Conditional symmetry and spectrum of the one-dimensional Schr\"odinger equation

We develop an algebraic approach to studying the spectral properties of the stationary Schr\"odinger equation in one dimension based on its high order conditional symmetries. This approach makes it possible to obtain in explicit form representations of the Schr\"odinger operator by $n\times n$ matrices for any $n\in {\bf N}$ and, thus, to reduce a spectral problem to a purely algebraic one of finding eigenvalues of constant $n\times n$ matrices. The connection to so called quasi exactly solvable models is discussed. It is established, in particular, that the case, when conditional symmetries reduce to high order Lie symmetries, corresponds to exactly solvable Schr\"odinger equations. A symmetry classification of Sch\"odinger equation admitting non-trivial high order Lie symmetries is carried out, which yields a hierarchy of exactly solvable Schr\"odinger equations. Exact solutions of these are constructed in explicit form. Possible applications of the technique developed to multi-dimensional linear and one-dimensional nonlinear Schr\"odinger equations is briefly discussed.Comment: LaTeX-file, 31 pages, to appear in J.Math.Phys., v.37, N7, 199

Remote measurement of the water content of snowpacks

Electronic equipment for sensing moisture content of snowpacks is described. Components of electronic test equipment are illustrated and methods of conducting tests are explained. Possibilities for airborne sensing are examined

Metabolic rate meter and method

A method is described for measuring the dynamic metabolic rate of a human or animal. The ratio of the exhaled carbon dioxide to a known amount of C(13)02 introduced into the exhalation is determined by mass spectrometry. This provides an instantaneous measurement of the carbon dioxide generated

A portable absorbed dose measuring instrument with gamma discrimination

The characteristics of an electronic instrument for measuring the radiation dose absorbed by tissues are presented. The detector is a sphere of tissue-equivalent plastic with a single wire located on a diameter of the sphere. The electronic circuits and method of operation of the detector are described. Advantages are the small size and easy portability plus ability to selectively measure neutron and gamma plus neutron events

Out-of-plane fluctuation conductivity of layered superconductors in strong electric fields

The non-Ohmic effect of a high electric field on the out-of-plane magneto-conductivity of a layered superconductor near the superconducting transition is studied in the frame of the Langevin approach to the time-dependent Ginzburg-Landau equation. The transverse fluctuation conductivity is computed in the self-consistent Hartree approximation for an arbitrarily strong electric field and a magnetic field perpendicular to the layers. Our results indicate that high electric fields can be effectively used to suppress the out-of-plane fluctuation conductivity in high-temperature superconductors and a significant broadening of the transition induced by a strong electric field is predicted. Extensions of the results are provided for the case when the electric field is applied at an arbitrary angle with respect to the layers, as well as for the three-dimensional anisotropic regime of a strong interlayer coupling.Comment: to be published in Phys. Rev.

Reduced gravity liquid configuration simulator

Reduced gravity liquid configuration simulator to study propellant behavior in rocket fuel tank

Cosmic Evolution and Primordial Black Hole Evaporation

A cosmological model in which primordial black holes (PBHs) are present in the cosmic fluid at some instant t=t_0 is investigated. The time t_0 is naturally identified with the end of the inflationary period. The PBHs are assumed to be nonrelativistic in the comoving fluid, to have the same mass, and may be subject to evaporation for t>t_0. Our present work is related to an earlier paper of Zimdahl and Pavon [Phys. Rev. D {\bf 58}, 103506 (1998)], but in contradistinction to these authors we assume that the (negative) production rate of the PBHs is zero. This assumption appears to us to be more simple and more physical. Consequences of the formalism are worked out. In particular, the four-divergence of the entropy four-vector in combination with the second law in thermodynamics show in a clear way how the the case of PBH evaporation corresponds to a production of entropy. Accretion of radiation onto the black holes is neglected. We consider both a model where two different sub-fluids interact, and a model involving one single fluid only. In the latter case an effective bulk viscosity naturally appears in the formalism.Comment: 18 pages, LaTeX, no figures. Extended discussion of the black hole evaporation process. Version to appear in Phys. Rev.