Related papers: Constraints on scalar diffusion anomaly in three-d…
We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection-diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our…
Given a velocity field $u(x,t)$, we consider the evolution of a passive tracer $\theta$ governed by $\partial_t\theta + u\cdot\nabla\theta = \Delta\theta + g$ with time-independent source $g(x)$. When $\|u\|$ is small in some sense,…
We consider self-similar solutions to the full compressible Euler system for an ideal gas in two and three space dimensions. The system admits a 2-parameter family of similarity solutions depending on parameters $\lambda$ and $\kappa$.…
We consider scaling limits of random quadrangulations obtained by applying the Cori-Vauquelin-Schaeffer bijection to Bienaym\'e-Galton-Watson trees with stably-decaying offspring tails with an exponent $\alpha$ in (1, 2). We show that these…
The field theoretic renormalization group and operator product expansion are applied to the problem of a passive scalar advected by the Gaussian nonsolenoidal velocity field with finite correlation time, in the presence of large-scale…
In this note we study the singular vanishing-viscosity limit of a gradient flow set in a finite-dimensional Hilbert space and driven by a smooth, but possibly non convex, time-dependent energy functional. We resort to ideas and techniques…
Electromagnetic decays of the scalar mesons are shown to be constrained by chiral symmetry as a consequence of the fact that, in the chiral limit, the two and three-point functions $<SS-PP>$ and $<VVS>$ satisfy super-convergent dispersion…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
Forced advection of passive scalar by a smooth $d$-dimensional incompressible velocity in the presence of a linear damping is studied. Acting separately advection and dumping do not lead to an essential intermittency of the steady scalar…
The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian,…
Since the pioneering work of Richardson in 1926, later refined by Batchelor and Obukhov in 1950, it is predicted that the rate of separation of pairs of fluid elements in turbulent flows with initial separation at inertial scales, grows…
We investigate a one-dimensional quantum system with a self-similar arrangement of delta-function potential barriers, exhibiting discrete scale invariance. The singular potential induces kinematically enforced symmetry breaking at $x=0$,…
We consider the scattering theory for the Schrodinger equation with $-\Delta -|x|^{\alpha}$ as a reference Hamiltonian, for $0< \alpha \leq 2$, in any space dimension. We prove that when this Hamiltonian is perturbed by a potential, the…
Kraichnan's model of passive scalar advection in which the driving velocity field has fast temporal decorrelation is studied as a case model for understanding the appearance of anomalous scaling in turbulent systems. We demonstrate how the…
We study the behaviour of the streamwise velocity variance in turbulent wall-bounded flows using a DNS database of pipe flow up to $Re_{\tau} \approx 12000$. The analysis of the spanwise spectra in the viscous near-wall region strongly…
We investigate horizontal dispersion of a passive scalar in a porous stratum with Rayleigh-Darcy convection initiated by a geothermal gradient. While increasing Rayleigh number ($Ra$) keeps enhancing convection, the horizontal dispersion…
For Kraichnan's problem of passive scalar advection by a velocity field delta-correlated in time, the limit of large space dimensionality $d\gg1$ is considered. Scaling exponents of the scalar field are analytically found to be…
We prove the hydrodynamic limit for the symmetric exclusion process with long jumps given by a mean zero probability transition rate with infinite variance and in contact with infinitely many reservoirs with density $\alpha$ at the left of…
We consider the Cauchy problem on nonlinear scalar conservation laws with a diffusion-type source term related to an index $s\in \R$ over the whole space $\R^n$ for any spatial dimension $n\geq 1$. Here, the diffusion-type source term…
The steady streaming flow pattern caused by a no-slip sphere oscillating in an unbounded viscous incompressible fluid is calculated exactly to second order in the amplitude. The pattern depends on a dimensionless scale number, determined by…