Quasi-Two-Dimensional Dynamics of Plasmas and Fluids

In the lowest order of approximation quasi-twa-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mirna (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in non ideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.U. S. Department of Energy DE-FG05-80ET-53088Ministry of Education, Science and Culture of JapanFusion Research Cente

Multidimensional Gaussian sums arising from distribution of Birkhoff sums in zero entropy dynamical systems

A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product dynamical system on the $\mathbb{T}^2$ torus, with zero Lyapounov exponents. The sequence, taking the values $\pm 1$, is pairwise independent (but not independent) ergodic sequence with infinite range dependence. The model corresponds to the motion of a particle on an infinite cylinder, hopping backward and forward along its axis, with a transversal acceleration parameter $\alpha$. We show that when the parameter $\alpha /\pi$ is rational then all the moments of the normalized sums $E((S_n/\sqrt{n})^k)$, but the second, are unbounded with respect to n, while for irrational $\alpha /\pi$, with bounded continuous fraction representation, all these moments are finite and bounded with respect to n.Comment: To be published in J. Phys.

'She's like a daughter to me': insights into care, work and kinship from rural Russia

This article draws on ethnographic research into a state-funded homecare service in rural Russia. The article discusses intersections between care, work and kinship in the relationships between homecare workers and their elderly wards and explores the ways in which references to kinship, as a means of authenticating paid care and explaining its emotional content, reinforce public and private oppositions while doing little to relieve the tensions and conflicts of care work. The discussion brings together detailed empirical insights into local ideologies and practices as a way of generating new theoretical perspectives, which will be of relevance beyond the particular context of study

Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the central limit theorem and a vector-valued almost sure invariance principle. We also obtain results on decay of correlations.Comment: 18 pages, minor revisions, to appear in Communications in Mathematical Physic

Canonical description of ideal magnetohydrodynamic flows and integrals of motion

In the framework of the variational principle the canonical variables describing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with spatially varying entropy and nonzero values of all topological invariants) are introduced. The corresponding complete velocity representation enables us not only to describe the general type flows in terms of single-valued functions, but also to solve the intriguing problem of the ``missing'' MHD integrals of motion. The set of hitherto known MHD local invariants and integrals of motion appears to be incomplete: for the vanishing magnetic field it does not reduce to the set of the conventional hydrodynamic invariants. And if the MHD analogs of the vorticity and helicity were discussed earlier for the particular cases, the analog of Ertel invariant has been so far unknown. It is found that on the basis of the new invariants introduced a wide set of high-order invariants can be constructed. The new invariants are relevant both for the deeper insight into the problem of the topological structure of the MHD flows as a whole and for the examination of the stability problems. The additional advantage of the proposed approach is that it enables one to deal with discontinuous flows, including all types of possible breaks.Comment: 16 page

Atrophy of the optic chiasm is associated with microvascular diabetic complications in type 1 diabetes

IntroductionDiabetic neuropathy and diabetic eye disease are well known complications of type 1 diabetes. We hypothesized that chronic hyperglycemia also damages the optic tract, which can be measured using routine magnetic resonance imaging. Our aim was to compare morphological differences in the optic tract between individuals with type 1 diabetes and healthy control subjects. Associations between optic tract atrophy and metabolic measures, cerebrovascular and microvascular diabetic complications were further studied among individuals with type 1 diabetes.MethodsWe included 188 subjects with type 1 diabetes and 30 healthy controls, all recruited as part of the Finnish Diabetic Nephropathy Study. All participants underwent a clinical examination, biochemical work-up, and brain magnetic resonance imaging (MRI). Two different raters manually measured the optic tract.ResultsThe coronal area of the optic chiasm was smaller among those with type 1 diabetes compared to non-diabetic controls (median area 24.7 [21.0-28.5] vs 30.0 [26.7-33.3] mm2, p<0.001). In participants with type 1 diabetes, a smaller chiasmatic area was associated with duration of diabetes, glycated hemoglobin, and body mass index. Diabetic eye disease, kidney disease, neuropathy and the presence of cerebral microbleeds (CMBs) in brain MRI were associated with smaller chiasmatic size (p<0.05 for all).ConclusionIndividuals with type 1 diabetes had smaller optic chiasms than healthy controls, suggesting that diabetic neurodegenerative changes extend to the optic nerve tract. This hypothesis was further supported by the association of smaller chiasm with chronic hyperglycemia, duration of diabetes, diabetic microvascular complications, as well as and CMBs in individuals with type 1 diabetes

Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page

The impact of human immunodeficiency virus infection on drug-resistant tuberculosis.

Infection with human immunodeficiency virus (HIV) has been associated with increased rates of single- and multidrug-resistant (MDR) tuberculosis in the New York City area. In order to examine the relationship of HIV infection to drug-resistant tuberculosis in other selected regions of the United States, we established a registry of cases of culture-proven tuberculosis. Data were collected from sites participating in an NIH-funded, community-based HIV clinical trials group. All cases of tuberculosis, regardless of HIV status, which occurred between January 1992 and June 1994 were recorded. Overall, 1,373 cases of tuberculosis were evaluated, including 425 from the New York City area, and 948 from seven other metropolitan areas. The overall prevalence of resistance to one or more drugs was 20.4%, and 5.6% of isolates were resistant to both isoniazid and rifampin (MDR). In the New York City area, HIV-infected patients were significantly more likely than persons not known to be HIV-infected, to have resistance to at least one drug (37% versus 19%) and MDR (19% versus 6%). In other geographic areas, overall drug resistance was 16%, and only 2.2% of isolates were MDR. In multiple logistic regression analyses, HIV infection was shown to be a risk factor for drug-resistant tuberculosis, independent of geographic location, history of prior therapy, age, and race. We concluded that HIV infection is associated with increased rates of resistance to antituberculosis drugs in both the New York City area and other geographic areas. MDR tuberculosis is occurring predominantly in the New York City area and is highly correlated with HIV infection

The impact of human immunodeficiency virus infection on drug-resistant tuberculosis.

Infection with human immunodeficiency virus (HIV) has been associated with increased rates of single- and multidrug-resistant (MDR) tuberculosis in the New York City area. In order to examine the relationship of HIV infection to drug-resistant tuberculosis in other selected regions of the United States, we established a registry of cases of culture-proven tuberculosis. Data were collected from sites participating in an NIH-funded, community-based HIV clinical trials group. All cases of tuberculosis, regardless of HIV status, which occurred between January 1992 and June 1994 were recorded. Overall, 1,373 cases of tuberculosis were evaluated, including 425 from the New York City area, and 948 from seven other metropolitan areas. The overall prevalence of resistance to one or more drugs was 20.4%, and 5.6% of isolates were resistant to both isoniazid and rifampin (MDR). In the New York City area, HIV-infected patients were significantly more likely than persons not known to be HIV-infected, to have resistance to at least one drug (37% versus 19%) and MDR (19% versus 6%). In other geographic areas, overall drug resistance was 16%, and only 2.2% of isolates were MDR. In multiple logistic regression analyses, HIV infection was shown to be a risk factor for drug-resistant tuberculosis, independent of geographic location, history of prior therapy, age, and race. We concluded that HIV infection is associated with increased rates of resistance to antituberculosis drugs in both the New York City area and other geographic areas. MDR tuberculosis is occurring predominantly in the New York City area and is highly correlated with HIV infection