Constraints on scalar diffusion anomaly in three-dimensional flows having bounded velocity gradients

This study is concerned with the decay behaviour of a passive scalar $\theta$ in three-dimensional flows having bounded velocity gradients. Given an initially smooth scalar distribution, the decay rate $d/dt$ of the scalar variance $$ is found to be bounded in terms of controlled physical parameters. Furthermore, in the zero diffusivity limit, $\kappa\to0$, this rate vanishes as $\kappa^{\alpha_0}$ if there exists an $\alpha_0\in(0,1]$ independent of $\kappa$ such that $<\infty$ for $\alpha\le\alpha_0$. This condition is satisfied if in the limit $\kappa\to0$, the variance spectrum $\Theta(k)$ remains steeper than $k^{-1}$ for large wave numbers $k$. When no such positive $\alpha_0$ exists, the scalar field may be said to become virtually singular. A plausible scenario consistent with Batchelor's theory is that $\Theta(k)$ becomes increasingly shallower for smaller $\kappa$, approaching the Batchelor scaling $k^{-1}$ in the limit $\kappa\to0$. For this classical case, the decay rate also vanishes, albeit more slowly -- like $(\ln P_r)^{-1}$, where $P_r$ is the Prandtl or Schmidt number. Hence, diffusion anomaly is ruled out for a broad range of scalar distribution, including power-law spectra no shallower than $k^{-1}$. The implication is that in order to have a $\kappa$-independent and non-vanishing decay rate, the variance at small scales must necessarily be greater than that allowed by the Batchelor spectrum. These results are discussed in the light of existing literature on the asymptotic exponential decay $\sim e^{-\gamma t}$, where $\gamma>0$ is independent of $\kappa$.Comment: 6-7 journal pages, no figures. accepted for publication by Phys. Fluid

Teleparallel origin of the Fierz picture for spin-2 particle

A new approach to the description of spin-2 particle in flat and curved spacetime is developed on the basis of the teleparallel gravity theory. We show that such an approach is in fact a true and natural framework for the Fierz representation proposed recently by Novello and Neves. More specifically, we demonstrate how the teleparallel theory fixes uniquely the structure of the Fierz tensor, discover the transparent origin of the gauge symmetry of the spin 2 model, and derive the linearized Einstein operator from the fundamental identity of the teleparallel gravity. In order to cope with the consistency problem on the curved spacetime, similarly to the usual Riemannian approach, one needs to include the non-minimal (torsion dependent) coupling terms.Comment: 5 pages, Revtex4, no figures. Accepted for publication in Phys. Rev.

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

Joint Probability Distributions for a Class of Non-Markovian Processes

We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single time probability distributions to the case of N-time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.Comment: 13 pages, 1 figur

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

Matter Wave Turbulence: Beyond Kinetic Scaling

Turbulent scaling phenomena are studied in an ultracold Bose gas away from thermal equilibrium. Fixed points of the dynamical evolution are characterized in terms of universal scaling exponents of correlation functions. The scaling behavior is determined analytically in the framework of quantum field theory, using a nonperturbative approximation of the two-particle irreducible effective action. While perturbative Kolmogorov scaling is recovered at higher energies, scaling solutions with anomalously large exponents arise in the infrared regime of the turbulence spectrum. The extraordinary enhancement in the momentum dependence of long-range correlations could be experimentally accessible in dilute ultracold atomic gases. Such experiments have the potential to provide insight into dynamical phenomena directly relevant also in other present-day focus areas like heavy-ion collisions and early-universe cosmology.Comment: 18 pages, 2 figure

Catechol estrogens stimulate insulin secretion in pancreatic β-cells via activation of the transient receptor potential A1 (TRPA1) channel

Estrogen hormones play an important role in controlling glucose homeostasis and pancreatic β-cell function. Despite the significance of estrogen hormones for regulation of glucose metabolism, little is known about the roles of endogenous estrogen metabolites in modulating pancreatic β-cell function. In this study, we evaluated the effects of major natural estrogen metabolites, catechol estrogens, on insulin secretion in pancreatic β-cells. We show that catechol estrogens, hydroxylated at positions C2 and C4 of the steroid A ring, rapidly potentiated glucose-induced insulin secretion via a nongenomic mechanism. 2-Hydroxyestrone, the most abundant endogenous estrogen metabolite, was more efficacious in stimulating insulin secretion than any other tested catechol estrogens. In insulin-secreting cells, catechol estrogens produced rapid activation of calcium influx and elevation in cytosolic free calcium. Catechol estrogens also generated sustained elevations in cytosolic free calcium and evoked inward ion current in HEK293 cells expressing the transient receptor potential A1 (TRPA1) cation channel. Calcium influx and insulin secretion stimulated by estrogen metabolites were dependent on the TRPA1 activity and inhibited with the channel-specific pharmacological antagonists or the siRNA. Our results suggest the role of estrogen metabolism in a direct regulation of TRPA1 activity with potential implications for metabolic diseases

On the exact Foldy-Wouthuysen transformation for a Dirac spinor in torsion and other CPT and Lorentz violating backgrounds

We discuss the possibility to perform and use the exact Foldy-Wouthuysen transformation (EFWT) for the Dirac spinor coupled to different CPT and Lorentz violating terms. The classification of such terms is performed, selecting those of them which admit EFWT. For the particular example of an axial vector field, which can be associated with the completely antisymmetric torsion, we construct an explicit EFWT in the case when only a timelike component of this axial vector is present. In the cases when EFWT is not possible, one can still use the corresponding technique for deriving the perturbative Foldy-Wouthuysen transformation, as is illustrated in a particular example in the Appendix