相关论文: Remark on the relation between passive scalars and…

This paper is devoted to the study of the dynamical behavior of the critically dissipative quasi-geostrophic equation in $\textbf{T}^2$. We prove that this system possesses time-dependent periodic solutions, bifurcating from a smooth steady…

We establish exact inequalities for the structure-function scaling exponents of a passively advected scalar in both the inertial-convective and viscous-convective ranges. These inequalities involve the scaling exponents of the velocity…

The Nelson stochastic mechanics of inhomogeneous quantum diffusion in flat spacetime with a tensor of diffusion can be described as a homogeneous one in a Riemannian manifold where this tensor of diffusion plays the role of a metric tensor.…

We explain how the invariant subspace method can be extended to a scalar and coupled system of time-space fractional partial differential equations. The effectiveness and applicability of the method have been illustrated through time-space…

The mixing of passive scalars of decreasing diffusivity, advected in each case by the same three-dimensional Navier-Stokes turbulence, is studied. The mixing becomes more isotropic with decreasing diffusivity. The local flow in the vicinity…

Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical…

Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…

We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions (in real space or in inverse space) where mixing is less efficient. We examine two situations. The first is…

We extend deterministic port-Hamiltonian systems (PHS) to a stochastic framework by means of stochastic differential equations. As the dissipation inequality plays a crucial role for deterministic PHS, we develop several passivity concepts…

The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. The effects of assigning different turning probabilities to the forward and…

Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different…

We consider statistics of the passive scalar on distances much larger than the pumping scale. Such statistics is determined by statistics of Lagrangian contraction that is by probabilities of initially distant fluid particles to come close.…

The background field equations for homogeneous and isotropic spacetime are derived in conformal scalar-tensor gravity. The background temporal evolution is entirely driven by the dynamical evolution of the scalar field, i.e. particle…

A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…

The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the…

The influence of compressibility on the stability of the scaling regimes of the passive scalar advected by a Gaussian velocity field with finite correlation time is investigated by the field theoretic renormalization group within two-loop…

Spatial and temporal noise power spectra of stripe patterns are investigated, using as a model a Swift-Hohenberg equation with a stochastic term. In particular, the analytical and numerical investigations show: 1) the temporal noise spectra…

The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range…

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find…

The dispersion of a passive scalar in a fluid through the combined action of advection and molecular diffusion is often described as a diffusive process, with an effective diffusivity that is enhanced compared to the molecular value.…