Symmetry breaking: Abnormal transport induced by mass modulation.

The phenomena of absolute negative mobility (ANM) and multiple current reversals(MCR) are investigated numerically in an inertial Brownian motor with time-delayedfeedback under the influence of a time-periodic and a constant, biasing drivingforce. Within tailored parameter regimes, the increasing delay time diminishes thenoise-induced ANM and the deterministic ANM while it induces the ANM in anormal transport regime. When an asymmetric parameter is added in the periodicpotential, the presence and absence of MCR are controlled by manipulating the delaytime.

Collective directional transport of particles in symmetric periodic potentials is studied. An example is given to reveal the directed motion of a single particle in a symmetric periodic potential and subject to an asymmetric ac force with zero mean. It is then shown that the asymmetric coupling can give rise to a directed transport. The transport failure (pinning of the lattice) is related to the phase delocalization (crisis) in the circle map. For symmetric couplings, it is found that a train of plane wave can also lead to a directed transport. The mode-locking steps of the transport velocity is found and analyzed. The collective transport can be well optimized by adjusting parameters in the system.

Defect modes are studied in parity-time (PT) symmetric periodic complex potentials for both positive and negative defects. Such new kinds of linear localized modes may conserve their energy or endure gain or loss upon propagating. The existence domain of the conserved modes would be prolonged by positive defects or shortened by negative defects, and the dissipative modes would appear before the phase transition point of the PT symmetric potential at stronger negative defects.

Transport of an inertial Brownian particle driven by the multiplicative Lévy noise was investigated here. Numerical results indicate that: (i) The Lévy noise is able to induce absolute negative mobility (ANM) in the system, while disappearing in the deterministic case; (ii) the ANM can occur in the region of superdiffusion while disappearing in the region of normal diffusion, and the appropriate stable index of the Lévy noise makes the particle move along the opposite direction of the bias force to the maximum degree; (iii) symmetry breaking of the Lévy noise also causes the ANM effect. In addition, the intrinsic physical mechanism and conditions for the ANM to occur are discussed in detail. Our results have the implication that the Lévy noise plays an important role in the occurrence of the ANM phenomenon.

Enhancement of current commensurate with mutual noise–noise correlation in a symmetric periodic substrate: The benefits of noise and nonlinearity

Transport of Brownian particles in a periodic channel coexisting with an energetic barrier is investigated in the presence of a curl-free force and a divergence-free force. It is found that the phase difference between the energetic barrier and the entropic barrier can determine the direction of transport without pressure-driven flow. The pressure-driven flow induces the negative current. When the four driving factors (the ac driving force, the pressure-driven flow, the energetic barrier, and the entropic barrier) compete with each other, the system exhibits peculiar properties. Remarkably, we can obtain multiple current reversals by suitably tailoring the system parameters.

Near-surface Brownian motor with synchronously fluctuating symmetric potential and applied force

Absolute negative mobility and current reversals of a meandering Brownian particle

Ratchet effect in an underdamped periodic potential and its characterisation

We investigate an overdamped Brownian motion in symmetric periodic potential switching by Markovian dichotomous noise between two configurations. Second configuration differs from the first one by the half of spatial period displacement when the maxima of a potential profile become the minima and vice versa. We establish a validity of the formula for effective diffusion constant previously obtained in the case of fixed periodic potentials and, thus, reduce the problem to calculation of mean first-passage times (MFPTs). At the same time the MFPT in this formula should be substituted for the semi-sum of MFPTs regarding two initial configurations of potential profile. A set of equations for MFPTs in flipping potentials can be solved for the sawtooth periodic potential. As a result, after cumbersome calculations we obtain the exact complex expression for effective diffusion coefficient of Brownian particles in such a medium which is valid for arbitrary mean frequency of potential switchings. We detect the acceleration of diffusion in comparison with the case of fixed sawtooth potential profile as it was demonstrated for a symmetric periodic potential modulating by external Gaussian white noise.

Fundamental, dipole, and vortex solitons in fractional nonlinear Schrödinger equation with a parity-time-symmetric periodic potential

Chaos-like properties such as noise or fluctuations arising from quantum effects have recently investigated on a single barrier potential and on a one-dimensional periodic potential barrier. They used either the planewave of light or a wavepacket (pulse) passing through the potential barrier, demonstrating the chaos created by the bounded one-dimensional multibarrier potential (Bar and Horwitz, 2002; Hondou and Sawada, 1995), and proved it is an ordered and periodic phenomenon. Also another group demonstrated unexpected behavior of a dissipative particle in simple multiscale systems subject to chaotic noise and clarified the reason for the particular behavior because it is under a periodic potential (Chialvo et al., 1997). They concluded the occurrence of drift in a symmetric periodic potential would be expected to be a common feature of noise-driven systems. Essentially this effect is quite similar to the problem of a particle placed in a potential well of finite barrier (Cohen-Tannoudji et al., 1977) and the present issue of the photon distribution on a crystallite surface. When the crystallite size decreases to a few nanometers, the light absorption or photoluminescence in air moves to the direction of smaller wavelength, which is known as the blueshift (Kale and Lokhande, 2000; Nanda et al., 1999; Tsunekawa et al., 2003; Von Behren et al., 2000). The basic theory for this phenomenon is the quantum confinement effect (Andersen et al., 2002; Sharma et al., 2005). According to this theory the number of photons confined in each unit cell increases with the decreasing crystallite size. It is also said to enlarge the band gap between the valence band and the conduction band. Another approach is to take crystalline unit cells as numerical elements and employ different potential energies over a unit cell (Choi, 2007; Choi and Kim, 2007), realizing light intensity fluctuations. The effect of the film thickness on the blueshift was investigated by one of the authors (Choi and Pyun, 2008) about cellular crystalline surfaces with periodic potential, getting the blueshift numerically demonstrated in good agreement with experiments. In this paper we deal with surface nanostructures and try to prove the blueshift numerically by predicting the location of absorption wavelength. One of the best ways to uphold the present numerical method would be to demonstrate the blueshift phenomenon observed widely experimentally (Lu et al., 2008; Miyake et al., 1999; Tan et al., 2005; Tsunekawa et al., 2000). They demonstrated experimentally the dependence of the blueshift on the crystallite size for CeO and CdS. One of the authors has been studying this problem recently, publishing a few papers (Choi, 2007; Choi and Kim, 2007; Choi and Pyun, 2008), and this paper may be taken as an extension of these consecutive efforts. Another publication (Choi and Choi, 2009) predicting the blueshift with respect to the shell layer thickness has been already accomplished and led the present investigation to be made. 17

We analyze the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low-friction regime in which the diffusion coefficient shows giant damped quasiperiodic oscillations as a function of the amplitude of the time-periodic force [I. G. Marchenko et al., Chaos 32, 113106 (2022)1054-150010.1063/5.0117902]. We find out that when temperature grows the diffusion coefficient increases at its minima; however, it decreases at the maxima within a finite temperature window. This curious behavior is explained in terms of the deterministic dynamics perturbed by thermal fluctuations and mean residence time of the particle in the locked and running trajectories. We demonstrate that temperature dependence of the diffusion coefficient can be accurately reconstructed from the stationary probability to occupy the running trajectories.

The discharge and plasma plume characteristics of the cylindrical Hall thruster were studied in regimes with external modulations of the applied voltage. It is found that the amplitude and the root mean square (rms) value of the discharge and ion currents increase with the amplitude of the external modulation exhibiting two different regimes. For smaller amplitudes of the modulation voltage, the oscillations amplitude and rms value of the discharge and ion currents follow the amplitude of modulations approximately linearly. For larger voltage modulations, the amplitude and the rms value of the discharge and ion currents grow faster and nonlinearly. In the nonlinear regime, the discharge and the ion currents demonstrate pronounced dependence on the frequency of the external modulations. Moreover, the rms value of the ion current is amplified stronger than the rms value of the discharge current resulting in an increase of the current utilization (of about 5%) and the propellant utilization efficiencies (of about 40%). The thruster efficiency, defined as a product of the current and propellant utilization coefficients, shows an increase of the about 20%. We also present the results of theoretical modeling of a plasma response to driven oscillations in a simplified 1D model of resistive-ionization mode in quasineutral plasma. This modeling demonstrates the nonlinear property of the fundamental breathing mode similar to the experimental results.

The dynamic properties of Renshaw cells located in the lumbar spinal cord of intercollicular decerebrate cats were measured. The responses of these interneurones were recorded extracellularly, while the ventral root was stimulated with sinusoidally frequency-modulated trains of electrical pulses. The frequency of the Renshaw cell discharges resulting from such stimulation varied sinusoidally. The amplitude of modulation about the average (or "carrier") rate of discharge exhibited a linear dependence on the modulation amplitude of the stimulus pulse train. Renshaw cells were able to follow modulated stimulus trains in the entire range of modulation frequencies (0.2 to 80 Hz) encompassed by the present study. Above modulation frequencies between 20 and 50 Hz, the amplitude of modulation of the responses declined. Frequency responses measured at low average frequencies of the stimulus pulse train (centre frequencies 30 and 40 Hz) showed comparatively little dependence on modulation frequency. The higher the centre frequency, however, the greater was the enhancement of the modulation amplitudes at high modulation frequencies compared with those observed at low modulation frequencies. Some aspects of the functional implications of these results are considered and an approximate formula for the transfer function of Renshaw cells is presented.