Alexandre Rosas

Observation of two-wave structure in strongly nonlinear dissipative granular chains.

In a strongly nonlinear viscous granular chain impacted by a single grain we observe a wave disturbance that consists of two parts exhibiting two time scales of dissipation. Above a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shocklike attenuating pulse.

Pulse propagation in tapered granular chains: An analytic study

We study pulse propagation in one-dimensional tapered chains of spherical granules. Analytic results for the pulse velocity and other pulse features are obtained using a binary collision approximation. Comparisons with numerical results show that the binary collision approximation provides quantitatively accurate analytic results for these chains.

Pulse propagation in decorated granular chains: An analytical approach

We study pulse propagation in one-dimensional chains of spherical granules decorated with small grains placed between large granules. The effect of the small granules can be captured by replacing the decorated chains by undecorated chains of large granules of appropriately renormalized mass and effective interaction between the large granules. This allows us to obtain simple analytic expressions for the pulse propagation properties using a generalization of the binary collision approximation introduced in our earlier work [Phys. Rev. E 80, 031303 (2009); Phys. Rev. E 69, 037601 (2004)].

Landau quantization and curvature effects in a two-dimensional quantum dot

In this work we have investigated the influence of topology in quantum dynamics in two-dimensional quantum dots in a conic surface. We analyze the quantum dynamics of particles in this dot when submitted to an external magnetic field and Aharonov-Bohm flux in the dot center. We obtain the eigenvalues and eigenfunctions exactly. We investigated the influence of geometry and topology on the magnetization, the Fermi energy, and the persistent currents. It is shown that the curvature of the space changes the oscillation pattern of those physical quantities.

Pulse velocity in a granular chain.

We discuss the applicability of two very different analytic approaches to the study of pulse propagation in a chain of particles interacting via a Hertz potential, namely, a continuum model and a binary collision approximation. While both methods capture some qualitative features equally well, the first is quantitatively good for softer potentials and the latter is better for harder potentials.

Self-similarity in random collision processes

Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long-time limit and the similarity functions have algebraic or stretched exponential tails. The characteristic exponents are roots of transcendental equations and vary continuously with the mixing parameters. In the presence of conservation laws, the velocity distributions become universal.

Pulse dynamics in a chain of granules with friction

We study the dynamics of a pulse in a chain of granules with friction. We present theories for chains of cylindrical granules (Hertz potential with exponent n=2) and of granules with other geometries (n>2). Our results are supported via numerical simulations for cylindrical and for spherical granules (n=5/2).

Short-pulse dynamics in strongly nonlinear dissipative granular chains.

We study the energy decay properties of a pulse propagating in a strongly nonlinear granular chain with damping proportional to the relative velocity of the grains. We observe a wave disturbance that at low viscosities consists of two parts exhibiting two entirely different time scales of dissipation. One part is an attenuating solitary wave, dominated by discreteness and nonlinearity effects as in a dissipationless chain, and has the shorter lifetime. The other is a purely dissipative shocklike structure with a much longer lifetime and exists only in the presence of dissipation. The range of viscosities and initial configurations that lead to this complex wave disturbance are explored.

Exact quantum motion of a particle trapped by oscillating fields

The exact wavefunctions for a particle trapped by oscillating fields are obtained in terms of Mathieu functions with the help of linear invariants and the dynamical invariant method. In addition, we construct Gaussian wave packet solutions and calculate the quantum fluctuations in the coordinate and momentum as well as the quantum correlations between coordinate and momentum.

Pulse Propagation in Granular Chains

We study pulse propagation in one‐dimensional granular chains of spherical granules. Our goal is to develop an analytic approach that makes it possible to predict pulse properties as a function of time. Our method is based on a binary collision approximation that reduces the problem to collisions involving only two granules at a time. We illustrate the procedure and show quantitative agreement with exact numerical simulations for chains with smoothly varying granular profiles. For some more complex configurations (specifically, for decorated chains) we first replace the actual chain with a chain of smooth profile with renormalized masses and intergranular interactions. The binary collision approximation is then applied to this effective chain. Quantitative agreement with numerical simulations of the original chain is again shown. Further applications of the approach are briefly mentioned.