On thermodynamically consistent Stefan problems with variable surface energy

A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities, it is proved that it exists globally in time and converges towards an equilibrium of the problem. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable if surface heat capacity is small; however, if kinetic undercooling is absent, they are stable if surface heat capacity is sufficiently large.Comment: To appear in Arch. Ration. Mech. Anal. The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0938-y. arXiv admin note: substantial text overlap with arXiv:1101.376

Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation

In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist to leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation

Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension

The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities in a sense made precise below, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable, reminiscent of the onset of Ostwald ripening.Comment: 56 pages. Expanded introduction, added references. This revised version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-66

The impact of the environment on health by country: a meta-synthesis

<p>Abstract</p> <p>Background</p> <p>Health gains that environmental interventions could achieve are main questions when choosing environmental health action to prevent disease. The World Health Organization has recently released profiles of environmental burden of disease for 192 countries.</p> <p>Methods</p> <p>These country profiles provide an estimate of the health impacts from the three major risk factors 'unsafe water, sanitation & hygiene', 'indoor air pollution from solid fuel use' and 'outdoor air pollution'. The profiles also provide an estimate of preventable health impacts by the environment as a whole. While the estimates for the three risk factors are based on country exposures, the estimates of health gains for total environmental improvements are based on a review of the literature supplemented by expert opinion and combined with country health statistics.</p> <p>Results</p> <p>Between 13% and 37% of the countries' disease burden could be prevented by environmental improvements, resulting globally in about 13 million deaths per year. It is estimated that about four million of these could be prevented by improving water, sanitation and hygiene, and indoor and outdoor air alone. The number of environmental DALYs per 1000 capita per year ranges between 14 and 316 according to the country. An analysis by disease group points to main preventions opportunities for each country.</p> <p>Conclusion</p> <p>Notwithstanding the uncertainties in their calculation, these estimates provide an overview of opportunities for prevention through healthier environments. The estimates show that for similar national incomes, the environmental burden of disease can typically vary by a factor five. This analysis also shows that safer water, sanitation and hygiene, and safer fuels for cooking could significantly reduce child mortality, namely by more than 25% in 20 of the lowest income countries.</p

Conditional stability of unstable viscous shock waves in compressible gas dynamics and MHD

Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic--parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small $L^1\cap H^3$ perturbations, converging time-asymptotically to a translate of the unperturbed wave. That is, for a shock with $p$ unstable eigenvalues, we establish conditional stability on a codimension-$p$ manifold of initial data, with sharp rates of decay in all $L^p$. For $p=0$, we recover the result of unconditional stability obtained by Mascia and Zumbrun. The main new difficulty in the hyperbolic--parabolic case is to construct an invariant manifold in the absence of parabolic smoothing.Comment: 32p

On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow

In this article, we study the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older regular surfaces of revolution embedded in R^3 and satisfying periodic boundary conditions. We also give conditions for global existence of solutions and prove that solutions are real analytic in time and space. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability and bifurcation behavior, with the radius acting as a bifurcation parameter for the problem.Comment: 37 pages, 6 figures, To Appear in SIAM J. Math. Ana

Human cerebrospinal fluid monoclonal LGI1 autoantibodies increase neuronal excitability

OBJECTIVE: Leucine-rich glioma-inactivated 1 (LGI1) encephalitis is the second most common antibody-mediatedencephalopathy, but insight into the intrathecal B-cell autoimmune response, including clonal relationships, isotype dis-tribution, frequency, and pathogenic effects of single LGI1 antibodies, has remained limited. METHODS: We cloned, expressed, and tested antibodies from 90 antibody-secreting cells (ASCs) and B cells from thecerebrospinalfluid (CSF) of several patients with LGI1 encephalitis. RESULTS: Eighty-four percent of the ASCs and 21% of the memory B cells encoded LGI1-reactive antibodies, whereasreactivities to other brain epitopes were rare. All LGI1 antibodies were of IgG1, IgG2, or IgG4 isotype and had under-gone affinity maturation. Seven of the overall 26 LGI1 antibodies efficiently blocked the interaction of LGI1 with itsreceptor ADAM22 in vitro, and their mean LGI1 signal on mouse brain sections was weak compared to the remaining,non–ADAM22-competing antibodies. Nevertheless, both types of LGI1 antibodies increased the intrinsic cellular excit-ability and glutamatergic synaptic transmission of hippocampal CA3 neurons in slice cultures. Interpretation: Our data show that the patients’intrathecal B-cell autoimmune response is dominated by LGI1 anti-bodies and that LGI1 antibodies alone are sufficient to promote neuronal excitability, a basis of seizure generation.Fundamental differences in target specificity and antibody hypermutations compared to the CSF autoantibody reper-toire in N-methyl-D-aspartate receptor encephalitis underline the clinical concept that autoimmune encephalitides arevery distinct entities

Assessing the impact of drinking water and sanitation on diarrhoeal disease in low- and middle-income settings: Systematic review and meta-regression

Objective: To assess the impact of inadequate water and sanitation on diarrhoeal disease in low- and middle-income settings. Methods: The search strategy used Cochrane Library, MEDLINE & PubMed, Global Health, Embase and BIOSIS supplemented by screening of reference lists from previously published systematic reviews, to identify studies reporting on interventions examining the effect of drinking water and sanitation improvements in low- and middle-income settings published between 1970 and May 2013. Studies including randomised controlled trials, quasi-randomised trials with control group, observational studies using matching techniques and observational studies with a control group where the intervention was well defined were eligible. Risk of bias was assessed using a modified Ottawa-Newcastle scale. Study results were combined using meta-analysis and meta-regression to derive overall and intervention-specific risk estimates. Results: Of 6819 records identified for drinking water, 61 studies met the inclusion criteria, and of 12 515 records identified for sanitation, 11 studies were included. Overall, improvements in drinking water and sanitation were associated with decreased risks of diarrhoea. Specific improvements, such as the use of water filters, provision of high-quality piped water and sewer connections, were associated with greater reductions in diarrhoea compared with other interventions. Conclusions: The results show that inadequate water and sanitation are associated with considerable risks of diarrhoeal disease and that there are notable differences in illness reduction according to the type of improved water and sanitation implemented

Maternal neurofascin-specific autoantibodies bind to structures of the fetal nervous system during pregnancy, but have no long term effect on development in the rat

Neurofascin was recently reported as a target for axopathic autoantibodies in patients with multiple sclerosis (MS), a response that will exacerbate axonal pathology and disease severity in an animal model of multiple sclerosis. As transplacental transfer of maternal autoantibodies can permanently damage the developing nervous system we investigated whether intrauterine exposure to this neurofascin-specific response had any detrimental effect on white matter tract development. To address this question we intravenously injected pregnant rats with either a pathogenic anti-neurofascin monoclonal antibody or an appropriate isotype control on days 15 and 18 of pregnancy, respectively, to mimic the physiological concentration of maternal antibodies in the circulation of the fetus towards the end of pregnancy. Pups were monitored daily with respect to litter size, birth weight, growth and motor development. Histological studies were performed on E20 embryos and pups sacrificed on days 2, 10, 21, 32 and 45 days post partum. Results: Immunohistochemistry for light and confocal microscopy confirmed passively transferred anti-neurofascin antibody had crossed the placenta to bind to distinct structures in the developing cortex and cerebellum. However, this did not result in any significant differences in litter size, birth weight, or general physical development between litters from control mothers or those treated with the neurofascin-specific antibody. Histological analysis also failed to identify any neuronal or white matter tract abnormalities induced by the neurofascin-specific antibody. Conclusions: We show that transplacental transfer of circulating anti-neurofascin antibodies can occur and targets specific structures in the CNS of the developing fetus. However, this did not result in any pre- or post-natal abnormalities in the offspring of the treated mothers. These results assure that even if anti-neurofascin responses are detected in pregnant women with multiple sclerosis these are unlikely to have a negative effect on their children