Related papers: Time Evolution of a Passive Scalar in a Turbulent …
Dynamical evolution of the quantum ground state (vacuum) is analyzed for time variant harmonic oscillators characterized by asymptotically constant frequency. The oscillatory density matrix in the asymptotic future is uniquely determined by…
We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and…
We investigate the dynamical behavior of a scalar field non-minimally coupled to Einstein's tensor and Ricci scalar in geometries of asymptotically de Sitter spacetimes. We show that the quasinormal modes remain unaffected if the scalar…
Dynamics of viscous shocks is considered in the modular Burgers equation, where the time evolution becomes complicated due to singularities produced by the modular nonlinearity. We prove that the viscous shocks are asymptotically stable…
Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different…
We consider the statistical description of steady state fully developed incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We show that turbulence statistics is scale but not conformally…
Some black hole mimickers, as well as black strings and other higher-dimensional spacetimes, exhibit stable light rings-regions where light or high-frequency gravitational waves can be trapped. In these regions, linear perturbations decay…
The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the…
Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) have been undergoing important improvements. In fact, many results obtained do not have an analogous for smooth vector fields. For example, the chaoticity of…
We study the spatio-temporal two-point correlation function of passively advected scalar fields in the inertial-convective range in three dimensions by means of numerical simulations. We show that at small time delays $t$ the correlations…
Recent work in the literature has studied a version of non-commutative Schwarzschild black holes where the effects of non-commutativity are described by a mass function depending on both the radial variable r and a non-commutativity…
We study stochastic evolution equations driven by Gaussian noise. The key features of the model are that the operators in the deterministic and stochastic parts can have the same order and the noise can be time-only, space-only, or…
The dynamics of expansion of the Universe and evolution of scalar perturbations are studied for the quintessential scalar fields $Q$ with the classical Lagrangian satisfying the additional condition $w=const$ or $c^2_a=0$. Both…
We consider transport of a passive scalar advected by an irregular divergence free vector field. Given any non-constant initial data $\bar \rho \in H^1_\text{loc}({\mathbb R}^d)$, $d\geq 2$, we construct a divergence free advecting velocity…
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and…
Universality of statistical properties of passive quantities advected by turbulent velocity fields at changing the passive forcing mechanism is discussed. In particular, we concentrate on the statistical properties of an hydrodynamic system…
In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…
The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and…
We exploit the possibility of existence of a repulsive gravity phase in the evolution of the Universe. A toy model with a free scalar field minimally coupled to gravity, but with the "wrong sign" for the energy and negative curvature for…
We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…