Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences

The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the classical transformations in the scalar case. It is demonstrated that Laplace transformations can be pulled back to the transformations of the corresponding hydrodynamic type systems. We discuss periodic Laplace sequences of with the emphasize on the simplest nontrivial case of period 2. For 3-component systems in Riemann invariants a complete discription of closed quadruples is proposed. They turn to be related to a special quadratic reduction of the (2+1)-dimensional 3-wave system which can be reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of the Lame and rotation coefficients Laplace transformations have a natural interpretation as the symmetries of the Dirac operator, associated with the (2+1)-dimensional n-wave system. The 2-component Laplace transformations can be interpreted also as the symmetries of the (2+1)-dimensional integrable equations of Davey-Stewartson type. Laplace transformations of hydrodynamic type systems originate from a canonical geometric correspondence between systems of conservation laws and line congruences in projective space.Comment: 22 pages, Late

Development of low-temperature thermochemical conversion reactors for coal power engineering

The main principles applied in developing a technology for low-temperature thermochemical conversion of brown coals to obtain fuel gas and semicoke intended for being fired in two-fuel power installations are considered on the basis of a set of experimental and calculated investigations. The obtained results are compared with the experimental data obtained using other methods and with the results of previous industrial tests. © 2013 Pleiades Publishing, Inc

The comet Halley dust and gas environment

Quantitative descriptions of environments near the nucleus of comet P /Halley have been developed to support spacecraft and mission design for the flyby encounters in March, 1986. To summarize these models as they exist just before the encounters, we review the relevant data from prior Halley apparitions and from recent cometary research. Orbital elements, visual magnitudes, and parameter values and analysis for the nucleus, gas and dust are combined to predict Halley's position, production rates, gas and dust distributions, and electromagnetic radiation field for the current perihelion passage. The predicted numerical results have been useful for estimating likely spacecraft effects, such as impact damage and attitude perturbation. Sample applications are cited, including design of a dust shield for spacecraft structure, and threshold and dynamic range selection for flight experiments. We expect that the comet's activity may be more irregular than these smoothly varying models predict, and that comparison with the flyby data will be instructive.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43774/1/11214_2004_Article_BF00175326.pd