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1

Perthame, Benoit, Weiran Sun, Min Tang, and Shugo Yasuda. "Multiple asymptotics of kinetic equations with internal states." Mathematical Models and Methods in Applied Sciences 30, no. 06 (2020): 1041–73. http://dx.doi.org/10.1142/s0218202520400060.

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The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However, the relation between the tumbling rate and the internal state of bacteria is poorly understood. This study aims at deriving macroscopic models as limits of the mesoscopic kinetic equation in different regimes. In particular, we are interested in the roles of the stiffness of the response and the adaptation time in the kinetic equation. Depending on the asymptotics chosen both the standard Keller–Segel equation and the flux-limited Keller–Segel (FLKS) equatio
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Sandoval, Mario, Navaneeth K. Marath, Ganesh Subramanian, and Eric Lauga. "Stochastic dynamics of active swimmers in linear flows." Journal of Fluid Mechanics 742 (February 21, 2014): 50–70. http://dx.doi.org/10.1017/jfm.2013.651.

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AbstractMost classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction, resulting in a transition from short-time ballistic dynamics to effective long-time diffusion. As most cells or synthetic swimmers are immersed in external flows, we consider theoretically in this paper the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. The stochasticity arises both from translational
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Banerjee, Tirthankar, Robert L. Jack, and Michael E. Cates. "Tracer dynamics in one dimensional gases of active or passive particles." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (2022): 013209. http://dx.doi.org/10.1088/1742-5468/ac4801.

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Abstract We consider one-dimensional systems comprising either active run-and-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer particle embedded in such a system—this tracer may be either active or passive, with hardcore exclusion from environmental particles. In an active hardcore environment, both active and passive tracers show long-time subdiffusion: displacements scale as t 1/4 with a density-dependent prefactor that is independent of tracer type, and differs from the
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SUBRAMANIAN, GANESH, and DONALD L. KOCH. "Critical bacterial concentration for the onset of collective swimming." Journal of Fluid Mechanics 632 (July 27, 2009): 359–400. http://dx.doi.org/10.1017/s002211200900706x.

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We examine the stability of a suspension of swimming bacteria in a Newtonian medium. The bacteria execute a run-and-tumble motion, runs being periods when a bacterium on average swims in a given direction; runs are interrupted by tumbles, leading to an abrupt, albeit correlated, change in the swimming direction. An instability is predicted to occur in a suspension of ‘pushers’ (e.g.E. Coli,Bacillus subtilis, etc.), and owes its origin to the intrinsic force dipoles of such bacteria. Unlike the dipole induced in an inextensible fibre subject to an axial straining flow, the forces constituting t
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Li, Hua, Yong Xu, Ralf Metzler, Jianwei Shen, and Kheder Suleiman. "Transition path dynamics for one-dimensional run and tumble particle." Chaos: An Interdisciplinary Journal of Nonlinear Science 35, no. 5 (2025). https://doi.org/10.1063/5.0249277.

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We study transition path properties such as the transient probability density, transition path time and its distribution, splitting probability, coefficient of variation, and the transition path shape of active run and tumble particles for unconstrained motion. In particular, we provide the theoretical description of the transition path properties using forward and backward master equations. The theoretical results are supported by Monte Carlo simulations. In particular, we prove that the system dynamics do not feature a symmetry breaking in the transition path properties for the case of run a
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6

Lee, Wanho, Yongsam Kim, and Sookkyung Lim. "Bio-inspired in silico microswimmer: Run and tumble kinematics." Physics of Fluids, February 28, 2023. http://dx.doi.org/10.1063/5.0142836.

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We present an in silico microswimmer motivated by peritrichous bacteria, E. coli, which can run and tumble by spinning their flagellar motors counterclockwise (CCW) or clockwise (CW). Runs are the directed movement driven by a flagellar bundle and tumbles are reorientations of cells caused by some motors' reversals from CCW to CW. In a viscous fluid without obstacles, our simulations reveal that material properties of the hook and the counterrotation of the cell body are important factors for efficient flagellar bundling, and that longer hooks in mutant cell models create an instability and di
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7

Guéneau, Mathis, and Léo Touzo. "Relating absorbing and hard wall boundary conditions for a one-dimensional run-and-tumble particle." Journal of Physics A: Mathematical and Theoretical, May 3, 2024. http://dx.doi.org/10.1088/1751-8121/ad4753.

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Abstract The connection between absorbing boundary conditions and hard walls is well established in the mathematical literature for a variety of stochastic models, including for instance the Brownian motion. In this paper we explore this duality for a different type of process which is of particular interest in physics and biology, namely the run-tumble-particle, a toy model of active particle. For a one-dimensional run-and-tumble particle subjected to an arbitrary external force, we provide a duality relation between the exit probability, i.e. the probability that the particle exits an interv
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8

Angelani, Luca, Alessandro De Gregorio, Roberto Garra, and Francesco Iafrate. "Anomalous Random Flights and Time-Fractional Run-and-Tumble Equations." Journal of Statistical Physics 191, no. 10 (2024). http://dx.doi.org/10.1007/s10955-024-03344-2.

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AbstractRandom flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained
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9

Berdakin, Iván, Alejandro Silhanek, Hernán Moyano Cortéz, Verónica Marconi, and Carlos Condat. "Quantifying the sorting efficiency of self-propelled run-and-tumble swimmers by geometrical ratchets." Open Physics 11, no. 12 (2013). http://dx.doi.org/10.2478/s11534-013-0300-7.

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AbstractSuitable asymmetric microstructures can be used to control the direction of motion in microorganism populations. This rectification process makes it possible to accumulate swimmers in a region of space or to sort different swimmers. Here we study numerically how the separation process depends on the specific motility strategies of the microorganisms involved. Crucial properties such as the separation efficiency and the separation time for two bacterial strains are precisely defined and evaluated. In particular, the sorting of two bacterial populations inoculated in a box consisting of
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10

Singh, Prashant, Saikat Santra, and Anupam Kundu. "Extremal statistics of a one dimensional run and tumble particle with an absorbing wall." Journal of Physics A: Mathematical and Theoretical, November 11, 2022. http://dx.doi.org/10.1088/1751-8121/aca230.

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Abstract We study the extreme value statistics of a run and tumble particle (RTP) in one dimension till its first passage to the origin starting from the position $x_0~(>0)$. This model has recently drawn a lot of interest due to its biological application in modelling the motion of certain species of bacteria. Herein, we analytically study the exact time-dependent propagators for a single RTP in a finite interval with absorbing conditions at its two ends. By exploiting a path decomposition technique, we use these propagators appropriately to compute the joint distribution $\mathscr{P}(M,t_
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11

Vourc'h, Thomas, Julien Léopoldès, and Hassan Peerhossaini. "Light Control of the Diffusion Coefficient of Active Fluids." Journal of Fluids Engineering 142, no. 3 (2020). http://dx.doi.org/10.1115/1.4045951.

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Abstract Active fluids refer to the fluids that contain self-propelled particles such as bacteria or microalgae, whose properties differ fundamentally from the passive fluids. Such particles often exhibit an intermittent motion, with high-motility “run” periods broken by low-motility “tumble” periods. The average motion can be modified with external stresses, such as nutrient or light gradients, leading to a directed movement called chemotaxis and phototaxis, respectively. Using cyanobacterium Synechocystis sp. PCC 6803, a model microorganism to study photosynthesis, we track the bacterial res
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12

Angelani, Luca, Alessandro De Gregorio, and Roberto Garra. "Generalized time-fractional kinetic-type equations with multiple parameters." Chaos: An Interdisciplinary Journal of Nonlinear Science 35, no. 2 (2025). https://doi.org/10.1063/5.0243533.

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In this paper, we study a new generalization of the kinetic equation emerging in run-and-tumble models [see, e.g., Angelani et al., J. Stat. Phys. 191, 129 (2024) for a time-fractional version of the kinetic equation]. We show that this generalization leads to a wide class of generalized fractional kinetic (GFK) and telegraph-type equations that depend on two (or three) parameters. We provide an explicit expression of the solution in the Laplace domain and show that, for a particular choice of the parameters, the fundamental solution of the GFK equation can be interpreted as the probability de
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13

Guseva, Ksenia, and Ulrike Feudel. "Advantages of run-reverse motility pattern of bacteria for tracking light and small food sources in dynamic fluid environments." Journal of The Royal Society Interface 22, no. 227 (2025). https://doi.org/10.1098/rsif.2025.0037.

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Marine bacteria are fundamental to the processes and cycles that sustain ocean ecosystems. Their activity at small scales, where they search for food sources in a highly heterogeneous and dynamic environment, for example controls the decomposition of organic matter. To be effective, these microorganisms have evolved sophisticated behaviours, which include extremely rapid swimming speeds, a precise chemosensing ability and particular swimming patterns. One of these peculiar motility patterns often recorded in the ocean is run-reverse (Mitchell et al 1996 Clustering of marine bacteria in seawate
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14

Dinelli, Alberto, Jérémy O’Byrne, and Julian Tailleur. "Fluctuating hydrodynamics of active particles interacting via taxis and quorum sensing: static and dynamics." Journal of Physics A: Mathematical and Theoretical, August 22, 2024. http://dx.doi.org/10.1088/1751-8121/ad72bc.

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Abstract In this article we derive and test the fluctuating hydrodynamic description of active particles interacting via taxis and quorum sensing, both for mono-disperse systems and for mixtures of co-existing species of active particles. We compute the average steady-state density profile in the presence of spatial motility regulation, as well as the structure factor and intermediate scattering function for interacting systems. By comparing our predictions to microscopic numerical simulations, we show that our fluctuating hydrodynamics correctly predicts the large-scale static and dynamical prop
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15

Costello, Moya. "Reading the Senses: Writing about Food and Wine." M/C Journal 16, no. 3 (2013). http://dx.doi.org/10.5204/mcj.651.

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"verbiage very thinly sliced and plated up real nice" (Barrett 1)IntroductionMany of us share in an obsessive collecting of cookbooks and recipes. Torn or cut from newspapers and magazines, recipes sit swelling scrapbooks with bloated, unfilled desire. They’re non-hybrid seeds, peas under the mattress, an endless cycle of reproduction. Desire and narrative are folded into each other in our drive, as humans, to create meaning. But what holds us to narrative is good writing. And what can also drive desire is image—literal as well as metaphorical—the visceral pleasure of the gaze, or looking and
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