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The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient information, and evolves both quantities in a fully coupled fashion. This maintains the coherence between function… (More)

Some phenomena involving intersection of weak shock waves at small angles are considered: the focusing of curved fronts at a&es, the transition between regular and irregular reflection of oblique shock waves on rigid walls and the diffraction patterns arising behind obstacles. The intersection of three shock waves plays a central role in most of these… (More)

- Brian D Sutton, Alan Edelman, Ttj Esis Supervisor, Rodolfo R Rosales, Archivtis

Classical random matrix models are formed from dense matrices with Gaussian entries. Their eigenvalues have features that have been observed in combinatorics, statistical mechanics, quantum mechanics, and even the zeros of the Riemann zeta function. However, their eigenvectors are Haar-distributed-completely random. Therefore , these classical random… (More)

We unify step bunching ͑SB͒ instabilities occurring under various conditions on crystal surfaces below roughening. We show that when attachment-detachment of atoms at step edges is the rate-limiting process, the SB of interacting, concentric circular steps is equivalent to the commonly observed SB of interacting straight steps under deposition, desorption,… (More)

In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic ("inviscid") continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling… (More)

- Andrew J Majda, Rodolfo R Rosales, Esteban G Tabak, Cristina V Turner
- 1999

A new theoretical mechanism is developed in which large-scale equatorial Kelvin waves can modify their speed through dispersion and interaction with other large-scale equatorial waves, such as Yanai or Rossby modes, through topographic resonance. This resonance mechanism can prevent the breaking of a propagating nonlinear Kelvin wave, slow down its speed,… (More)

- Irene M Gamba, Rodolfo R Rosales, Esteban G Tabak
- 1999

We discuss the singular behavior of solutions to two-dimensional, general second-order, uniformly elliptic equations in divergence form, with bounded measurable coefficients and discontinuous Dirichlet data along a portion of a Lipschitz boundary. We show that the conjugate to the solution develops a singularity that is at least logarithmic along the… (More)

Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries, resulting in weakly convergent solutions. We recast the Navier-Stokes incompress-ibility constraint as a pressure… (More)

We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from superdiffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the superdiffusive (but sub-ballistic) regime, which occurs before a particle… (More)

The surface of a nanostructure relaxing on a substrate consists of a finite number of interacting steps and often involves the expansion of facets. Prior theoretical studies of facet evolution have focused on models with an infinite number of steps, which neglect edge effects caused by the presence of the substrate. By considering diffusion of adsorbed… (More)