Chaos Synchronization Using Active Control and Backstepping Control: A Comparative Analysis

This paper examines the synchronization performance of two widely used chaos synchronization techniques: active control and backstepping control. It is shown that the two methods have excellent performance, with the active control marginally outperforming the backstepping control in terms of transient analysis. However, the complexity of active controllers suggests that the backstepping control would be more attainable in engineering applications

Synchronization and Control of directed transport in chaotic ratchets via active control,” Phys

Abstract Using a technique derived from nonlinear control theory, we demonstrate that two identical inertial ratchets transporting particles in two directions can be synchronized such that both ratchets transport particles in a desired direction. This novel approach to control of directed transport is applicable when there are multiple co-existing attractors in phase space transporting particles in different directions. Numerical simulations are employed to illustrate the approach

Artificial Brownian motors: Controlling transport on the nanoscale

In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with symmetric external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases, one speaks of "Brownian motors". In this review the constructive role of Brownian motion is exemplified for various one-dimensional setups, mostly inspired by the cell molecular machinery: working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are reviewed with particular attention to transport in artificial nanopores and optical traps, where single particle currents have been first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented hereby. Another area with promising potential for realization of artificial Brownian motors are microfluidic or granular set-ups.....Comment: 57 pages, 39 figures; submitted to Reviews Modern Physics, revised versio

Cooperative surmounting of bottlenecks

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport

Dinámica estocástica en física y biología

Tesis de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Estructura de la Materia, Física Térmica y Electrónica, leída el 26-10-2018Stochastic processes are present in virtually any field of science. Actually, in general deterministic processes are no more than an approximation of more complex stochastic processes in some regime of validity. In the present thesis, we will study some systems that appear in Physics and Biology where the presence of these stochastic processes plays a major role. First, we will study the Brownian ratchet systems, which are able to generate a directed motion simply by rectifying the thermal fluctuations to which Brownian particles are subjected. These Brownian ratchets began to be studied in the field of Statistical Physics as a Gedanken experiment that apparently broke the Second Law of Thermodynamics. Later they were applied to study the operation of some molecular motors. In this thesis we will study different types of Brownian ratchets, characterizing the average flux, the efficiency, and the quality of the transport of particles they produce..En prácticamente cualquier rama de la ciencia están presentes los procesos estocásticos. De hecho, en general los procesos deterministas no son más que una aproximación de procesos estocásticos más complejos en algún régimen de validez. En la presente tesis, estudiaremos algunos sistemas que aparecen en Física y Biología donde la presencia de dichos procesos es crucial.Primero, estudiaremos los conocidos como trinquetes brownianos, que son capaces de generar movimiento dirigido simplemente a través de la rectificación de las fluctuaciones térmicas a las que se ven sometidas las partículas Brownianas. Estos trinquetes Brownianos se empezaron a estudiar en el campo de la Física Estadística como un experimento mental que aparentemente rompía la Segunda Ley de la Termodinámica. Sin embargo, más adelante se ha visto que pueden ser aplicados para estudiar el funcionamiento de algunos motores moleculares. En esta tesis estudiaremos distintos tipos de trinquetes Brownianos, caracterizando el flujo medio, la eficiencia, y la calidad del transporte de partículas que producen...Depto. de Estructura de la Materia, Física Térmica y ElectrónicaFac. de Ciencias FísicasTRUEunpu

Separation and collective phenomena of colloidal particles in Brownian ratchets

Ph.DDOCTOR OF PHILOSOPH