Trkalian fields and Radon transformation

We write the spherical curl transformation for Trkalian fields using differential forms. Then we consider Radon transform of these fields. The Radon transform of a Trkalian field satisfies a corresponding eigenvalue equation on a sphere in transform space. The field can be reconstructed using knowledge of the Radon transform on a canonical hemisphere. We consider relation of the Radon transformation with Biot-Savart integral operator and discuss its transform introducing Radon-Biot- Savart operator. The Radon transform of a Trkalian field is an eigenvector of this operator. We also present an Ampere law type relation for these fields. We apply these to Lundquist solution. We present a Chandrasekhar-Kendall type solution of the corresponding equation in the transform space. Lastly, we focus on the Euclidean topologically massive Abelian gauge theory. The Radon transform of an anti-self-dual field is related by antipodal map on this sphere to the transform of the self-dual field obtained by inverting space coordinates. The Lundquist solution provides an example of quantization of topological mass in this context.Comment: 23 page

Hamilton-Jacobi Approach to Pre-Big Bang Cosmology at Long-wavelengths

We apply the long-wavelength approximation to the low energy effective string action in the context of Hamilton-Jacobi theory. The Hamilton-Jacobi equation for the effective string action is explicitly invariant under scale factor duality. We present the leading order, general solution of the Hamilton-Jacobi equation. The Hamilton-Jacobi approach yields a solution consistent with the with the Lagrange formalism. The momentum constraints take an elegant, simple form. Furthermore this general solution reduces to the quasi-isotropic one, if the evolution of the gravitational field is neglected. Duality transformation for the general solution is written as a coordinate transformation in an abstract field space

Topologically Massive Gauge Theory: A Lorentzian Solution

We obtain a lorentzian solution for the topologically massive non-abelian gauge theory on AdS space by means of a SU(1, 1) gauge transformation of the previously found abelian solution. There exists a natural scale of length which is determined by the inverse topological mass. The topological mass is proportional to the square of the gauge coupling constant. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an abelian gauge transformation. Then we present the map from the AdS space to the pseudo-sphere including the topological mass. This is the lorentzian analog of the Hopf map. This map yields a global decomposition of the AdS space as a trivial circle bundle over the upper portion of the pseudo-sphere which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the abelian field equation onto the pseudo-sphere using a global section of the solution on the AdS space. Then we discuss the integration of the field equation using the Archimedes map from the pseudo-sphere to the cylinder over the ideal Poincare circle. We also present a brief discussion of the holonomy of the gauge potential and the dual-field strength on the upper portion of the pseudo-sphere.Comment: 23 pages, 1 postscript figur

Distribution and Excretion of TEGDMA in Guinea Pigs and Mice

The monomer triethyleneglycoldimethacrylate (TEGDMA) is used as a diluent in many resin-based dental materials. It was previously shown in vitro that TEGDMA was released into the adjacent biophase from such materials during the first days after placement. In this study, the uptake, distribution, and excretion of 14C-TEGDMA applied via gastric, intradermal, and intravenous administration at dose levels well above those encountered in dental care were examined in vivo in guinea pigs and mice as a test of the hypothesis that TEGDMA reaches cytotoxic levels in mammalian tissues. 14C-TEGDMA was taken up rapidly from the stomach and small intestine after gastric administration in both species and was widely distributed in the body following administration by each route. Most 14C was excreted within one day as 14 CO2. The peak equivalent TEGDMA levels in all mouse and guinea pig tissues examined were at least 1000-fold less than known toxic levels. The study therefore did not support the hypothesis

Initial Hypersurface Formulation: Hamilton-Jacobi Theory for Strongly Coupled Gravitational Systems

Strongly coupled gravitational systems describe Einstein gravity and matter in the limit that Newton's constant G is assumed to be very large. The nonlinear evolution of these systems may be solved analytically in the classical and semiclassical limits by employing a Green function analysis. Using functional methods in a Hamilton-Jacobi setting, one may compute the generating functional (`the phase of the wavefunctional') which satisfies both the energy constraint and the momentum constraint. Previous results are extended to encompass the imposition of an arbitrary initial hypersurface. A Lagrange multiplier in the generating functional restricts the initial fields, and also allows one to formulate the energy constraint on the initial hypersurface. Classical evolution follows as a result of minimizing the generating functional with respect to the initial fields. Examples are given describing Einstein gravity interacting with either a dust field and/or a scalar field. Green functions are explicitly determined for (1) gravity, dust, a scalar field and a cosmological constant and (2) gravity and a scalar field interacting with an exponential potential. This formalism is useful in solving problems of cosmology and of gravitational collapse.Comment: 30 pages Latex (IOP) file with 2 IOP style files, to be published in Classical and Quantum Gravity (1998

Topologically massive magnetic monopoles

We show that in the Maxwell-Chern-Simons theory of topologically massive electrodynamics the Dirac string of a monopole becomes a cone in anti-de Sitter space with the opening angle of the cone determined by the topological mass which in turn is related to the square root of the cosmological constant. This proves to be an example of a physical system, {\it a priory} completely unrelated to gravity, which nevertheless requires curved spacetime for its very existence. We extend this result to topologically massive gravity coupled to topologically massive electrodynamics in the framework of the theory of Deser, Jackiw and Templeton. These are homogeneous spaces with conical deficit. Pure Einstein gravity coupled to Maxwell-Chern-Simons field does not admit such a monopole solution

A perspective on using experiment and theory to identify design principles in dye-sensitized solar cells

Dye-sensitized solar cells (DSCs) have been the subject of wide-ranging studies for many years because of their potential for large-scale manufacturing using roll-to-roll processing allied to their use of earth abundant raw materials. Two main challenges exist for DSC devices to achieve this goal; uplifting device efficiency from the 12 to 14% currently achieved for laboratory-scale ‘hero’ cells and replacement of the widely-used liquid electrolytes which can limit device lifetimes. To increase device efficiency requires optimized dye injection and regeneration, most likely from multiple dyes while replacement of liquid electrolytes requires solid charge transporters (most likely hole transport materials – HTMs). While theoretical and experimental work have both been widely applied to different aspects of DSC research, these approaches are most effective when working in tandem. In this context, this perspective paper considers the key parameters which influence electron transfer processes in DSC devices using one or more dye molecules and how modelling and experimental approaches can work together to optimize electron injection and dye regeneration. This paper provides a perspective that theory and experiment are best used in tandem to study DSC device

Trkalian fields: ray transforms and mini-twistors

We study X-ray and Divergent beam transforms of Trkalian fields and their relation with Radon transform. We make use of four basic mathematical methods of tomography due to Grangeat, Smith, Tuy and Gelfand-Goncharov for an integral geometric view on them. We also make use of direct approaches which provide a faster but restricted view of the geometry of these transforms. These reduce to well known geometric integral transforms on a sphere of the Radon or the spherical Curl transform in Moses eigenbasis, which are members of an analytic family of integral operators. We also discuss their inversion. The X-ray (also Divergent beam) transform of a Trkalian field is Trkalian. Also the Trkalian subclass of X-ray transforms yields Trkalian fields in the physical space. The Riesz potential of a Trkalian field is proportional to the field. Hence, the spherical mean of the X-ray (also Divergent beam) transform of a Trkalian field over all lines passing through a point yields the field at this point. The pivotal point is the simplification of an intricate quantity: Hilbert transform of the derivative of Radon transform for a Trkalian field in the Moses basis. We also define the X-ray transform of the Riesz potential (of order 2) and Biot-Savart integrals. Then, we discuss a mini-twistor respresentation, presenting a mini-twistor solution for the Trkalian fields equation. This is based on a time-harmonic reduction of wave equation to Helmholtz equation. A Trkalian field is given in terms of a null vector in C3 with an arbitrary function and an exponential factor resulting from this reduction.Comment: 37 pages, http://dx.doi.org/10.1063/1.482610