Related papers: Eulerian dynamics with a commutator forcing II: fl…
The two dimensional crossover from independent particle towards collective motion is studied using 2 spinless fermions interacting via a U/r Coulomb repulsion in a LxL square lattice with periodic boundary conditions and nearest neighbor…
We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering towards a weighted average heading. We consider the class of so-called $p$-alignment hydrodynamics, based on $2p$-Laplacians, and weighted by a general…
We analyze a family of degenerate parabolic equations with linear growth Lagrangian having the form $u_t=\div (\varphi(u)\psi(\nabla u/u))$. Here $|\psi|\le 1$ and saturates at infinity. We present a simple and natural set of assumptions on…
We propose \emph{Euler Mean Flows (EMF)}, a flow-based generative framework for one-step and few-step generation that enforces long-range trajectory consistency with minimal sampling cost. The key idea of EMF is to replace the trajectory…
In this paper, we study the following class of fractional Hamiltonian systems: \begin{eqnarray*} \begin{aligned}\displaystyle \left\{ \arraycolsep=1.5pt \begin{array}{ll} (-\Delta)^{\frac{1}{2}} u + u = \Big(I_{\mu_{1}}\ast G(v)\Big)g(v) \…
The collective behaviour of confluent cell sheets is strongly influenced both by polar forces, arising through cytoskeletal propulsion and by active inter-cellular forces, which are mediated by interactions across cell-cell junctions. We…
We investigate the joint density-velocity evolution in $f(R)$ gravity using smooth, compensated spherical top-hats as a proxy for the non-linear regime. Using the Hu-Sawicki model as a working example, we solve the coupled continuity, Euler…
On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…
A one-dimensional flocking model using active Ising spins is studied, where the system evolves through the reinforcement learning approach \textit{via} defining state, action, and cost function for each spin. The orientation of spin with…
We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the stan- dard Laplacian…
This paper investigates the asymptotic behavior of the solutions of the Fisher-KPP equation in a heterogeneous medium, $$\partial_t u = \partial_{xx} u + f(x,u),$$ associated with a compactly supported initial datum. A typical nonlinearity…
Motivated by applications in conditional sampling, given a probability measure $\mu$ and a diffeomorphism $\phi$, we consider the problem of simultaneously approximating $\phi$ and the pushforward $\phi_{\#}\mu$ by means of the flow of a…
Using numerical simulations we examine the velocity fluctuations of a probe particle driven with constant force through a two-dimensional disordered assembly of disks which has a well-defined jamming point J at a density of \phi_J=0.843. As…
For an orientable surface with an area form, there are two invariants of area-preserving dynamics, the flux homomorphism and the Calabi invariant. Tsuboi found a remarkable connection between the Calabi invariant on the closed disk and a…
We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent…
We study the (hydro-)dynamics of multi-species driven by alignment. What distinguishes the different species is the protocol of their interaction with the rest of the crowd: the collective motion is described by different communication…
Many models of flocking involve alignment rules based on the mean orientation of neighboring particles, which we show introduces microscopic non-reciprocal interactions. In the absence of this microscopic non-reciprocity an exceptional…
Dynamical simulations of polaron transport in conjugated polymers in the presence of an external time-dependent electric field have been performed within a combined extended Hubbard model (EHM) and Su-Schrieffer-Heeger (SSH) model. Nearly…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
The Euler phi function on a given integer $n$ yields the number of positive integers less than $n$ that are relatively prime to $n$. Equivalently, it gives the order of the group of units in the quotient ring $\mathbb{Z}/(n)$. We generalize…