Related papers: Critical thresholds in flocking hydrodynamics\\wit…
We consider a hydrodynamic model of self-organized evolution of agents, with singular interaction kernel $\phi_\alpha(x)=1/|x|^{1+\alpha}$ ($0<\alpha<2$), in the presence of an additional external force. Well-posedness results are already…
Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale. We employ an agent-based model to describe the microscopic…
We consider one-dimensional, locally finite interacting particle systems with two conservation laws. The models have a family of stationary measures with product structure and we assume the existence of a uniform bound on the inverse of the…
Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a…
We investigate a continuum Lagrangian $p$-alignment system given by a nonlocal mean-field system of ordinary differential equations for interacting agents with weak initial data. We first establish global well-posedness of the Lagrangian…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel motion of agents, and are globally well-posed in…
Collective behaviour in biological systems pitches us against theoretical challenges way beyond the borders of ordinary statistical physics. The lack of concepts like scaling and renormalization is particularly grievous, as it forces us to…
In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation…
We demonstrate that hyperuniformity, the suppression of density fluctuations at large length scales, emerges generically from the interplay between conservation laws and non-equilibrium driving. The underlying mechanism for this emergence…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in…
In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in critical Besov spaces to the considered system with small…
We study the critical dynamics of a scalar field theory with $Z_2$ symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the…
We investigate global solutions to the Euler-alignment system in $d$ dimensions with unidirectional flows and strongly singular communication protocols $\phi(x) = |x|^{-(d+\alpha)}$ for $\alpha \in (0,2)$. Our paper establishes global…
The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
With the use of the general variational principle of self-organization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the…
In this paper, we study the well-posedness in critical Besov spaces for two-fluid Euler-Maxwell equations, which is different from the one fluid case. We need to deal with the difficulties mainly caused by the nonlinear coupling and…
This article concludes a series of papers (R. Folk, Yu. Holovatch, and G. Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)) where the tools of the field theoretical renormalization group were employed to explain…