RTCC requirements for mission G - Trajectory computers for TLI and MCC processors, part 1 Final report

Functional properties of trajectory computers for translunar injection and midcourse correction procedures on lunar orbit

Abelian gauge theories on compact manifolds and the Gribov ambiguity

We study the quantization of abelian gauge theories of principal torus bundles over compact manifolds with and without boundary. It is shown that these gauge theories suffer from a Gribov ambiguity originating in the non-triviality of the bundle of connections whose geometrical structure will be analyzed in detail. Motivated by the stochastic quantization approach we propose a modified functional integral measure on the space of connections that takes the Gribov problem into account. This functional integral measure is used to calculate the partition function, the Greens functions and the field strength correlating functions in any dimension using the fact that the space of inequivalent connections itself admits the structure of a bundle over a finite dimensional torus. The Greens functions are shown to be affected by the non-trivial topology, giving rise to non-vanishing vacuum expectation values for the gauge fields.Comment: 33 page

Ginzburg-Landau model with small pinning domains

We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from 1 only on finitely many disjoint domains, called the {\it pinning domains}. These pinning domains model small impurities in a homogeneous superconductor and shrink to single points in the limit $\v\to0$; here, \v is the inverse of the Ginzburg-Landau parameter. We study the energy minimization in a smooth simply connected domain $\Omega \subset \mathbb{C}$ with Dirichlet boundary condition $g$ on \d \O, with topological degree {\rm deg}_{\d \O} (g) = d >0. Our main result is that, for small \v, minimizers have $d$ distinct zeros (vortices) which are inside the pinning domains and they have a degree equal to 1. The question of finding the locations of the pinning domains with vortices is reduced to a discrete minimization problem for a finite-dimensional functional of renormalized energy. We also find the position of the vortices inside the pinning domains and show that, asymptotically, this position is determined by {\it local renormalized energy} which does not depend on the external boundary conditions.Comment: 39 page

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

Symmetries of Higher Dimensional Black Holes

We prove that if a stationary, real analytic, asymptotically flat vacuum black hole spacetime of dimension $n\geq 4$ contains a non-degenerate horizon with compact cross sections that are transverse to the stationarity generating Killing vector field then, for each connected component of the black hole's horizon, there is a Killing field which is tangent to the generators of the horizon. For the case of rotating black holes, the stationarity generating Killing field is not tangent to the horizon generators and therefore the isometry group of the spacetime is at least two dimensional. Our proof relies on significant extensions of our earlier work on the symmetries of spacetimes containing a compact Cauchy horizon, allowing now for non closed generators of the horizon.Comment: 57 page

Maintenance of bone mineral density after implantation of a femoral neck hip prosthesis

<p>Abstract</p> <p>Background</p> <p>Stress shielding of the proximal femur has been observed in a number of conventional cementless implants used in total hip arthroplasty. Short femoral-neck implants are claiming less interference with the biomechanics of the proximal femur. The goal of this study was to investigate the changes of bone-mineral density in the proximal femur and the clinical outcome after implantation of a short femoral-neck prosthesis.</p> <p>Methods</p> <p>We prospectively assessed the clinical outcome and the changes of bone mineral density of the proximal femur up to one year after implantation of a short femoral neck prosthesis in 20 patients with a mean age of 47 years (range 17 to 65). Clinical outcome was assessed using the Harris Hip Score. The WOMAC was used as a patient-relevant outcome-measure. The bone mineral density was determined using dual energy x-ray absorptiometry, performed 10 days, three months and 12 months after surgery.</p> <p>Results</p> <p>The Harris Hip Score improved from an average preoperative score of 46 to a postoperative score at 12 months of 89 points, the global WOMAC index from 5,3 preoperatively to 0,8 at 12 months postoperatively. In contrast to conventional implants, the DEXA-scans overall revealed a slight increase of bone mineral density in the proximal femur in the 12 months following the implantation.</p> <p>Conclusion</p> <p>The short femoral neck stem lead to a distinct bone reaction. This was significantly different when compared to the changes in bone mineral density reported after implantation of conventional implants.</p

Treatment of Late Stage Disease in a Model of Arenaviral Hemorrhagic Fever: T-705 Efficacy and Reduced Toxicity Suggests an Alternative to Ribavirin

A growing number of arenaviruses are known to cause viral hemorrhagic fever (HF), a severe and life-threatening syndrome characterized by fever, malaise, and increased vascular permeability. Ribavirin, the only licensed antiviral indicated for the treatment of certain arenaviral HFs, has had mixed success and significant toxicity. Since severe arenaviral infections initially do not present with distinguishing symptoms and are difficult to clinically diagnose at early stages, it is of utmost importance to identify antiviral therapies effective at later stages of infection. We have previously reported that T-705, a substituted pyrazine derivative currently under development as an anti-influenza drug, is highly active in hamsters infected with Pichinde virus when the drug is administered orally early during the course of infection. Here we demonstrate that T-705 offers significant protection against this lethal arenaviral infection in hamsters when treatment is begun after the animals are ill and the day before the animals begin to succumb to disease. Importantly, this coincides with the time when peak viral loads are present in most organs and considerable tissue damage is evident. We also show that T-705 is as effective as, and less toxic than, ribavirin, as infected T-705-treated hamsters on average maintain their weight better and recover more rapidly than animals treated with ribavirin. Further, there was no added benefit to combination therapy with T-705 and ribavirin. Finally, pharmacokinetic data indicate that plasma T-705 levels following oral administration are markedly reduced during the latter stages of disease, and may contribute to the reduced efficacy seen when treatment is withheld until day 7 of infection. Our findings support further pre-clinical development of T-705 for the treatment of severe arenaviral infections

Characterization of Generalized Young Measures Generated by Symmetric Gradients

This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer\ue2\u80\u93Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The \ue2\u80\u9clocal\ue2\u80\u9d proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti\ue2\u80\u99s rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences

Whirl mappings on generalised annuli and the incompressible symmetric equilibria of the dirichlet energy

In this paper we show a striking contrast in the symmetries of equilibria and extremisers of the total elastic energy of a hyperelastic incompressible annulus subject to pure displacement boundary conditions.Indeed upon considering the equilibrium equations, here, the nonlinear second order elliptic system formulated for the deformation u=(u1,…,uN) : EL[u,X]=⎧⎩⎨⎪⎪Δu=div(P(x)cof∇u)det∇u=1u≡φinX,inX,on∂X, where X is a finite, open, symmetric N -annulus (with N≥2 ), P=P(x) is an unknown hydrostatic pressure field and φ is the identity mapping, we prove that, despite the inherent rotational symmetry in the system, when N=3 , the problem possesses no non-trivial symmetric equilibria whereas in sharp contrast, when N=2 , the problem possesses an infinite family of symmetric and topologically distinct equilibria. We extend and prove the counterparts of these results in higher dimensions by way of showing that a similar dichotomy persists between all odd vs. even dimensions N≥4 and discuss a number of closely related issues