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ABSTRACT: We present numerical results for a chemical reaction of colloidal particles
which are transported by a laminar fluid and are focused by periodic obstacles
in such a way that the two components are well mixed and consequently the
chemical reaction is speeded up. The roles of the various system parameters
(diffusion coefficients, reaction rate, obstacles sizes) are studied. We show
that focusing speeds up the reaction from the diffusion limited rate (t to the
power -1/2) to very close to the perfect mixing rate, (t to the power -1).
12/2012;
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ABSTRACT: Non-interacting Brownian particles obey Langevin equations fulfilling a fluctuation–dissipation relation between friction
and thermal noise. Under a linear potential (constant force) Einstein found a relation between diffusion and transport through
mobility. In nonlinear potentials this prediction is only satisfied within the limits of very small and large constant external
forces. Moreover, other more interesting behaviors do appear, such as: dispersionless transport, sorting, giant diffusion,
subdiffusion, superdiffusion, subtransport, etc. All these phenomena depend on the characteristics of the nonlinear potential
landscape: periodic or random, the symmetries and boundary conditions. Moreover, the presence of transport is the keystone
of most of this phenomenology. In this review, we present numerical simulations illustrating these facts and theoretical analysis
when possible.
The European Physical Journal Special Topics 04/2012; 187(1):49-62. · 1.56 Impact Factor
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ABSTRACT: We carry out a detailed study of the motion of particles driven by a constant external force over a landscape consisting of a periodic potential corrugated by a small amount of spatial disorder. We observe anomalous behavior in the form of subdiffusion and superdiffusion and even subtransport over very long time scales. Recent studies of transport over slightly random landscapes have focused only on parameters leading to normal behavior, and while enhanced diffusion has been identified when the external force approaches the critical value associated with the transition from locked to running solutions, the regime of anomalous behavior had not been recognized. We provide a qualitative explanation for the origin of these anomalies, and make connections with a continuous time random walk approach.
Physical Review Letters 03/2011; 106(9):090602. · 7.37 Impact Factor
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ABSTRACT: We uncover and characterize different chaotic transport scenarios in perfect two-dimensional periodic potentials by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect (i.e., with no directed transport by symmetry breaking of zero-mean forces). After identifying relevant symmetries of the equations of motion, analytical estimates in parameter space for the occurrence of different transport scenarios are provided and confirmed by numerical simulations. These scenarios are highly sensitive to variations of the system's asymmetry parameters, including the eccentricity of the two-dimensional periodic potential and the direction of dc and ac forces, which could be useful for particle sorting purposes in those cases where chaos is unavoidable.
Physical Review E 10/2010; 82(4 Pt 2):046207. · 2.26 Impact Factor
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ABSTRACT: We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying relevant {\it symmetries} of chaotic solutions, analytical estimates in parameter space for the occurrence of different transport scenarios are provided and confirmed by numerical simulations. These scenarios are highly sensitive to variations of the system's asymmetry parameters, including the eccentricity of the periodic surface and the direction of dc and ac forces, which could be useful for particle sorting purposes in those cases where chaos is unavoidable.
03/2010;
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ABSTRACT: Transport and diffusion of particles on modulated surfaces is a nonequilibrium problem which is receiving a great deal of attention due to its technological applications, but analytical calculations are scarce. In earlier work, we developed a perturbative approach to begin to provide an analytic platform for predictions about particle trajectories over such surfaces. In some temperature and forcing regimes, we successfully reproduced results for average particle velocities obtained from numerical simulations. In this paper, we extend the perturbation theory to the calculation of higher moments, in particular the diffusion tensor and the skewness. Numerical simulations are used to check the domain of validity of the perturbative approach.
Physical Review E 08/2009; 80(2 Pt 1):021123. · 2.26 Impact Factor
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ABSTRACT: Using numerical methods the authors study the annihilation reactions A+A-->0 and A+B-->0 in one and two dimensions in the presence of inertial contributions to the motion of the particles. The particles move freely following Langevin dynamics at a fixed temperature. The authors focus on the role of friction.
The Journal of Chemical Physics 11/2007; 127(17):174506. · 3.33 Impact Factor
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ABSTRACT: We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.
Physical Review Letters 02/2007; 98(2):020602. · 7.37 Impact Factor
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ABSTRACT: We propose a set of Langevin equations of motion together with a reaction rule for the study of binary reactions. Our scheme is designed to address this problem for arbitrary friction γ and temperature T. It easily accommodates the inclusion of a substrate potential, and it lends itself to straightforward numerical integration. We test this approach on diffusion-limited () as well as ballistic (γ = 0) reactions for which there are extensive exact and approximate theoretical results as well as extensive Monte Carlo results. We reproduce the known results using our integration scheme, and also present new results for the ballistic reactions.
Journal of Physics Condensed Matter 01/2007; 19(6):065108. · 2.55 Impact Factor
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ABSTRACT: A simple model of a stochastic bistable medium is analytically shown to exhibit pulse propagation sustained by external spatiotemporal noise. In particular, signal transmission is seen to be optimal for a certain nonzero value of the noise intensity, which can be determined theoretically. Numerical simulations confirm the analytical predictions. This property of noise enables the use of the bistable medium as an information channel through which a continuous (in general nonperiodic) string of bits can be transmitted.
EPL (Europhysics Letters) 01/2007; 50(4):427. · 2.17 Impact Factor
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ABSTRACT: There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.
Physical Review E 05/2006; 73(4 Pt 1):041102. · 2.26 Impact Factor
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ABSTRACT: An inchworm processive mechanism is proposed to explain the motion of dimeric molecular motors such as kinesin. We present here preliminary results for this mechanism focusing on observables like mean velocity, coupling ratio and efficiency versus ATP concentration and the external load F. Comment: 6 pages, 2 figures
02/2006;
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ABSTRACT: We study the interaction between two independent nonlinear oscillators competing through a neutral excitable element. The first oscillator, completely deterministic, acts as a normal pacemaker sending pulses to the neutral element which fires when it is excited by these pulses. The second oscillator, endowed with some randomness, though unable to make the excitable element to beat, leads to the occasional suppression of its firing. The missing beats or errors are registered and their statistics analyzed in terms of the noise intensity and the periods of both oscillators. This study is inspired in some complex rhythms such as a particular class of heart arrhythmia.
Physical Review E 02/2006; 73(1 Pt 2):016206. · 2.26 Impact Factor
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ABSTRACT: We present a model that allows for the derivation of the experimentally accessible observables: spatial steps, mean velocity, stall force, useful power, efficiency and randomness, etc. as a function of the [adenosine triphosphate] concentration and an external load F. The model presents a minimum of adjustable parameters and the theoretical predictions compare well with the available experimental results.
Physical Review E 10/2005; 72(3 Pt 1):031918. · 2.26 Impact Factor
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ABSTRACT: Particles moving on crystalline surfaces and driven by external forces or flow fields can acquire velocities along directions that deviate from that of the external force. This effect depends upon the characteristics of the particles, most notably particle size or particle index of refraction, and can therefore be (and has been) used to sort different particles. We introduce a simple model for particles subject to thermal fluctuations and moving in appropriate potential landscapes. Numerical results are compared to recent experiments on landscapes produced with holographic optical tweezers and microfabricated technology. Our approach clarifies the relevance of different parameters, the direction and magnitude of the external force, particle size, and temperature.
Physical Review Letters 05/2005; 94(16):160601. · 7.37 Impact Factor
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ABSTRACT: We present a numerical study of classical particles obeying a Langevin equation and moving on a solid crystalline surface under an external force that may either be constant or modulated by periodic oscillations. We focus on the particle drift velocity and diffusion. The roles of friction and equilibrium thermal fluctuations are studied for two nonlinear dynamical regimes corresponding to low and to high but finite friction. We identify a number of resonances and antiresonances, and provide phenomenological interpretations of the observed behaviour.
New Journal of Physics 01/2005; 7(1):29. · 4.18 Impact Factor
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ABSTRACT: Particles moving on perfect periodic surfaces under the influence of external forces may move along directions that deviate from that of the force. We briefly recall previous results for transport of particles on surfaces with periodic traps or periodic obstacles driven by a constant external force, and present new results for particles moving in a harmonic periodic potential. The sorting properties are explored as a function of a number of control parameters, specifically the friction, force amplitude and direction, temperature, and lattice constants.
J. Phys.: Condens. Matter. 01/2005; 17:4151-4163.
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Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series; 01/2005
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ABSTRACT: We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.
Physical Review E 12/2004; 70(5 Pt 1):051104. · 2.26 Impact Factor
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ABSTRACT: We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two-dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.
Physical Review Letters 07/2004; 92(25 Pt 1):250601. · 7.37 Impact Factor
