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We present molecular mechanics {and spectroscopic} calculations on prototype artificial light harvesting systems consisting of chromophores attached to a tobacco mosaic virus (TMV) protein scaffold. These systems have been synthesized and characterized spectroscopically, but information about the microscopic configurations and geometry of these TMV-templated chromophore assemblies is largely unknown. We use a Monte Carlo conformational search algorithm to determine the preferred positions and orientations of two chromophores, Coumarin 343 together with its linker, and Oregon Green 488, when these are attached at two different sites (104 and 123) on the TMV protein. The resulting geometric information shows that the extent of disorder and aggregation properties, and therefore the optical properties of the TMV-templated chromophore assembly, are highly dependent on the choice of chromophores and protein site to which they are bound. We used the results of the conformational search as geometric parameters together with an improved tight-binding Hamiltonian to simulate the linear absorption spectra and compare with experimental spectral measurements. The ideal dipole approximation to the Hamiltonian is not valid since the distance between chromophores can be very small. We found that using the geometries from the conformational search is necessary to reproduce the features of the experimental spectral peaks.

Based on the CR formalism of algebraically special spacetimes by Hill, Lewandowski and Nurowski, we derive a nonlinear system of two real ODEs, of which the general solution determines a twisting type II (or more special) vacuum spacetime with two Killing vectors (commuting or not) and at most seven real parameters in addition to the cosmological constant Lambda. To demonstrate a broad range of interesting spacetimes that these ODEs can capture, special solutions of various Petrov types are presented and described as they appear in this approach. They include Kerr-NUT, Kerr and Debney/Demia\'{n}ski's type II, Lun's type II and III (subclasses of Held-Robinson), MacCallum and Siklos' type III (Lambda<0), and the type N solutions (Lambda<>0) we found in an earlier paper, along with a new class of type II solutions as a nontrivial limit of Kerr and Debney's type II solutions. Also, we discuss a situation in which the two ODEs can be reduced to one. However, constructing the general solution still remains an open problem., Comment: 22 pages

We investigate a new class of twisting type N vacuum solutions with nonzero (positive) cosmological constant Lambda by studying the equations of geodesic deviations along the privileged radial timelike geodesics, generalizing J. Bicak and J. Podolsky's results on non-twisting type N solutions. It is shown that these twisting radiative spacetimes can be interpreted as exact transverse gravitational waves propagating in the de-Sitter universe, with a distinctive feature that all the wave amplitudes are proportional to Lambda (dark energy/matter source coupling). Moveover, we demonstrate the cosmic no-hair conjecture in these spacetimes and discuss their Killing horizons., Comment: 12 pages

In the search for vacuum solutions, with or without a cosmological constant, of the Einstein field equations of Petrov type N with twisting principal null directions, the CR structures to describe the parameter space for a congruence of such null vectors provide a very useful tool. A work of Hill, Lewandowski and Nurowski has given a good foundation for this, reducing the field equations to a set of differential equations for two functions, one real, one complex, of three variables. Under the assumption of the existence of one Killing vector, the (infinite-dimensional) classical symmetries of those equations are determined and group-invariant solutions are considered. This results in a single ODE of the third order which may easily be reduced to one of the second order. A one-parameter class of power series solutions, g(w), of this second-order equation is realized, holomorphic in a neighborhood of the origin and behaving asymptotically as a simple quadratic function plus lower-order terms for large values of w, which constitutes new solutions of the twisting type N problem. The solution found by Leroy, and also by Nurowski, is shown to be a special case in this class. Cartan's method for determining equivalence of CR manifolds is used to show that this class is indeed much more general. In addition, for a special choice of a parameter, this ODE may be integrated once, to provide a first-order Abel equation. It can also determine new solutions to the field equations although no general solution has yet been found for it., Comment: 28 pages

The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits., Comment: 28 pages, 11 figures

We present the general solution to the Plebanski equation for an H-space that admits Killing vectors for an entire SU(2) of symmetries, which is therefore also the general solution of the sDiff(2)Toda equation that allows these symmetries. Desiring these solutions as a bridge toward the future for yet more general solutions of the sDiff(2)Toda equation, we generalize the earlier work of Olivier, on the Atiyah-Hitchin metric, and re-formulate work of Babich and Korotkin, and Tod, on the Bianchi IX approach to a metric with an SU(2) of symmetries. We also give careful delineations of the conformal transformations required to ensure that a metric of Bianchi IX type has zero Ricci tensor, so that it is a self-dual, vacuum solution of the complex-valued version of Einstein's equations, as appropriate for the original Plebanski equation., Comment: 27 pages

HH-spaces, i.e., complex spacetimes, of Petrov type NxN are determined by a trio of pde's for two functions, lambda and a, of three independent variables (and also two gauge functions, chosen to be two of the independent variables if one prefers). As in common integrable systems, these form a second order, linear system for lambda; howver, here the integrability conditions, involving a, are more complicated than is common. Therefore, with the hope of finding new solutions, these equations are now constrained to also admit both one and two homothetic or Killing vectors. The case with one Killing and one homothetic vector reduces these equations to two ode's for two unknown functions of the one remaining variable. In addition, we also describe in detail the explicit forms of the metric, tetrad, connections, and curvature for twisting HH-spaces of Petrov type NxN, modulo the determining equations. This simplifies considerably the process of obtaining these details cleanly from earlier articles on the subject, thus simplifying access to the research area., Comment: 7 pages, TeX file, from a talk at GR16, Durban, South Africa, July, 2001