Optimal transport in a ratchet coupled to a modulated environment: The role of Levy walks

We consider a Brownian particle in a ratchet potential coupled to a modulated environment and subjected to an external oscillating force. The modulated environment is modelled by a finite number N of uncoupled harmonic oscillators. Superdiffusive motion and Levy walks (anomalous random walks) are observed for any N and for low values of the external amplitude F. The coexistence of left and right running states enhances the power α from the time dependence of the mean square displacement (MSD). It is shown that α is twice the average of the power of the separated left and right MSDs. Normal random walks are obtained by increasing F. We show that the maximal mobility of particles along the periodic structure occurs just before superdiffusive motion disappears and Levy walks are transformed into normal random walks.     

Anomalous transport controlled via potential fluctuations

In this paper, we investigate the transport of an inertial Brownian motor moving in an asymmetric periodic potential, where it is driven by a time periodic and a constant biasing driving force, and potential fluctuations generated by a Gaussian white noise. It is found that some anomalous transports (ATs) appear in the presence of the potential fluctuations. For smaller potential fluctuations, we detect that the phenomenons of absolute negative mobility (ANM) near zero bias, and negative nonlinear mobility (NNM) at larger bias away from equilibrium, which means that the inertial Brownian motor moves opposite to the bias force in the two parameter regimes. However for larger potential fluctuations, the phenomenons of both the ANM and NNM vanish. Furthermore, the asymmetry of the potential can also cause the ATs (i.e., both ANM and NNM) to disappear.     

Forcing inertial Brownian motors: Efficiency and negative differential mobility

The noise-assisted, directed transport in a one-dimensional dissipative, inertial Brownian motor of the rocking type that is exposed to an external bias is investigated. We demonstrate that the velocity–load characteristics is distinctly non-monotonic, possessing regimes with a negative differential mobility. In addition, we evaluate several possible efficiency quantifiers which are compared among each other. These quantifiers characterize the mutual interplay between the viscous drag and the external load differently, weighing the inherent rectification features from different physical perspectives.     

Absolute negative mobility induced by thermal equilibrium fluctuations

A novel transport phenomenon is identified that is induced by inertial Brownian particles which move in simple one-dimensional, symmetric periodic potentials under the influence of both a time periodic and a constant, biasing driving force. Within tailored parameter regimes, thermal equilibrium fluctuations induce the phenomenon of absolute negative mobility (ANM), which means that the particle noisily moves backwards against a small constant bias. When no thermal fluctuations act, the transport vanishes identically in these tailored regimes. ANM can also occur in the absence of fluctuations on grounds which are rooted solely in the complex, inertial deterministic dynamics. The experimental verification of this new transport scheme is elucidated for the archetype symmetric physical system: a convenient setup consisting of a resistively and capacitively shunted Josephson junction device.     

Resonant current in coupled inertial Brownian particles with delayed-feedback control

The transport of a walker in rocking feedback-controlled ratchets is investigated. The walker consists of two coupled “feet” that allow the interchange of the order of particles while the walker moves. In the underdamped case, the deterministic dynamics of the walker in a tilted asymmetric ratchet with an external periodic force is considered. It is found that delayed feedback ratchets with a switching-onand-off dependence of the states of the system can lead to absolute negative mobility. In such a novel phenomenon, the particles move against the bias. Moreover, the walker can acquire a series of resonant steps for different values of the current. It is interesting to find that the resonant currents of the walker are induced by the phase locked motion that corresponds to the synchronization of the motion with the change in the frequency of the external driving. These resonant steps can be well predicted in terms of time-space symmetry analysis, which is in good agreement with dynamics simulations. The transport performances can be optimized and controlled by suitably adjusting the parameters of the delayed-feedback ratchets.     

Adiabatic Brownian ratchets with the inclusion of inertia

Inertial corrections to the drift velocity of a Brownian particle have been calculated for two main classes of Brownian ratchets operating in the adiabatic regime of fluctuations of the potential energy: first, the stationary periodic potential and dichotomic fluctuations of an external force with zero average value (rocking ratchet) and, second, dichotomic fluctuations of the periodic potential itself. It has been shown that, in contrast to passive transport at which the inertial correction always reduces the effective mobility and diffusion coefficients, inertial corrections for Brownian ratchets can play a constructive role, increasing the drift velocity at least at high temperatures.     

Synchronization, anti-synchronization and current transports in non-identical chaotic ratchets

The synchronization (CS) and anti-synchronization (AS) of two non-identical inertial ratchets moving in different asymmetric potentials and transporting particles chaotically is demonstrated based on a technique derived from nonlinear control theory. It is shown that in the CS state, particle current is enhanced; while in the AS state, the particles transport current in different directions, suggesting that AS phenomenon could be exploited as a mechanism for particle separation.     

Experimental control of transport and current reversals in a deterministic optical rocking ratchet

We present an experimental demonstration of a deterministic optical rocking ratchet. A periodic and asymmetric light pattern is created to interact with dielectric microparticles in water, giving rise to a ratchet potential. The sample is moved with respect to the pattern with an unbiased time-periodic rocking function, which tilts the potential in alternating opposite directions. We obtain a current of particles whose direction can be controlled in real time and show that particles of different sizes may experience opposite currents. Moreover, we observed current reversals as a function of the magnitude and period of the rocking force.     

Anomalous transport and diffusion phenomena induced by biharmonic forces in deformable potential systems

We study transport properties of an inertial Brownian motor which moves in a deformable Remoissenet-Peyrad periodic potential and is subjected to both a static bias force and time periodic driving biharmonic force. By modifying the shape of the potential, the anomalous transport is identified for a particular set of the system parameters. For a particular potential shape, the mean velocity of a particle is modified by going from negative to positive values according to the external bias force. These features also depend on both the biharmonic parameter and the phase-lag of two signals. A remarkable transition of the negative velocity depending on the shape of the potential is observed. We also focus on the efficiency of the motor and discuss velocity fluctuation. In addition, within selected system parameters, different types of diffusion particle such as subdiffusion, superdiffusion, normal diffusion, ballistic diffusion, hyperdiffusion and dispersionless transport phenomena are generated in the system.     

Anomalous diffusion with absorption: exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a nonextensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion, and the absorption process are discussed.     

Non-Smooth Bifurcation and Chaos in a DC-DC Buck Converter

A direct-current-direct-current （DC-DC） buck converter with integrated load current feedback is studied with three kinds of Poincaré maps. The external corner-collision bifurcation occurs when the crossing number per period varies, and the internal corner-collision bifurcations occur along with period-doubling and period-tripling bifurcations in this model. The multi-band chaos roots in external corner-collision bifurcation and often grows into 1-band chaos. A new kind of chaotic sliding orbits, which is more complex for non-smooth systems, is also found in this model.     

Simple stochastic models showing strong anomalous diffusion

We show that strong anomalous diffusion, i.e. where is a nonlinear function of q, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of systems it is possible to compute analytically where n is an integer number. The presence of strong anomalous diffusion implies that the data collapse of the probability density function cannot hold, a part (sometimes) in the limit of very small , now . Moreover the comparison with previous numerical results shows that the shape of is not universal, i.e., one can have systems with the same but different F. Received 14 April 2000     

Uphill anomalous transport in a deterministic system with speed-dependent friction coefficient

We investigate the transport of a deterministic Brownian particle theoretically, which moves in simple onedimensional, symmetric periodic potentials under the influence of both a time periodic and a static biasing force. The physical system employed contains a friction coefficient that is speed-dependent. Within the tailored parameter regime, the absolute negative mobility, in which a particle can travel in the direction opposite to a constant applied force, is observed.This behavior is robust and can be maximized at two regimes upon variation of the characteristic factor of friction coefficient. Further analysis reveals that this uphill motion is subdiffusion in terms of localization(diffusion coefficient with the form D(t) ~t~(-1) at long times). We also have observed the non-trivially anomalous subdiffusion which is significantly deviated from the localization; whereas most of the downhill motion evolves chaotically, with the normal diffusion.     

Current Reversals of an Underdamped Brownian Particle in an Asymmetric Deformable Potential

Transport of an underdamped Brownian particle in a one-dimensional asymmetric deformable potential is investigated in the presence of both an ac force and a static force,respectively.From numerical simulations,we obtain the current average velocity.The current reversals and the absolute negative mobility are presented.The increasing of the deformation of the potential can cause the absolute negative mobility to be suppressed and even disappear.When the static force is small,the increase of the potential deformation suppresses the absolute negative mobility.When the force is large,the absolute negative mobility disappears.In particular,when the potential deformation is equal to0.015,the two current reversals present with the increasing of the force.Remarkably,when the potential deformation is small,there are three current reversals with the increasing of the friction coefficient and the average velocity presents a oscillation behavior.     

Numerical studies on boundary effects on the FPU paradox

We study numerically the dynamics of a chain of particles subjected to an on site restoring nonlinear force and a first neighbor harmonic coupling. We excite the first linear mode and investigate the distribution of the average harmonic energies at metastable regime, in the spirit of Fermi Pasta Ulam experiment. The limit distribution turns out to strongly depend on the boundary conditions. A theoretical discussion of the phenomenon is also given.     

Stochastic resonance in time-delayed bistable systems driven by weak periodic signal

We study theoretically a bistable system with time-delayed feedback driven by a weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of the signal. The maximum of SNR decreases with increasing the feedback intensity ?. When ? is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon.     

Negative mobility and multiple current reversals induced by colored thermal fluctuation in an asymmetric periodic potential

The phenomena of negative mobility (NM) and multiple current reversals (MCR) are investigated numerically in an asymmetric periodic potential with a Gaussian colored noise under the influence of a periodic driving and a constant bias. Two cases have been considered: the case of noise-induced normal transport and the case of noise-induced anomalous transport. The results indicate: (1) within tailored parameter regimes, a robust and wide range of NM can be obtained for a fixed regime of correlation time; (2) nonzero correlation time can induce and diminish MCR; (3) the asymmetry can induce and significantly facilitate the anomalous transport of inertial Brownian particle.     

Current transport and mass separation for an asymmetric fluctuation system with correlated noises

We discuss the transport of an underdamped particle driven by an external fluctuation force in a spatially periodic asymmetric potential with correlated noises. The corresponding mathematical model is established. The movement of the steady current of an underdamped particle is presented by the method of the numerical simulation. It is indicated that the value of the current may be negative, zero, or positive. The external fluctuation force and correlated noises can effect the current direction. Under the appropriate parameters, the correlated noises intensity may even raise a reversal of the current.Besides, we have noticed a phenomenon that particles with different weight have different directions during movement by the impact of the correlated noises and external fluctuation force. Therefore, the Brownian particles can be effectively separated according to their masses.     

非高斯噪声对惯性棘轮中粒子负迁移率的影响

利用随机模拟方法研究了惯性棘轮中非高斯噪声对负迁移率的影响. 分别模拟了绝对负迁移率(ANM), 非线性迁移率(NNM) 和负微分迁移率(NDM) 等三种反常输运现象. 计算结果表明: 1) 在不同的参数空间里, 非高斯噪声参数q 能够增强或者削弱ANM, 诱导NNM 和NDM; 2) 当q 较大时, 反常输运现象转化为正常输运; 3) 随着q 逐渐增大, 平均速度- 关联时间特性曲线朝着关联时间较小的方向移动并且其峰值逐渐减小. 关键词： 反常输运 负迁移率 非高斯噪声     

Wave Grouping of a Drifting Spiral Wave in the Presence of an External Field

The phenomenon of wave grouping, in which the dense waves and the sparse waves can form groups in front of the spiral tip when the spiral wave is meandering, has been reported in a chemical reaction system recently. We present a method to realize the phenomenon of wave grouping by applying an external field to the system. The numerical simulations are carried out on the basis of the FitzHugh-Nagumo equations.