Surface wave techniques for the study of engineering structures and materials

A wire drive pulse echo method of measuring the spectrum of solid bodies described. Using an 's' plane representation, a general analysis of the transient response of such solids has been carried out. This was used for the study of the stepped amplitude transient of high order modes of disks and for the case where there are two adjacent resonant frequencies. The techniques developed have been applied to the measurenent of the elasticities of refractory materials at high temperatures. In the experimental study of the high order in-plane resonances of thin disks it was found that the energy travelled at the edge of the disk and this initiated the work on one dimensional Rayleigh waves.Their properties were established for the straight edge condition by following an analysis similar to that of the two dimensional case. Experiments were then carried out on the velocity dispersion of various circuits including the disk and a hole in a large plate - the negative curvature condition.Theoretical analysis established the phase and group velocities for these cases and experimental tests on aluminium and glass gave good agreement with theory. At high frequencies all velocities approach that of the one dimensional Rayleigh waves. When applied to crack detection it was observed that a signal burst travelling round a disk showed an anomalous amplitude effect. In certain cases the signal which travelled the greater distance had the greater amplitude.An experiment was designed to investigate the phenanenon and it was established that the energy travelled in two nodes with different velocities.It was found by analysis that as well as the Rayleigh surface wave on the edge, a seoond node travelling at about the shear velocity was excited and the calculated results gave reasonable agreement with the experiments.

Solitons: permanent waves

Communications engineers are learning to create an electromagnet wave at will, to transmit information. This wave, the optical soliton, is the subject of astounding recent developments in nonlinear optics and lasers. The author describes the principles behind the use of solitons in optical communications and shows that in the context of such communications the most important property of solitons is that they are extremely stable. Not only do they not disperse, but an encounter with a perturbation (e.g. a joint in optical fibre) will usually leave the soliton unaltered.

Fundamental characteristics of space-charge waves in photorefractive sillenite crystals

We investigate experimentally the fundamental characteristics of space-charge waves excited in a photorefractive crystal of Bi12SiO20. Features such as their transient rise and decay as well as their steady-state frequency response are investigated. Based on this, we find the dependence of the space-charge waves' quality factor on spatial frequency and electric-field biasing. The experimental findings are compared with the linear space-charge wave theory developed previously by Sturman et al. [J. Opt. Sec. Am. B 10, 1919 (1993)].

Range of validity of weakly non-linear theory in Rayleigh-Bénard problem

In this paper we examine the equilibrium states of finite amplitude flow in a horizontal fluid layer with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau constants and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infinitesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighborhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable. © 2009 The Physical Society of Japan.

Ultra-long raman laser with a feedback based on the Rayleigh scattering

This paper reports the Rayleigh scattering effects in ultra-long Raman fibre laser. It has been found that in a long fibre cavity (-100 km) the distributed feedback due to Rayleigh back scattering at propagation of light between fibre Bragg grating reflectors may be comparable with the lumped feedback provided by the FBG itself. As a result, Raman lasing in the fibre span limited by lumped (FBG) reflector at one side only appears possible due to significant reflection from the RS-based "random" distributed mirror at the other side. Thus, it concludes that a distributed Rayleigh scattering "random" mirror can form a cavity together with a single FBG spliced to the opposite cavity end.

Dual-wavelength, ultralong Raman laser with Rayleigh-scattering feedback

We present experimental demonstration of a 200-km-long, dual-wavelength Raman laser utilizing two slightly different-wavelength fiber Bragg gratings, one on each side of the fiber span. The obtained results clearly prove the generation of two independent Raman lasers with a distributed “random” Rayleigh scattering mirror forming a cavity together with each of the individual fiber Bragg grating reflectors.

Business cycles, long waves, and company langevity in Birmingham area metal industries 1780-1980

This doctoral thesis originates from an observational incongruence between the perennial aims and aspirations of economic endeavour and actually recorded outcomes, which frequently seem contrary to those intended and of a recurrent, cyclical type. The research hypothesizes parallel movement between unstable business environments through time, as expressed by periodically fluctuating levels of economic activity, and the precipitation rates of industrial production companies. A major problem arose from the need to provide theoretical and empirical cohesion from the conflicting, partial and fragmented interpretations of several hundred historians and economists, without which the research question would remain unanswerable. An attempt to discover a master cycle, or superimposition theorem, failed, but was replaced by minute analysis of both the concept of cycles and their underlying data-bases. A novel technique of congregational analysis emerged, resulting in an integrated matrix of numerical history. Two centuries of industrial revolution history in England and Wales was then explored and recomposed for the first time in a single account of change, thereby providing a factual basis for the matrix. The accompanying history of the Birmingham area provided the context of research into the failure rates and longevities of firms in the city's staple metal industries. Sample specific results are obtained for company longevities in the Birmingham area. Some novel presentational forms are deployed for results of a postal questionnaire to surviving firms. Practical demonstration of the new index of national economic activity (INEA) in relation to company insolvencies leads to conclusions and suggestions for further applications of research into the tempo of change, substantial Appendices support the thesis and provide a compendium of information covering immediately contiguous domains.

Fundamental characteristics of space-charge waves in photorefractive sillenite crystals

We investigate experimentally the fundamental characteristics of space-charge waves excited in a photorefractive crystal of Bi12SiO20. Features such as their transient rise and decay as well as their steady-state frequency response are investigated. Based on this, we find the dependence of the space-charge waves' quality factor on spatial frequency and electric-field biasing. The experimental findings are compared with the linear space-charge wave theory developed previously by Sturman et al. [J. Opt. Sec. Am. B 10, 1919 (1993)].

Distributed temperature change sensor, based on Rayleigh backscattering in an optical fibre

A frequency-modulated continuous-wave technique is used to detect the presence of frequency shifts in the Rayleigh-backscattered light in a single-mode optical fiber as a result of a changing temperature. The system is able to detect a rate of temperature change of 0.014 K/s, when a 20-cm length of fiber is heated. The system is also able to demonstrate a spatial resolution of better than 15 cm.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Localized waves in optical systems with periodic dispersion and nonlinearity management

We overview our recent developments in the theory of dispersion-managed (DM) solitons within the context of optical applications. First, we present a class of localized solutions with a period multiple to that of the standard DM soliton in the nonlinear Schrödinger equation with periodic variations of the dispersion. In the framework of a reduced ordinary differential equation-based model, we discuss the key features of these structures, such as a smaller energy compared to traditional DM solitons with the same temporal width. Next, we present new results on dissipative DM solitons, which occur in the context of mode-locked lasers. By means of numerical simulations and a reduced variational model of the complex Ginzburg-Landau equation, we analyze the influence of the different dissipative processes that take place in a laser.