5,746 research outputs found
Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency
We study origin, parameter optimization, and thermodynamic efficiency of
isothermal rocking ratchets based on fractional subdiffusion within a
generalized non-Markovian Langevin equation approach. A corresponding
multi-dimensional Markovian embedding dynamics is realized using a set of
auxiliary Brownian particles elastically coupled to the central Brownian
particle (see video on the journal web site). We show that anomalous
subdiffusive transport emerges due to an interplay of nonlinear response and
viscoelastic effects for fractional Brownian motion in periodic potentials with
broken space-inversion symmetry and driven by a time-periodic field. The
anomalous transport becomes optimal for a subthreshold driving when the driving
period matches a characteristic time scale of interwell transitions. It can
also be optimized by varying temperature, amplitude of periodic potential and
driving strength. The useful work done against a load shows a parabolic
dependence on the load strength. It grows sublinearly with time and the
corresponding thermodynamic efficiency decays algebraically in time because the
energy supplied by the driving field scales with time linearly. However, it
compares well with the efficiency of normal diffusion rocking ratchets on an
appreciably long time scale
On the role of initial velocities in pair dispersion in a microfluidic chaotic flow
Chaotic flows drive mixing and efficient transport in fluids, as well as the
associated beautiful complex patterns familiar to us from our every day life
experience. Generating such flows at small scales where viscosity takes over is
highly challenging from both the theoretical and engineering perspectives. This
can be overcome by introducing a minuscule amount of long flexible polymers,
resulting in a chaotic flow dubbed \textit{elastic turbulence}. At the basis of
the theoretical frameworks for its study lie the assumptions of a spatially
smooth and random-in-time velocity field. Previous measurements of elastic
turbulence have been limited to two-dimensions. Using a novel three-dimensional
particle tracking method, we conduct a microfluidic experiment, allowing us to
explore elastic turbulence from the perspective of particles moving with the
flow. Our findings show that the smoothness assumption breaks already at scales
smaller than a tenth of the system size. Moreover, we provide conclusive
experimental evidence that \textit{ballistic} separation prevails in the
dynamics of pairs of tracers over long times and distances, exhibiting a memory
of the initial separation velocities. The ballistic dispersion is universal,
yet it has been overlooked so far in the context of small scales chaotic flows.Comment: 28 pages (Main Article: 17 pages ; Supplementary Information: 11
pages), 5 Main Figures, 6 Supplementary Figures, 3 Supplementary Notes,
Supplementary Reference
Crossover to self-organized criticality in an inertial sandpile model
We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the system no longer evolves to a self-organized critical state. A range of mean-field theories based on a kinetic equation approach is presented which confirm the numerical findings. We conclude by considering the physical applications of this model, particularly with reference to recent experimental results
Stochastic suspensions of heavy particles
Turbulent suspensions of heavy particles in incompressible flows have gained
much attention in recent years. A large amount of work focused on the impact
that the inertia and the dissipative dynamics of the particles have on their
dynamical and statistical properties. Substantial progress followed from the
study of suspensions in model flows which, although much simpler, reproduce
most of the important mechanisms observed in real turbulence. This paper
presents recent developments made on the relative motion of a pair of particles
suspended in time-uncorrelated and spatially self-similar Gaussian flows. This
review is complemented by new results. By introducing a time-dependent Stokes
number, it is demonstrated that inertial particle relative dispersion recovers
asymptotically Richardson's diffusion associated to simple tracers. A
perturbative (homogeneization) technique is used in the small-Stokes-number
asymptotics and leads to interpreting first-order corrections to tracer
dynamics in terms of an effective drift. This expansion implies that the
correlation dimension deficit behaves linearly as a function of the Stokes
number. The validity and the accuracy of this prediction is confirmed by
numerical simulations.Comment: 15 pages, 12 figure
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