The Hamiltonian formalism and the action-angle variables for a generalized version of the Davey-Stewartson system is developed. Special cases include the usual Davey-Stewartson II system and the partial-differential-e...
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The Hamiltonian formalism and the action-angle variables for a generalized version of the Davey-Stewartson system is developed. Special cases include the usual Davey-Stewartson II system and the partial-differential-equation limit of the Davey-Stewartson I equations.
We consider the self-dual Yang-Mills system along with its hyperbolic version. We solve the corresponding initial value problem in the second case, and a boundary value problem for self-dual Yang-Mills equation.
We consider the self-dual Yang-Mills system along with its hyperbolic version. We solve the corresponding initial value problem in the second case, and a boundary value problem for self-dual Yang-Mills equation.
A formula governing the evolution of twist in moving filaments or ribbons of finite extent is derived. This evolution is shown to be made up of a 'dynamic' part corresponding to physical properties of the fila...
A formula governing the evolution of twist in moving filaments or ribbons of finite extent is derived. This evolution is shown to be made up of a 'dynamic' part corresponding to physical properties of the filament or ribbon and a 'geometric' part due to the motion of the filament or ribbon core itself. These results are used to extend classical elastic rod theory to the case of motion including dynamically evolving twist. In addition, the averaged geometric contribution is noted to be minus the time rate of change of the writhing number and it is shown that the writhe is a conserved quantity for closed filaments moving according to certain integrable curve dynamics.
We judge symplectic integrators by the accuracy with which they represent the Hamiltonian function. This accuracy is computed, compared and tested for several different methods. We develop new, highly accurate explici...
We judge symplectic integrators by the accuracy with which they represent the Hamiltonian function. This accuracy is computed, compared and tested for several different methods. We develop new, highly accurate explicit fourth- and fifth-order methods valid when the Hamiltonian is separable with quadratic kinetic energy. For the near-integrable case, we confirm several of their properties expected from KAM theory;convergence of some of the characteristics of chaotic motions are also demonstrated. We point out cases in which long-time stability is intrinsically lost.
This paper addresses the question of how the zero and small diffusivity solutions to the kinematic magnetic induction equation are related. It is shown that, in the case of perturbed linear toral automorphisms, hyperb...
This paper addresses the question of how the zero and small diffusivity solutions to the kinematic magnetic induction equation are related. It is shown that, in the case of perturbed linear toral automorphisms, hyperbolicity properties allow a connection between the zero diffusivity Cauchy solution and the non-zero diffusivity Wiener ensemble solution using shadowing theory. A formula is derived that calculates over finite times the small diffusivity magnetic field in terms of the local zero diffusivity magnetic field by averaging against a Gaussian density with variance proportional to diffusivity. For linear toral automorphisms, it is proven that the infinite time fast dynamo growth rate can be calculated using a local Cauchy flux average in agreement with a conjecture by Finn and Ott.
The magnetostatic energies and forces derived from axisymmetric models appropriate for magnetic force microscopy (MFM) of superconductors are examined. For models with a semi-infinite sample, closed form representatio...
The magnetostatic energies and forces derived from axisymmetric models appropriate for magnetic force microscopy (MFM) of superconductors are examined. For models with a semi-infinite sample, closed form representations are obtained for arbitrary probe height. Specific boundary value problems considered are appropriate for a vortex penetrating a type-II superconductor, or for a magnetic monopole or dipole above or within a superconductor. Physically important limits such as complete flux expulsion become transparent with the new results. It is shown that previously employed approximations and numerical quadrature are unnecessary.
The critical properties of Ising model on the dynamical triangulated random surface embedded in D-dimensional Euclidean space are investigated. The strong coupling expansion method is used. The transition to thermodyn...
The critical properties of Ising model on the dynamical triangulated random surface embedded in D-dimensional Euclidean space are investigated. The strong coupling expansion method is used. The transition to thermodynamical limit is performed by means of continuous fractions.
It is surprising that last two decades many works in time series data mining and clustering were concerned with measures of similarity of time series but not with measures of association that can be used for measuring...
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It is surprising that last two decades many works in time series data mining and clustering were concerned with measures of similarity of time series but not with measures of association that can be used for measuring possible direct and inverse relationships between time series. Inverse relationships can exist between dynamics of prices and sell volumes, between growth patterns of competitive companies, between well production data in oilfields, between wind velocity and air pollution concentration etc. The paper develops a theoretical basis for analysis and construction of time series shape association measures. Starting from the axioms of time series shape association measures it studies the methods of construction of measures satisfying these axioms. Several general methods of construction of such measures suitable for measuring time series shape similarity and shape association are proposed. Time series shape association measures based on Minkowski distance and data standardization methods are considered. The cosine similarity and the Pearson's correlation coefficient are obtained as partial cases of the proposed general methods that can be used also for construction of new association measures in data analysis.
Summary form only given. In recent years, much attention has been given to wavelength-division multiplexed (WDM) systems due to their ability to maximize lightwave communications. In practice, the combined effects of ...
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ISBN:
(纸本)1557524432
Summary form only given. In recent years, much attention has been given to wavelength-division multiplexed (WDM) systems due to their ability to maximize lightwave communications. In practice, the combined effects of linear dispersion and nonlinear self phase modulation impose severe limitations on the long-haul performance of non-return-to-zero (NRZ) systems. The aim of this presentation is to provide an analytic description of the nonlinear pulse evolution in a NRZ communications system under a dispersion-management scheme.
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