A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the ...
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A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the gauge potentials and their first derivatives, and also on certain gauge-dependent parameters whose properties are suggested by the interaction of an isotopic spin particle with a classical Yang-Mills field. It is shown that the necessary and sufficient conditions for the invariance of the given objects under a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a Lagrangian be gauge-invariant, uniquely determines the structure of these equations.
Two classes of controlled systems evolving in function spaces on the circle are considered in this paper. The first, in which the control is distributed around the circle, is shown to be strongly controllable and mimi...
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ISBN:
(纸本)354013168X
Two classes of controlled systems evolving in function spaces on the circle are considered in this paper. The first, in which the control is distributed around the circle, is shown to be strongly controllable and mimics the finite dimensional case. The second, in which the control is a simple time varying function, is more subtle. Approximation techniques are introduced which approximate the infinite dimensional system by a finite dimensional system. Authors show that the approximations converge in a weak sense giving a well founded definition of approximate systems.
"This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynami...
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ISBN:
(数字)9781461211402
ISBN:
(纸本)9780387908199;9781461270201
"This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #;#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #;#2
We examine a particle-production mechanism for scalar λϕ4 theory in de Sitter space which has the feature that the rate of particle production is proportional to the number of particles present, yielding an exponenti...
We examine a particle-production mechanism for scalar λϕ4 theory in de Sitter space which has the feature that the rate of particle production is proportional to the number of particles present, yielding an exponentially increasing rate of production. General arguments strongly suggest that this process is generic to any renormalizable interacting theory on de Sitter space. The interpretation of this process and its relation to the response of freely falling "particle detectors" is discussed.
A linear model of a wave packet in a laminar Ekman boundary layer is proposed for tracing the development of an initially localized pulsed perturbation at the boundary. The model disturbance was built up from a linear...
A linear model of a wave packet in a laminar Ekman boundary layer is proposed for tracing the development of an initially localized pulsed perturbation at the boundary. The model disturbance was built up from a linear combination of growing modes summed numerically over all wavenumbers and frequencies. The input spectrum was assumed to be flat so that there was no biasing at any wavenumber or frequency and the evolution was calculated on the basis of linear-stability theory. The wave packet generated by the summation of modes developed uniformly downstream of the disturbance source location and, depending upon the choice of the Reynolds number, vividly displayed results representative of the different kinds of instabilities that are present in the Ekman layer. Outputs in the form of perspective plots are given in order to explain the evolution of the packet into either a single wave patch or a sum of individual wave patches.
The on-going debate regarding the merits of large versus small aircraft carriers raises several issues concerning the ability of various ship configurations to support sea based air operations. One such issue is the q...
The on-going debate regarding the merits of large versus small aircraft carriers raises several issues concerning the ability of various ship configurations to support sea based air operations. One such issue is the question of the relative seakeeping performance of ship alternatives. In an effort to shed some light on the matter, a comparative seakeeping assessment of nine air capable ships covering a wide range of size and hull form was performed. An evaluation of the impact of aircraft and ship motion limitations on sea based air operations and a comparison of the relative ability of the ships to conduct air operations while in a seaway are presented. The specific air operations considered are launch, recovery, and support of aircraft. The ships evaluated are CVN-71, CVA-67 (MR), CVV, LHA-1, VSS-D, DDV-2, DDV-1D, DD-963, and SWATH-6. These ships have the combined capability to operate Vertical Takeoff and Landing (VTOL), Conventional Takeoff and Landing (CTOL), Short Takeoff and Arrested Landing (STOAL), and Short Takeoff and Vertical Landing (STOVL) type aircraft. Results indicate that seakeeping performance generally degrades with decreasing displacement, that SWATH-6 performance is the least degraded, that elevator wetness can be an important degrader for ships with lower freeboards, that roll motion can be an important degrader for ships under 60,000 tons, and that percent time of operation is strongly dependent on the prevailing wave and wind environment.
Guided by the example of gauge transformations associated with classical Yang-Mills fields, a very general class of transformations is considered. The explicit representation of these transformations involves not only...
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Guided by the example of gauge transformations associated with classical Yang-Mills fields, a very general class of transformations is considered. The explicit representation of these transformations involves not only the independent and the dependent field variables, but also a set of position-dependent parameters together with their first derivatives. The stipulation that an action integral associated with the field variables be invariant under such transformations gives rise to a set of three conditions involving the Lagrangian and its derivatives, together with derivatives of the functions that define the transformations. These invariance identities constitute an extension of the classical theorem of Noether to general transformations of this kind. An application to the case of gauge fields demonstrates the existence of two distinct types of conservation laws for such fields.
The finite element and spectral methods are applied to two-dimensional bound state problems. A comparison of the spectral method, which requires a global basis set expansion of the wave functions, and the finite eleme...
The Benjamin-Ono equation is shown to admit a two-parameter family of Miura transformations, leading to a proof that the equation has an infinite number of conserved densities. Linearized equations are derived from a ...
The Benjamin-Ono equation is shown to admit a two-parameter family of Miura transformations, leading to a proof that the equation has an infinite number of conserved densities. Linearized equations are derived from a special case of the transformation.
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