161 research outputs found
Nonlinear Response of Inertial Tracers in Steady Laminar Flows: Differential and Absolute Negative Mobility
We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence ofthermal noise and under the actionof an external force. We show, with extensive numerical simulations, that the force-velocity rela-tion for the tracer, in the nonlinear regime, displays complex and rich behaviors, including negativedifferential and absolute mobility. These effects rely upon asubtle coupling between inertia andapplied force which induce the tracer to persist in particular regions of phase space with a velocityopposite to the force. The relevance of this coupling is revisited in the framework of non-equilibriumresponse theory, applying a generalized Einstein relationto our system. The possibility of experi-mental observation of these results is also discussed
Anomalous mobility of a driven active particle in a steady laminar flow
We study, via extensive numerical simulations, the force-velocity curve of an
active particle advected by a steady laminar flow, in the nonlinear response
regime. Our model for an active particle relies on a colored noise term that
mimics its persistent motion over a time scale . We find that the
active particle dynamics shows non-trivial effects, such as negative
differential and absolute mobility (NDM and ANM, respectively). We explore the
space of the model parameters and compare the observed behaviors with those
obtained for a passive particle () advected by the same laminar flow.
Our results show that the phenomena of NDM and ANM are quite robust with
respect to the details of the considered noise: in particular for finite
a more complex force-velocity relation can be observed.Comment: 12 pages, 9 figures, paper submitted for the Special Issue of Journal
of Physics: Condensed Matter, "Transport in Narrow Channels", Guest Editors
P. Malgaretti, G. Oshanin, J. Talbo
Anomalous force-velocity relation of driven inertial tracers in steady laminar flows
We study the nonlinear response to an external force of an inertial tracer
advected by a two-dimensional incompressible laminar flow and subject to
thermal noise. In addition to the driving external field , the main
parameters in the system are the noise amplitude and the characteristic
Stokes time of the tracer. The relation velocity vs force shows
interesting effects, such as negative differential mobility (NDM), namely a
non-monotonic behavior of the tracer velocity as a function of the applied
force, and absolute negative mobility (ANM), i.e. a net motion against the
bias. By extensive numerical simulations, we investigate the phase chart in the
parameter space of the model, , identifying the regions where NDM,
ANM and more common monotonic behaviors of the force-velocity curve are
observed.Comment: 5 pages, 13 figures. Contribution to the Topical Issue "Fluids and
Structures: Multi-scale coupling and modeling", edited by Luca Biferale,
Stefano Guido, Andrea Scagliarini, Federico Toschi. The final publication is
available at Springer via http://dx.doi.org/10.1140/epje/i2017-11571-
Nonlinear susceptibilities and the measurement of a cooperative length
We derive the exact beyond-linear fluctuation dissipation relation,
connecting the response of a generic observable to the appropriate correlation
functions, for Markov systems. The relation, which takes a similar form for
systems governed by a master equation or by a Langevin equation, can be derived
to every order, in large generality with respect to the considered model, in
equilibrium and out of equilibrium as well. On the basis of the fluctuation
dissipation relation we propose a particular response function, namely the
second order susceptibility of the two-particle correlation function, as an
effective quantity to detect and quantify cooperative effects in glasses and
disordered systems. We test this idea by numerical simulations of the
Edwards-Anderson model in one and two dimensions.Comment: 5 pages, 2 figure
Brownian ratchet in a thermal bath driven by Coulomb friction
The rectification of unbiased fluctuations, also known as the ratchet effect,
is normally obtained under statistical non-equilibrium conditions. Here we
propose a new ratchet mechanism where a thermal bath solicits the random
rotation of an asymmetric wheel, which is also subject to Coulomb friction due
to solid-on-solid contacts. Numerical simulations and analytical calculations
demonstrate a net drift induced by friction. If the thermal bath is replaced by
a granular gas, the well known granular ratchet effect also intervenes,
becoming dominant at high collision rates. For our chosen wheel shape the
granular effect acts in the opposite direction with respect to the
friction-induced torque, resulting in the inversion of the ratchet direction as
the collision rate increases. We have realized a new granular ratchet
experiment where both these ratchet effects are observed, as well as the
predicted inversion at their crossover. Our discovery paves the way to the
realization of micro and sub-micrometer Brownian motors in an equilibrium
fluid, based purely upon nano-friction.Comment: main paper: 4 pages and 4 figures; supplemental material joined at
the end of the paper; a movie of the experiment can be viewed
http://www.youtube.com/watch?v=aHrdY4BC71k ; all the material has been
submitted for publication [new version with substantial changes in the order
of the presentation of the results; differences with previous works have been
put in evidence
Nonlinear response and fluctuation dissipation relations
A unified derivation of the off equilibrium fluctuation dissipation relations
(FDR) is given for Ising and continous spins to arbitrary order, within the
framework of Markovian stochastic dynamics. Knowledge of the FDR allows to
develop zero field algorithms for the efficient numerical computation of the
response functions. Two applications are presented. In the first one, the
problem of probing for the existence of a growing cooperative length scale is
considered in those cases, like in glassy systems, where the linear FDR is of
no use. The effectiveness of an appropriate second order FDR is illustrated in
the test case of the Edwards-Anderson spin glass in one and two dimensions. In
the second one, the important problem of the definition of an off equilibrium
effective temperature through the nonlinear FDR is considered. It is shown
that, in the case of coarsening systems, the effective temperature derived from
the second order FDR is consistent with the one obtained from the linear FDR.Comment: 24 pages, 6 figure
On anomalous diffusion and the out of equilibrium response function in one-dimensional models
We study how the Einstein relation between spontaneous fluctuations and the
response to an external perturbation holds in the absence of currents, for the
comb model and the elastic single-file, which are examples of systems with
subdiffusive transport properties. The relevance of non-equilibrium conditions
is investigated: when a stationary current (in the form of a drift or an energy
flux) is present, the Einstein relation breaks down, as is known to happen in
systems with standard diffusion. In the case of the comb model, a general
relation, which has appeared in the recent literature, between the response
function and an unperturbed suitable correlation function, allows us to explain
the observed results. This suggests that a relevant ingredient in breaking the
Einstein formula, for stationary regimes, is not the anomalous diffusion but
the presence of currents driving the system out of equilibrium.Comment: 10 pages, 4 figure
Identification of the critical temperature from non-equilibrium time-dependent quantities
We present a new procedure able to identify and measure the critical
temperature. This method is based on the divergence of the relaxation time
approaching the critical point in quenches from infinite temperature. We
introduce a dimensionless quantity that turns out to be time-independent at the
critical temperature. The procedure does not need equilibration and allows for
a relatively fast identification of the critical temperature. The method is
first tested in the ferromagnetic Ising model and then applied to the
one-dimensional Ising spin glass with power-law interactions. Here we always
find a finite critical temperature also in presence of a uniform external
field, in agreement with the mean-field picture for the low temperature phase
of spin glasses.Comment: 6 pages, 10 figure
Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: a non-equilibrium potential approach
Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, such as stochastic resonance, noise induced bistability, and noise-induced oscillations, to name but a few. Here we revisit a mechanism-first investigated in the context of neuroscience-by which relatively small intrinsic (demographic) fluctuations can lead to the emergence of avalanching behavior in systems that are deterministically characterized by a single stable fixed point (up state). The anomalously large response of such systems to stochasticity stems from (or is strongly associated with) the existence of a 'non-normal' stability matrix at the deterministic fixed point, which may induce the system to be 'reactive'. By employing a number of analytical and computational approaches, we further investigate this mechanism and explore the interplay between non-normality and intrinsic stochasticity. In particular, we conclude that the resulting dynamics of this type of systems cannot be simply derived from a scalar potential but, additionally, one needs to consider a curl flux which describes the essential non-equilibrium nature of this type of noisy non-normal systems. Moreover, we shed further light on the origin of the phenomenon, introduce the novel concept of 'non-linear reactivity', and rationalize the observed values of avalanche exponents.We are grateful to the Spanish-MINECO for financial support (under grants FIS2013-43201-P and FIS2017-84256-P; FEDER funds). MAM also acknowledges the support from TeachinParma and the Cariparma foundation
Einstein, Planck and Vera Rubin: Relevant Encounters Between the Cosmological and the Quantum Worlds
In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of? that, even after 40 years from the Vera Rubin seminal discovery [1] does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic Dark Matter particle candidates may play a role in framing the Dark Matter mystery that seems to be accomplice of new unknown Physics. Observations and experiments have clearly indicated that the above phenomenon cannot be considered as already theoretically framed, as hoped for decades. The Special Topic to which this review belongs wants to penetrate this newly realized mystery from different angles, including that of a contamination of different fields of Physics apparently unrelated. We show with the works of this ST that this contamination is able to guide us into the required new Physics. This review wants to provide a good number of these \u201cpaths or contamination\u201d beyond/among the three worlds above; in most of the cases, the results presented here open a direct link with the multi-scale dark matter phenomenon, enlightening some of its important aspects. Also in the remaining cases, possible interesting contacts emerges. Finally, a very complete and accurate bibliography is provided to help the reader in navigating all these issues
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