On the One Class of Hyperbolic Systems

The classification problem is solved for some type of nonlinear lattices. These lattices are closely related to the lattices of Ruijsenaars-Toda type and define the Backlund auto-transformations for the class of two-component hyperbolic systems.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Topical cyclone rainfall characteristics as determined from a satellite passive microwave radiometer

Data from the Nimbus-5 Electrically Scanning Microwave Radiometer (ESMR-5) were used to calculate latent heat release and other rainfall parameters for over 70 satellite observations of 21 tropical cyclones in the tropical North Pacific Ocean. The results indicate that the ESMR-5 measurements can be useful in determining the rainfall characteristics of these storms and appear to be potentially useful in monitoring as well as predicting their intensity. The ESMR-5 derived total tropical cyclone rainfall estimates agree favorably with previous estimates for both the disturbance and typhoon stages. The mean typhoon rainfall rate (1.9 mm h(-1)) is approximately twice that of disturbances (1.1 mm h(-1))

Satellite-observed latent heat release in a tropical cyclone

Data from the Nimbus 5 electrically scanning microwave radiometer (ESMR) are used to make calculations of the latent heat release (L.H.R.) and the distribution of rainfall rate in a tropical cyclone as it grows from a tropical disturbance to a typhoon. The L.H.R. (calculated over a circular area of 4 deg latitude radius) increases during the development and intensification of the storm from a magnitude of 2.7 X 10 to the 21st power ergs/s (in the disturbance stage) to 8.8 X 10 to the 21st power ergs (typhoon stage). The latter value corresponds to a mean rainfall rate of 2.0 mm hr/s. The more intense the cyclone and the greater the L.H.R., the greater the percentage contribution of the larger rainfall rates to the L.H.R. In the disturbance stage the percentage contribution of rainfall rates less than or minus 6 mm hr/s is typically 8%; for the typhoon stage, the value is 38%. The distribution of rainfall rate as a function of radial distance from the center indicates that as the cyclone intensifies, the higher rainfall rates tend to concentrate toward the center of the circulation

Classification of integrable equations on quad-graphs. The consistency approach

A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional consistency. This property yields, among other features, the existence of the discrete zero curvature with a spectral parameter. For all integrable systems of the obtained exhaustive list, the so called three-leg forms are found. This establishes Lagrangian and symplectic structures for these systems, and the connection to discrete systems of the Toda type on arbitrary graphs. Generalizations of these ideas to the three-dimensional integrable systems and to the quantum context are also discussed

Classification of integrable discrete equations of octahedron type

We use the consistency approach to classify discrete integrable 3D equations of the octahedron type. They are naturally treated on the root lattice $Q(A_3)$ and are consistent on the multidimensional lattice $Q(A_N)$. Our list includes the most prominent representatives of this class, the discrete KP equation and its Schwarzian (multi-ratio) version, as well as three further equations. The combinatorics and geometry of the octahedron type equations are explained. In particular, the consistency on the 4-dimensional Delaunay cells has its origin in the classical Desargues theorem of projective geometry. The main technical tool used for the classification is the so called tripodal form of the octahedron type equations.Comment: 53 pp., pdfLaTe