Exact magnetohydrodynamic equilibria with flow and effects on the Shafranov shift

Exact solutions of the equation governing the equilibrium magetohydrodynamic states of an axisymmetric plasma with incompressible flows of arbitrary direction [H. Tasso and G.N.Throumoulopoulos, Phys. Pasmas {\bf 5}, 2378 (1998)] are constructed for toroidal current density profiles peaked on the magnetic axis in connection with the ansatz $S=-ku$, where $S=d/d u [\varrho (d\Phi/du)^2]$ ($k$ is a parameter, $u$ labels the magnetic surfaces; $\varrho(u)$ and $\Phi(u)$ are the density and the electrostatic potential, respectively). They pertain to either unbounded plasmas of astrophysical concern or bounded plasmas of arbitrary aspect ratio. For $k=0$, a case which includes flows parallel to the magnetic field, the solutions are expressed in terms of Kummer functions while for $k\neq 0$ in terms of Airy functions. On the basis of a tokamak solution with $k\neq 0$ describing a plasma surrounded by a perfectly conducted boundary of rectangular cross-section it turns out that the Shafranov shift is a decreasing function which can vanish for a positive value of $k$. This value is larger the smaller the aspect ratio of the configuration.Comment: 13 pages, 2 figures. v2:Eq (3) has been corrected. A new figure (Fig. 2) has been added in order to illustrate u-contours in connection with solution (24) and the Shafranov shift. Also, a sentence referring to Fig. 2 has been added after Eq. (25

Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross section shape

The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, conscequently, the general two dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function $\psi$, in which four profile functionals of $\psi$ appear. Apart from a singularity occuring when the modulus of Mach number associated with the Alfv\'en velocity for the poloidal magnetic field is unity, this equation is always elliptic and permits the construction of several classes of analytic solutions. Specific exact equlibria for a plasma confined within a perfectly conducting circular cylindrical boundary and having i) a flat current density and ii) a peaked current density are obtained and studied.Comment: Accepted to Plasma Physics & Controlled Fusion, 14 pages, revte

Robust Aeroelastic Control of Very Flexible Wings using Intrinsic Models

This paper explores the robust control of large exible wings when their dynamics are written in terms of intrinsic variables, that is, velocities and stress resultants. Assuming 2-D strip theory for the aerodynamics, the resulting nonlinear aeroelastic equations of motion are written in modal coordinates. It is seen that a system which experiences large displacements can nonetheless be accurately described by a system with only weak nonlinear couplings in this description of the wing dynamics. As result, a linear robust controller acting on a control surface is able to effectively provide gust load alleviation and flutter suppression even when the wing structure undergoes large deformations. This is numerically demonstrated on various representative test cases. © 2013 by Yinan Wang, Andrew Wynn and Rafael Palacios

Quantum transport and momentum conserving dephasing

We study numerically the influence of momentum-conserving dephasing on the transport in a disordered chain of scatterers. Loss of phase memory is caused by coupling the transport channels to dephasing reservoirs. In contrast to previously used models, the dephasing reservoirs are linked to the transport channels between the scatterers, and momentum conserving dephasing can be investigated. Our setup provides a model for nanosystems exhibiting conductance quantization at higher temperatures in spite of the presence of phononic interaction. We are able to confirm numerically some theoretical predictions.Comment: 7 pages, 4 figure

Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions

We present a systematic approach to studying the geometric aspects of Vinberg theta-representations. The main idea is to use the Borel-Weil construction for representations of reductive groups as sections of homogeneous bundles on homogeneous spaces, and then to study degeneracy loci of these vector bundles. Our main technical tool is to use free resolutions as an "enhanced" version of degeneracy loci formulas. We illustrate our approach on several examples and show how they are connected to moduli spaces of Abelian varieties. To make the article accessible to both algebraists and geometers, we also include background material on free resolutions and representation theory.Comment: 41 pages, uses tabmac.sty, Dedicated to David Eisenbud on the occasion of his 65th birthday; v2: fixed some typos and added reference

Experimental investigation and modeling attempt on the effects of ultraviolet aging on the fatigue behavior of an LDPE semi-crystalline polymer

The objective of this study was to investigate the effect of UV irradiation on the fatigue life of a bulk semi-crystalline polymer. Low-density polyethylene samples exposed to different UV irradiation doses were fatigue tested. Fatigue indicator based on dissipated energy per cycle was found to present the best correlation with the experimental fatigue results. A master curve unifying the experimental fatigue results for as-received and UV-aged materials was obtained when subtracting the dissipated energy threshold from the total dissipated energy. Finally, the evolution of the damage with cyclic loading was analyzed and preliminary modeling was attempted.This research was supported by the Qatar National Research Fund (NPRP grant No. 7-1562-2-571). We would like to acknowledge the fruitful discussions with Profs. Eddine Gherdaoui and Jean-Michel Gloaguen of the University of Lille

On the geometry of C^3/D_27 and del Pezzo surfaces

We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D_27, the noncompact complex manifold underlying the brane quiver standard model recently proposed by Verlinde and Wijnholt. We explicitly realize a map between X and the total space of the canonical bundle over a degree 1 quasi del Pezzo surface, thus defining a desingularization of X. Our analysis relys essentially on the relationship existing between the normalizer group of D_27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.Comment: 23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co

Haptic Perception of Object Curvature in Parkinson's Disease

The haptic perception of the curvature of an object is essential for adequate object manipulation and critical for our guidance of actions. This study investigated how the ability to perceive the curvature of an object is altered by Parkinson's disease (PD).Eight healthy subjects and 11 patients with mild to moderate PD had to judge, without vision, the curvature of a virtual "box" created by a robotic manipulandum. Their hands were either moved passively along a defined curved path or they actively explored the curved curvature of a virtual wall. The curvature was either concave or convex (bulging to the left or right) and was judged in two locations of the hand workspace--a left workspace location, where the curved hand path was associated with curved shoulder and elbow joint paths, and a right workspace location in which these joint paths were nearly linear. After exploring the curvature of the virtual object, subjects had to judge whether the curvature was concave or convex. Based on these data, thresholds for curvature sensitivity were established. The main findings of the study are: First, 9 out 11 PD patients (82%) showed elevated thresholds for detecting convex curvatures in at least one test condition. The respective median threshold for the PD group was increased by 343% when compared to the control group. Second, when distal hand paths became less associated with proximal joint paths (right workspace), haptic acuity was reduced substantially in both groups. Third, sensitivity to hand trajectory curvature was not improved during active exploration in either group.Our data demonstrate that PD is associated with a decreased acuity of the haptic sense, which may occur already at an early stage of the disease