Stability of the coastline from Manakkodam to Thottappally along the Kerala coast

Wave refraction studies were undertaken to assess the stability of the coastline from Manakkodam to Thottappally, along the Kerala coast. Refraction diagrams were constructed for waves of different periods and directions of approach and the cumulative effect of the sediment transport was assessed for the particular region under study. The study reveals that the coastline north of Alleppey is on the whole a stable one. The stability of the beaches on the southern side from Alleppey Pier to Thottappally spillway, is more dependent on the changes in offshore relief.     

Difference approximations for wave equations via finite elements. I. Construction and performance

Many practical applications of wave equations involve media in which there are interfaces, or discontinuities in material properties. The accurate numerical representation of these interfaces is important in mathematical models. One can develop generalizations of standard finite-difference methods that accommodate sharp interfaces by modifying a straightforward finite-element approach. In two space dimensions, these methods yield explicit, 5-point or 9-point difference schemes that accurately capture reflection, transmission, and refraction at interfaces. The approach also extends readily to the simulation of waves in elastic media. A companion article presents an error analysis for the approach. © 1995 John Wiley & Sons, Inc.     

A Lattice of Varieties of Completely Regular Semigroups

In a previous communication, we defined a countably infinite sequence of varieties of completely regular semigroups, termed canonical. Finite intersections of these varieties constitute the upper ends of the intervals which are the classes of the congruence induced by the complete homomorphism 𝒱 → 𝒱 ∩ ?, where ? is the variety of all bands. We construct here the lattice generated by the first few of these varieties in some detail. In particular, we determine their bases and illustrate our findings by three diagrams.     

Explicit green matrices for linear elasticity in the half space

This paper studies traveling-wave solutions of the partial differential equations which model waves in a horizontal water channel traveling in both directions. The existence of solitary-wave solutions for a number of systems is proved. Interesting new multi-pulsed traveling-wave solutions which consist of an arbitrary number of troughs are found numerically. The bifurcation diagrams of N-trough solutions with respect to phase speed and system parameters are presented.     

The near ultraviolet absorption spectra ofortho- andmeta-thiocresols

The absorption spectra ofortho- andmeta-thiocresols have been studied in the present investigation. The ortho-thiocresol spectrum consists of about forty-five bands of rather a diffuse nature and in general low intensity in the region from 2873 Å to 2600 Å. The maximum number of bands is obtained by using a path length of 330 cm. for absorption, the temperature of the bulb being maintained at 14°C. Several of these bands are assigned as due tov-v-transitions. The (0, 0) band is chosen at 35386 cm.^?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 729, 957 and 1159 and combinations and overtones of these are present. Themeta-thiocresol spectrum consists of about forty bands of rather a diffuse nature and very weak intensities in the region from 2900 Å to 2590 Å. The maximum number of bands is obtained by using a path length 200 cm. for absorption and by keeping the temperature of the bulb at 20° C. The (0, 0) band is chosen to be that at 34793 cm.^?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 492, 611, 720, 845, 965, 1016 and 1155 cm.^?1 and combinations and overtones of these are present.     

Normal waves in orthotropic plates and prismatic bodies with thin face coatings

We construct and study the dispersion equations that describe the spectra of normal waves with various kinds of wave motion symmetry in a cross section of the waveguides. We compute the dispersion curve diagrams of symmetric waves for several directions of propagation in the plane of a plate and for the axial direction of a prismatic body of monocrystal Rochelle salt. Four figures. Bibliography: 4 titles Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 90–97.     

Modulational Stability of Travelling Waves in 2D Anisotropic Systems

The modulational stability of travelling waves in 2D anisotropic systems is investigated. We consider normal travelling waves, which are described by solutions of a globally coupled Ginzburg–Landau system for two envelopes of left- and right-travelling waves, and oblique travelling waves, which are described by solutions of a globally coupled Ginzburg–Landau system for four envelopes associated with two counterpropagating pairs of travelling waves in two oblique directions. The Eckhaus stability boundary for these waves in the plane of wave numbers is computed from the linearized Ginzburg–Landau systems. We identify longitudinal long and finite wavelength instabilities as well as transverse long wavelength instabilities. The results of the stability calculations are confirmed through numerical simulations. In these simulations we observe a rich variety of behaviors, including defect chaos, elongated localized structures superimposed to travelling waves, and moving grain boundaries separating travelling waves in different oblique directions. The stability classification is applied to a reaction–diffusion system and to the weak electrolyte model for electroconvection in nematic liquid crystals.      

Anisotropic characters in two-dimensional hexagonal crystal

The anisotropic characters of two-dimensional hexagonal crystal are investigated in this paper. The dispersion relation has been studied numerically. It is shown that the dispersion relation strongly dependents on the directions of wave propagation. Generally, the direction of waves has the inclination angle with respect to particle displacement. There are compressional waves  = 0 or transverse waves  = π/2 for long wavelength. However, for short wavelength compressional and transverse waves exists only for some special directions. For most cases, neither compressional nor transverse waves exists. The nonlinear waves in this crystal have also been studied. The characters of solitons, such as amplitude and width, have been investigated.     

On linear and nonlinear Rossby waves in an ocean

This paper deals with recent developments of linear and nonlinear Rossby waves in an ocean. Included are also linear Poincaré, Rossby, and Kelvin waves in an ocean. The dispersion diagrams for Poincaré, Kelvin and Rossby waves are presented. Special attention is given to the nonlinear Rossby waves on a β-plane ocean. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a modified nonlinear Schrödinger equation. The solution of this equation represents solitary waves in a dispersive medium. In other words, the envelope of the amplitude of the waves has a soliton structure and these envelope solitons propagate with the group velocity of the Rossby waves. Finally, a nonlinear analytical model is presented for long Rossby waves in a meridional channel with weak shear. A new nonlinear wave equation for the amplitude of large Rossby waves is derived in a region where fluid flows over the recirculation core. It is shown that the governing amplitude equations for the inner and outer zones are both KdV type, where weak nonlinearity is balanced by weak dispersion. In the inner zone, the nonlinear amplitude equation has a new term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude, and this term occurs to account for a nonlinearity due to the flow over the vortex core. The solution of the amplitude equations with the linear shear flow represents the solitary waves. The present study deals with the lowest mode (n=1) analysis. An extension of the higher modes (n?2) of this work will be made in a subsequent paper.     

Riemann theta functions periodic wave solutions and rational characteristics for the (1+1)-dimensional and (2+1)-dimensional Ito equation

In this paper, based on a multidimensional Riemann theta function, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta functions periodic waves solutions for nonlinear differential equation such as the (1+1)-dimensional and (2+1)-dimensional Ito equations. Among these periodic waves, the one-periodic waves are well-known cnoidal waves, their surface pattern is one-dimensional, and often they are used as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two dimensional that they have two independent spatial periods in two independent horizontal directions. A limiting procedure is presented to analyze asymptotic behavior of the multiperiodic periodic waves in details and the relations between the periodic wave solutions and soliton solutions are rigorously established.     

Nonstationary love waves of theSH type in an anisotropic elastic medium. A kinematic approach. II

In this paper, the study of the high-frequency Love waves (simular to the well-known transverse waves of theSH type) near the surface of an anisotropic elastic body is continued. The formulation of the boundary-value problem, independent of a specific form of the elasticity tensor, provides the possibility of developing a kinematic approach, which is essential for constructing the asymptotics of these high-frequency waves. To this end, an algorithm is proposed that allows one to relate the transversality of the polarization of surface waves to the directions of their propagation on the surface and to obtain the conditions necessary for the origination of such waves. The algorithm suggested makes it possible to indicate those types of symmetry of media (special cases of anisotropy) for which the directions obtained correspond to the field of rays of Love waves. In these cases, the space-time ray method provides a mathematical tool for constructing uniform asymptotics of the surface waves in question. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol 218, 1994, pp. 206–219. This work was supported by the Russian Foundation of Fundamental Research (Grant 93-011-16148). Translated by Z. A. Yanson.     

On conditions of the dynamic equivalence of waves in multilayer elastic media

Necessary and sufficient conditions for the dynamic equivalence of two waves propagating in an elastic p-layer medium and undergoing all kinds of exchanges on the medium interfaces are formulated. These conditions are represented in the form of equalities involving powers of the reflection and refraction coefficients occurring in the expressions for the intensities of these waves. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 218, 1994, pp. 166–175. This work was supported by the Russian Foundation of Fundamental Research (Grant 93-011-16148). Translated by N. S. Zabavnikova.     

The near ultraviolet absorption spectrum of tetrahydro-naphthalene

The near ultraviolet absorption spectrum of tetrahydronaphthalene commonly known as tetralin consists of sharp bands in the region from 2800 to 2500 Å. The spectrum consists of about sixty bands. The maximum number of bands is obtained by using a path length of 200 cm. at room temperature which was nearly 30° C. Several of these very sharp bands have to be assigned tov-v transitions. The 0, 0 band is chosen to be at 36790 cm^?1. Vibrational frequencies in the excited state have values 1185, 951 and 682 and combinations and overtones of these are present. Assignments of the different frequencies are discussed.     

Anisotropic smoothness spaces via level sets

It has been understood for sometime that the classical smoothness spaces, such as the Sobolev and Besov classes, are not satisfactory for certain problems in image processing and nonlinear PDEs. Their deficiency lies in their isotropy. Functions in these smoothness spaces must be simultaneously smooth in all directions. The anisotropic generalizations of these spaces also have the deficiency that they are biased in coordinate directions. While they allow different smoothness in certain directions, these directions must be aligned to the coordinate axes. In the application areas mentioned above, it would be desirable to measure smoothness in new ways that would allow one to have more local control over the smoothness directions. We introduce one possible approach to this problem based on defining smoothness via level sets. We present this approach in the case of functions defined on ?^d. Our smoothness spaces depend on two smoothness indices (s₁, s₂). The first reflects the smoothness of the level sets of the function, while the second index reflects how smoothly the level sets themselves are changing. As a motivation, we start with d = 2 and investigate Besov smooth domains. © 2007 Wiley Periodicals, Inc.     

On the calculation of wave fields propagating in multilayer media

A program for evaluating elastic waves in multilayer media is composed on the basis of the algorithm previously stated. The waves under consideration undergo all possible acts of reflection and refraction on the interfaces of the media. Exchanges on these interfaces are also taken into account. Two examples illustrating the calculation of theoretical seismograms of elastic waves are presented. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 156–165. Translated by N. S. Zabavnikova     

具有两个驰豫时间的热弹性立方晶体材料中平面波的传播

研究具有两个驰豫时间的、两个不同弹性和热性质的、广义传热立方晶体固体半空间的有缺陷结合面上,热弹性平面波的反射和折射问题.具有两个驰豫时间的广义热弹性理论,是1972年由Green和Lindsay提出并应用于问题的研究.对有缺陷边界,给出了反射系数和折射系数(即反射波和折射波振幅与入射波振幅之比)的表达式,并推演了法向刚性边界、横向刚性边界、接触传热边界、滑动边界和结合面边界时的表达式.给出了在不同边界条件及出射角时,不同的反射波和折射波的振幅比,在不同的入射波时的变化图.发现反射波和折射波振幅比受到介质刚性和热性质的影响.     

Transmission of sound in a wedge-shaped layer of fluid with a rigid bottom

The theory of generalized rays is applied to the problem of determining the exact shape of the pressure pulse received at very large ranges, in the case of a sound source in a 3° perfect wedge of fluid. The time variation of the pressure at the point source is assumed to be given by a Heaviside unit function H(t). It is found that horizontal refraction and backscattering have a pronounced effect on the overall appearance of the received pulse: at very large down–slope (normal to the apex line) ranges, the shape of the received pulse does not change much, while, at very large cross–slope (parallel to the apex line) ranges, it changes drastically. Thus, in a 3° perfect wedge of fluid, long–range down–slope propagation (exclusively affected by backscattering) seems to be nondispersive, but long–range cross–slope propagation (affected by horizontal refraction and backscattering) seems to be highly dispersive. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On surface waves in diffraction gratings

We discuss the existence criterion of surface waves based on the augmented scattering matrices. Such matrices arise if one takes into account not only oscillating waves but also those which grow (attenuate) in amplitude far from the grating. A family of planar dielectric gratings with periodic modulation of the refraction index is considered. Asymptotic and numerical analysis of the model are given. We represent various examples of gratings which support (or do not support) surface waves. Copyright © 2000 John Wiley & Sons, Ltd.     

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω ² u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.