arXiv subjects

Rodolfo R. Rosales

Publications and source records attributed to Rodolfo R. Rosales.

12 recordsLinked to original sources

arXiv2026

Anomalous interference drives oscillatory dynamics in wave-dressed active particles

A recent surge of discoveries has sparked significant interest in active systems where a particle moves autonomously in resonance with its self-generated wave field, leading to notable wave-mediated effects including new propulsion mechanisms, self-sustained speed modulations, and quantum-like phenomena. Drawing from walking droplets, an archetypical model of wave-dressed active particles, we identify a wave-mediated non-local force driving their oscillatory dynamics, arising from the particle's path memory and an unconventional form of wave interference near jerking points, locations where the particle's velocity changes rapidly. In contrast to the typical case of constructive interference at points of stationary phase, waves excited by the particle near jerking points avoid cancellation through rapid changes in frequency. Through an asymptotic analysis, we derive the wave force from jerking points, revealing it as an exponentially small yet crucial remnant of the particle's past motion. This previously unrecognized force underlies a range of phenomena that have thus far been treated independently, including in-line speed oscillations, wave-like statistics in potential wells, and non-specular reflections, thereby unifying them within a common framework rooted in generic wave superposition principles.

cond-mat.soft↗

arXiv2020

A discrete complex Ginzburg-Landau equation for a hydrodynamic active lattice

A discrete and periodic complex Ginzburg-Landau equation, coupled to a discrete mean equation, is systematically derived from a driven and dissipative oscillator model, close to the onset of a supercritical Hopf bifurcation. The oscillator model is inspired by recent experiments exploring active vibrations of quasi-one-dimensional lattices of self-propelled millimetric droplets bouncing on a vertically vibrating fluid bath. Our systematic derivation provides a direct link between the constitutive properties of the lattice system and the coefficients of the resultant amplitude equations, paving the way to compare the emergent nonlinear dynamics---namely discrete bright and dark solitons, breathers, and traveling waves---against experiments. Further, the amplitude equations allow us to rationalize the successive bifurcations leading to these distinct dynamical states. The framework presented herein is expected to be applicable to a wider class of oscillators characterized by the presence of a dynamic coupling potential between particles. More broadly, our results point to deeper connections between nonlinear oscillators and the physics of active and driven matter.

nlin.PS↗

arXiv2020

Collective vibrations of a hydrodynamic active lattice

Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling.By modelling the droplet lattice as a memory-endowed system with spatially nonlocal coupling, we herein rationalise the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or sub-critical Hopf bifurcation \emph{via} a systematic weakly nonlinear analysis, rationalising experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory-rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system.

physics.flu-dyn↗

arXiv2017

Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we propose to match at the level of the equations involved, via a "uniform expansion" whose equations enfold those of the approximations to be matched. This has the advantage that one does not need to explicitly solve the asymptotic equations to do the matching, which can be quite impossible for some problems. In addition, it allows matching to proceed in certain wave situations where the traditional approach fails because the time behaviors differ (e.g., one of the expansions does not include dissipation). On the other hand, this approach does not provide the fairly explicit approximations resulting from standard matching. In fact, this is not even its aim, which to produce the "simplest" set of equations that capture the behavior.

physics.flu-dyn↗

arXiv2015

Study of a model equation in detonation theory: multidimensional effects

We extend the reactive Burgers equation presented in Kasimov et al. Phys. Rev. Lett., 110 (2013) and Faria et al. SIAM J. Appl. Maths, 74 (2014), to include multidimensional effects. Furthermore, we explain how the model can be rationally justified following the ideas of the asymptotic theory developed in Faria et al. JFM (2015). The proposed model is a forced version of the unsteady small disturbance transonic flow equations. We show that for physically reasonable choices of forcing functions, traveling wave solutions akin to detonation waves exist. It is demonstrated that multidimensional effects play an important role in the stability and dynamics of the traveling waves. Numerical simulations indicate that solutions of the model tend to form multi-dimensional patterns analogous to cells in gaseous detonations.

math.AP↗

arXiv2014

Theory of weakly nonlinear self sustained detonations

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations.

physics.flu-dyn↗

arXiv2013

Study of a model equation in detonation theory

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales. Model for shock wave chaos. Physical Review Letters, 110(10):104104, 2013]. The equation is \[ u_{t}+\frac{1}{2}\left(u^{2}-uu\left(0_{-},t\right)\right)_{x}=f\left(x,u\left(0_{-},t\right)\right),\quad x\le0,\quad t>0. \] It describes a detonation shock at $x=0$ with the reaction zone in $x<0$. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos.

nlin.CD↗

arXiv2012

A model for shock wave chaos

We propose the following model equation: \[u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}), \] that predicts chaotic shock waves. It is given on the half-line $x<0$ and the shock is located at $x=0$ for any $t\ge0$. Here $u_{s}(t)$ is the shock state and the source term $f$ is assumed to satisfy certain integrability constraints as explained in the main text. We demonstrate that this simple equation reproduces many of the properties of detonations in gaseous mixtures, which one finds by solving the reactive Euler equations: existence of steady traveling-wave solutions and their instability, a cascade of period-doubling bifurcations, onset of chaos, and shock formation in the reaction zone.

nlin.CD↗

arXiv2008

Self-sustained nonlinear waves in traffic flow

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, termed "jamitons," 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 wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway (Sugiyama et al., New Journal of Physics, 10, 2008), our numerical calculations show that, under appropriate road conditions, jamitons are attracting solutions, with the time evolution of the system converging towards a jamiton-dominated configuration. Jamitons are characterized by a sharp increase in density over a relatively compact section of the roadway. Applications of our analysis to traffic modeling and control are examined by way of a detailed example.

physics.soc-ph↗

arXiv2008

Multirate integration of axisymmetric step-flow equations

We present a multirate method that is particularly suited for integrating the systems of Ordinary Differential Equations (ODEs) that arise in step models of surface evolution. The surface of a crystal lattice, that is slightly miscut from a plane of symmetry, consists of a series of terraces separated by steps. Under the assumption of axisymmetry, the step radii satisfy a system of ODEs that reflects the steps' response to step line tension and step-step interactions. Two main problems arise in the numerical solution of these equations. First, the trajectory of the innermost step can become singular, resulting in a divergent step velocity. Second, when a step bunching instability arises, the motion of steps within a bunch becomes very strongly stable, resulting in "local stiffness". The multirate method introduced in this paper ensures that small time steps are taken for singular and locally stiff components, while larger time steps are taken for the remaining ones. Special consideration is given to the construction of high order interpolants during run time which ensures fourth order accuracy of scheme for components of the solution sufficiently far away from singular trajectories.

math.NA↗

arXiv2008

On "jamitons," self-sustained nonlinear traffic waves

"Phantom jams," traffic blockages that arise without apparent cause, have long frustrated transportation scientists. Herein, we draw a novel homology between phantom jams and a related class of self-sustained transonic waves, namely detonations. Through this analogy, we describe the jam structure; favorable agreement with reported measurements from congested highways is observed. Complementary numerical simulations offer insights into the jams' development. Our results identify conditions likely to result in a dangerous concentration of vehicles and thereby lend guidance in traffic control and roadway design.

math.AP↗

arXiv1995

Mechanisms for Stable Sonoluminescence

A gas bubble trapped in water by an oscillating acoustic field is expected to either shrink or grow on a diffusive timescale, depending on the forcing strength and the bubble size. At high ambient gas concentration this has long been observed in experiments. However, recent sonoluminescence experiments show that in certain circumstances when the ambient gas concentration is low the bubble can be stable for days. This paper presents mechanisms leading to stability which predict parameter dependences in agreement with the sonoluminescence experiments.

chao-dyn↗