are performed. Our results suggest that parallel tempering might offer a simple but powerful alternative to simulated annealing for combinatorial optimization problems. [ABSTRACT FROM AUTHOR]

Judy and Motta developed a customizable electrodeposition process for fabrication of very small metal structures on a substrate. In this process, layers of metal of various shapes are placed on the substrate, then the substrate is inserted in an electroplating solution. Some of the metal layers have power applied to them, while the rest of the metal layers are not connected to the power initially. Metal ions in the plating solution start depositing on the powered layers and a surface grows from the powered layers. As the surface grows, it will touch metal layers that were initially unpowered, causing them to become powered and to start growing with the rest of the surface. The metal layers on the substrate are known as seed layer patterns, and different seed layer patterns can produce different shapes. This paper presents a mathematical model, a forward simulation method, and an inverse problem solution for the growth of a surface from a seed layer pattern. The model describes the surface evolution as uniform growth in the direction normal to the surface. This growth is simulated in two and three dimensions using the level set method. The inverse problem is to design a seed layer pattern that produces a desired surface shape. Some surface shapes are not attainable by any seed layer pattern. For smooth attainable shapes, we present a computational method that solves this inverse problem. [ABSTRACT FROM AUTHOR]

Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson-type formula and the associated step stiffness as a function of the step edge orientation angle, θ. Basic ingredients of the model are (i) the diffusion of point defects ("adatoms") on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a mean-field approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, β͂(θ), is determined via perturbations of the kinetic steady state for small edge Péclet number P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, β͂ is found to satisfy β͂ = O(θ-1) for O(P1/3) < θ ≫ 1, which is in agreement with independent, equilibrium-based calculations. [ABSTRACT FROM AUTHOR]

In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. [ABSTRACT FROM AUTHOR]

Exact periodic solutions are found for the relative motion of three spheres sedimenting in a Stokes fluid. Nearby solutions are found to be nearly periodic for a long time. Existence of the exact periodic solutions is proved using the point-particle approximation and symmetry properties of Stokes equations. Numerical simulations for finite-sized particles are performed using a method of multipole expansions. [ABSTRACT FROM AUTHOR]

Entropy increase and comparison principles are found for the Fokker–Planck equation for the radiation field in a homogeneous plasma with constant electron temperature. When emission– absorption is neglected, this is used to find equilibrium distributions that have the form of a Planck distribution plus a δ function at zero photon energy. For distributions below the Planck and with emission–absorption included, a rate of entropy increase is obtained. Numerical results confirm these conclusions. [ABSTRACT FROM AUTHOR]

Examines numerical solutions for the steady flow corresponding to a two-dimensional moving droplet with circulation. Effect of differences in droplet density on buoyancy force; Role of the Magnus effect in lift force balancing; Assumption of constant vorticity in the droplet interior.