相关论文: On the Mathematics of Swarming: Emergent Behavior …
We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group $\mathrm{SO}(3)$ by identifying closed form expressions for geometric quantities such as covariant derivative and parallel transport in exponential…
We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of…
We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in…
We show that hydrodynamic theories of polar active matter generically possess inhomogeneous traveling solutions. We introduce a unifying dynamical-system framework to establish the shape of these intrinsically nonlinear patterns, and show…
In this paper we study the steady state of the fluctuations of the surface for a model of surface growth with relaxation to any of its lower nearest neighbors (SRAM) [F. Family, J. Phys. A {\bf 19}, L441 (1986)] in scale free networks. It…
We study the energy distribution in the extended resonant level model at equilibrium. Previous investigations [Phys. Rev. B {\bf 89}, 161306 (2014), Phys. Rev. B {\bf 93}, 115318 (2016)] have found, for a resonant electronic level…
A lot of efforts have been devoted in the last decade to the investigation of the high-frequency behaviour of geometric functionals for the excursion sets of random spherical harmonics, i.e., Gaussian eigenfunctions for the spherical…
We provide a bird's eye view on developments in analyzing the long time, large crowd behavior of Cucker-Smale alignment dynamics. We consider a class of (fully-)discrete models, paying particular attention to general alignment protocols in…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-time…
We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
A hallmark of far-from-equilibrium systems is the emergence of a spectral cascade, where energy is transferred across length-scales following a simple power law. The universal nature of this phenomenon has led to advances in a range of…
This is a study of the Euler equations for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem…
Starting from symmetry considerations, we derive the generic hydrodynamic equation of non-equilibrium $XY$ spin systems with $N$-atic symmetry under weak fluctuations. Through a systematic treatment we demonstrate that, in two dimensions,…
Many organisms in nature use local interactions to generate global cooperative phenomena. To unravel how the behavior of individuals generates effective interactions within a group, we introduce a simple model, wherein each agent senses the…
A general expression for the momentum equation in the Smooth Particle Hydrodynacis approximation is derived for an arbitrary kernel, and compared with its spherical counterpart for various degrees of ellipsoidicity. For such an ellsipsoidal…
This note introduces a new method for establishing alignment in systems of collective behavior with degenerate communication protocol. The communication protocol consists of a kernel defining interaction between pairs of agents. Degeneracy…
Averaging and evolving inhomogeneities are non-commuting operations. This implies the existence of deviations of an averaged model from the standard Friedmann-Lemaitre cosmologies. We quantify these deviations, encoded in a backreaction…
By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and…