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ABSTRACT: The motion of self-propelled particles can be rectified by asymmetric or
ratchet-like periodic patterns in space. Here we show that a non-zero average
drift can already be induced in a periodic potential with symmetric barriers
when the self-propulsion velocity is also symmetric and periodically modulated
but phase-shifted against the potential. In the adiabatic limit of slow
rotational diffusion we determine the mean drift analytically and discuss the
influence of temperature. In the presence of asymmetric barriers modulating the
self-propulsion can largely enhance the mean drift or even reverse it.
02/2013;
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ABSTRACT: We investigate a driven, one-dimensional system of colloidal particles in a
periodically currogated narrow channel subject to a time-delayed feedback
control. Our goal is to identify conditions under which the control induces
oscillatory, time-periodic states. The investigations are based on the
Fokker-Planck equation involving the density distribution of the system. First,
by using the numerical continuation technique, we determine the linear
stability of a stationary density. Second, the nonlinear regimes are analyzed
by studying numerically the temporal evolution of the first moment of the
density distribution. In this way we construct a bifurcation diagram revealing
the nature of the instability. Apart from the case of a system with periodic
boundary conditions, we also consider a microchannel of finite length. Finally,
we study the influence of (repulsive) particle interactions based on Dynamical
Density Functional Theory (DDFT).
09/2012;
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ABSTRACT: We consider the unidirectional particle transport in a suspension of colloidal particles which interact with each other via a pair potential having a hard-core repulsion plus an attractive tail. The colloids are confined within a long narrow channel and are driven along by a dc or an ac external potential. In addition, the walls of the channel interact with the particles via a ratchetlike periodic potential. We use dynamical density functional theory to compute the average particle current. In the case of dc drive, we show that as the attraction strength between the colloids is increased beyond a critical value, the stationary density distribution of the particles loses its stability leading to depinning and a time-dependent density profile. Attraction induced symmetry breaking gives rise to the coexistence of stable stationary density profiles with different spatial periods and time-periodic density profiles, each characterized by different values for the particle current.
Physical Review E 06/2011; 83(6 Pt 1):061401. · 2.26 Impact Factor
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ABSTRACT: We consider a two-dimensional gas of colliding charged particles confined to
finite size containers of various geometries and subjected to a uniform
orthogonal magnetic field. The gas spectral densities are characterized by a
broad peak at the cyclotron frequency. Unlike for infinitely extended gases,
where the amplitude of the cyclotron peak grows linearly with temperature, here
confinement causes such a peak to go through a maximum for an optimal
temperature. In view of the fluctuation-dissipation theorem, the reported
resonance effect has a direct counterpart in the electric susceptibility of the
confined magnetized gas.
05/2011;
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ABSTRACT: Relativistic Brownian motion can be inexpensively demonstrated on a graphene
chip. The interplay of stochastic and relativistic dynamics, governing the
transport of charge carrier in graphene, induces noise-controlled effects such
as (i) a stochastic effective mass, detectable as a suppression of the particle
mobility with increasing the temperature; (ii) a transverse ratchet effect,
measurable as a net current orthogonal to an ac drive on an asymmetric
substrate, and (iii) a chaotic stochastic resonance. Such properties can be of
practical applications in the emerging graphene technology.
03/2011;
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ABSTRACT: The rectification of a single file of attracting particles subjected to a low
frequency ac drive is proposed as a working mechanism for particle shuttling in
an asymmetric narrow channel. Increasing the particle attraction results in the
file condensing, as signalled by the dramatic enhancement of the net particle
current. Magnitude and direction of the current become extremely sensitive to
the actual size of the condensate, which can then be made to shuttle between
two docking stations, transporting particles in one direction, with an
efficiency much larger than conventional diffusive models predict.
04/2010;
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ABSTRACT: We consider an elastic neutral dimer formed by two bound equal masses carrying opposite charges and moving along an electrically active filament in one dimension. An ac electrical field drives the two dimer heads, when set free or bound together to form a rigid rod, to opposite directions, thus yielding a zero net dimer current for zero and infinite elastic constants. Under the same driving conditions, an elastically deformable dimer can get rectified and the ensuing net current maximized for an optimal value of dimer elastic constant. The dependence of the dimer current on the periodic charge distribution along the filament is analyzed in terms of global symmetries of the dimer dynamics.
Physical Review E 03/2010; 81(3 Pt 1):031114. · 2.26 Impact Factor
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ABSTRACT: We consider a network of deterministic and stochastic locally coupled oscillators with positive or negative dissipation and local time-delayed feedback. (i) For a deterministic system, we study propagation of waves through the network. We show that time delay leads to a coexistence of several neutral modes with different wave numbers and group velocities, which we compute analytically. (ii) For noisy system, we study the response of the network to external random forcing correlated in space and uncorrelated in time. Below the threshold of spatial instability, noise induces spatiotemporal fluctuations, which can be characterized by the structure function. We give an analytical expression for the structure function and demonstrate the effect of the time delay and of the correlation length of noise on the wave number of the most excited mode.
Physical Review E 12/2009; 80(6 Pt 2):066203. · 2.26 Impact Factor
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ABSTRACT: We present an approach for the analytical treatment of excitable systems with noise-induced dynamics in the presence of time delay. An excitable system is modeled as a bistable system with a time delay, while another delay enters as a control term taken after Pyragas [K. Pyragas, Phys. Lett. A 170, 421 (1992)] as a difference between the current system state and its state tau time units before. This approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term.
Physical Review E 04/2008; 77(3 Pt 1):031113. · 2.26 Impact Factor
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ABSTRACT: Here we address the effect of large delay on the statistical characteristics of noise-induced oscillations in a nonlinear system below Andronov-Hopf bifurcation. In particular, we introduce a theory of these oscillations that does not involve the eigenmode expansion, and can therefore be used for arbitrary delay time. In particular, we show that the correlation matrix (CM) oscillates on two different time scales: on the scale of the main period of noise-induced oscillations, and on the scale close to the delay time. At large values of the delay time, the CM is shown to decay exponentially only for large values of its argument, while for the arguments comparable with the value of the delay, the CM remains finite disregarding the delay time. The definition of the correlation time of the system with delay is discussed.
Physical Review E 12/2007; 76(5 Pt 2):056208. · 2.26 Impact Factor
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ABSTRACT: We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100-nm thickness, or due to temperature-gradient-caused Marangoni flows in the heated case. Using a long-wave approximation, we derive coupled evolution equations for the interface profiles for the general nonisothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers, taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag, or mixed type. However, in the nonlinear stage of the evolution the mode type, and therefore the pattern morphology, can change via switching between two different branches of stationary solutions or via coarsening along a single branch.
The Journal of Chemical Physics 07/2005; 122(22):224711. · 3.33 Impact Factor
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ABSTRACT: We consider two stacked ultrathin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Depending on the long-range van der Waals forces and the ratio of the layer thicknesses, the system follows different pathways of dewetting. The instability may be driven by varicose or zigzag modes and leads to film rupture either at the liquid-gas interface or at the substrate. We predict that the faster layer drives the evolution and may accelerate the rupture of the slower layer by orders of magnitude, thereby promoting the rupture of rather thick films.
Physical Review E 09/2004; 70(2 Pt 2):025201. · 2.26 Impact Factor
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ABSTRACT: We consider two stacked ultra-thin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Linear and non-linear analyses show that depending on the long-range van-der-Waals forces and the ratio of the layer thicknesses, the system follows different pathways of dewetting. The instability may be driven by varicose or zigzag modes and leads to film rupture either at the liquid-gas interface or at the substrate.
01/2004;
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ABSTRACT: We propose two methods to control the structuring of unstable thin films of soft matter. The first one is a non-contact method, where an external disturbance can be used to move a single drop, front or hole in a certain direction. The principle is illustrated by incorporating a sonic disturbance in a thin film equation to study the evolution of ultrathin films unstable due to their wetting properties. The second one is based on inhomogeneous templating of the substrate. Here, we study the influence of periodic modulation on coarsening in the long-time limit. Finally, the fully nonlinear evolution of a 3D system is presented by numerical integration.
Physica D: Nonlinear Phenomena.
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ABSTRACT: We study synchronization as a means of control of collective behavior of an ensemble of coupled stochastic units in which oscillations are induced merely by external noise. For a large number of one-dimensional continuous stochastic elements coupled non-homogeneously through the mean field with delay we developed an approach to find a boundary of synchronization domain and the frequency of the mean-field oscillations on it. Namely, the exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker–Planck equation. Here the synchronization threshold is found by solving this BVP numerically. Approximate analytics is obtained by expanding the solution of the linearized Fokker–Planck equation into a series of eigenfunctions of the stationary Fokker–Planck operator. Bistable systems with a polynomial and piece-wise linear potential are considered as examples. Multistability and hysteresis in the mean-field behavior are observed in the stochastic network at finite noise intensities. In the limit of small noise intensities the critical coupling strength is shown to remain finite, provided that the delay in the coupling function is not infinitely small. Delay in the coupling term can be used as a control parameter that manipulates the location of the synchronization threshold.
Physica D: Nonlinear Phenomena.
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ABSTRACT: ¡ (t) in the sense of the averaging over all possible histories U are introduced. Based on this concept we derive an equation for the equilibriumeq ¡ (t) which is valid for an arbitrary delay time ¿1 ˆeq ¡ (t) = Z u2U P(ˆ eq ¡ (u))ˆ u ¡(t)du.
