Related papers: Lagrangian Dynamics in High-Dimensional Point-Vort…
Pairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical…
The statistical distribution of the radial pairwise peculiar velocity of galaxies is known to have an exponential form as implied by observations and explicitly shown in N-body simulations. Here we calculate its statistical distribution…
Conditional statistics of homogeneous isotropic turbulent flow is investigated by means of high-Reynolds number direct numerical simulations performed with $2048^3$ collocation points. Eulerian as well as Lagrangian velocity increment…
Motivated by systems in which droplets grow and shrink in a turbulence-driven supersaturation field, we investigate the problem of turbulent condensation in a general manner. Using direct numerical simulations we show that the turbulent…
Lagrangian pair dispersion provides insights into mixing in turbulent flows. By direct numerical simulations (DNS) we show that the statistics of pair dispersion in the randomly forced two-dimensional Burgers equation, which is a typical…
Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before…
Most approaches in Lagrangian fluid dynamics simulations proceed from the definition of particle volumes, from which discrete versions of the spatial differential operators are derived. Recently, Gallou\"et and M\'erigot [1] simultaneously…
Geophysical flows are often turbulent and subject to rotation. This rotation modifies the structure of turbulence and is thereby expected to sensibly affect its Lagrangian properties. Here, we investigate the relative dispersion and…
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…
We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh-B\'enard convection in a reduced Rayleigh-number range $1.3{\le}Ra/Ra_{c}{\le}166$. Under slow rotations ($Ra{\gtrsim}10Ra_{c}$), the vortices are…
We review some of the properties of higher-dimensional superstatistical stochastic models. As an example, we analyse the stochastic properties of a superstatistical model of 3-dimensional Lagrangian turbulence, and compare with experimental…
The orientation dynamics of small anisotropic tracer particles in turbulent flows is studied using direct numerical simulation (DNS) and results are compared with Lagrangian stochastic models. Generalizing earlier analysis for axisymmetric…
A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert…
The present paper derives the post-Newtonian Lagrangian of translational motion of N arbitrary-structured bodies with all mass and spin multipoles in a scalar-tensor theory of gravity. The multipoles depend on time and evolve in accordance…
Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The…
This two-part paper aims to provide a Lagrangian perspective of the final southern warming in spring of 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting. We approach the subject from a dynamical systems…