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The derivation of effective descriptions for interacting many-body systems is an important branch of applied mathematics. We prove a propagation of chaos result for a system of $N$ particles subject to Newtonian time evolution with or…
This paper discusses the leading-order correction induced by cosmological perturbations on the average expansion rate of an expanding spacetime, containing one or many perfect fluids. The calculation is carried out up to the second order in…
The dynamics of the torsion field is analyzed in the framework of the Covariant Canonical Gauge Theory of Gravity (CCGG), a De~Donder-Weyl Hamiltonian formulation of gauge gravity. The action is quadratic in both, the torsion and the…
It is shown that a first-order relativistic perturbation theory for the open, flat or closed Friedmann-Lemaitre-Robertson-Walker universe admits one, and only one, gauge-invariant quantity which describes the perturbation to the energy…
We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
In this article, we study the asymptotic behavior of the spatial integral of the solution to the hyperbolic Anderson model in dimension $d\leq 2$, as the domain of the integral gets large (for fixed time $t$). This equation is driven by a…
Caustics in the dynamics of heavy particles in turbulence accelerate particle collisions. The rate $\mathscr{J}$ at which these singularities form depends sensitively on the Stokes number St, the non-dimensional inertia parameter. Exact…
In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation…
Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics can be represented by population rate equations based on a mean field assumption, according to…
Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles, whose average value agrees with expressions derived previously. We analyze the relation…
Velocity and absorption coefficient of the plane sound waves in classical gases are obtained by solving the Boltzmann kinetic equation. This is done within the linear response theory as a reaction of the single-particle distribution…
Rayleigh-Taylor (RT) instability commonly arises in compressible systems with time-dependent acceleration in practical applications. To capture the complex dynamics of such systems, a two-component discrete Boltzmann method is developed to…
In this paper, we consider an inference problem for the first order autoregressive process with non-zero mean driven by a long memory stationary Gaussian process. Suppose that the covariance function of the noise can be expressed as…
The goal of this paper is to propose a theoretical framework to study homogeneous and isotropic turbulence in a viscoelastic fluid, regarded as a perturbation of a Newtonian incompressible fluid, where the fluid relaxation time, or else the…
We investigate the behavior of microscopic heavy particles settling in homogeneous air turbulence. The regimes are relevant to the airborne transport of dust and droplets: the Taylor-microscale Reynolds number is Re = 289 - 462, the…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
Upon its inception the theory of regularity structures allowed for the treatment for many semilinear perturbations of the stochastic heat equation driven by space-time white noise. When the driving noise is non-Gaussian the machinery of…
When a physical system evolves in a thermal bath at a constant temperature, it arrives eventually to an equilibrium state whose properties are independent of the kinetic parameters and of the precise evolution scenario. This is generically…
This paper consists of two parts. In the first part, we focus on the average of a functional over shifted Gaussian homogeneous noise and as the averaging domain covers the whole space, we establish a Breuer-Major type Gaussian fluctuation…