Spontaneous curvature cancellation in forced thin sheets

In this paper we report numerically observed spontaneous vanishing of mean curvature on a developable cone made by pushing a thin elastic sheet into a circular container. We show that this feature is independent of thickness of the sheet, the supporting radius and the amount of deflection. Several variants of developable cone are studied to examine the necessary conditions that lead to the vanishing of mean curvature. It is found that the presence of appropriate amount of radial stress is necessary. The developable cone geometry somehow produces the right amount of radial stress to induce just enough radial curvature to cancel the conical azimuthal curvature. In addition, the circular symmetry of supporting container edge plays an important role. With an elliptical supporting edge, the radial curvature overcompensates the azimuthal curvature near the minor axis and undercompensates near the major axis. Our numerical finding is verified by a crude experiment using a reflective plastic sheet. We expect this finding to have broad importance in describing the general geometrical properties of forced crumpling of thin sheets.Comment: 13 pages, 12 figures, revtex

A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating through this marginally stable plasma will neither grow nor damp. The dispersion relation of these waves, {\omega} (k), smoothly rises from the usual MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow \pm\infty. The proton distribution function has constant phase-space density along the characteristic resonant surfaces defined by this dispersion relation. Our equation contains a free function describing the variation of the proton phase-space density across these surfaces. Taking this free function to be a simple "box function", we obtain specific solutions of the marginally stable state for a range of proton parallel betas. The phase speeds of these waves are larger than those given by the cold plasma dispersion relation, and the characteristic surfaces are more sharply peaked in the v\bot direction. The threshold anisotropy for generation of ion cyclotron waves is also larger than that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma

TURBULENT HEATING OF THE DISTANT SOLAR WIND BY INTERSTELLAR PICKUP PROTONS IN A DECELERATING FLOW

Previous models of solar wind heating by interstellar pickup proton-driven turbulence have assumed that the wind speed is a constant in heliocentric radial position. However, the same pickup process, which is taken to provide the turbulent energy, must also decelerate the wind. In this paper, we extend our phenomenological turbulence model to include variable wind speed, and then incorporate the deceleration due to interstellar pickup protons into the model. We compare the model results with plasma and field data from Voyager 2, taking this opportunity to present an extended and improved data set of proton core temperature, magnetic field fluctuation intensity, and correlation length along the Voyager trajectory. A particular motivation for including the solar wind deceleration in this model is the expectation that a slower wind would reduce the resulting proton core temperature in the region beyond ~60 AU, where the previous model predictions were higher than the observed values. However, we find instead that the deceleration of the steady-state wind increases the energy input to the turbulence, causing even higher temperatures in that region. The increased heating is shown to result from the larger values of the ratio of Alfven speed to solar wind speed that develop in the decelerating wind.Jet Propulsion Laboratory (U.S.) (NASA contract 959203)United States. National Aeronautics and Space Administration (NASA grant NNX08A147G)United States. National Aeronautics and Space Administration (NASA Guest Investigator grant NNX07AH75G)United States. National Aeronautics and Space Administration (NASA Guest Investigator grant NNX08AJ19G

Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

Direct Oral Anticoagulants for Thromboprophylaxis in Patients with Antiphospholipid Syndrome

The current mainstay of the treatment and secondary thromboprophylaxis of thrombotic antiphospholipid syndrome (APS) is anticoagulation with warfarin or other vitamin K antagonists (VKAs). In addition to their well-known limitations, VKAs are often problematic in APS patients because of the variable sensitivity of thromboplastins to lupus anticoagulant. As a result, the international normalized ratio may not accurately reflect the intensity of anticoagulation. Direct oral anticoagulants (DOACs) are established as therapeutic alternatives to VKAs for a wide range of indications, including the treatment and secondary prevention of venous thromboembolism. Definition of the role of DOACs in the treatment of thrombotic APS is emerging with the results of recent and ongoing clinical studies. This review focuses on the current situation with regard to DOACs for secondary thromboprophylaxis in APS and issues pertinent to DOAC use in APS patients, as well as potential future directions

The constraint equations for the Einstein-scalar field system on compact manifolds

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum Gravit

Thrombotic antiphospholipid syndrome: A practical guide to diagnosis and management

Thrombotic antiphospholipid syndrome (APS) is characterised by venous, arterial and/or small vessel thrombosis in the context of persistently positive antiphospholipid antibodies (aPL). The diagnosis and management of thrombotic APS continues to prove challenging for clinicians. We provide a practical guide to the diagnosis of APS including who to test for aPL and which tests to do. We also consider clinical practice points on the management of venous, arterial and small vessel thrombosis, in the context of first and recurrent thrombotic events. Non-criteria manifestations of APS are reviewed. An approach to recurrent thrombosis and anticoagulant-refractory APS is discussed, with options including increasing the anticoagulation intensity of vitamin K antagonists, switching to low-molecular-weight-heparin, the use of fondaparinux and/or the addition of antiplatelet treatment. Adjunctive options such as vitamin D, hydroxychloroquine and statins are also addressed

Heating the outer heliosphere by pickup protons

There is a growing body of literature that demonstrates the ability of a turbulent cascade within the solar wind to heat the thermal protons. Several sources of energy are required to accomplish the observed heating. Wind shear and shocks originating with the multiple source of wind plasma heat the wind inside ∽AU. However, beyond this distance little is left of these sources and all that remains is the energy injected into the plasma by the pickup of newborn protons originating from interstellar neutrals. Recent advances in the theory of wave excitation by the newborn protons allows us to return to the published heating theory and remove a previously unexplained parameterization of the heating due to pickup protons. Furthermore, recent observational evidence suggests that large-scale correlations between the wind speed and the proton temperature exist into the distant outer heliosphere that motivate an attempt to connect the two within the structure of the heating theory

On the area of the symmetry orbits in T2T^2 symmetric spacetimes with Vlasov matter

This paper treats the global existence question for a collection of general relativistic collisionless particles, all having the same mass. The spacetimes considered are globally hyperbolic, with Cauchy surface a 3-torus. Furthermore, the spacetimes considered are isometrically invariant under a two-dimensional group action, the orbits of which are spacelike 2-tori. It is known from previous work that the area of the group orbits serves as a global time coordinate. In the present work it is shown that the area takes on all positive values in the maximal Cauchy development.Comment: 27 pages, version 2 minor changes and correction

Numerical method for binary black hole/neutron star initial data: Code test

A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each object; the third patch extends to the asymptotic region. As in the Komatsu-Eriguchi-Hachisu method, nonlinear elliptic field equations are decomposed into a flat space Laplacian and a remaining nonlinear expression that serves in each iteration as an effective source. The equations are solved iteratively, integrating a Green's function against the effective source at each iteration. Detailed convergence tests for the essential part of the code are performed for a few types of selected Green's functions to treat different boundary conditions. Numerical computation of the gravitational potential of a fluid source, and a toy model for a binary black hole field are carefully calibrated with the analytic solutions to examine accuracy and convergence of the new code. As an example of the application of the code, an initial data set for binary black holes in the Isenberg-Wilson-Mathews formulation is presented, in which the apparent horizons are located using a method described in Appendix A.Comment: 19 pages, 18 figure