The Experts below are selected from a list of 1002 Experts worldwide ranked by ideXlab platform
Alexander G. Chefranov - One of the best experts on this subject based on the ideXlab platform.
-
Point vortices dynamics on a rotating sphere and modeling of global atmospheric vortices interaction
Physics of Fluids, 2020Co-Authors: Igor I. Mokhov, Sergey Chefranov, Alexander G. ChefranovAbstract:It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of Antipodal Point vortices (APVs), in contrast to the stream function of a single Point vortex on a sphere with a background of a uniform opposite sign vorticity. A simple zero solution of the equation of the absolute vorticity conservation is used for bypassing the well-known nonlinear problem of a Point vortices interaction with a regular vorticity field, and an exact solution for the APV dynamics problem on a rotating sphere is obtained. Due to this, a new stable stationary solution for the dynamics of APV is obtained, which can model the dynamics of the global vortex structures, such as atmospheric centers of action.
-
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.
-
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.
C Anil P Kumar - One of the best experts on this subject based on the ideXlab platform.
-
Antipodal Point arrangements on spheres and classification of normal systems
arXiv: Combinatorics, 2018Co-Authors: C Anil P KumarAbstract:For any positive integer $k>1$, we classify the Antipodal Point arrangements on the sphere $S^k$ up to an isomorphism, by associating a finite complete set of cycle invariants.
-
Antipodal Point arrangements on spheres classification of normal systems and very generic hyperplane arrangements over ordered fields
2018Co-Authors: C Anil P KumarAbstract:For any positive integer $k$, we classify the Antipodal Point arrangements (Definitions $[2.1,3.1,3.2,5.1,5.2]$) on the sphere $\mathbb{PF}^{k+}_{\mathbb{F}}$ over an ordered field $\mathbb{F}$ (Definition $1.1$), up to an isomorphism, by associating a finite complete set of cycle invariants. The classification for dimension $k = 2$ is done in Theorem $3.7$ and the classification for dimension $k > 2$ is done in first main Theorem $\Omega$. Very Generic Normal systems (Definitions $[1.2,1.4]$) arise as coarse invariants during classification of very generic hyperplane arrangements (Definition $[1.7,1.8,1.12]$), that is, they classify very generic hyperplane arrangements modulo translation of any hyperplane (Theorem $1.16$, Note $1.17$). Theorem $\Omega$ in turn classifies the normal system associated to a hyperplane arrangement (Definition $1.14$) up to an isomorphism via its Antipodal Point arrangement. With one more invariant, the concurrency arrangement sign function (Definition $1.18$), we completely classify the isomorphism classes of very generic hyperplane arrangements over an ordered field in Section $8$ in second main Theorem $\Sigma$. Finally in last Section $9$ we pose open Question $9.1$ about normal systems.
-
Antipodal Point arrangements on spheres classification of normal systems and hyperplane arrangements
arXiv: Combinatorics, 2018Co-Authors: C Anil P KumarAbstract:For any positive integer k, we classify the Antipodal Point arrangements (refer to Definitions $[3.1,3.2,5.1,5.2]$) on the sphere $\mathbb{PF}^{k+}_{\mathbb{F}}$ over a field $\mathbb{F}$ with $1-ad$ structure (refer to Definition $1.1$), upto isomorphism, by associating a finite complete set of cycle invariants. The classification for dimension $k = 2$ is done in Theorem $3.6$ and the classification for dimension $k > 2$ is done in Theorem $5.6$. Normal systems (refer to Definitions $[1.2,1.3]$) arise as coarse invariants during classification of hyperplane arrangements i.e. they classify hyperplane arrangements modulo translations. Theorem $5.6$ in turn classifies the normal system associated to an hyperplane arrangement upto an isomorphism. With one more invariant, the concurrency arrangement sign function (refer to Definition $6.1$), we completely classify the isomorphism classes of hyperplane arrangements over the field of reals in the last Section $6$ in Theorem $6.6$.
Igor I. Mokhov - One of the best experts on this subject based on the ideXlab platform.
-
Point vortices dynamics on a rotating sphere and modeling of global atmospheric vortices interaction
Physics of Fluids, 2020Co-Authors: Igor I. Mokhov, Sergey Chefranov, Alexander G. ChefranovAbstract:It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of Antipodal Point vortices (APVs), in contrast to the stream function of a single Point vortex on a sphere with a background of a uniform opposite sign vorticity. A simple zero solution of the equation of the absolute vorticity conservation is used for bypassing the well-known nonlinear problem of a Point vortices interaction with a regular vorticity field, and an exact solution for the APV dynamics problem on a rotating sphere is obtained. Due to this, a new stable stationary solution for the dynamics of APV is obtained, which can model the dynamics of the global vortex structures, such as atmospheric centers of action.
-
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.
-
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.
Herschel Rabitz - One of the best experts on this subject based on the ideXlab platform.
-
Minimal time trajectories for two-level quantum systems with two bounded controls
Journal of Mathematical Physics, 2015Co-Authors: Ugo Boscain, Ruixing Long, Fredrik Grönberg, Herschel RabitzAbstract:In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we treat the time-optimal control problem with techniques of optimal synthesis on 2D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the Antipodal Point of the initial condition.
-
Time minimal trajectories for two-level quantum systems with two bounded controls
2012Co-Authors: Ugo Boscain, Ruixing Long, Fredrik Grönberg, Herschel RabitzAbstract:In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we tackle the time-optimal control problem with techniques of optimal synthesis on 2-D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the Antipodal Point of the starting Point.
-
Time minimal trajectories for two-level quantum systems with two bounded controls
2012Co-Authors: Boscain Ugo, Ruixing Long, Grönberg Fredrik, Herschel RabitzAbstract:In this paper we consider the minimum time population transfer problem for a two level quantum system driven by {\em two} external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we tackle the time-optimal control problem with techniques of optimal synthesis on 2-D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the Antipodal Point of the starting Point
Sergey Chefranov - One of the best experts on this subject based on the ideXlab platform.
-
Point vortices dynamics on a rotating sphere and modeling of global atmospheric vortices interaction
Physics of Fluids, 2020Co-Authors: Igor I. Mokhov, Sergey Chefranov, Alexander G. ChefranovAbstract:It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of Antipodal Point vortices (APVs), in contrast to the stream function of a single Point vortex on a sphere with a background of a uniform opposite sign vorticity. A simple zero solution of the equation of the absolute vorticity conservation is used for bypassing the well-known nonlinear problem of a Point vortices interaction with a regular vorticity field, and an exact solution for the APV dynamics problem on a rotating sphere is obtained. Due to this, a new stable stationary solution for the dynamics of APV is obtained, which can model the dynamics of the global vortex structures, such as atmospheric centers of action.
-
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.
-
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.