804,543 research outputs found
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 matrices for
any and, thus, to reduce a spectral problem to a purely
algebraic one of finding eigenvalues of constant 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.
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