The Experts below are selected from a list of 75 Experts worldwide ranked by ideXlab platform
Alexander G. Chefranov - One of the best experts on this subject based on the ideXlab platform.
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interaction between global scale atmospheric vortices modeling with Hamiltonian Dynamic system of antipodal point vortices on a rotating sphere
arXiv: Fluid Dynamics, 2016Co-Authors: Igor I. Mokhov, Sergey Chefranov, Alexander G. ChefranovAbstract:We get point vortices Dynamics equations on a rotating sphere surface directly from the hydroDynamic equations as representing their weak exact solution contrary to the conventional case of the use of a kinematic relationship between a given singular vortex field and velocity field. It is first time that the effect of a sphere rotation on the vortices interaction is accounted for in exact form. We show that only the stream function of a vortex pair of antipodal vortices (APV), and only it satisfies the original three-dimensional hydroDynamics equations on a sphere. We prove that only APV pair with two point vortices in the diameter-conjugated points of a sphere with equal by quantity but different sign circulations may be correctly considered as an elementary (stationary, not self-affecting) singular point object on a sphere. We suggest using the axis connecting the two point vortices in an APV for describing of an axis of rotation of the global vortices introduced in (Barrett, 1958) to reflect the observed global rotation of atmospheric masses with the rotation axes not coinciding with the planet rotation axis and precessing about it. Up to now, the question about interaction of global vortices corresponding to such solutions with rotations about different axis was not even posed. This is the first model describing interaction of the Barrett-type global vortices corresponding to atmospheric centers of action (ACA). The new steady-state and its stability conditions for N=2 are obtained and used for the analysis of coupled cyclone-anticyclone ACAs over oceans in the Northern Hemisphere. On the base of corresponding exact solutions, we show acceptability of modelling of the stable blocks of splitting flow type when in line with the exact accounting for the sphere rotation, we define also conditions of the polar vortices affecting on the stability boundaries of the block modes.
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Interaction of Global-scale Atmospheric Vortices: Modeling based on Hamiltonian Dynamic System of Antipodal Point Vortices on Rotating Sphere☆
Procedia IUTAM, 2013Co-Authors: Igor I. Mokhov, Sergey Chefranov, Alexander G. ChefranovAbstract:Abstract It is shown for the first time that only an antipodal vortex pair (APV) is the elementary singular vortex object on the rotating sphere compatible with the hydroDynamic equations. The exact weak solution of the absolute vorticity equation on the rotating sphere is obtained in the form of Hamiltonian Dynamic system for N interacting APVs. This is the first model describing interaction of Barrett vortices corresponding to atmospheric centers of action (ACA). In particular, new steady-state conditions for N = 2 are obtained. These analytical conditions are used for the analysis of coupled cyclone-anticyclone ACAs over oceans in the Northern Hemisphere.
Martin Bohner - One of the best experts on this subject based on the ideXlab platform.
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Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems
Abstract and Applied Analysis, 2010Co-Authors: Shurong Sun, Martin Bohner, Shaozhu ChenAbstract:We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian Dynamic systems on a time scale𝕋, which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for𝕋=ℝand𝕋=ℤwithin one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian Dynamic systems. These investigations are part of a larger program which includes the following: (i)M(λ)theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian Dynamic systems.
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an eigenvalue problem for linear Hamiltonian Dynamic systems
Fasciculi Mathermatici, 2005Co-Authors: Martin Bohner, Roman Simon HilscherAbstract:In this paper we consider eigenvalue problems on time scales involving linear Hamiltonian Dynamic systems. We give conditions that ensure that the eigenvalues of the problem are isolated and bounded below. The presented results are applicable also to Sturm{Liouville Dynamic equations of higher order, and further special cases of our systems are linear Hamiltonian dierential systems as well as linear Hamiltonian dierence systems.
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linear Hamiltonian Dynamic systems on time scales sturmian property of the principal solution
Nonlinear Analysis-theory Methods & Applications, 2001Co-Authors: Martin Bohner, O Dos, Roman Simon HilscherAbstract:Basic results of the oscillation and transformation theories of linear Hamiltonian Dynamic systems on time scales are presented. In particular, a Sturmian-type property for the principal solutions is established.
K B Chandran - One of the best experts on this subject based on the ideXlab platform.
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image based point cloud Hamiltonian Dynamic analysis for biomechanical systems
International Journal for Numerical Methods in Biomedical Engineering, 2011Co-Authors: A I Nadareyshvili, K B ChandranAbstract:The paper presents a discrete method for the Dynamic analysis of biomechanical systems. The method works directly on a point-cloud representation of a material domain. An elastic body is represented by a set of interacting particles, and the Dynamic behavior is described by Hamilton's equations. A first-order symplectic integrator, which also conserves the total linear and angular momentum, is utilized for numerical integration. The discrete formulation and integration method are presented in detail. Numerical examples are presented to show the numerical properties and demonstrate the method. Copyright © 2011 John Wiley & Sons, Ltd.
Igor I. Mokhov - One of the best experts on this subject based on the ideXlab platform.
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interaction between global scale atmospheric vortices modeling with Hamiltonian Dynamic system of antipodal point vortices on a rotating sphere
arXiv: Fluid Dynamics, 2016Co-Authors: Igor I. Mokhov, Sergey Chefranov, Alexander G. ChefranovAbstract:We get point vortices Dynamics equations on a rotating sphere surface directly from the hydroDynamic equations as representing their weak exact solution contrary to the conventional case of the use of a kinematic relationship between a given singular vortex field and velocity field. It is first time that the effect of a sphere rotation on the vortices interaction is accounted for in exact form. We show that only the stream function of a vortex pair of antipodal vortices (APV), and only it satisfies the original three-dimensional hydroDynamics equations on a sphere. We prove that only APV pair with two point vortices in the diameter-conjugated points of a sphere with equal by quantity but different sign circulations may be correctly considered as an elementary (stationary, not self-affecting) singular point object on a sphere. We suggest using the axis connecting the two point vortices in an APV for describing of an axis of rotation of the global vortices introduced in (Barrett, 1958) to reflect the observed global rotation of atmospheric masses with the rotation axes not coinciding with the planet rotation axis and precessing about it. Up to now, the question about interaction of global vortices corresponding to such solutions with rotations about different axis was not even posed. This is the first model describing interaction of the Barrett-type global vortices corresponding to atmospheric centers of action (ACA). The new steady-state and its stability conditions for N=2 are obtained and used for the analysis of coupled cyclone-anticyclone ACAs over oceans in the Northern Hemisphere. On the base of corresponding exact solutions, we show acceptability of modelling of the stable blocks of splitting flow type when in line with the exact accounting for the sphere rotation, we define also conditions of the polar vortices affecting on the stability boundaries of the block modes.
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Interaction of Global-scale Atmospheric Vortices: Modeling based on Hamiltonian Dynamic System of Antipodal Point Vortices on Rotating Sphere☆
Procedia IUTAM, 2013Co-Authors: Igor I. Mokhov, Sergey Chefranov, Alexander G. ChefranovAbstract:Abstract It is shown for the first time that only an antipodal vortex pair (APV) is the elementary singular vortex object on the rotating sphere compatible with the hydroDynamic equations. The exact weak solution of the absolute vorticity equation on the rotating sphere is obtained in the form of Hamiltonian Dynamic system for N interacting APVs. This is the first model describing interaction of Barrett vortices corresponding to atmospheric centers of action (ACA). In particular, new steady-state conditions for N = 2 are obtained. These analytical conditions are used for the analysis of coupled cyclone-anticyclone ACAs over oceans in the Northern Hemisphere.
Roman Simon Hilscher - One of the best experts on this subject based on the ideXlab platform.
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an eigenvalue problem for linear Hamiltonian Dynamic systems
Fasciculi Mathermatici, 2005Co-Authors: Martin Bohner, Roman Simon HilscherAbstract:In this paper we consider eigenvalue problems on time scales involving linear Hamiltonian Dynamic systems. We give conditions that ensure that the eigenvalues of the problem are isolated and bounded below. The presented results are applicable also to Sturm{Liouville Dynamic equations of higher order, and further special cases of our systems are linear Hamiltonian dierential systems as well as linear Hamiltonian dierence systems.
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riccati inequality disconjugacy and reciprocity principle for linear Hamiltonian Dynamic systems
Dynamic Systems and Applications, 2003Co-Authors: Roman Simon Hilscher, Pavel řehakAbstract:We investigate linear Hamiltonian Dynamic systems (H). In particular, we charac- terize the disconjugacy of (H) in terms of the solvability of a Riccati inequality. This generalizes the known result of linear Hamiltonian dierential systems and yields a new result for the discrete case. Further, we investigate a connection between eventual disconjugacy of (H) and its reciprocal system. AMS (MOS) Subject Classication. 39A10, 34C10.
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linear Hamiltonian Dynamic systems on time scales sturmian property of the principal solution
Nonlinear Analysis-theory Methods & Applications, 2001Co-Authors: Martin Bohner, O Dos, Roman Simon HilscherAbstract:Basic results of the oscillation and transformation theories of linear Hamiltonian Dynamic systems on time scales are presented. In particular, a Sturmian-type property for the principal solutions is established.
