Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMulti-flocks: emergent dynamics in systems with multi-scale collective behavior
145
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 turn peak at different time scales. We derive a `master-equation which describes a complex multi-flock congregations governed by two ingredients: (i) a fast inner-flock communication; and (ii) a slow(-er) inter-flock communication. The latter is driven by macroscopic observables which feature the up-scaling of the problem. We extend the current mono-flock theory, proving a series of results which describe rates of multi-flocking with natural dependencies on communication strengths. Both agent-based, kinetic, and hydrodynamic descriptions are considered, with particular emphasis placed on the discrete and macroscopic descriptions.
rate research
Read More
We overview recent developments in the study of alignment hydrodynamics, driven by a general class of symmetric communication kernels. A main question of interest is to characterize the emergent behavior of such systems, which we quantify in terms of the spectral gap of a weighted Laplacian associated with the alignment operator. Our spectral analysis of energy fluctuation covers both long-range and short-range kernels and does not require thermal equilibrium (no closure for the pressure). In particular, in the prototypical case of metric-based short-range kernels, the spectral gap admits a lower-bound expressed in terms of the discrete Fourier coefficients of the radial kernel, which enables us to quantify an emerging flocking behavior for non-vacuous solutions. These large-time behavior results apply as long as the solutions remain smooth. It is known that global smooth solutions exist in one and two spatial dimensions, subject to sub-critical initial data. We settle the question for arbitrary dimension, obtaining non-trivial initial threshold conditions which guarantee existence of multiD global smooth solutions.
In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which identifies a group to which they belong. Besides interacting within and across the groups, the agents may change label according to a state-dependent Markov-type jump process. We derive general kinetic equations for the joint interaction/label switch processes in each group. For prototypical birth/death dynamics, we characterise the transient and equilibrium kinetic distributions of the groups via a Fokker-Planck asymptotic analysis. Then we introduce and analyse a simple model for the contagion of infectious diseases, which takes advantage of the joint interaction/label switch processes to describe quarantine measures.
This paper is devoted to the construction of generalized multi-scale Young measures, which are the extension of Pedregals multi-scale Young measures [Trans. Amer. Math. Soc. 358 (2006), pp. 591-602] to the setting of generalized Young measures introduced by DiPerna and Majda [Comm. Math. Phys. 108 (1987), pp. 667-689]. As a tool for variational problems, these are well-suited objects for the study (at different length-scales) of oscillation and concentration effects of convergent sequences of measures. Important properties of multi-scale Young measures such as compactness, representation of non-linear compositions, localization principles, and differential constraints are extensively developed in the second part of this paper. As an application, we use this framework to address the $Gamma$-limit characterization of the homogenized limit of convex integrals defined on spaces of measures satisfying a general linear PDE constraint.
In the fermionic systems with topologically stable Fermi points the emergent two - component Weyl fermions appear. We propose the topological classification of these fermions based on the two invariants composed of the two - component Green function. We define these invariants using Wigner - Weyl formalism also in case of essentially non - homogeneous systems. In the case when values of these invariants are minimal ($pm 1$) we deal with emergent relativistic symmetry. The emergent gravity appears, and our classification of Weyl fermions gives rise to the classification of vierbein. Transformations between emergent relativistic Weyl fermions of different types correspond to parity conjugation, time reversal, and charge conjugation.
The presence of correlations between particles significantly separated in pseudorapidity in proton-proton and proton-nucleus collisions has raised questions about whether collective effects are observed in small collision systems as well as in heavy-ion collisions. The quantification of these long-range correlations by $v_n$ coefficients is of particular interest. A selection of the latest $v_n$ measurements is presented, including results from the recent $d$+Au beam energy scan at RHIC where a significant non-zero $v_2$ is measured down to low center-of-mass energies ($sqrt{s_{rm{NN}}}$ = 39 GeV). Results from a collision system scan - comprising $p$+Au, $d$+Au, and $^3$He+Au collisions - are also shown to address the role of the initial nuclear geometry in the final state anisotropy. Finally, the challenge of measuring multi-particle cumulants, particularly $c_2{4}$, in $p$+$p$ collisions is discussed, and new methods for reducing the effects of non-flow are shown to produce a more robust measurement of $v_2{4}$ in $p$+$p$ collisions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
