Related papers: On reduced inertial PDE models for Cucker-Smale fl…
We analyze the one dimensional Cucker-Smale (in short CS) model with a weak singular communication weight $\psi(x) = |x|^{-\beta}$ with $\beta \in (0,1)$. We first establish a global-in-time existence of measure-valued solutions to the…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
We study emergent behaviors of thermomechanical Cucker-Smale (TCS) ensemble confined in a harmonic potential field. In the absence of external force field, emergent dynamics of TCS particles has been extensively studied recently under…
Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
We consider a particle system with a mean-field-type interaction perturbed by some common and individual noises. When the interacting kernels are sublinear and only locally Lipschitz-continuous, relying on arguments based on the tightness…
We derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with non-symmetric interaction weights. The condition prescribes smallness of the delay length relative to…
In this work we derive and analyze coarse-grained descriptions of self-propelled particles with selective attraction-repulsion interaction, where individuals may respond differently to their neighbours depending on their relative state of…
In this paper, we deal with a Cucker-Smale model with time-dependent time delay and communication failures. Namely, we investigate the situation in which the agents involved in a flocking process can possibly suspend the exchange of…
We prove existence of global $C^1$ piecewise weak solutions for the discrete Cucker-Smale's flocking model with the communication weight $\psi(s)=s^{-\alpha}, 0<\alpha<1.$ We also discuss the possibility of finite in time alignment of the…
In this work, we perform modulation analysis of monokinetic limits from the kinetic Cucker- Smale model to the pressureless Euler alignment system. Two regimes are considered -- a strong Fokker- Planck force with vanishing noise and Knudsen…
Particle filters (PFs) are recursive Monte Carlo algorithms for Bayesian tracking and prediction in state space models. This paper addresses continuous-discrete filtering problems, where the hidden state evolves as an It\^o stochastic…
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…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…
In this paper, we study the behavior of systems of individuals in confined environments that are driven by laws of self-organization. We propose that, under certain conditions, the long-term behavior of such systems will be global…
Inertial microfluidics has been limited to dilute particle concentrations due to defocusing (spreading out) at high particle concentrations. We observe a counterintuitive shift of focusing to the outer curved wall under high concentration…
We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We…
We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…
To understand the process of pattern formation in a low-density granular flow, we propose a simple particle model. This model considers spherical particles moving over an inclined flat surface based on three forces: gravity as the driving…