Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

A Nonlinear System Under Combined Periodic and Random Excitation

The anharmonic oscillator under combined sinusoidal and white noise excitation is studied using the Gaussian closure approximation. The mean response and the steady-state variance of the system is obtained by the WKBJ approximation and also by the Fokker Planck equation. The multiple steadystate solutions are obtained and their stability analysis is presented. Numerical results are obtained for a particular set of system parameters. The theoretical results are compared with a digital simulation study to bring out the usefulness of the present approximate theory.

Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

A new method for generation of quasi-periodic structures withn fold axes: Application to five and seven folds

A new geometrical method for generating aperiodic lattices forn-fold non-crystallographic axes is described. The method is based on the self-similarity principle. It makes use of the principles of gnomons to divide the basic triangle of a regular polygon of 2n sides to appropriate isosceles triangles and to generate a minimum set of rhombi required to fill that polygon. The method is applicable to anyn-fold noncrystallographic axis. It is first shown how these regular polygons can be obtained and how these can be used to generate aperiodic structures. In particular, the application of this method to the cases of five-fold and seven-fold axes is discussed. The present method indicates that the recursion rule used by others earlier is a restricted one and that several aperiodic lattices with five fold symmetry could be generated. It is also shown how a limited array of approximately square cells with large dimensions could be detected in a quasi lattice and these are compared with the unit cell dimensions of MnAl6 suggested by Pauling. In addition, the recursion rule for sub-dividing the three basic rhombi of seven-fold structure was obtained and the aperiodic lattice thus generated is also shown.

Sequence generator for periodic sampling of transient phenomena

A simple instrument that can provide a sequence of timed pulses for first initiating a transient process and then enabling sampling and recording periodically during the course of the transient event is described. The time delay between the first of these sampling pulses and the start of the transient event is adjustable. This sequence generator has additional features that make it ideal for use in acquiring the waveforms when a storage oscilloscope is used as the recording device. For avoiding the clutter caused by many waveforms being recorded at the same place on an oscilloscope screen such features as displacements of waveforms in the X and Y directions and trace blanking at places where the waveform is not required, have been incorporated. This sequence generator has been employed to acquire a sequence of Raman scattered radiation signals from an adiabatically expanding saturated vapour probed by a flashlamp-pumped dye laser.

Vibrations of a periodic rail-sleeper system excited by an oscillating stationary transverse force

The rail-sleeper system is idealized as an infinite, periodic beam-mass system. Use is made of the periodicity principle for the semi-infinite halves on either side of the forcing point for evaluation of the wave propagation constants and the corresponding modal vectors. It is shown that the spread of acceleration away from the forcing point depends primarily upon one of the wave propagation constants. However, all the four modal vectors (two for the left-hand side and two for the right-hand side) determine the driving point impedance of the rail-sleeper system, which in combination with the driving point impedance of the wheel (which is adopted from the preceding companion paper) determines the forces generated by combined surface roughness and the resultant accelerations. The compound one-third octave acceleration levels generated by typical roughness spectra are generally of the same order as the observed levels.

Periodic oscillations in feedback systems with combined pulse modulation

This paper presents a systematic method of investigating the existence of limit cycle oscillations in feedback systems with combined integral pulse frequency-pulse width (IPF-P/V) modulation. The method is based on the non-linear discrete equivalence of the continuous feedback system containing the IPF-PW modulator.

On the stability of a nonlinear system with periodic coefficients

A quasi-geometric stability criterion for feedback systems with a linear time invariant forward block and a periodically time varying nonlinear gain in the feedback loop is developed.

Tumour necrosis factor receptor-associated periodic syndrome (TRAPS) : Identification of novel TNFRSF1A mutations and intracellular signalling defects

The systemic autoinflammatory disorders are a group of rare diseases characterized by periodically recurring episodes of acute inflammation and a rise in serum acute phase proteins, but with no signs of autoimmunity. At present eight hereditary syndromes are categorized as autoinflammatory, although the definition has also occasionally been extended to other inflammatory disorders, such as Crohn s disease. One of the autoinflammatory disorders is the autosomally dominantly inherited tumour necrosis factor receptor-associated periodic syndrome (TRAPS), which is caused by mutations in the gene encoding the tumour necrosis factor type 1 receptor (TNFRSF1A). In patients of Nordic descent, cases of TRAPS and of three other hereditary fevers, hyperimmunoglobulinemia D with periodic fever syndrome (HIDS), chronic infantile neurologic, cutaneous and articular syndrome (CINCA) and familial cold autoinflammatory syndrome (FCAS), have been reported, TRAPS being the most common of the four. Clinical characteristics of TRAPS are recurrent attacks of high spiking fever, associated with inflammation of serosal membranes and joints, myalgia, migratory rash and conjunctivitis or periorbital cellulitis. Systemic AA amyloidosis may occur as a sequel of the systemic inflammation. The aim of this study was to investigate the genetic background of hereditary periodically occurring fever syndromes in Finnish patients, to explore the reliability of determining serum concentrations of soluble TNFRSF1A and metalloproteinase-induced TNFRSF1A shedding as helpful tools in differential diagnostics, as well as to study intracellular NF-κB signalling in an attempt to widen the knowledge of the pathomechanisms underlying TRAPS. Genomic sequencing revealed two novel TNFRSF1A mutations, F112I and C73R, in two Finnish families. F112I was the first TNFRSF1A mutation to be reported in the third extracellular cysteine-rich domain of the gene and C73R was the third novel mutation to be reported in a Finnish family, with only one other TNFRSF1A mutation having been reported in the Nordic countries. We also presented a differential diagnostic problem in a TRAPS patient, emphasizing for the clinician the importance of differential diagnostic vigiliance in dealing with rare hereditary disorders. The underlying genetic disease of the patient both served as a misleading factor, which possibly postponed arrival at the correct diagnosis, but may also have predisposed to the pathologic condition, which led to a critical state of the patient. Using a method of flow cytometric analysis modified for the use on fresh whole blood, we studied intracellular signalling pathways in three Finnish TRAPS families with the F112I, C73R and the previously reported C88Y mutations. Evaluation of TNF-induced phosphorylation of NF-κB and p38, revealed low phosphorylation profiles in nine out of ten TRAPS patients in comparison to healthy control subjects. This study shows that TRAPS is a diagnostic possibility in patients of Nordic descent, with symptoms of periodically recurring fever and inflammation of the serosa and joints. In particular in the case of a family history of febrile episodes, the possibility of TRAPS should be considered, if an etiology of autoimmune or infectious nature is excluded. The discovery of three different mutations in a population as small as the Finnish, reinforces the notion that the extracellular domain of TNFRSF1A is prone to be mutated at the entire stretch of its cysteine-rich domains and not only at a limited number of sites, suggesting the absence of a founder effect in TRAPS. This study also demonstrates the challenges of clinical work in differentiating the symptoms of rare genetic disorders from those of other pathologic conditions and presents the possibility of an autoinflammatory disorder as being the underlying cause of severe clinical complications. Furthermore, functional studies of fresh blood leukocytes show that TRAPS is often associated with a low NF-κB and p38 phosphorylation profile, although low phosphorylation levels are not a requirement for the development of TRAPS. The aberrant signalling would suggest that the hyperinflammatory phenotype of TRAPS is the result of compensatory NF-κB-mediated regulatory mechanisms triggered by a deficiency of the innate immune response.

Quasi-periodic, global oscillations in sea level pressure on intraseasonal timescales

The sea level pressure (SLP) variability in 30-60 day intraseasonal timescales is investigated using 25 years of reanalysis data addressing two issues. The first concerns the non-zero zonal mean component of SLP near the equator and its meridional connections, and the second concerns the fast eastward propagation (EP) speed of SLP compared to that of zonal wind. It is shown that the entire globe resonates with high amplitude wave activity during some periods which may last for few to several months, followed by lull periods of varying duration. SLP variations in the tropical belt are highly coherent from 25A degrees S to 25A degrees N, uncorrelated with variations in mid latitudes and again significantly correlated but with opposite phase around 60A degrees S and 65A degrees N. Near the equator (8A degrees S-8A degrees N), the zonal mean contributes significantly to the total variance in SLP, and after its removal, SLP shows a dominant zonal wavenumber one structure having a periodicity of 40 days and EP speeds comparable to that of zonal winds in the Indian Ocean. SLP from many of the atmospheric and coupled general circulation models show similar behaviour in the meridional direction although their propagation characteristics in the tropical belt differ widely.

Electric-polarization and structure of molecular complexes of the metallic halides of group II of the periodic table

Dielectric measurements have been made on a number of molecular complexes of beryllium, zinc, cadmium and mercuric halides. The polarizations observed have been interpreted in terms of a tetrahedral configuration for the undissociated beryllium, zinc and cadmium halide complexes. In other cases the observed polarization has been shown to be due to the dissociation of the complex in solution.

Detection of a periodic structure hidden in random background: the role of signal amplitude in the matched filter detection method

The matched filter method for detecting a periodic structure on a surface hidden behind randomness is known to detect up to (r(0)/Lambda) gt;= 0.11, where r(0) is the coherence length of light on scattering from the rough part and 3 is the wavelength of the periodic part of the surface-the above limit being much lower than what is allowed by conventional detection methods. The primary goal of this technique is the detection and characterization of the periodic structure hidden behind randomness without the use of any complicated experimental or computational procedures. This paper examines this detection procedure for various values of the amplitude a of the periodic part beginning from a = 0 to small finite values of a. We thus address the importance of the following quantities: `(a)lambda) `, which scales the amplitude of the periodic part with the wavelength of light, and (r(0))Lambda),in determining the detectability of the intensity peaks.