Strong clustering of noninteracting, sliding passive scalars driven by fluctuating surfaces

Nagar, Apoorva; Majumdar, Satya N.; Barma, Mustansir

doi:10.1103/physreve.74.021124

Cited by 28 publications

(48 citation statements)

References 30 publications

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“…For the case of antiadvection (AA), the exponent z of the particles was estimated numerically by Drossel and Kardar [8] and found to be nonuniversal, changing continuously with a [8,14]. For a = 1 they obtained z 1.74 consistent with the numerical findings in [15,21] as also in the current work. As the coupling constant a decreases from 1 to 0, the exponent z increases from approximately 1.74 to 2, with a = 0 corresponding to a simple random walk.…”

Section: Antiadvectionsupporting

confidence: 88%

“…The scaling form for the steady state correlations in Ref. [15] is fully consistent with Eq. 5, if we make the replacement L(t) = L In a similar vein, the problem of two passive particles on a fluctuating KPZ surface is closely related to the problem of two second-class particles in the ASEP.…”

Section: A Pdf Of Separation Between Two Particlessupporting

confidence: 69%

“…Later, the same value of the dynamic exponent was obtained by modeling the surface dynamics through the Kim-Kosterlitz model [17] and the single step model [15]. As emphasized in [17], with KPZ driving the particle motion becomes slaved to the fluctuations of the surface so that z = z s .…”

Section: A Kpz Drivingmentioning

confidence: 79%

“…R(t) grows as t 1/z , and the question is whether z = z s . For KPZ advection, earlier work has established z = z s = 3/2 [14,18] while for KPZ-AA, z was found to be very different from z s [8,14,15]. With EW driving, there appears to be a marginal difference, in that z = z s = 2, but there is a multiplicative logarithm R(t) ∼ t 1/2 [ln(t/t 0 )] α/2 .…”

Section: Single Particle On a Fluctuating Surfacementioning

confidence: 89%

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Clustering, intermittency, and scaling for passive particles on fluctuating surfaces

Singha

Barma

2018

Phys. Rev. E

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We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for passive particles sliding on one-dimensional Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) surfaces, with particles moving either along (advection) or against (antiadvection) the growth direction in the latter case. Extensive numerical simulations are supplemented by analytical results for a sticky slider model in which particles coalesce when they meet. Results for single particle displacement versus time show to what extent particle dynamics is slaved to the surface, while scaling properties of the probability distribution of the separation of two particles determine the scaling form of average overlap of a pair of trajectories. For the manyparticle system, clustering in steady state is studied via moments of particle number fluctuations in a single stretch, revealing different degrees of spatial multiscaling with different drivings. Temporal intermittency in steady state is established by showing that the scaled flatness diverges as the stretch size scaled by system size approaches zero for all the three drivings, but with different exponents, reflecting strongest clustering for KPZ advection and weakest for KPZ antiadvection. Finally we consider the approach to the steady state, study both the flatness and the evolution of equal-time correlation functions as in coarsening of phase ordering systems. Our studies give clear evidence for a simple scaling description of the approach to steady state, with the scale set by a length which grows in time. An investigation of aging properties reveals that flatness is nonmonotonic in time with two distinct branches, and that a scaling description holds for each one.

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Section: Antiadvectionsupporting

confidence: 88%

Section: A Pdf Of Separation Between Two Particlessupporting

confidence: 69%

Section: A Kpz Drivingmentioning

confidence: 79%

Section: Single Particle On a Fluctuating Surfacementioning

confidence: 89%

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Clustering, intermittency, and scaling for passive particles on fluctuating surfaces

Singha

Barma

2018

Phys. Rev. E

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“…Further understanding of this system could be obtained from an analysis similar to the one in [270] for the symmetric motion of non-interacting particles in fluctuating energy landscapes. Here the effective 'potential' landscape emerges spontaneously from the particle jamming.…”

Section: Mean-field Approximationmentioning

confidence: 99%

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

2015

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Cells are the elementary units of living organisms, which are able to carry out many vital functions. These functions rely on active processes on a microscopic scale. Therefore, they are strongly out-of-equilibrium systems, which are driven by continuous energy supply. The tasks that have to be performed in order to maintain the cell alive require transportation of various ingredients, some being small, others being large. Intracellular transport processes are able to induce concentration gradients and to carry objects to specific targets. These processes cannot be carried out only by diffusion, as cells may be crowded, and quite elongated on molecular scales. Therefore active transport has to be organized.The cytoskeleton, which is composed of three types of filaments (microtubules, actin and intermediate filaments), determines the shape of the cell, and plays a role in cell motion. It also serves as a road network for a special kind of vehicles, namely the cytoskeletal motors. These molecules can attach to a cytoskeletal filament, perform directed motion, possibly carrying along some cargo, and then detach.It is a central issue to understand how intracellular transport driven by molecular motors is regulated. The interest for this type of question was enhanced when it was discovered that intracellular transport breakdown is one of the signatures of some neuronal diseases like the Alzheimer.We give a survey of the current knowledge on microtubule based intracellular transport. Our review includes on the one hand an overview of biological facts, obtained from experiments, and on the other hand a presentation of some modeling attempts based on cellular automata. We present some background knowledge on the original and variants of the TASEP (Totally Asymmetric Simple Exclusion Process), before turning to more application oriented models. After addressing microtubule based transport in general, with a focus on in vitro experiments, and on cooperative effects in the transportation of large cargos by multiple motors, we concentrate on axonal transport, because of its relevance for neuronal diseases. Some important characteristics of axonal transport is that it takes place in a confined environment; Besides several types of motors are involved, that move in opposite directions. It is a challenge to understand how this bidirectional transport is organized. We review several features that could contribute to the efficiency of bidirectional transport in the axon, including in particular the role of motor-motor interactions and of the dynamics of the underlying microtubule network. Finally, we also discuss some open questions that may be relevant for future research in this field.

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SLE on Doubly-Connected Domains and the Winding of Loop-Erased Random Walks

Hagendorf

Doussal

2008

J Stat Phys

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Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE κ with parameter κ = 2. In this note, some properties of an SLE κ trace on doubly-connected domains are studied and a connection to passive scalar diffusion in a Burgers flow is emphasised. In particular, the endpoint probability distribution and winding probabilities for SLE 2 on a cylinder, starting from one boundary component and stopped when hitting the other, are found. A relation of the result to conditioned one-dimensional Brownian motion is pointed out. Moreover, this result permits to study the statistics of the winding number for SLE 2 with fixed endpoints. A solution for the endpoint distribution of SLE 4 on the cylinder is obtained and a relation to reflected Brownian motion pointed out.

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Strong clustering of noninteracting, sliding passive scalars driven by fluctuating surfaces

Cited by 28 publications

References 30 publications

Clustering, intermittency, and scaling for passive particles on fluctuating surfaces

Clustering, intermittency, and scaling for passive particles on fluctuating surfaces

Intracellular transport driven by cytoskeletal motors: General mechanisms and defects

SLE on Doubly-Connected Domains and the Winding of Loop-Erased Random Walks

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