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Highlights • Determination of dominating relaxation mechanisms from temperature-dependent spectra. • Comparison of Fokker–Planck simulations with experimental MPS data. • Sharp bends in harmonic spectra attributed to superimposing and coupled relaxation. Abstract Magnetic Particle Spectroscopy (MPS) is a characterization method for investigating the nonlinear properties of magnetic nanoparticles (MNP) using magnetic field strengths in the order of a few tens of millitesla. Its exploitation for particle characterization is of high significance for biomedical applications such as Magnetic Particle Imaging (MPI) and magnetic hyperthermia. Since the dynamic characteristics of MNP are influenced by both the Néel and the Brownian relaxation mechanism, harmonic spectra in MPS measurements are directly linked to ambient influences like temperature or viscosity of the surrounding medium. Experimental data of multiparametric measurements helps one to evaluate and validate mathematical models of dynamic particle magnetization. This contribution deals with the investigation of temperature-dependent harmonic spectra of different commercially available single-core and multi-core particle systems. It is shown, that dominating relaxation mechanisms can be determined from temperature-dependent MPS measurements. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract Multiple experiments show that various submicron particles such as magnetosomes, RNA messengers, viruses, and even much smaller nanoparticles such as globular proteins diffuse anomalously slow in viscoelastic cytosol of living cells. Hence, their sufficiently fast directional transport by molecular motors such as kinesins is crucial for the cell operation. It has been shown recently that the traditional flashing Brownian ratchet models of molecular motors are capable to describe both normal and anomalous transport of such subdiffusing cargos by molecular motors with a very high efficiency. This work elucidates further an important role of mechanochemical coupling in such an anomalous transport. It shows a natural emergence of a perfect subdiffusive ratchet regime due to allosteric effects, where the random rotations of a "catalytic wheel" at the heart of the motor operation become perfectly synchronized with the random stepping of a heavily loaded motor, so that only one ATP molecule is consumed on average at each motor step along microtubule. However, the number of rotations made by the catalytic engine and the traveling distance both scale sublinearly in time. Nevertheless, this anomalous transport can be very fast in absolute terms. [ABSTRACT FROM AUTHOR]

Abstract Under the background of subdiffusion in cytosol, the nonlinear-coupling fractional Langevin equations is proposed to model the stepping modes of the double-headed molecular motor: inchworm and hand-over-hand mechanisms, and the transport properties in flashing asymmetrical periodic potential are investigated. By numerical simulations, the influences of noise intensity, height of potential barriers, and external load force on the average velocity of coupled particles current in the overdamped limit are assessed. With the exception of conventional directed transport, we observe some anomalous phenomena, including inverse transport and cooperative transport, which cannot be described by the integral-order models. Moreover, the average transport velocity varies non-monotonously with the noise intensity and the height of potential barrier, which shows there exists generalized stochastic resonance (GSR) phenomenon in proposed coupled fractional systems. The results also indicate that the damping force involving the weighted sum of historical velocity leads to the nonlocal memory property and blocks the traditional dissipative behaviors, and it even plays a cooperative role of the driving force in drift motion. Highlights • The model of fractional nonlinear-coupling Brownian motors are established. • Nonlinear coupling is considered to mimics the stepping modes in cytosol. • Subdiffusive transport behaviors of double-headed molecular motor are analyzed. • Inverse transport and generalized stochastic resonance are observed by simulations. • The directed transport and energy conversion can be controlled by the system parameters. [ABSTRACT FROM AUTHOR]

Abstract The dynamics of autonomous Brownian motors that achieve rectified motion due to morphological changes is analyzed. These motors are assumed to be deformable, with restitution internal forces, and to be able to adapt their shapes as function of their total elongation. A generic protocol for morphology adaptation is presented which guarantees unidirectional motion at a constant average speed. This protocol is illustrated by diverse particular examples. Motors operating under non-linear internal forces are analyzed. It is shown that non-linear forces produce considerable variations of the average speed and could serve as a control mechanism for the biased dynamics. The effects of hydrodynamic interactions are quantified as function of the morphological asymmetry. Such interactions are found to promote a very slight reduction of the rectification phenomenon, and could be observable only for motors operating at extremely reduced velocities. The theoretical analysis is found to be in very good agreement with the results of Brownian Dynamics simulations. Highlights • Rectified speed of BMs under diverse morphologic changes is rigorously calculated. • It is shown that nonlinear restitution forces could control the rectified speed. • It is shown that hydrodynamic interactions do not affect the rectification mechanism. • Numerical simulations are used to support these predictions. • The model can be used as a tool for designing novel autonomous BMs. [ABSTRACT FROM AUTHOR]

In some complex viscoelastic mediums, it is ubiquitous that absorbing and desorbing surrounding Brownian particles randomly occur in coupled systems. The conventional method is to model a variable-mass system driven by both multiplicative and additive noises. In this paper, an improved mathematical model is created based on generalized Langevin equations (GLE) to characterize the random interaction with locally fluctuating number of coupled particles in the elastically coupled factional Brownian motors (FBM). By the numerical simulations, the effect of fluctuating interactions on collective transport behaviors is investigated, and some abnormal phenomena, such as cooperative behaviors, stochastic resonance (SR) and anomalous transport, are observed in the regime of sub-diffusion. [ABSTRACT FROM AUTHOR]

We study the temporal correlations in the evolution of the order parameter ϕ t for the Vicsek model with vectorial noise by estimating its Hurst exponent H with detrended fluctuation analysis (DFA). We present results on this parameter as a function of noise amplitude η introduced in simulations. We also compare with well known order–disorder phase transition for that same noise range. We find that – regardless of detrending degree – H spikes at the known coexistence noise for phase transition, and that this is due to nonstationarities introduced by the transit of the system between two well defined states with lower exponents. We statistically support this claim by successfully synthesizing equivalent cases derived from a transformed fractional Brownian motion (TfBm). [ABSTRACT FROM AUTHOR]

In this paper we have presented the dynamics of a Brownian particle which is coupled to a thermal bath in the presence of a fluctuating magnetic field (FMF). By virtue of the FMF the Brownian particle experiences a time dependent damping strength for the x − direction motion even in the presence of a stationary Markovian thermal bath. There is a transition state along this direction. The time dependent damping strength leads to appear a bi-turnover phenomenon in the variation of the barrier crossing rate as a function of the thermal bath induced damping strength. It is a generic signature of the fluctuating magnetic field. [ABSTRACT FROM AUTHOR]

In the paper, we investigate the transport properties of coupled flashing ratchets in viscoelastic media. Using generalized Langevin equation, subvelocity V α , subdiffusive coefficient D α and generalized Peclet number P e α are calculated as functions of the temperature T and the flashing period τ with different subdiffusive exponents α . The results show that the transport of coupled flashing ratchets can be optimized in viscoelastic media. [ABSTRACT FROM AUTHOR]

The directed transport in a one-dimensional overdamped, Brownian motor subjected to a travelling wave potential with variable shape and exposed to an external bias is studied numerically. We focus our attention on the class of Remoissenet–Peyrard parametrized on-site potentials with slight modification, whose shape can be varied as a function of a parameter s , recovering the sine–Gordon shape as the special case. We demonstrate that in the presence of the travelling wave potential the observed dynamical properties of the Brownian motor which crucially depends on the travelling wave speed, the intensity of the noise and the external load is significantly influenced also by the geometry of the system. In particular, we notice that systems with sharp wells and broad barriers favour the transport under the influence of an applied load. The efficiency of transport of Brownian motors in deformable systems remains equal to 1 (in the absence of an applied load) up to a critical value of the travelling wave speed greater than that of the pure sine–Gordon shape. [ABSTRACT FROM AUTHOR]

Abstract: The transport properties of coupled Brownian particles in a two-dimensional rocking ratchet are investigated via Langevin simulation. The results show that the average center-of-mass velocity is multi-peaks function of the frequency of the driving force. Furthermore, in the 2D coupled Brownian motor system there are the collective effect and ratchet behavior, which can switch depending on the frequency of driving force. It turns out that the cooperative effect between the interaction of coupled particles and external rocking driving force facilitates collective directional motion and energy conversion. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Based on recent work [B. Lindner and E. M., Nicola, Phys. Rev. Lett. 101 (2008) 190603], the transport of globally coupled Brownian motors with diversity is investigated. By applying the mean-field approximation, the effects of the diversity disturbance and the coupling strength on the transport of the coupled system are discussed both theoretically and numerically. It is found that the diversity reduces the diffusion dramatically for small bias and increases the diffusion gradually for large bias. The collective motion shows a resonant dependence on the coupling strength in a region of small bias. [Copyright &y& Elsevier]

Abstract: The transport of the coupled Brownian ratchets with two different kinds of time delays is investigated. The increase of the feedback delay reduces the transport with oscillations. While increasing the coupling delay increases the transport with some irregular oscillations and finally saturates to a constant for the large driving force. [Copyright &y& Elsevier]

Abstract: Here, the volume-amplified magnetic nanobead detection assay (VAM-NDA) is for the first time applied for detection of rolling circle amplified (RCA) DNA molecules in a portable, commercial AC susceptometer that operates at ambient temperatures and with an analysis time of about 20min. The performance of the assay is investigated using three different magnetic nanobead sizes: 50, 130 and 250nm. The performance of the assay using the AC susceptometer is compared to the performance achieved using a superconducting quantum interference device (SQUID). It is found that the performance of the assay is comparable in the two setups with a quantitative detection limit of ∼4pM for all bead sizes under study. The findings show that the VAM-NDA holds promise for future wide-spread implementation in commercial AC susceptometer setups thus opening up for the possibility to perform magnetic bead-based DNA detection in point-of-care and outpatient settings. [Copyright &y& Elsevier]

Abstract: We have found, by varying two parameters, several stationary trajectories in a system consisting in many elastically coupled particles that are placed in a periodic ratchet potential on a ring. The system is assumed to be over-damped and driven by an external potential that is periodic both in space and time. The transport properties of these orbits are quite different and their values are quantified. The symmetries allow us to study the orbits with and without the presence of thermal fluctuations and there is found current inversions due to the addition of white Gaussian noise. [Copyright &y& Elsevier]

Abstract: Molecular motors can exhibit Brownian ratchet or power stroke mechanisms. These mechanistic categories are related to transition state position: An early transition state suggests that chemical energy is stored and then released during the step (stroke) while a late transition state suggests that the release of chemical energy rectifies thermally activated motion that has already occurred (ratchet). Cellular RNA polymerases are thought to be ratchets that can push each other forward to reduce pausing during elongation. Here, by constructing a two-dimensional energy landscape from the individual landscapes of active and backtracked enzymes, we identify a new pushing mechanism which is the result of a saddle trajectory that arises in the two-dimensional energy landscape of interacting enzymes. We show that this mechanism is more effective with an early transition state suggesting that interacting RNAPs might translocate via a power stroke. [Copyright &y& Elsevier]

Abstract: A generalized model of an irreversible thermal Brownian refrigerator, which consists of Brownian particles moving in a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate, is established in this paper. The heat flows driven by both potential and kinetic energies of the particles as well as the heat leakage between the hot and cold reservoirs are taken into account. The optimum performance of the generalized model is analyzed using the theory and method of finite time thermodynamics. The analytical expressions for cooling load, coefficient of performance (COP) and power input of the Brownian refrigerator are derived. It is shown by numerical examples that due to the heat leakage between the heat reservoirs and heat flow via the change of kinetic energy of the particles, the Brownian refrigerator is always irreversible and the COP can never attain the Carnot COP. The influences of the heat leakage, the external force, barrier height of the potential, asymmetry of the sawtooth potential and temperature ratio of the heat reservoirs on the performance of the Brownian refrigerator are also investigated in detail. The effective regions of external force and barrier height of the potential in which the Brownian motor can operate as a refrigerator are determined. It is found that the performance of the Brownian refrigerator depends strictly on the design parameters. If these design parameters are properly chosen, the Brownian refrigerator can be controlled to operate in the optimal regimes. The results obtained herein about the general Brownian refrigerator model include those obtained in many previous literatures. [Copyright &y& Elsevier]

Abstract: The magnetic field induced change in the viscosity of a ferrofluid, commonly known as the magnetoviscous effect and parameterized through the magnetoviscosity, is one of the most interesting and practically relevant aspects of ferrofluid phenomena. Although the steady state behavior of ferrofluids under conditions of applied constant magnetic fields has received considerable attention, comparatively little attention has been given to the transient response of the magnetoviscosity to changes in the applied magnetic field or rate of shear deformation. Such transient response can provide further insight into the dynamics of ferrofluids and find practical application in the design of devices that take advantage of the magnetoviscous effect and inevitably must deal with changes in the applied magnetic field and deformation. In this contribution Brownian dynamics simulations and a simple model based on the ferrohydrodynamics equations are applied to explore the dependence of the transient magnetoviscosity for two cases: (I) a ferrofluid in a constant shear flow wherein the magnetic field is suddenly turned on, and (II) a ferrofluid in a constant magnetic field wherein the shear flow is suddenly started. Both simulations and analysis show that the transient approach to a steady state magnetoviscosity can be either monotonic or oscillatory depending on the relative magnitudes of the applied magnetic field and shear rate. [Copyright &y& Elsevier]

Abstract: We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski-reactive like equation; for the particle’s momentum density, a generalized Ohm’s-like equation; and for the particle’s energy density, a Maxwell–Cattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann’s entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. [Copyright &y& Elsevier]

Abstract: Previous works have shown that time asymmetric forcing on the one hand, as well as non-Gaussian noises on the other, can separately enhance the efficiency and current of a Brownian motor. Here, we study the result of subjecting a Brownian motor to both effects simultaneously. Our results have been compared with those obtained for the Gaussian white noise regime in the adiabatic limit. We find that, although the inclusion of the time asymmetry parameter increases the efficiency value up to a certain extent, for the present case this increase is much less appreciable than in the white noise case. We also present a comparative study of the transport coherence in the context of colored noise. Though the efficiency in some cases becomes higher for the non-Gaussian case, the Péclet number is always higher in the Gaussian colored noise case than in the white noise as well as non-Gaussian colored noise cases. [Copyright &y& Elsevier]

Abstract: We study transport properties of an inertial Brownian particle moving in viscous symmetric periodic structures and driven by an oscillating signal of two harmonic components. We analyze the influence of symmetric, antisymmetric and asymmetric signals on directed transport and reveal the shift symmetry of the stationary averaged velocity of the Brownian particle with respect to the relative phase of two components of the signal. The shift symmetry holds true in all regimes. [ABSTRACT FROM AUTHOR]

Abstract: We study phase synchronization for a walker on a ratchet potential. The walker consist of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the deterministic and the stochastic dynamics of the center of mass of the walker in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues and show that the local maxima in the average velocity of the center of mass of the walker, both in the deterministic case and in the presence of noise, correspond to the borders of these Arnold tongues. In this way, we established a connection between optimal transport in ratchets and the phenomenon of phase synchronization. [ABSTRACT FROM AUTHOR]

Abstract: We analyze the transport properties of inertial deterministic rocking ratchets in the presence of an external constant force. For small values of this load, we can obtain a positive current for a negative load, and vice versa. This phenomenon, in which the direction of the current is opposed to the sign of the external force, is a signature of anomalous negative mobility. We show that this anomalous mobility is possible in the deterministic case, and explain this phenomenon as current reversals associated to bifurcations in an inertial deterministic rocking ratchet in the presence of an external load. [Copyright &y& Elsevier]

Abstract: Unidirectional solitonic wave-mediated transport is shown to be possible for a class of anharmonic lattice problems where, due to wave asymmetry, the waves can be used as a traveling periodic ratchet. Using a (mesoscopic) probabilistic description we have assessed the role of both viscous friction and temperature in both the direction of transport and its quantitative features. No asymmetry is required on the potential. Furthermore its actual form and even that of the periodic wave, save its asymmetry, play no significant role in the results obtained and hence they exhibit rather universal value. [Copyright &y& Elsevier]

Abstract: We study phase synchronization for a ratchet system. We consider the deterministic dynamics of a particle in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues, which represent regions of synchronization in parameter space, and discuss their implications for transport in ratchets. [Copyright &y& Elsevier]

Abstract: We analyze a system consisting in many elastically coupled particles that are placed in a periodic ratchet potential on a ring. The system is assumed to be overdamped and driven by an external potential that is periodic both in space and time. The symmetries of the model allow to study the orbits with and without the presence of thermal fluctuations and for a changing intensity of the elastic coupling and the external driving force. We investigate the dependence of the transport current on the intensity of the elastic interaction. The direction of the current may be understood as resulting from the competition of collective transport modes in opposite directions and presents an inversion as the elastic coupling is increased. [Copyright &y& Elsevier]

Abstract: Cooperative Parrondo''s games on a regular two-dimensional lattice are analyzed based on computer simulations and on the discrete-time Markov chain model with exact transition probabilities. The paradox appears in the vicinity of the probabilites characteristic of the “voter model”, suggesting practical applications. As in the one-dimensional case, winning and the occurrence of the paradox depend on the number of players. [Copyright &y& Elsevier]

Abstract: We discuss the connections between Brownian ratchets (BR) and stochastic resonance (SR). We consider a periodic potential energy landscape with no left–right symmetry that is driven by an external force which can be derived from a potential that is periodic both in time and space. We show that this system presents two thermal enhancements within two different windows of the temperature. One is associated with a “coherent diffusion” by which particles jump back and forth between the minima of the periodic potential in synchrony with the external driving. The other is instead associated with a “coherent directional transport” by which particles hop synchronically from one minimum of the ratchet to the next. We calculate the current and the diffusion coefficients and show how transport undergoes a resonant enhancement. While the former is always present, the second only appears when left–right symmetry is broken. [Copyright &y& Elsevier]

Abstract: We investigate the one-dimensional diffusion of the particle in piecewise linear potentials in some physically relevant cases. The underlying potential profiles are a W-shaped double well and a periodic array of saw tooth. In both cases the potential is superimposed with step of harmonically oscillating height. Due to the simplified implementation of the driving process we are able to calculate exact (non-linear) time-resolved response represented by the particle mean position and by the particle current. The time-asymptotic and time-averaged response exhibits resonance-like features with respect to the temperature and some other model parameters. [Copyright &y& Elsevier]

Abstract: We report on an apparently self-consistent model for an asymmetric superconducting loop with two weak links that encloses a magnetic flux. This model mimics the circuit of a recent experiment. This circuit supports a DC voltage in thermal equilibrium. This result challenges the second law of thermodynamics. [Copyright &y& Elsevier]

Abstract: We study the coherence of transport of an overdamped Brownian particle in frictional ratchet system in the presence of external Gaussian white noise fluctuations. The analytical expressions for the particle velocity and diffusion coefficient are derived for this system and the reliability or coherence of transport is analysed by means of their ratio in terms of a dimensionless Péclet number. We show that the coherence in the transport can be enhanced or degraded depending sensitively on the frictional profile with respect to the underlying potential. [Copyright &y& Elsevier]

Abstract: We analyze a model for a walker moving on a ratchet potential. This model is motivated by the properties of transport of motor proteins, like kinesin and myosin. The walker consists of two feet that are represented as two particles coupled nonlinearly through a bistable potential. In contrast to linear coupling, the bistable potential admits a richer dynamics, where the ordering of the particles can alternate during the walking. The transitions between the two stable states on the bistable potential correspond to a walking with alternating particles. We distinguish between two main walking styles: alternating and no alternating, resembling the hand-over-hand and the inchworm walking in motor proteins, respectively. When the equilibrium distance between the two particles divided by the periodicity of the ratchet is an integer, we obtain a maximum for the current, indicating optimal transport. [Copyright &y& Elsevier]

Abstract: Recent studies on Brownian motors driven by colored non-Gaussian noises have shown that the departure of the noise distribution from Gaussian behavior induces an enhancement of its current and efficiency. Here, we discuss some new aspects of this phenomenon focusing on some analytical results based on an adiabatic approximation and in the analysis of the role of long probability distribution tails. [Copyright &y& Elsevier]

Abstract: A novel quantum Smoluchowski dynamics in an external, nonlinear potential has been derived recently. In its original form, this overdamped quantum dynamics is not compatible with the second law of thermodynamics if applied to periodic, but asymmetric ratchet potentials. An improved version of the quantum Smoluchowski equation with a modified diffusion function has been put forward in L. Machura et al. (Phys. Rev. E 70 (2004) 031107) and applied to study quantum Brownian motors in overdamped, arbitrarily shaped ratchet potentials. With this work we prove that the proposed diffusion function, which is assumed to depend (in the limit of strong friction) on the second-order derivative of the potential, is uniquely determined from the validity of the second law of thermodynamics in thermal, undriven equilibrium. Put differently, no approximation-induced quantum Maxwell demon is operating in thermal equilibrium. Furthermore, the leading quantum corrections correctly render the dissipative quantum equilibrium state, which distinctly differs from the corresponding Gibbs state that characterizes the weak (vanishing) coupling limit. [Copyright &y& Elsevier]

We investigate different mechanisms for the control of directed transport of particles on two-dimensional periodic and symmetric substrates, based on the application of a crossed static and a bi-harmonic (harmonic mixing) field. We focus on inertial systems in the low friction regime, using a prototypical model for atom-surface diffusion, and demonstrate that a proper control of current reversals can be achieved at moderate field strengths by tuning either the static field or changing the relative phase of the harmonic mixing signal, respectively. [Copyright &y& Elsevier]

A system of periodically coupled nonlinear phase oscillators—submitted to both additive and multiplicative white noises—has been recently shown to exhibit ratchetlike transport, negative zero-bias conductance, and anomalous hysteresis. These features stem from the asymmetry of the stationary probability distribution function, arising through a noise-induced non-equilibrium phase transition which is re-entrant as a function of the multiplicative noise intensity. Using an explicit mean-field approximation we analyse the effect of the multiplicative noises being coloured, finding a contraction of the ordered phase (and a re-entrance as a function of the coupling) on one hand, and a shift of the transition from anomalous to normal hysteresis inside this phase on the other. [Copyright &y& Elsevier]