Chiral anomaly for local boundary conditions

It is known that in the zeta function regularization and in the Fujikawa method chiral anomaly is defined through a coefficient in the heat kernel expansion for the Dirac operator. In this paper we apply the heat kernel methods to calculate boundary contributions to the chiral anomaly for local (bag) boundary conditions. As a by-product some new results on the heat trace asymptotics are also obtained.Comment: 20 p., late

Extremal metrics for spectral functions of Dirac operators in even and odd dimensions

Let (M^n, g) be a closed smooth Riemannian spin manifold and denote by D its Atiyah-Singer-Dirac operator. We study the variation of Riemannian metrics for the zeta function and functional determinant of D^2, and prove finiteness of the Morse index at stationary metrics, and local extremality at such metrics under general, i.e. not only conformal, change of metrics. In even dimensions, which is also a new case for the conformal Laplacian, the relevant stability operator is of log-polyhomogeneous pseudodifferential type, and we prove new results of independent interest, on the spectrum for such operators. We use this to prove local extremality under variation of the Riemannian metric, which in the important example when (M^n, g) is the round n-sphere, gives a partial verification of Branson's conjecture on the pattern of extremals. Thus det(D^2) has a local (max, max, min, min) when the dimension is (4k, 4k + 1, 4k + 2, 4k + 3), respectively.Comment: 45 pages; title and content edited to reflect subsequent related wor

Statistical mechanics approach to some problems in conformal geometry

A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in \bbR^n, or \bbS^n, n\in \bbN, which are distributed according to the configurational microcanonical measure $\delta(E-H)$, or rather some regularization thereof, where H is the configurational Hamiltonian and E the configurational energy. When $N\to\infty$ with non-extensive energy scaling E=N^2 \vareps, the particle positions become i.i.d. according to a self-consistent Boltzmann distribution, respectively a superposition of such distributions. The self-consistency condition in n dimensions is some nonlinear elliptic PDE of order n (pseudo-PDE if n is odd) with an exponential nonlinearity. When n=2, this PDE is known in statistical mechanics as Poisson-Boltzmann equation, with applications to point vortices, 2D Coulomb and magnetized plasmas and gravitational systems. It is then also known in conformal differential geometry, where it is the central equation in Nirenberg's problem of prescribed Gaussian curvature. For constant Gauss curvature it becomes Liouville's equation, which also appears in two-dimensional so-called quantum Liouville gravity. The PDE for n=4 is Paneitz' equation, and while it is not known in statistical mechanics, it originated from a study of the conformal invariance of Maxwell's electromagnetism and has made its appearance in some recent model of four-dimensional quantum gravity. In differential geometry, the Paneitz equation and its higher order n generalizations have applications in the conformal geometry of n-manifolds, but no physical applications yet for general n. Interestingly, though, all the Paneitz equations have an interpretation in terms of statistical mechanics.Comment: 17 pages. To appear in Physica

Inflammatory monocytes require type I interferon receptor signaling to activate NK cells via IL-18 during a mucosal viral infection

The requirement of type I interferon (IFN) for natural killer (NK) cell activation in response to viral infection is known, but the underlying mechanism remains unclear. Here, we demonstrate that type I IFN signaling in inflammatory monocytes, but not in dendritic cells (DCs) or NK cells, is essential for NK cell function in response to a mucosal herpes simplex virus type 2 (HSV-2) infection. Mice deficient in type I IFN signaling, Ifnar(-/-) and Irf9(-/-) mice, had significantly lower levels of inflammatory monocytes, were deficient in IL-18 production, and lacked NK cell-derived IFN-gamma. Depletion of inflammatory monocytes, but not DCs or other myeloid cells, resulted in lower levels of IL-18 and a complete abrogation of NK cell function in HSV-2 infection. Moreover, this resulted in higher susceptibility to HSV-2 infection. Although Il18(-/-) mice had normal levels of inflammatory monocytes, their NK cells were unresponsive to HSV-2 challenge. This study highlights the importance of type I IFN signaling in inflammatory monocytes and the induction of the early innate antiviral response

Singular limits for the bi-laplacian operator with exponential nonlinearity in R4\R^4

Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^{4}$ such that for some integer $d\geq1$ its $d$-th singular cohomology group with coefficients in some field is not zero, then problem {\Delta^{2}u-\rho^{4}k(x)e^{u}=0 & \hbox{in}\Omega, u=\Delta u=0 & \hbox{on}\partial\Omega, has a solution blowing-up, as $\rho\to0$, at $m$ points of $\Omega$, for any given number $m$.Comment: 30 pages, to appear in Ann. IHP Non Linear Analysi

The Dirichlet-to-Robin Transform

A simple transformation converts a solution of a partial differential equation with a Dirichlet boundary condition to a function satisfying a Robin (generalized Neumann) condition. In the simplest cases this observation enables the exact construction of the Green functions for the wave, heat, and Schrodinger problems with a Robin boundary condition. The resulting physical picture is that the field can exchange energy with the boundary, and a delayed reflection from the boundary results. In more general situations the method allows at least approximate and local construction of the appropriate reflected solutions, and hence a "classical path" analysis of the Green functions and the associated spectral information. By this method we solve the wave equation on an interval with one Robin and one Dirichlet endpoint, and thence derive several variants of a Gutzwiller-type expansion for the density of eigenvalues. The variants are consistent except for an interesting subtlety of distributional convergence that affects only the neighborhood of zero in the frequency variable.Comment: 31 pages, 5 figures; RevTe

Geometries with Killing Spinors and Supersymmetric AdS Solutions

The seven and nine dimensional geometries associated with certain classes of supersymmetric $AdS_3$ and $AdS_2$ solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further elucidate their properties and also generalise them to higher odd dimensions by introducing a new class of complex geometries in $2n+2$ dimensions, specified by a Riemannian metric, a scalar field and a closed three-form, which admit a particular kind of Killing spinor. In particular, for $n\ge 3$, we show that when the geometry in $2n+2$ dimensions is a cone we obtain a class of geometries in $2n+1$ dimensions, specified by a Riemannian metric, a scalar field and a closed two-form, which includes the seven and nine-dimensional geometries mentioned above when $n=3,4$, respectively. We also consider various ansatz for the geometries and construct infinite classes of explicit examples for all $n$.Comment: 28 page

Design of a pneumatic muscle based continuum robot with embedded tendons

© 1996-2012 IEEE. Continuum robots have attracted increasing focus in recent years due to their intrinsic compliance that allows for dexterous and safe movements. However, the inherent compliance in such systems reduces the structural stiffness, and therefore leads to the issue of reduced positioning accuracy. This paper presents the design of a continuum robot employing tendon embedded pneumatic muscles. The pneumatic muscles are used to achieve large-scale movements for preliminary positioning, while the tendons are used for fine adjustment of position. Such hybrid actuation offers the potential to improve the accuracy of the robotic system, while maintaining large displacement capabilities. A three-dimensional dynamic model of the robot is presented using a mass-damper-spring-based network, in which elastic deformation, actuating forces, and external forces are taken into account. The design and dynamic model of the robot are then validated experimentally with the help of an electromagnetic tracking system

Invasion of Europe by the western corn rootworm, Diabrotica virgifera virgifera: multiple transatlantic introductions with various reductions of genetic diversity

The early stages of invasion involve demographic bottlenecks that may result in lower genetic variation in introduced populations as compared to source population/s. Low genetic variability may decrease the adaptive potential of such populations in their new environments. Previous population genetic studies of invasive species have reported varying levels of losses of genetic variability in comparisons of source and invasive populations. However, intraspecific comparisons are required to assess more thoroughly the repeatability of genetic consequences of colonization events. Descriptions of invasive species for which multiple introductions from a single source population have been demonstrated may be particularly informative. The western corn rootworm (WCR), Diabrotica virgifera virgifera, native to North America and invasive in Europe, offers us an opportunity to analyse multiple introduction events within a single species. We investigated within- and between-population variation at eight microsatellite markers in WCR in North America and Europe to investigate the routes by which WCR was introduced into Europe, and to assess the effect of introduction events on genetic variation. We detected five independent introduction events from the northern USA into Europe. The diversity loss following these introductions differed considerably between events, suggesting substantial variation in introduction, foundation and/or establishment conditions. Genetic variability at evolutionarily neutral loci does not seem to underlie the invasive success of WCR in Europe. We also showed that the introduction of WCR into Europe resulted in the redistribution of genetic variance from the intra- to the interpopulational level contrary to most examples of multiple introductions