Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

КРИЗИС ВЛАСТИ В КАБАРДИНО-БАЛКАРИИ В АВГУСТЕ 1991 ГОДА Статья посвящена исследованию влияния путча 1991 г. на этнополитическую обстановку в Кабардино-Балкарской Республике. Анализируется процесс "включения" национального фактора в разгоревшееся политическое противоборство, вылившееся в кризис власти. Авторами впервые сформулирована и обоснована мысль о том, что события августа 1991 г. привели к объединению к тому времени уже нелояльных по отношению друг к другу национальных движений "титульных" народов Кабардино-Балкарии, что нашло выражение в выдвижении общего требования отставки первых лиц республиканской власти. Адрес статьи: www.gramota.net/materials/3/2017/9/58.html

1991년도 사업경과 보고

Beyond Equilibrium Thermodynamics

Some general properties of compatible Poisson brackets of hydrodynamic type are discussed, in particular: (a) an invariant differential-geometric criterion of the compatibility based on the Nijenhuis tensor which is slightly different from those existing in the literature; (b) the Lax pair with a spectral parameter governing compatible Poisson brackets in the diagonalizable case; (c) the connection of this problem with the class of surfaces in Euclidean space which possess non-trivial deformations preserving the Weingarten operator.

https://iopscience.iop.org/article/10.1088/0305-4470/34/11/328/pdf

Compatible Poisson brackets of hydrodynamic type

differential geometry and lie groups for physicists is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the differential geometry and lie groups for physicists is universally compatible with any devices to read.

Differential Geometry And Lie Groups For Physicists

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one‐form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two‐monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)‐valued connection and belongs to a nontrivial Godbillon–Vey class. On the other hand, for the Euler top and a special case of three‐species Lotka–Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi‐Hamiltonian structures. The globally integrable bi‐Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one‐form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one‐form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack–McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka–Volterra, May–Leonard, and Maxwell–Bloch systems admit globally integrable bi‐Hamiltonian structure.

/pdf/poisson-structure-of-dynamical-systems-with-three-degrees-of-2eyzszbts2.pdf

Poisson structure of dynamical systems with three degrees of freedom

The discussion of the Hamiltonian structure of two‐component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler’s equation governing the motion of plane sound waves of finite amplitude and another quasilinear second‐order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow‐water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama’s generalization of the shallow‐water equations admits bi‐Hamiltonian structure.

/pdf/multi-hamiltonian-structure-of-equations-of-hydrodynamic-3wqf0o1xyf.pdf

Multi‐Hamiltonian structure of equations of hydrodynamic type

The dynamics of collisionless plasma described by the Poisson–Vlasov equations is connected to the Hamiltonian motions of particles and their symmetries. The group of canonical diffeomorphisms of particle phase space is described and adopted as the configuration space. The dual space of its Lie algebra of Hamiltonian vector fields is identified with the space of nonclosed one-forms. The Poisson equation is obtained as a constraint arising from the gauge symmetries of particle dynamics. Variational derivative constrained by the Poisson equation is used to obtain reduced dynamical equations. Usual Lie–Poisson reduction for the group of canonical diffeomorphisms gives the momentum-Vlasov equations. Plasma density is defined as the divergence of symplectic dual of momentum variables. This definition is also given a momentum map description associated with the action of additive group of functions of particle phase space. Equivalence of Hamiltonian functionals in momentum and density formulations is shown. As an alternative formulation in momentum variables, a canonical Hamiltonian system with a quadratic Hamiltonian functional is described. In the case that the groups of Hamiltonian and volume preserving diffeomorphisms coincide, a comparison of one-dimensional plasma and two-dimensional incompressible fluid is presented.

Geometry of plasma dynamics. I. Group of canonical diffeomorphisms

Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on T * T * Q ) of (both compressible and incompressible) Euler’s fluid and Vlasov’s plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

https://www.mdpi.com/1099-4300/21/9/907/pdf

Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy

Taking conguration space as a Lie group, the trivialized Euler-Lagrange and Hamilton’s equations are obtained and presented as Lagrangian submanifolds of the trivialized Tulczyjew’s symplectic space. Euler-Poincar e and Lie-Poisson equations are presented as Lagrangian submanifolds of the reduced Tulczyjew’s symplectic space. Tulczyjew’s generalized Legendre transformations for trivialized and reduced dynamics are constructed. Key words Trivialized Euler-Lagrange equations, trivialized Hamilton’s equations, EulerPoincar e equations, Lie-Poisson equations, Morse families, Tulczyjew’s triplet, Legendre transformation, Lagrangian submanifold, dieomorphisms group.

Hasan Gümral

Papers

Poisson structure of dynamical systems with three degrees of freedom

Multi‐Hamiltonian structure of equations of hydrodynamic type

Geometry of plasma dynamics. I. Group of canonical diffeomorphisms

Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy

Tulczyjew's Triplet for Lie Groups II: Dynamics