Entire solutions of hydrodynamical equations with exponential dissipation

We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as \ue ^{|k|/\kd} at high wavenumbers $|k|$. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than \ue ^{-C(k/\kd) \ln (|k|/\kd)} for any $C<1/(2\ln 2)$. The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with $C= C_\star =1/\ln2$. The same behavior with a universal constant $C_\star$ is conjectured for the Navier--Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier--Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.Comment: 29 pages, 3 figures, Comm. Math. Phys., in pres

Analytic solutions and Singularity formation for the Peakon b--Family equations

Using the Abstract Cauchy-Kowalewski Theorem we prove that the $b$-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to $H^s$ with $s > 3/2$, and the momentum density $u_0 - u_{0,{xx}}$ does not change sign, we prove that the solution stays analytic globally in time, for $b\geq 1$. Using pseudospectral numerical methods, we study, also, the singularity formation for the $b$-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity approaches the real axis, estimating the rate of decay of the Fourier spectrum

Turbulence in a free surface

We report an experimental and numerical study of turbulent fluid motion in a free surface. The flow is realized experimentally on the surface of a tank filled with water stirred by a vertically oscillating grid positioned well below the surface. Particles floating on the surface are used to visualize the flow. The effect of surface waves appears to be negligible. The flow is unconventional in that it is confined to two dimensions but does not have squared vorticity as a conservation law, that it is not divergence free and that it inherits scaling features of the mean square velocity differences S_2(R) and the vorticity fluctuations Omega(R) from the bulk 3-d turbulence.Comment: 4 pages, 4 Postscript figure

The First Magnetic Fields

We review current ideas on the origin of galactic and extragalactic magnetic fields. We begin by summarizing observations of magnetic fields at cosmological redshifts and on cosmological scales. These observations translate into constraints on the strength and scale magnetic fields must have during the early stages of galaxy formation in order to seed the galactic dynamo. We examine mechanisms for the generation of magnetic fields that operate prior during inflation and during subsequent phase transitions such as electroweak symmetry breaking and the quark-hadron phase transition. The implications of strong primordial magnetic fields for the reionization epoch as well as the first generation of stars is discussed in detail. The exotic, early-Universe mechanisms are contrasted with astrophysical processes that generate fields after recombination. For example, a Biermann-type battery can operate in a proto-galaxy during the early stages of structure formation. Moreover, magnetic fields in either an early generation of stars or active galactic nuclei can be dispersed into the intergalactic medium.Comment: Accepted for publication in Space Science Reviews. Pdf can be also downloaded from http://canopus.cnu.ac.kr/ryu/cosmic-mag1.pd

Oxidation of Aqueous Phosphorous Acid Electrolyte in Contact with Pt Studied by X ray Photoemission Spectroscopy

The oxidation of the aqueous H3PO3 in contact with Pt was investigated for a fundamental understanding of the Pt aqueous H3PO3 interaction with the goal of providing a comprehensive basis for the further optimization of high temperature polymer electrolyte membrane fuel cells HT PEMFCs . Ion exchange chromatography IEC experiments suggested that in ambient conditions, Pt catalyzes H3PO3 oxidation to H3PO4 with H2O. X ray photoelectron spectroscopy XPS on different substrates, including Au and Pt, previously treated in H3PO3 solutions was conducted to determine the catalytic abilities of selected metals toward H3PO3 oxidation. In situ ambient pressure hard X ray photoelectron spectroscopy AP HAXPES combined with the dip and pull method was performed to investigate the state of H3PO3 at the Pt H3PO3 interface and in the bulk solution. It was shown that whereas H3PO3 remains stable in the bulk solution, the catalyzed oxidation of H3PO3 by H2O to H3PO4 accompanied by H2 generation occurs in contact with the Pt surface. This catalytic process likely involves H3PO3 adsorption at the Pt surface in a highly reactive pyramidal tautomeric configuratio

Symptom patterns in women with premenstrual syndrome complaints: a prospective assessment using a marker for ovulation and screening criteria for adequate ovarian function

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72929/1/j.1365-2648.1991.tb01727.x.pd

COMPOSIÇÃO CORPORAL, NO 1º ESTRO, DE RATAS SUBMETIDAS A DIFERENTES GRAUS DE RESTRIÇÃO ALIMENTAR

As autoras estudaram a composição corporal em proteína, água e gordura, em 2 grupos de ratas com restrição alimentar, que recebiam, respectivamente, 6g dia e 4g dia de uma dieta com 20% de proteína de caseína. Como percentagem de peso corporal houve aumento do teor de proteína e diminuição de água e de gordura nos grupos com restrição alimentar, em relação ao grupo controle. Na época do 19 estro a média ponderai não diferia, significativamente, nos 3 grupos.At first estrus the feed-restricted rats were older and, proportionally to the age, leaner than the well fed animals. They had attained a greater proportion of protein and lesser proportion of water and fat; however the animals of the two restricted diet groups and the well fed group had the same weight. First estrus was simultaneous with vaginal opening in 90% of the well fed animals, in 20% of the group I and in 0% of the group II