A variational approach to the derivation of high-order shallow-water equations

Summary It is shown that the Airy, Boussinesq, Su and Gardner and extended Boussinesq equations for the propagation of shallow-water waves can be easily obtained from Luke's variational principle. The technique of derivation of the equations is examined in detail and used to extend the range of application of the highest-order theories to the case of variable depth. The approach is relatively straightforward and, moreover, points out the hypotheses under which the various equations are derived.     

Variational principle for derivation of macroscopic equations

It is pointed out that the Schwinger variational principle of scattering theory applies to the case of linear and nonlinear relaxation problems in quantum statistics. By means of this principle it is possible to derive closed sets of equations for expectation values. To illustrate this variational method and to clarify the connection to other standard approaches some simple examples are treated for which the equations of motion are already known.     

Towards a general solution of the Hamiltonian constraints of General Relativity

The present work has a double aim. On the one hand, we call attention on the relationship existing between the Ashtekar formalism and other gauge-theoretical approaches to gravity, in particular the Poincaré Gauge Theory. On the other hand, we study two kinds of solutions for the constraints of General Relativity, consisting of two mutually independent parts, namely a general three-metric-dependent contribution to the extrinsic curvature K _ab in terms of the Cotton–York tensor, and besides it further metric independent contributions, which we analyze in particular in the presence of isotropic three-metrics.     

Exact Pollard-like internal water waves

In this paper we construct a new solution which represents Pollard-like three-dimensional nonlinear geophysical internal water waves. The Pollard-like solution includes the effects of the rotation of Earth and describes the internal water wave which exists at all latitudes across Earth and propagates above the thermocline. The solution is provided in Lagrangian coordinates. In the process we derive the appropriate dispersion relation for the internal water waves in a stable stratification and discuss the particles paths. An analysis of the dispersion relation for the constructed model identifies one mode of the internal water waves.     

On the fully-nonlinear shallow-water generalized Serre equations

A fully-nonlinear weakly dispersive system for the shallow water wave regime is presented. In the simplest case the model was first derived by Serre in 1953 and rederived various times since then. Two additions to this system are considered: the effect of surface tension, and that of using a different reference fluid level to describe the velocity field. It is shown how the system can be further expanded by consistent exchanges of spatial and time derivatives. Properties of the solitary waves of the resulting system as well as a symmetric splitting of the equations based on the Riemann invariants of the hyperbolic shallow water system are presented. The latter leads to a fully-nonlinear one-way model and, upon further approximations, existing weakly nonlinear models. Our study also helps clarify the differences or similarities between existing models.     

Frequency separation of surface acoustic waves in layered structures with acoustic metamaterials

We show theoretically that in elastic layered structures containing an upper layer of smoothly varied thickness and a substrate of a highly dispersive metametarial it is possible to significantly enhance spatial frequency separation of surface acoustic waves. Theory of Love surface acoustic waves propagation in waveguides with varied thickness, taking into account mutual modes coupling, is built. Appropriate structure of metamatererial with resonant frequency dependence of material parameters, making frequency separation effective, is provided. Efficiency of spatial frequency separation and modes coupling is calculated for various metamaterial parameters and wave frequencies.     

An improved approximate solution of Altarelli-Parisi equations

We have presented here an improved solution to Altarelli-Parisi equations, and it is found to be in good agreement with SLAC-MIT data up tox⩾0.1.     

Exact plasma wave solutions for isothermal electron fluid plasma

Quasistationary electron plasma waves of arbitrary amplitude and speed that are exact solutions of the isothermal electron fluid equations are shown to exist.     

Variational derivation of KdV-type models for surface water waves

Using the Hamiltonian formulation of surface waves, we approximate the kinetic energy and restrict the governing generalized action principle to a submanifold of uni-directional waves. Different from the usual method of using a series expansion in parameters related to wave height and wavelength, the variational methods retains the Hamiltonian structure (with consequent energy and momentum conservation) and makes it possible to derive equations for any dispersive approximation. Consequentially, the procedure is valid for waves above finite and above infinite depth, and for any approximation of dispersion, while quadratic terms in the wave height are modeled correctly. For finite depth this leads to higher-order KdV type of equations with terms of different spatial order. For waves above infinite depth, the pseudo-differential operators cannot be approximated by finite differential operators and all quadratic terms are of the same spatial order.     

On the equivalence of some exact master equations

In this note we show the equivalence of two procedures for obtaining exact, convolutionless master equations.     

Formulation of Hamiltonian Equations for Fractional Variational Problems

An extension of Riewes fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional constrained systems are analyzed in details.On leave of absence from Institute of Space Sciences, P.O.BOX MG-23, R 76900, Magurele–Bucharest, Romania     

On the derivation of thermohydrodynamic equations from the Boltzmann equations

The Boltzmann equation deals with a distributionf(x, ), wherex denotes the space variable and is the momentum. The hydrodynamic equations deal with-moments of the distribution. The paper deals with the derivation of the hydrodynamic equations in the case that the collision kernel is Maxwellian, i.e., independent of the velocity. For such a kernel, a computational tool, based on the theory of representations of the orthogonal group, is developed. With this tool it is possible to derive systems of equations for any number of moments. The construction of closed systems is based on asymptotic estimates for solutions of Boltzmann equations. These show that, in some definite sense, an approximating system involving moments of high order is more accurate than a system of lower order.     

Physically transparent derivation of the Hartree-Fock equations

A simple and physically transparent derivation of the Hartree-Fock equation is given. This derivation reveals the physical essence of this approximation.     

色散作用能更简捷的推导

基于色散作用的本质，利用宏观电介质形式，更一般且更简捷地得到了各种维度的色散作用能。     

等离子体部分填充的波纹慢波结构中电磁波色散特性

 对有限厚环形等离子体层填充的波纹慢波结构中电磁波色散特性进行了分析。研究结果表明，对于ω＞ω_p的高频TM_0n模，模式色散曲线随等离子体密度的增加而上移；ω≤ω_p的低频等离子体模为一系列呈周期变化的密度谱，部分模式能与电子注发生较强的同步互作用。等离子体模的时间增长率随等离子体密度的增加快速增加，而TM_0n模则快速减小或缓慢增加，因此在较高的等离子体密度下，高频模式可能被抑制。     

On the spectra of periodic waves for infinite-dimensional Hamiltonian systems

We consider the problem of determining the spectrum for the linearization of an infinite-dimensional Hamiltonian system about a spatially periodic traveling wave. By using a Bloch-wave decomposition, we recast the problem as determining the point spectra for a family of operators J_γL_γ, where J_γ is skew-symmetric with bounded inverse and L_γ is symmetric with compact inverse. Our main result relates the number of unstable eigenvalues of the operator J_γL_γ to the number of negative eigenvalues of the symmetric operator L_γ. The compactness of the resolvent operators allows us to greatly simplify the proofs, as compared to those where similar results are obtained for linearizations about localized waves. The theoretical results are general, and apply to a larger class of problems than those considered herein. The theory is applied to a study of the spectra associated with periodic and quasi-periodic solutions to the nonlinear Schrödinger equation, as well as periodic solutions to the generalized Korteweg-de Vries equation with power nonlinearity.     

On the microscopic derivation of mode-mode coupling equations

Alternative results derived on a microscopic basis for the mode-mode coupling kinetic equations are shown to be identical. It is also emphasized that nonlinear kinetic equations for the gross variables describing the system are only suggested but not implied by the corresponding equations obeyed by their dynamical variables. Finally an equivalent closed form for the renormalized transport coefficients is shown to hold in mode-mode coupling theory.Miembro del Colegio Nacional. On sabbatical leave from UAM—Iztapalapa, Mexico.     

Measurments of attenuation and refractive dispersion due to atmospheric water vapor at 80 and 240 GHz

Field line-of-sight propagation experiments were made at 80 and 240 GHz on a horizontal path of 810 m. The measured attenuations showed quadratic dependences on atmospheric water vapor density, and absorptions in excess of theoretical predictions were observed at both frequencies, while the measured refractive dispersion between these two frequencies showed a linear dependence on water vapor density and was in good agreement with theoretical prediction. Liebe's model for water vapor attenuation including empirical continuum absorption is confirmed to be effective for 80 and 240 GHz.     

Diffraction of SH waves at a mixed interface

Summary We study the diffraction of SH-type elastic waves propagating along the plane interface between two dissimilar elastic half-spaces. It is assumed that the contact between the half-spaces is perfect except for a part of semi-infinite extension where the contact is loosely coupled. We use the Wiener-Hopf technique to obtain the diffracted field in a closed form.