Degenerate dispersive equations arising in the study of magma dynamics

An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive, nonlinear wave equations. We establish a general local well-posedness for a physical class of data (roughly $H^1$) via fixed point methods. The strategy requires positive lower bounds on the solution. This is extended to global existence for a subset of possible nonlinearities by making use of certain conservation laws associated with the equations. Furthermore, we construct a Lyapunov energy functional, which is locally convex about the uniform state, and prove (global in time) nonlinear dynamic stability of the uniform state for any choice of nonlinearity. We compare the dynamics to that of other problems and discuss open questions concerning a larger range of nonlinearities, for which we conjecture global existence.Comment: 27 Pages, 7 figures are not present in this version. See http://www.columbia.edu/~grs2103/ for a PDF with figures. Submitted to Nonlinearit

Veneziano-Yankielowicz Superpotential Terms in N=1 SUSY Gauge Theories

The Veneziano-Yankielowicz glueball superpotential for an arbitrary N=1 SUSY pure gauge theory with classical gauge group is derived using an approach following recent work of Dijkgraaf, Vafa and others. These non-perturbative terms, which had hitherto been included by hand in the above approach, are thus seen to arise naturally, and the approach is rendered self-contained. By minimising the glueball superpotential for theories with fundamental matter added, the expected vacuum structure with gaugino condensation and chiral symmetry breaking is obtained. Various possible extensions are also discussed.Comment: 9 page

A Simulation Study of the Factors Influencing the Risk of Intraoperative Slipping

AbstractBackgroundTo identify the impact of weight, table surface, and table type on slipping in a simulation of minimally invasive gynecologic surgery.MethodsA mannequin was placed into increasing Trendelenburg until a slip was observed; the table angle at the time of the event was measured (slip angle). The influence of mannequin position (supine vs. lithotomy), weight, table surface, and model was evaluated. A linear regression model was used to analyze the data.ResultsMannequin weight, bed surface, and bed type all significantly impacted the slip angles. In general, higher mannequin weights tolerated significantly more Trendelenburg before slipping in the supine position but less in lithotomy compared to lower weights. In lithotomy, the disposable sheet and gelpad performed worse than the bean bag, egg crate foam, and bedsheet. There was no difference in slipping because of bed surface in the supine model. The Skytron operating table performed significantly better than the Steris operating table when tested with the bedsheet.ConclusionOperative position, patient weight, and bed surface together influence the slipping propensity. In lithotomy, heavier patients were more prone to slipping while the inverse was true in supine. The egg crate foam, bean bag, and bedsheet were the best antislip surfaces. Operating room table choice can mitigate slippage

Geometrical Tachyon Kinks and NS5 Branes

We further investigate the $NS$5 ring background using the tachyon map. Mapping the radion fields to the rolling tachyon helps to explain the motion of a probe $Dp$-brane in this background. It turns out that the radion field becomes tachyonic when the brane is confined to one dimensional motion inside the ring. We find explicit solutions for the geometrical tachyon field that describe stable kink solutions which are similar to those of the open string tachyon. Interestingly in the case of the geometric tachyon, the dynamics is controlled by a cosine potential. In addition, we couple a constant electric field to the probe-brane, but find that the only stable kink solutions occur when there is zero electric field or a critical field value. We also investigate the behaviour of Non-BPS branes in this background, and find that the end state of any probe brane is that of tachyonic matter 'trapped' around the interior of the ring. We conclude by considering compactification of the ring solution in one of the transverse directions.Comment: Latex, 24 pages, 1 eps fig; clarifying comments added to Section 2; typos correcte

Electrified Fuzzy Spheres and Funnels in Curved Backgrounds

We use the non-Abelian DBI action to study the dynamics of $N$ coincident $Dp$-branes in an arbitrary curved background, with the presence of a homogenous world-volume electric field. The solutions are natural extensions of those without electric fields, and imply that the spheres will collapse toward zero size. We then go on to consider the $D1-D3$ intersection in a curved background and find various dualities and automorphisms of the general equations of motion. It is possible to map the dynamical equation of motion to the static one via Wick rotation, however the additional spatial dependence of the metric prevents this mapping from being invertible. Instead we find that a double Wick rotation leaves the static equation invariant. This is very different from the behaviour in Minkowski space. We go on to construct the most general static fuzzy funnel solutions for an arbitrary metric either by solving the static equations of motion, or by finding configurations which minimise the energy. As a consistency check we construct the Abelian $D3$-brane world-volume theory in the same generic background and find solutions consistent with energy minimisation. In the $NS$5-brane background we find time dependent solutions to the equations of motion, representing a time dependent fuzzy funnel. These solutions match those obtained from the $D$-string picture to leading order suggesting that the action in the large $N$ limit does not need corrections. We conclude by generalising our solutions to higher dimensional fuzzy funnels.Comment: 38 pages, Latex; references adde

Evolving a photosynthetic organelle

The evolution of plastids from cyanobacteria is believed to represent a singularity in the history of life. The enigmatic amoeba Paulinella and its 'recently' acquired photosynthetic inclusions provide a fascinating system through which to gain fresh insight into how endosymbionts become organelles

Natural Killer T Cell Ligand α-Galactosylceramide Enhances Protective Immunity Induced by Malaria Vaccines

The important role played by CD8+ T lymphocytes in the control of parasitic and viral infections, as well as tumor development, has raised the need for the development of adjuvants capable of enhancing cell-mediated immunity. It is well established that protective immunity against liver stages of malaria parasites is primarily mediated by CD8+ T cells in mice. Activation of natural killer T (NKT) cells by the glycolipid ligand, α-galactosylceramide (α-GalCer), causes bystander activation of NK, B, CD4+, and CD8+ T cells. Our study shows that coadministration of α-GalCer with suboptimal doses of irradiated sporozoites or recombinant viruses expressing a malaria antigen greatly enhances the level of protective anti-malaria immunity in mice. We also show that coadministration of α-GalCer with various different immunogens strongly enhances antigen-specific CD8+ T cell responses, and to a lesser degree, Th1-type responses. The adjuvant effects of α-GalCer require CD1d molecules, Vα14 NKT cells, and interferon γ. As α-GalCer stimulates both human and murine NKT cells, these findings should contribute to the design of more effective vaccines against malaria and other intracellular pathogens, as well as tumors

Biochemistry of the sphingolipides. X. Phytoglycolipide, a complex phytosphingosine‐containing lipide from plant seeds

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141721/1/aocs0335.pd

The Importance of Biologically Active Vitamin D for Mineralization by Osteocytes After Parathyroidectomy for Renal Hyperparathyroidism

Hypomineralized matrix is a factor determining bone mineral density. Increased perilacunar hypomineralized bone area is caused by reduced mineralization by osteocytes. The importance of vitamin D in the mineralization by osteocytes was investigated in hemodialysis patients who underwent total parathyroidectomy (PTX) with immediate autotransplantation of diffuse hyperplastic parathyroid tissue. No previous reports on this subject exist. The study was conducted in 19 patients with renal hyperparathyroidism treated with PTX. In 15 patients, the serum calcium levels were maintained by subsequent administration of alfacalcidol (2.0 μg/day), i.v. calcium gluconate, and oral calcium carbonate for 4 weeks after PTX (group I). This was followed in a subset of 4 patients in group I by a reduced dose of 0.5 μg/day until 1 year following PTX; this was defined as group II. In the remaining 4 patients, who were not in group I, the serum calcium (Ca) levels were maintained without subsequent administration of alfacalcidol (group III). Transiliac bone biopsy specimens were obtained in all groups before and 3 or 4 weeks after PTX to evaluate the change of the hypomineralized bone area. In addition, patients from group II underwent a third bone biopsy 1 year following PTX. A significant decrease of perilacunar hypomineralized bone area was observed 3 or 4 weeks after PTX in all group I and II patients. The area was increased again in the group II patients 1 year following PTX. In group III patients, an increase of the hypomineralized bone area was observed 4 weeks after PTX. The maintenance of a proper dose of vitamin D is necessary for mineralization by osteocytes, which is important to increase bone mineral density after PTX for renal hyperparathyroidism

Ischaemic strokes in patients with pulmonary arteriovenous malformations and hereditary hemorrhagic telangiectasia: associations with iron deficiency and platelets.

<div><p>Background</p><p>Pulmonary first pass filtration of particles marginally exceeding ∼7 µm (the size of a red blood cell) is used routinely in diagnostics, and allows cellular aggregates forming or entering the circulation in the preceding cardiac cycle to lodge safely in pulmonary capillaries/arterioles. Pulmonary arteriovenous malformations compromise capillary bed filtration, and are commonly associated with ischaemic stroke. Cohorts with CT-scan evident malformations associated with the highest contrast echocardiographic shunt grades are known to be at higher stroke risk. Our goal was to identify within this broad grouping, which patients were at higher risk of stroke.</p><p>Methodology</p><p>497 consecutive patients with CT-proven pulmonary arteriovenous malformations due to hereditary haemorrhagic telangiectasia were studied. Relationships with radiologically-confirmed clinical ischaemic stroke were examined using logistic regression, receiver operating characteristic analyses, and platelet studies.</p><p>Principal Findings</p><p>Sixty-one individuals (12.3%) had acute, non-iatrogenic ischaemic clinical strokes at a median age of 52 (IQR 41–63) years. In crude and age-adjusted logistic regression, stroke risk was associated not with venous thromboemboli or conventional neurovascular risk factors, but with low serum iron (adjusted odds ratio 0.96 [95% confidence intervals 0.92, 1.00]), and more weakly with low oxygen saturations reflecting a larger right-to-left shunt (adjusted OR 0.96 [0.92, 1.01]). For the same pulmonary arteriovenous malformations, the stroke risk would approximately double with serum iron 6 µmol/L compared to mid-normal range (7–27 µmol/L). Platelet studies confirmed overlooked data that iron deficiency is associated with exuberant platelet aggregation to serotonin (5HT), correcting following iron treatment. By MANOVA, adjusting for participant and 5HT, iron or ferritin explained 14% of the variance in log-transformed aggregation-rate (p = 0.039/p = 0.021).</p><p>Significance</p><p>These data suggest that patients with compromised pulmonary capillary filtration due to pulmonary arteriovenous malformations are at increased risk of ischaemic stroke if they are iron deficient, and that mechanisms are likely to include enhanced aggregation of circulating platelets.</p></div