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Related papers: On the Stochastic Singular Cucker--Smale Model: We…

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We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…

Statistical Mechanics · Physics 2019-07-24 Trilochan Bagarti , Shakti N. Menon

We establish the existence of martingale solutions to a class of stochastic conservation equations. The underlying models correspond to random perturbations of kinetic models for collective motion such as the Cucker-Smale and Motsch-Tadmor…

Probability · Mathematics 2020-07-06 Arnaud Debussche , Angelo Rosello

We prove that certain types of measure-valued mappings are monokinetic i.e. the distribution of velocity is concentrated in a Dirac mass. These include weak measure-valued solutions to the strongly singular Cucker-Smale model with…

Analysis of PDEs · Mathematics 2022-11-04 Michał Fabisiak , Jan Peszek

The purpose of this paper is to study the existence, uniqueness and lifespan of solutions for a fractional Stokes-Transport system. This problem should be understood as a model for sedimentation in a fluid where the viscosity law is given…

Analysis of PDEs · Mathematics 2023-01-26 Dimitri Cobb

Experimental observations of animal collective behavior have shown stunning evidence for the emergence of large-scale cooperative phenomena resembling phase transitions in physical systems. Indeed, quantitative studies have found scale-free…

Statistical Mechanics · Physics 2013-03-27 Gabriel Baglietto , Ezequiel V. Albano , Julián Candia

We analyze the Cucker-Smale model under hierarchical leadership in presence of a time delay. By using a Lyapunov functional approach and some induction arguments we will prove convergence to consensus for every positive delay $\tau$. These…

Optimization and Control · Mathematics 2018-07-06 Cristina Pignotti , Irene Reche Vallejo

We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $\phi$ and a non-linear coupling of velocities given by the power…

Analysis of PDEs · Mathematics 2026-01-01 Vinh Nguyen , Roman Shvydkoy , Changhui Tan

We consider SDEs driven by two different sources of additive noise, which we refer to as intrinsic and common. We establish almost sure existence and uniqueness of pullback attractors with respect to realisations of the common noise only.…

Dynamical Systems · Mathematics 2021-08-12 Federico Graceffa , Jeroen S. W. Lamb

Natural systems are inextricably affected by noise. Within recent decades, the manner in which noise affects the collective behavior of self-organized systems, specifically, has garnered considerable interest from researchers and developers…

Optimization and Control · Mathematics 2016-07-12 Ge Chen

While it is well established that self-propelled particles with alignment interactions can exhibit orientational order, the impact of self-replication and annihilation, which are key characteristics in cellular systems, on spatiotemporal…

Populations and Evolution · Quantitative Biology 2025-09-09 Seiya Takamura , Nen Saito

We study the clustering of passive, non-interacting particles moving under the influence of a fluctuating field and random noise, in one dimension. The fluctuating field in our case is provided by a surface governed by the…

Statistical Mechanics · Physics 2013-05-29 Apoorva Nagar , Satya N. Majumdar , Mustansir Barma

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…

Soft Condensed Matter · Physics 2019-01-15 Tapas Singha , Mustansir Barma

A hallmark in natural systems, self-organization often stems from very simple interaction rules between individual agents. While single-species self-propelled particle (SPP) systems are well understood, the behavior of binary mixtures with…

Soft Condensed Matter · Physics 2026-03-05 Eloise Lardet , Letian Chen , Thibault Bertrand

Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…

Dynamical Systems · Mathematics 2018-04-24 Inom Mirzaev , David M. Bortz

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the…

Analysis of PDEs · Mathematics 2015-05-19 Jacob Bedrossian , Nancy Rodríguez , Andrea Bertozzi

A microscopic, stochastic, minimal model for collective and cohesive motion of identical self-propelled particles is introduced. Even though the particles interact strictly locally in a very noisy manner, we show that cohesion can be…

Statistical Mechanics · Physics 2010-01-05 Guillaume Gregoire , Hugues Chate , Yuhai Tu

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…

Statistical Mechanics · Physics 2014-10-06 César Parra-Rojas , Joseph D. Challenger , Duccio Fanelli , Alan J. McKane

It is well-known that the two-dimensional Keller-Segel system admits finite time blowup solutions, which is the case if the initial density has a total mass greater than $8\pi$ and a finite second moment. Several constructive examples of…

Analysis of PDEs · Mathematics 2024-09-10 Charles Collot , Tej-Eddine Ghoul , Nader Masmoudi , Van Tien Nguyen

The results of the author and Gess [27] develop a robust well-posedness theory for a broad class of conservative stochastic PDEs, with both probabilistically stationary and non-stationary Stratonovich noise, and with irregular noise…

Probability · Mathematics 2025-04-28 Benjamin Fehrman

In this paper we prove well-posedness and stabibility of a class of stochastic delay differential equations with singular drift. Moreover, we show local well-posedness under localized assumptions.

Probability · Mathematics 2017-08-04 Stefan Bachmann