Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

Amplitude of accommodation in type 1 diabetes

Purpose People with diabetes have accelerated age-related biometric ocular changes compared with people without diabetes. We determined the effect of Type 1 diabetes on amplitude of accommodation. Method There were 43 participants (33 ± 8 years) with type 1 diabetes and 32 (34 ± 8 years) age-balanced participants without diabetes. There was no significant difference in the mean equivalent refractive error and visual acuity between the two groups. Amplitude of accommodation was measured using two techniques: objective — by determining the accommodative response to a stimulus in a COAS-HD wavefront aberrometer (Wavefront Sciences), and subjective — with a Badal hand optometer (Rodenstock). The influences of age and diabetes duration (in years) on amplitude of accommodation were analyzed using multiple regression analysis. Results Across both groups, objective amplitude was less than subjective amplitude by 1.4 ± 1.2 D. People with diabetes had lower objective (2.7 ± 1.6 D) and subjective (4.0 ± 1.7 D) amplitudes than people without diabetes (objective 4.1 ± 2.1 D, subjective 5.6 ± 2.1 D). For objective amplitude and the whole group, the duration of diabetes contributed 57% of the variation as did age. For the objective amplitude and only the diabetes group this was 78%. For subjective amplitude, the corresponding proportions were 68% and 103%. Conclusions Both objective and subjective techniques showed lowered amplitude of accommodation in participants with type 1 diabetes when compared with age-matched controls. The loss correlated strongly with duration of diabetes. The results suggest that individuals with diabetes will experience presbyopia earlier in life than people without diabetes, possibly due to metabolic changes in the lens.

Effect of diabetes on amplitude of accommodation

Purpose: To determine the effect of Type 1 diabetes (DM1) on amplitude of accommodation. Method: There were 43 participants (33 ± 8 years) with DM1 and 32 (34 ± 8 years) age-balanced controls. Amplitude was measured objectively with a COAS wavefront aberrometer and subjectively with a Badal hand optometer. Results: Across both groups, objective amplitude was less than subjective amplitude by 1.4 ± 1.2 D. People with diabetes had lower objective (2.7±1.6 D) and subjective (4.0±1.7 D) amplitudes than people without diabetes (objective 4.1±2.1 D, subjective 5.6±2.1 D). For the DM1 group, the objective and subjective multivariate linear regressions were 7.1 – 0.097Age – 0.076DiabDur (R2 0.51) and 9.1 –0.103Age – 0.106DiabDur (R2 0.63), respectively. Conclusion: Objective and subjective techniques showed lowered amplitude of accommodation in DM1 participants compared with age-matched controls. Loss was affected strongly by duration of diabetes. People with diabetes will experience presbyopia earlier in life than people without diabetes.

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.

Small-amplitude cyclic voltammetry: Part I. A simple fourier synthesis approach

Current-potential relationships are derived for small-amplitude periodic inputs for linear electrochemical systems using a Fourier synthesis procedure. Specific results have been obtained for a triangular potential waveform for two simple model systems.

Surface acoustic waves of finite amplitude excited by a monochromatic line source

A technique for obtaining a uniformly valid solution to the problem of nonlinear propagation of surface acoustic waves excited by a monochromatic line source is presented. The method of solution is an extension of the method of strained coordinates wherein both the dependent and independent variables are expanded in perturbation series. A special transformation is proposed for the independent variables so as to make the expansions uniformly valid and also to satisfy all the boundary conditions. This perturbation procedure, carried out to the second order, yields a solution containing a second harmonic surface wave whose amplitude and phase exhibit an oscillatory variation along the direction of propagation. In addition, the solution also contains a second harmonic bulk wave of constant amplitude but varying phase propagating into the medium.

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.

Small amplitude cyclic voltammetry - a simple fourier synthesis approach

Abstaract is not available.

Finite-amplitude love-waves on an isotropic layered half-space

A pair of semi-linear hyperbolic partial differential equations governing the slow variations in amplitude and phase of a quasi-monochromatic finite-amplitude Love-wave on an isotropic layered half-space is derived using the method of multiple-scales. The analysis of the exact solution of these equations for a signalling problem reveals that the amplitude of the wave remains constant along its characteristic and that the phase of the wave increases linearly behind the wave-front.

Coupled amplitude theory of nonlinear surface acoustic waves

The nonlinear propagation characteristics of surface acoustic waves on an isotropic elastic solid have been studied in this paper. The solution of the harmonic boundary value problem for Rayleigh waves is obtained as a generalized Fourier series whose coefficients are proportional to the slowly varying amplitudes of the various harmonics. The infinite set of coupled equations for the amplitudes when solved exhibit an oscillatory slow variation signifying a continuous transfer of energy back and forth among the various harmonics. A conservation relation is derived among all the harmonic amplitudes.

Prediction of frequency and amplitude of foundations at resonance

This note presents the statistical analysis carried out on some of the available experimental results to predict the resonant frequency and maximum displacement amplitude of a machine foundation – soil system under vertical vibration as a function of the size and weight of the foundation and of the excitation level. A total of 442 experimental results of Fry, Novak, and Raman have been analysed using nonlinear regression analysis. The results obtained compared well with predictions obtained from the popular theoretical models, and the coefficient of correlation obtained from the analysis was satisfactory in most of the cases.

The neutron-antineutron transition amplitude in the MIT Bag Model

The neutron-antineutron transition amplitude caused by an effective six fermion interaction with strength λeff is calculated within the context of the MIT Bag Model. The transition mass δm is found to have the value λeff×3×10−4(GeV6).

Analyticity of the charge-monopole scattering amplitude

We study the analyticity in cosθ of the exact quantum-mechanical electric-charge-magnetic-monopole scattering amplitude by ascribing meaning to its formally divergent partial-wave expansion as the boundary value of an analytic function. This permits us to find an integral representation for the amplitude which displays its analytic structure. On the physical sheet we find only a branch-point singularity in the forward direction, while on each of the infinitely many unphysical sheets we find a logarithmic branch-point singularity in the backward direction as well as the same forward structure.