692 research outputs found
On cosmic rotation
We overview our recent studies of cosmological models with expansion and
global rotation. Problems of the early rotating models are discussed, and the
class of new viable cosmologies is described in detail. Particular attention is
paid to the observational effects of the cosmic rotation.Comment: 22 pages, Revte
Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection
We investigate experimentally the statistical properties of active and
passive scalar fields in turbulent Rayleigh-B\'{e}nard convection in water, at
. Both the local concentration of fluorescence dye and the local
temperature are measured near the sidewall of a rectangular cell. It is found
that, although they are advected by the same turbulent flow, the two scalars
distribute differently. This difference is twofold, i.e. both the quantities
themselves and their small-scale increments have different distributions. Our
results show that there is a certain buoyant scale based on time domain, i.e.
the Bolgiano time scale , above which buoyancy effects are significant.
Above , temperature is active and is found to be more intermittent than
concentration, which is passive. This suggests that the active scalar possesses
a higher level of intermittency in turbulent thermal convection. It is further
found that the mixing of both scalar fields are isotropic for scales larger
than even though buoyancy acts on the fluid in the vertical direction.
Below , temperature is passive and is found to be more anisotropic than
concentration. But this higher degree of anisotropy is attributed to the higher
diffusivity of temperature over that of concentration. From the simultaneous
measurements of temperature and concentration, it is shown that two scalars
have similar autocorrelation functions and there is a strong and positive
correlation between them.Comment: 13 pages and 12 figure
The Kelvin-wave cascade in the vortex filament model
The energy transfer mechanism in zero temperature superfluid turbulence of
helium-4 is still a widely debated topic. Currently, the main hypothesis is
that weakly nonlinear interacting Kelvin waves transfer energy to sufficiently
small scales such that energy is dissipated as heat via phonon excitations.
Theoretically, there are at least two proposed theories for Kelvin-wave
interactions. We perform the most comprehensive numerical simulation of weakly
nonlinear interacting Kelvin-waves to date and show, using a specially designed
numerical algorithm incorporating the full Biot-Savart equation, that our
results are consistent with nonlocal six-wave Kelvin wave interactions as
proposed by L'vov and Nazarenko.Comment: 6 pages, 6 figure
An assessment of Evans' unified field theory II
Evans developed a classical unified field theory of gravitation and
electromagnetism on the background of a spacetime obeying a Riemann-Cartan
geometry. In an accompanying paper I, we analyzed this theory and summarized it
in nine equations. We now propose a variational principle for Evans' theory and
show that it yields two field equations. The second field equation is algebraic
in the torsion and we can resolve it with respect to the torsion. It turns out
that for all physical cases the torsion vanishes and the first field equation,
together with Evans' unified field theory, collapses to an ordinary Einstein
equation.Comment: 11 pages of late
A stochastic model of cascades in 2D turbulence
The dual cascade of energy and enstrophy in 2D turbulence cannot easily be
understood in terms of an analog to the Richardson-Kolmogorov scenario
describing the energy cascade in 3D turbulence. The coherent up- and downscale
fluxes points to non-locality of interactions in spectral space, and thus the
specific spatial structure of the flow could be important. Shell models, which
lack spacial structure and have only local interactions in spectral space,
indeed fail in reproducing the correct scaling for the inverse cascade of
energy. In order to exclude the possibility that non-locality of interactions
in spectral space is crucial for the dual cascade, we introduce a stochastic
spectral model of the cascades which is local in spectral space and which shows
the correct scaling for both the direct enstrophy - and the inverse energy
cascade.Comment: 4 pages, 3 figure
Kraichnan model of passive scalar advection
A simple model of a passive scalar quantity advected by a Gaussian
non-solenoidal ("compressible") velocity field is considered. Large order
asymptotes of quantum-field expansions are investigated by instanton approach.
The existence of finite convergence radius of the series is proved, a position
and a type of the corresponding singularity of the series in the regularization
parameter are determined. Anomalous exponents of the main contributions to the
structural functions are resummed using new information about the series
convergence and two known orders of the expansion.Comment: 21 page
From non-Brownian Functionals to a Fractional Schr\"odinger Equation
We derive backward and forward fractional Schr\"odinger type of equations for
the distribution of functionals of the path of a particle undergoing anomalous
diffusion. Fractional substantial derivatives introduced by Friedrich and
co-workers [PRL {\bf 96}, 230601 (2006)] provide the correct fractional
framework for the problem at hand. In the limit of normal diffusion we recover
the Feynman-Kac treatment of Brownian functionals. For applications, we
calculate the distribution of occupation times in half space and show how
statistics of anomalous functionals is related to weak ergodicity breaking.Comment: 5 page
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