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

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

Saethre-Chotzen syndrome : cranofacial anomalies caused by genetic changes in the TWIST gene

In this thesis, one of the most frequently occurring and most variable craniosynostosis syndromes was investigated; Saethre-Chotzen syndrome. Craniosynostosis is the premature obliteration of cranial sutures in the developing embryo. It can also occur in the first few months of life. Saethre-Chotzen syndrome is, besides craniosynostosis, characterized by specific facial and limb abnormalities, of which the most frequently reported are ptosis, prominent crus helicis, cutaneous syndactyly of digit 2 and 3 on both hands and feet, and broad halluces. Saethre-Chotzen syndrome has been linked to the TWIST gene on chromosome 7p21.1. Mutations in and variably sized deletions of this gene can be found in patients with clinical features of Saethre-Chotzen syndrome. The latter, TWIST deletions, often also include part of the surrounding chromosome 7p and are reported to be associated with mental retardation. In Saethre-Chotzen patients, in whom neither a mutation nor a deletion of TWIST had been found, the FGFR3 P250R mutation was in some cases detected. This mutation has specifically been linked to Muenke syndrome that is characterized by unior bicoronal synostosis and slight facial dysmorphology. However, a Saethre-Chotzen like phenotype can also result from this mutation. Because of the possible overlap of Saethre-Chotzen with Muenke syndrome, these syndromes were studied in order to provide clinical criteria that discriminate between the two (chapter 4). Many phenotypic features occur in both syndromes. In addition, although unicoronal synostosis occurs slightly more frequently in Muenke syndrome, unicoronal and bicoronal synostosis are seen in both syndromes. The discrimination between Saethre-Chotzen and Muenke is often not made easily and the associated genes, TWIST and FGFR3, respectively, are simultaneously tested for pathogenic m