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We study the asymptotic emergent dynamics of two models that can be thought of as extensions of the well known Schr\"odinger-Lohe model for quantum synchronization. More precisely, the interaction strength between different oscillators is…
We study the short-time dynamics of a mean-field model with non-conserved order parameter (Curie-Weiss with Glauber dynamics) by solving the associated Fokker-Planck equation. We obtain closed-form expressions for the first moments of the…
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…
We consider the problem of understanding the coordinated movements of biological or artificial swarms. In this regard, we propose a learning scheme to estimate the coordination laws of the interacting agents from observations of the swarm's…
We study the evolution of a flat Friedmann-Robertson- Walker Universe, filled with a bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The dimensional analysis of the model suggest a…
This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic…
We study the problem of consensus emergence in multi-agent systems via external feedback controllers. We consider a set of agents interacting with dynamics given by a Cucker-Smale type of model, and study its consensus stabilization by…
The paper introduces a model of collective behavior where agents receive information only from sufficiently dense crowds in their immediate vicinity. The system is an asymmetric, density-induced version of the Cucker-Smale model with…
We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses…
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…
We analyze the long time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type scattering operator, subject to confining potentials of harmonic oscillator type. We establish the conditions under…
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the…
Collective motion in animal groups provide examples of emergent, decentralised coordination. Here, we examine a bottom-up model of collective behavior based on Future State Maximisation (FSM). In this model agents seek to maximise the…
This paper studies the problem of decentralized continuum deformation coordination of multi-agent systems aided by cooperative localization. We treat agents as particles inside a triangular continuum (deformable body) in a2-D motion space…
We compute the full probability distribution of the spectral form factor in the self-dual kicked Ising model by providing an exact lower bound for each moment and verifying numerically that the latter is saturated. We show that at large…
We investigate the hydrodynamic limit problem for a kinetic flocking model. We develop a GCI-based Hilbert expansion method, and establish rigorously the asymptotic regime from the kinetic Cucker-Smale model with a confining potential in a…
Populations of self-propelled mobile agents - animal groups, robot swarms or crowds of people - that exchange information with their surrounding, host fascinating cooperative behaviors. While in many situations of interest the agents motion…
Fish, birds, insects and robots frequently swim or fly in groups. During their 3 dimensional collective motion, these agents do not stop, they avoid collisions by strong short-range repulsion, and achieve group cohesion by weak long-range…
We study the large-time behavior of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dynamics, e.g., Cucker-Smale and Motsch-Tadmor models…
From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization,…