R. R. Rosales

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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)
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)
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)
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)
Pak-Wing Fok,1 Rodolfo R. Rosales,2 and Dionisios Margetis3 1Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125, USA 2Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 3Department of Mathematics and Institute for Physical Science and Technology, University(More)
Pak-Wing Fok,1,2 Rodolfo R. Rosales,3 and Dionisios Margetis4 1Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125, USA 2Department of Biomathematics, University of California–Los Angeles, Los Angeles, California 90095, USA 3Department of Mathematics, Massachusetts Institute of Technology, Cambridge,(More)
A crystal lattice with a small miscut from the plane of symmetry has a surface which consists of a series of atomic height steps separated by terraces. If the surface of this crystal is not in equilibrium with the surrounding medium, then its evolution is strongly mediated by the presence of these steps, which act as sites for attachment and detachment of(More)
We present the results of a theoretical investigation of droplets bouncing on a vertically vibrating fluid bath. An integro-differential equation describing the horizontal motion of the drop is developed by approximating the drop as a continuous moving source of standing waves. Our model indicates that, as the forcing acceleration is increased, the bouncing(More)
We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x = 0 for any t ≥ 0. Here, u(s)(t) is the shock state and the source term f is taken to mimic the chemical(More)