366 research outputs found
The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-B\'enard convection
When the classical Rayleigh-B\'enard (RB) system is rotated about its
vertical axis roughly three regimes can be identified. In regime I (weak
rotation) the large scale circulation (LSC) is the dominant feature of the
flow. In regime II (moderate rotation) the LSC is replaced by vertically
aligned vortices. Regime III (strong rotation) is characterized by suppression
of the vertical velocity fluctuations. Using results from experiments and
direct numerical simulations of RB convection for a cell with a
diameter-to-height aspect ratio equal to one at ()
and we identified the characteristics of the
azimuthal temperature profiles at the sidewall in the different regimes. In
regime I the azimuthal wall temperature profile shows a cosine shape and a
vertical temperature gradient due to plumes that travel with the LSC close to
the sidewall. In regime II and III this cosine profile disappears, but the
vertical wall temperature gradient is still observed. It turns out that the
vertical wall temperature gradient in regimes II and III has a different origin
than that observed in regime I. It is caused by boundary layer dynamics
characteristic for rotating flows, which drives a secondary flow that
transports hot fluid up the sidewall in the lower part of the container and
cold fluid downwards along the sidewall in the top part.Comment: 21 pages, 12 figure
Ground state of a resonantly interacting Bose gas
We show that a two-channel mean-field theory for a Bose gas near a Feshbach
resonance allows for an analytic computation of the chemical potential, and
therefore the universal constant \beta, at unitarity. To improve on this
mean-field theory, which physically neglects condensate depletion, we study a
variational Jastrow ansatz for the ground-state wave function and use the
hypernetted-chain approximation to minimize the energy for all positive values
of the scattering length. We also show that other important physical quantities
such as Tan's contact and the condensate fraction can be directly obtained from
this approach.Comment: Replaced with published version; 11 pages, 7 figure
On anomalous diffusion in a plasma in velocity space
The problem of anomalous diffusion in momentum space is considered for
plasma-like systems on the basis of a new collision integral, which is
appropriate for consideration of the probability transition function (PTF) with
long tails in momentum space. The generalized Fokker-Planck equation for
description of diffusion (in momentum space) of particles (ions, grains etc.)
in a stochastic system of light particles (electrons, or electrons and ions,
respectively) is applied to the evolution of the momentum particle distribution
in a plasma. In a plasma the developed approach is also applicable to the
diffusion of particles with an arbitrary mass relation, due to the small
characteristic momentum transfer. The cases of an exponentially decreasing in
momentum space (including the Boltzmann-like) kernel in the PT-function, as
well as the more general kernels, which create the anomalous diffusion in
velocity space due to the long tail in the PT-function, are considered.
Effective friction and diffusion coefficients for plasma-like systems are
found.Comment: 18 pages, no figure
Diffusion in a Time-dependent External Field
The problem of diffusion in a time-dependent (and generally inhomogeneous)
external field is considered on the basis of a generalized master equation with
two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck
approximation, when the probability transition function for diffusion
(PTD-function) does not possess a long tail in coordinate space and can be
expanded as a function of instantaneous displacements. The more complicated
case of long tails in the PTD will be discussed separately. We also discuss
diffusion on the basis of hydrodynamic and kinetic equations and show the
validity of the phenomenological approach. A new type of "collision" integral
is introduced for the description of diffusion in a system of particles, which
can transfer from a moving state to the rest state (with some waiting time
distribution). The solution of the appropriate kinetic equation in the external
field also confirms the phenomenological approach of the generalized master
equation.Comment: 18 pages, no figure
Anomalous Transport in Velocity Space, from Fokker-Planck to General Equation
The problem of anomalous diffusion in momentum (velocity) space is considered
based on the master equation and the appropriate probability transition
function (PTF). The approach recently developed by the author for coordinate
space, is applied with necessary modifications to velocity space. A new general
equation for the time evolution of the momentum distribution function in
momentum space is derived. This allows the solution of various problems of
anomalous transport when the probability transition function (PTF) has a long
tail in momentum space. For the opposite cases of the PTF rapidly decreasing as
a function of transfer momenta (when large transfer momenta are strongly
suppressed), the developed approach allows us to consider strongly
non-equilibrium cases of the system evolution. The stationary and
non-stationary solutions are studied. As an example, the particular case of the
Boltzmann-type PT-function for collisions of heavy and light particles with the
determined (prescribed) distribution function, which can be strongly
non-equilibrium, is considered within the proposed general approach. The
appropriate diffusion and friction coefficients are found. The Einstein
relation between the friction and diffusion coefficients is shown to be
violated in these cases.Comment: 23 pages, 0 figure
Kramers-Kronig Relations For The Dielectric Function And The Static Conductivity Of Coulomb Systems
The mutual influence of singularities of the dielectric permittivity e(q,w)
in a Coulomb system in two limiting cases w tends to zero, q tends to zero, and
opposite q tends to zero, w tends to zero is established. It is shown that the
dielectric permittivity e(q,w) satisfies the Kramers-Kronig relations, which
possesses the singularity due to a finite value of the static conductivity.
This singularity is associated with the long "tails" of the time correlation
functions.Comment: 9 pages, 0 figure
Kinetic theory of Jeans instability
Kinetic treatment of the Jeans gravitational instability, with collisions taken into account, is presented. The initial-value problem for the distribution function which obeys the kinetic equation, with the collision integral conserving the number of particles, is solved. Dispersion relation is obtained and analyzed. New modes are found. Collisions are shown not to affect the Jeans instability criterion. Although the instability growth rate diminishes, the collisions they cannot quench the instability. However, the oscillation spectrum is modified significantly: even in the neighborhood of the threshold frequency =0 (separating stable and unstable modes) the spectrum of oscillations can strongly depend on the collision frequency. Propagating (rather than aperiodic) modes are also found. These modes, however, are strongly damped
Duration and Time Trends in Hospital Stay for Very Preterm Infants Differ Across European Regions
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