Gary K. Leaf

Bifurcation of Pulsating and Spinning Reaction Fronts in Condensed Two-Phase Combustion

Abstract We employ a nonlinear stability analysis to describe the bifurcation of pulsating and spinning modes of combustion in condensed media. We adopt the two-phase model of Margolis (1983) in which the modified nondimensional activation energy Δ of the reaction is large, but finite, and in which the limiting component of the mixture melts during the reaction process, as characterized by a nondimensional melting parameter M. We identify several types of non-steady solution branches which bifurcate from the steady palanar solution and show that they are supercritical and stable only for certain realistic ranges of M. For example, the spinning modes, though supercritical and stable for a range of M > 0, are subcritical and unstable for M = 0.

Sputter-induced surface composition changes in alloys

Abstract Radiation-induced redistribution of alloying elements in the near-surface region of dilute binary alloys during low-energy Ar+ ion sputtering was calculated using a kinetic model that includes the effects of radiation-induced segregation and preferential sputtering. Changes in the alloy surface composition were calculated as functions of sputtering time, temperature, ion flux and initial alloy composition for Ni-based model alloys. In the temperature range 200–850°C, radiation-induced segregation is dominant initially and the surface is enriched with or depleted of solutes whose fluxes are coupled predominantly to interstitial or vacancy fluxes, respectively. As the bombardment time increases, the effects of preferential sputtering become dominant and the surface composition approaches a steady-state value determined by the sputtering coefficients of the alloy components. Below 200 and above 850°C, the surface composition is altered by preferential sputtering because radiation-induced segregation is insignificant. The time required to achieve steady state increases with increasing temperature and decreasing ion flux. The present calculations may be of importance in the areas of sputter depth-profiling, sputter etching, and plasma contamination in fusion reactors.

Inner product computations using periodized Daubechies wavelets

Inner products of wavelets and their derivatives are presently known as connection coefficients. The numerical calculation of inner products of periodized Daubechies wavelets and their derivatives is reviewed, with the aim at providing potential users of the publicly-available numerical scheme, details of its operation. The numerical scheme for the calculation of connection coefficients is evaluated in the context of approximating differential operators, information which is useful in the solution of partial differential equations using wavelet-Galerkin techniques. Specific details of the periodization of inner products in the solution differential equations are included in the presentation. Wavelets have found a well-deserved niche in such areas of applied mathematics and engineering as approximation theory, signal analysis, and projection techniques for the solution of differential equations.

Circumventing Storage Limitations in Variational Data Assimilation Studies

An application of Pontryagins maximum principle data assimilation is used to blend possibly incomplete or nonuniformly distributed spatio-temporal observational data into geophysical models. Used extensively in engineering control theory applications, data assimilation has been introduced relatively recently into meteorological forecasting, natural-resource recovery modeling, and climate dynamics. Variational data assimilation is a promising assimilation technique in which it is assumed that the optimal state of the system is an extrema of a carefully chosen cost function. Provided that an adjoint model is available, the required model gradient can be computed by integrating the model forward and its adjoint backward. The gradient is then used to extremize the cost function with a suitable iterative or conjugate gradient solver. The problem addressed in this study is the explosive growth in both on-line computer memory and remote storage requirements of computing the gradient by the forward/adjoint technique which characterizes large-scale assimilation studies. Storage limitations impose severe limitation on the size of assimilation studies, even on the largest computers. By using a recursive strategy, a schedule can be constructed that enables the forward/adjoint model runs to be performed in such a way that storage requirements can be traded for longer computational times. This generally applicable strategy enables data assimilation studies on significantly larger domains than would otherwise be possible, given the particular hardware constraints, without compromising the outcome in any way. Furthermore, it is shown that this tradeoff is indeed viable and that when the schedule is optimized, the storage and computational times grow at most logarithmically.

On Nonadiabatic Condensed Phase Combustion

Abstract We analyze the effects of melting and volumetric heat losses on the propagation of a reaction front in condensed phase combustion. Considering both homogeneous and heterogeneous models for the reaction rate, we calculate the propagation velocity for steady, planar burning as a function of the parameters in the problem. In particular, we show that this quantity is a multi-valued function of the heat loss parameter. We interpret the critical value of this parameter at which the propagation velocity has a vertical tangent, and which varies with the melting parameter, as an extinction limit beyond which a steady, planar combustion wave cannot sustain itself. We also present a model for nonsteady, nonplanar burning and consider the linear stability of the steady, planar solution. As in the adiabatic case, this basic solution is unstable to pulsating disturbances for sufficiently large values of a modified activation energy parameter. We show, in agreement with experimental results, that the effects of...

Time-dependent Ginzburg-Landau simulations of vortex guidance by twin boundaries

Abstract The driven motion of vortices in the presence of a planar defect is simulated by means of the time-dependent Ginzburg-Landau equations. Guided motion of the vortices, both internal and external to the twin boundary, is found to occur over a range of driving forces. Experimental transport data on a single crystal of YBa 2 Cu 3 O 7 are consistent with guided motion.

Forces on particles in oscillatory boundary layers

The lift and drag forces on an isolated particle resulting from an oscillating wall-bounded flow, are approximated using direct numerical simulation and extrapolation techniques. We also confirm the existence of anomalies in the lift force, which arise from the interaction of the vortical field with the particle. Anomalies can also occur for computational reasons and these are discussed as well. This study was motivated by a long-standing question about the importance of lift forces in the dynamics of sediments in oceanic settings. To answer this question we use the numerically generated data as well as extrapolations to compute the ratio of the lift to buoyancy forces on a particle. This analysis suggests that for particles and oceanic conditions typical of the nearshore, the lift force can play a role in the dynamics of sedimentary beds.

Pulsating and Chaotic Dynamics near the Extinction Limit

Abstract We numerically solve the problem of a premixed flame in the region between two concentric cylinders, in which the combustible mixture is fed in through The inner cylinder, and combustion products are removed through the outer cylinder and through the sides. We employ a model which accounts for the full coupling between fluid and transport effects and chemical reactions. The model accounts for heat loss through both the outer and inner cylindrical walls. We find that as heat loss is increased or as the inflow velocity is decreased, a transition from stationary to pulsating combustion occurs prior to extinction. For certain parameter ranges a transition to apparently chaotic dynamics occurs via a period doubling cascade.

Defect buildup and solute segregation in alloys under pulsed irradiation

Abstract The Johnson-Lam kinetic model, which is based on a combination of diffusion and chemical reaction rate equations, has been used to study the buildup of point defects and defect-solute complexes, and segregation of minor elements in alloys under pulsed irradiation. Concentrations of defects and solutes have been calculated for various defect-production rates, defect-solute binding energies and pulse durations, with Ni as the model material. Precipitation at the sink surface is taken into account when the solute concentration at the sink exceeds the solubility limit. For a fixed damage rate, the longer the pulse duration the smaller the number of cycles needed to achieve a cyclic state for defects and defect-solute complexes and quasi-steady state for solute segregation. In addition, for a fixed pulse duration, the higher the damage rate the fewer the cycles required to observe these states. The resultant solute segregation obtained under pulsed irradiation can be similar to, or different from segregation achieved during steady irradiation depending on whether the beam-off period is comparable to, or much longer than the pulse duration. The microstructures of the material can also be different from those formed by unpulsed bombardment due to cyclic production and annealing of mobile defects.

Quasi-periodic waves and the transfer of stability in condensed-phase surface combustion

This article is concerned with the structure and stability properties of a combustion front propagating in the axial direction along the outer surface of a cylindrical solid fuel element. A nonlinear analysis is given that explains the occurrence of spinning and standing wave patterns as bifurcations from a uniformly propagating plane circular front. Particular attention is given to a stability transfer mechanism between standing and spinning waves by means of quasi-periodic waves.