Related papers: Oscillating sequences, Gowers norms and Sarnak's c…
In the recently proposed generating systems for the (anti)holomorphic sector of the 4d higher spin theory and for the off-shell higher spin theory in generic dimension locality was achieved due to a peculiar limiting star product. Even…
We report on progress on the free surface flow in the presence of submerged oscillating line sources (2D) or point sources (3D) when a simple shear flow is present varying linearly with depth. Such sources are in routine use as Green…
Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…
In this work, we discuss how the linear and non-linear advection terms modify the scaling behavior of the continuous symmetry breaking and stabilize the long-range order, even in $d=2$ far from equilibrium, by means of simple scaling…
The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to…
We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby…
A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
We prove nonlinear asymptotic stability of a large class of monotonic shear flows among solutions of the 2D Euler equations in the channel $\mathbb{T}\times[0,1]$. More precisely, we consider shear flows $(b(y),0)$ given by a function $b$…
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating…
We establish Sarnak's conjecture on M\"obius disjointness for the dynamical system of a skew product on a circle and the three-dimensional Heisenberg nilmanifold, first studied by Wen Huang, Jianya Liu and Ke Wang. We advance the work of…
The ergodic properties of two uncoupled oscillators, a horizontal and vertical one, residing in a class of non rectangular star-shaped polygons with only vertical and horizontal boundaries and impacting elastically from its boundaries are…
Measurements of any property of a microscopic system are bound to show significant deviations from the average, due to thermal fluctuations. For time-integrated currents such as heat, work or entropy production in a steady state, it is in…
We study the ergodic properties (recurrence, discrepancy, diffusion coefficients and ergodicity itself) of a class of $\mathbb Z$-extensions over infinite interval exchange transformations called rotated odometers. The choice of a…
Estimating the causal structure of observational data is a challenging combinatorial search problem that scales super-exponentially with graph size. Existing methods use continuous relaxations to make this problem computationally tractable…
High resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussianity of velocity differences statistics are quantitatively investigated. The level of statistical…
We investigate a scaling limit of gradient stochastic dynamics associated to Gibbs states in classical continuous systems on ${\mathbb R}^d, d \ge 1$. The aim is to derive macroscopic quantities from a given micro- or mesoscopic system. The…
We show that oscillating flow of a simple fluid in both the Newtonian and the non-Newtonian regime can be described by a universal function of a single dimensionless scaling parameter $\omega\tau$, where $\omega$ is the oscillation…
In this paper, we study systems of time-invariant ordinary differential equations whose flows are non-expansive with respect to a norm, meaning that the distance between solutions may not increase. Since non-expansiveness (and…
We study the recurrence properties of certain skew products over symmetric interval exchange transformations, including rotations, with cocycles of the form $f(x)=-\frac{1}{x^a}+\frac{1}{(1-x)^a}$, where $a>1$. We prove that typically, such…