Boundary values as Hamiltonian variables. I. New Poisson brackets

The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift this restriction. The new brackets generalize a canonical bracket considered by Lewis, Marsden, Montgomery and Ratiu for the free boundary problem in hydrodynamics. Our definition of Poisson brackets permits to treat boundary values of a field on equal footing with its internal values and directly estimate the brackets between both surface and volume integrals. This construction is applied to any local form of Poisson brackets. A prescription for delta-function on closed domains and a definition of the {\it full} variational derivative are proposed.Comment: 26 pages, LaTex, IHEP 93-4

The calcareous nannofossils and magnetostratigraphic results from the Upper Tithonian-Berriasian of Feodosiya region (Eastern Crimea)

This article is concerned with nannofossil study of Tithonian-Berriasian sediments of Eastern Crimea. The NJT 16, NJT 17a, NJT 17b, NKT, and NK 1 nannofossil zones were determined. The occurrence of Nannoconus kamptneri minor, one of the potential marker-types of the Tithonian-Berriasian boundary (the base of the NKT Zone) of the Tethyan sequence in the Feodosiyan section is assigned here to the Pseudosubplanites grandis ammonite Subzone and the magnetic Chron M18n. The base of the NKT Zone is closer to the Grandis Subzone base than to the base of the Jacobi Subzone. Contradictions in the interpretation of magnetic chrons obtained by the present authors (Arkadiev et al. 2018) and by Bakhmutov et al. (2018) might be caused by mistakes admitted in the latter work on the compiled section.Fil: Arkadiev, V.. Saint Petersburg State University; RusiaFil: Lescano, Marina Aurora. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; ArgentinaFil: Concheyro, Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; ArgentinaFil: Guzhikov, A.. Saratov State University; RusiaFil: Baraboshkin, E.. Moscow State University; Rusi

An application of the Casoratian technique to the 2D Toda lattice equation

A general Casoratian formulation is proposed for the 2D Toda lattice equation, which involves coupled eigenfunction systems. Various Casoratian type solutions are generated, through solving the resulting linear conditions and using a Baecklund transformation.Comment: 11 page

Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism

We consider the algebra of spatial diffeomorphisms and gauge transformations in the canonical formalism of General Relativity in the Ashtekar and ADM variables. Modifying the Poisson bracket by including surface terms in accordance with our previous proposal allows us to consider all local functionals as differentiable. We show that closure of the algebra under consideration can be achieved by choosing surface terms in the expressions for the generators prior to imposing any boundary conditions. An essential point is that the Poisson structure in the Ashtekar formalism differs from the canonical one by boundary terms.Comment: 19 pages, Latex, amsfonts.sty, amssymb.st

Spectral decomposition for the Dirac system associated to the DSII equation

A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Davey--Stewartson II (DSII) equation. Discrete spectrum in the spectral problem corresponds to eigenvalues embedded into a two-dimensional essential spectrum. We show that these embedded eigenvalues are structurally unstable under small variations of the initial data. This instability leads to the decay of localized initial data into continuous wave packets prescribed by the nonlinear dynamics of the DSII equation

Combining scanning probe microscopy and x-ray spectroscopy

A new versatile tool, combining Shear Force Microscopy and X-Ray Spectroscopy was designed and constructed to obtain simultaneously surface topography and chemical mapping. Using a sharp optical fiber as microscope probe, it is possible to collect locally the visible luminescence of the sample. Results of tests on ZnO and on ZnWO4 thin layers are in perfect agreement with that obtained with other conventional techniques. Twin images obtained by simultaneous acquisition in near field of surface topography and of local visible light emitted by the sample under X-Ray irradiation in synchrotron environment are shown. Replacing the optical fibre by an X-ray capillary, it is possible to collect local X-ray fluorescence of the sample. Preliminary results on Co-Ti sample analysis are presented

Magnetostratigraphy of the Upper Berriasian “Zavodskaya Balka” section (East Crimea, Feodosiya

The results of magnetostratigraphic investigations in the Upper Berriasian Zavodskaya Balka section (Feodosiya, Crimea) are presented: magnetic polarity information, data on magnetic susceptibility, its anisotropy (АМS), frequency dependence (FD-factor) and other petromagnetic parameters. The analysis of the thermomagnetic and magnetic saturation curves has proved the presence of magnetite, being the main carrier of the remanent magnetization. Magnetic cleaning with alternating field and with temperature mostly has revealed the two-component composition of the magnetization, and the magnetostratigraphy is based on the directions of the most stable of them, with unblocking field from 35–50 mT and temperature from 300 to 540°C. The palaeomagnetic column presented specifies four heteropolar magnetozones – analogous to the M16 and M15 magnetic chrons (full M16n and M15r, parts of M16r and M15n). The existence of the M16n.1r subchron (“Feodosiya”) is substantiated, and it should be included into the Geomagnetic Polarity Time Scale. By bio- and magnetostratigraphic correlation, the section studied is an age analogue of the Paramimounum, Picteti and Alpillensis (probably Otopeta) subzones of the Boissieri Zone. The calculated sedimentation rate varied from 26.6 to 29.5 m/My

Integrated palaeontological characteristics (ammonites, ostracods, foraminifers, dinocysts) of the Berriasian deposits of central Crimea

The Berriasian deposits of the central Crimea have been studied in order to compose a composite sequence of the stage with detailed palaeontological characterization. The Berriasian includes the Bedenekyrskaya Formation (packstones), Bechku Formation (siltstones, sandstones) and Kuchkinskaya Formation (sponge packstones, clays, siltstones, and coral-algal bioherm framestones). The Jacobi, Occitanica and Boissieri zones were identified based on ammonites found in the sections. A micropalaeontological analysis determined the following: 6 foraminiferal assemblages, the Costacythere khiamii – Hechticythere belbekensis and Costacythere drushchitzi – Reticythere marfenini ostracod assemblages, and a Phoberocysta neocomica dinocyst assemblage. Palaeoecological analysis of the ostracod and foraminiferal associations indicates a moderately warm marine basin with normal salinity and shallow depths (tens of meters). Only the sponge horizon was probably deposited in a deeper-water environment