Future monitoring of charged particle energy deposition into the upper atmosphere and comments on possible relationships between atmospheric phenomena and solar and/or geomagnetic activity

Monitoring of earth's atmosphere was conducted for several years utilizing the ITOS series of low-altitude, polar-orbiting weather satellites. A space environment monitoring package was included in these satellites to perform measurements of a portion of earth's charged particle environment. The charged particle observations proposed for the low-altitude weather satellite TIROS N, are described which will provide the capability of routine monitoring of the instantaneous total energy deposition into the upper atmosphere by the precipitation of charged particles from higher altitudes. Such observations may be of use in future studies of the relationships between geomagnetic activity and atmospheric weather pattern developments. Estimates are given to assess the potential importance of this type of energy deposition. Discussion and examples are presented illustrating the importance of distinguishing between solar and geomagnetic activity as possible causative sources. Such differentiation is necessary because of the widely different spatial and time scales involved in the atmospheric energy input resulting from these various sources of activity

Ellipticity Conditions for the Lax Operator of the KP Equations

The Lax pseudo-differential operator plays a key role in studying the general set of KP equations, although it is normally treated in a formal way, without worrying about a complete characterization of its mathematical properties. The aim of the present paper is therefore to investigate the ellipticity condition. For this purpose, after a careful evaluation of the kernel with the associated symbol, the majorization ensuring ellipticity is studied in detail. This leads to non-trivial restrictions on the admissible set of potentials in the Lax operator. When their time evolution is also considered, the ellipticity conditions turn out to involve derivatives of the logarithm of the tau-function.Comment: 21 pages, plain Te

Klein-Gordon Solutions on Non-Globally Hyperbolic Standard Static Spacetimes

We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a technical condition: "acceptability") of (some variant of) the Laplace-Beltrami operator defined on test functions in an $L^2$-space of the static hypersurface. The proof of the existence of this construction completes and extends work originally done by Wald. Further results include the uniqueness of these solutions, their support properties, the construction of the space of solutions and the energy and symplectic form on this space, an analysis of certain symmetries on the space of solutions and of various examples of this method, including the construction of a non-bounded below acceptable self-adjoint extension generating the dynamics

Unravelling the mechanisms of vibrational relaxation in solution

We present a systematic study of the mode-specific vibrational relaxation of NO(2) in six weakly-interacting solvents (perfluorohexane, perfluoromethylcyclohexane, perfluorodecalin, carbon tetrachloride, chloroform, and d-chloroform), chosen to elucidate the dominant energy transfer mechanisms in the solution phase. Broadband transient vibrational absorption spectroscopy has allowed us to extract quantum state-resolved relaxation dynamics of the two distinct NO(2) fragments produced from the 340 nm photolysis of N(2)O(4) → NO(2)(X) + NO(2)(A) and their separate paths to thermal equilibrium. Distinct relaxation pathways are observed for the NO(2) bending and stretching modes, even at energies as high as 7000 cm(–1) above the potential minimum. Vibrational energy transfer is governed by different interaction mechanisms in the various solvent environments, and proceeds with timescales ranging from 20–1100 ps. NO(2) relaxation rates in the perfluorocarbon solvents are identical despite differences in acceptor mode state densities, infrared absorption cross sections, and local solvent structure. Vibrational energy is shown to be transferred to non-vibrational solvent degrees of freedom (V-T) through impulsive collisions with the perfluorocarbon molecules. Conversely, NO(2) relaxation in chlorinated solvents is reliant on vibrational resonances (V-V) while V-T energy transfer is inefficient and thermal excitation of the surrounding solvent molecules inhibits faster vibrational relaxation through direct complexation. Intramolecular vibrational redistribution allows the symmetric stretch of NO(2) to act as a gateway for antisymmetric stretch energy to exit the molecule. This study establishes an unprecedented level of detail for the cooling dynamics of a solvated small molecule, and provides a benchmark system for future theoretical studies of vibrational relaxation processes in solution