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Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends…

Anomalous diffusion phenomenon is an intriguing process that tracer diffusion presents in numerous complex systems. Current experimental and theoretical investigations have reported the emergence of random diffusivity scenarios accompanied…

Statistical Mechanics · Physics 2022-10-19 M. A. F. dos Santos , L. Menon Junior , D. Cius

Brownian motion is a well-known model for normal diffusion, but not all physical phenomena behave according to a Brownian motion. Many phenomena exhibit irregular diffusive behavior, called anomalous diffusion. Examples of anomalous…

Probability · Mathematics 2011-10-04 Meredith N. Burr

Nature suggests that exploiting the elasticities and natural dynamics of robotic systems could increase their locomotion efficiency. Prior work on elastic snake robots supports this hypothesis, but has not fully exploited the nonlinear…

Robotics · Computer Science 2026-05-14 Tristan Ehlert , Arne Sachtler , Annika Schmidt , Davide Calzolari , Alin Albu-Schäffer

The interplay between structure and dynamics in non-equilibrium steady-state is far from understood. We address this interplay by tracking Brownian Dynamics trajectories of particles in a binary colloid of opposite charges in an external…

Soft Condensed Matter · Physics 2016-12-08 Suman Dutta , J. Chakrabarti

Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which…

Statistical Mechanics · Physics 2017-03-15 C. Charalambous , G. Muñoz-Gil , A. Celi , M. F. Garcia-Parajo , M. Lewenstein , C. Manzo , M. A. García-March

Cell movement, for example during embryogenesis or tumor metastasis, is a complex dynamical process resulting from an intricate interplay of multiple components of the cellular migration machinery. At first sight, the paths of migrating…

Cell Behavior · Quantitative Biology 2009-04-17 Peter Dieterich , Rainer Klages , Roland Preuss , Albrecht Schwab

Microorganisms are able to overcome the thermal randomness of their surroundings by harvesting energy to navigate in viscous fluid environments. In a similar manner, synthetic colloidal microswimmers are capable of mimicking complex…

Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…

Statistical Mechanics · Physics 2019-03-22 T. Guggenberger , G. Pagnini , T. Vojta , R. Metzler

Active particles such as swimming bacteria or self-propelled colloids are known to spontaneously organize into fascinating large-scale dynamic structures. The emergence of these collective states from the motility pattern of the individual…

Soft Condensed Matter · Physics 2019-11-20 Hamid Karan , Gerardo E. Pradillo , Petia M. Vlahovska

The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…

Physics and Society · Physics 2021-04-01 Michael Schultz

Self-propelled active particles exhibit delayed responses to environmental changes, modulating their propulsion speed through intrinsic sensing and feedback mechanisms. This adaptive behavior fundamentally determines their dynamics and…

Soft Condensed Matter · Physics 2025-05-21 Viktor Holubec , Alexander Fischer , Giovanni Volpe , Frank Cichos

We consider active Brownian particles that intermittently switch between active and inactive states. Such behavior is ubiquitous at all scales, from bacteria to animals and in artificial active systems. We derive exact expressions for key…

Statistical Mechanics · Physics 2025-09-24 Fernando Peruani , Debasish Chaudhuri

Diffusion and anomalous diffusion are widely observed and used to study movement across organisms, resulting in extensive use of the mean and mean-squared displacement (MSD). However, these measures - corresponding to specific displacement…

Populations and Evolution · Quantitative Biology 2025-08-14 Ohad Vilk , Motti Charter , Sivan Toledo , Eli Barkai , Ran Nathan

Guiding active motion is important for targeted delivery, sensing, and search tasks. Many active systems exhibit circular swimming, ubiquitous in chemical, physical, and biological systems, that biases motion and reduces transport…

Soft Condensed Matter · Physics 2026-02-26 Amir Shee

Non-typical transport phenomena may arise when randomly driven particles remain in an active relationship with the environment instead of being passive. If we attribute to Brownian particles an ability to induce alterations of the…

Statistical Mechanics · Physics 2009-10-31 Piotr Garbaczewski

Biological machines harness targeted deformations that can be actuated by Brownian fluctuations. However, while synthetic micromachines can similarly leverage targeted deformations they are too stiff to be driven by thermal fluctuations and…

Soft Condensed Matter · Physics 2025-03-24 Julio Melio , Martin van Hecke , Silke E. Henkes , Daniela J. Kraft

The random motion of molecules in living cells has consistently been reported to deviate from standard Brownian motion, a behavior coined as ``anomalous diffusion''. Fluorescence Correlation Spectroscopy (FCS) is a powerful method to…

Quantitative Methods · Quantitative Biology 2024-07-18 Nathan Quiblier , Jan-Michael Rye , Pierre Leclerc , Henri Truong , Abdelkrim Hannou , Laurent Héliot , Hugues Berry

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…

Other Condensed Matter · Physics 2015-06-04 Pawel Romanczuk , Markus Bär , Werner Ebeling , Benjamin Lindner , Lutz Schimansky-Geier

In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied…

Statistical Mechanics · Physics 2019-10-23 Axel Masó-Puigdellosas , Daniel Campos , Vicenç Méndez