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The analysis of a stochastic interacting particle scheme for approximation of the measure valued solutions to the Keller-Segel system in 2D is continued. In previous work it has been shown that, in the limit of the regularized scheme when the number of particles N tends to infinity, solutions of the regularized Keller-Segel system are recovered. In the… (More)

We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels we provide a rigorous derivation of the mean-field kinetic equation. Moreover, we study the energy of the system, show that… (More)

We introduce and discuss the possible dynamics of groups of undistinguished agents, which are interacting according to their relative positions, with the aim of deriving hydrodynamical equations. These models are developed to mimic the collective motion of groups of living individuals such as bird flocks, fish schools, herds of quadrupeds or bacteria… (More)

- Massimo Fornasier, J. Haskovec, Jan Vybíral
- Multiscale Modeling & Simulation
- 2011

In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such systems, one has to deal with a large number of agents (typically millions) in spaces of parameters describing each agent… (More)

Abstract. We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighbourhood. In the first-order model the location of each individual is subject to a density-dependent random walk, while in the second-order model the… (More)

- J. Haskovec, Dietmar Oelz
- 2014

Abstract. On the d-dimensional torus we consider the drift-diffusion equation corresponding to the mean field limit of a stochastic model for direct aggregation which features a diffusion coefficient that depends on the locally measured empirical density. In particular, we consider the situation where the diffusion coefficient may take one of two possible… (More)

- J. Haskovec, Peter A. Markowich, Benôıt Perthame, Matthias Schlottbom, Luis Vázquez
- 2017

We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai [8, 10], which models the formation of biological transport networks. The model describes the pressure field using a Darcy’s type equation and the dynamics of the conductance network under pressure force effects.… (More)

The Spherical Harmonics Expansion (SHE) assumes a momentum distribution function only depending on the microscopic kinetic energy. The SHE-Poisson system describes carrier transport in semiconductors with self-induced electrostatic potential. Existence of weak solutions to the SHEPoisson system subject to periodic boundary conditions is established, based… (More)

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