Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

Extraction of electrical characteristics from pixels of multifrequency EIT images

Computer modelling has shown that electrical characteristics of individual pixels may be extracted from within multiple-frequency electrical impedance tomography (MFEIT) images formed using a reference data set obtained from a purely resistive, homogeneous medium. In some applications it is desirable to extract the electrical characteristics of individual pixels from images where a purely resistive, homogeneous reference data set is not available. One such application of the technique of MFEIT is to allow the acquisition of in vivo images using reference data sets obtained from a non-homogeneous medium with a reactive component. However, the reactive component of the reference data set introduces difficulties with the extraction of the true electrical characteristics from the image pixels. This study was a preliminary investigation of a technique to extract electrical parameters from multifrequency images when the reference data set has a reactive component. Unlike the situation in which a homogenous, resistive data set is available, it is not possible to obtain the impedance and phase information directly from the image pixel values of the MFEIT images data set, as the phase of the reactive reference is not known. The method reported here to extract the electrical characteristics (the Cole-Cole plot) initially assumes that this phase angle is zero. With this assumption, an impedance spectrum can be directly extracted from the image set. To obtain the true Cole-Cole plot a correction must be applied to account for the inherent rotation of the extracted impedance spectrum about the origin, which is a result of the assumption. This work shows that the angle of rotation associated with the reactive component of the reference data set may be determined using a priori knowledge of the distribution of frequencies of the Cole-Cole plot. Using this angle of rotation, the true Cole-Cole plot can be obtained from the impedance spectrum extracted from the MFEIT image data set. The method was investigated using simulated data, both with and without noise, and also for image data obtained in vitro. The in vitro studies involved 32 logarithmically spaced frequencies from 4 kHz up to 1 MHz and demonstrated that differences between the true characteristics and those of the impedance spectrum were reduced significantly after application of the correction technique. The differences between the extracted parameters and the true values prior to correction were in the range from 16% to 70%. Following application of the correction technique the differences were reduced to less than 5%. The parameters obtained from the Cole-Cole plot may be useful as a characterization of the nature and health of the imaged tissues.

Sample-induced RF perturbations in high-field, high-resolution NMR spectroscopy

Conducting dielectric samples are often used in high-resolution experiments at high held. It is shown that significant amplitude and phase distortions of the RF magnetic field may result from perturbations caused by such samples. Theoretical analyses demonstrate the spatial variation of the RF field amplitude and phase across the sample, and comparisons of the effect are made for a variety of sample properties and operating field strengths. Although the effect is highly nonlinear, it tends to increase with increasing field strength, permittivity, conductivity, and sample size. There are cases, however, in which increasing the conductivity of the sample improves the homogeneity of the amplitude of the RF field across the sample at the expense of distorted RF phase. It is important that the perturbation effects be calculated for the experimental conditions used, as they have the potential to reduce the signal-to-noise ratio of NMR experiments and may increase the generation of spurious coherences. The effect of RF-coil geometry on the coherences is also modeled, with the use of homogeneous resonators such as the birdcage design being preferred, Recommendations are made concerning methods of reducing sample-induced perturbations. Experimental high-field imaging and high-resolution studies demonstrate the effect. (C) 1997 Academic Press.

Classical and quantum signatures of competing chi((2)) nonlinearities

We report the observation of the quantum effects of competing chi((2)) nonlinearities. We also report classical signatures of competition, namely, clamping of the second-harmonic power and production of nondegenerate frequencies in the visible. Theory is presented that describes the observations as resulting from competition between various chi((2)) up-conversion and down-conversion processes. We show that competition imposes hitherto unsuspected limits to both power generation and squeezing. The observed signatures are expected to be significant effects in practical systems.

A methodology for current density calculations in high-frequency RF resonators

As nuclear magnetic resonance imaging and spectroscopy move inexorably toward higher field-strength magnets in search of improved signal-to-noise ratio, spectral resolution, and spatial resolution, the way in which radiofrequency (RF) probes are designed changes. At higher frequencies, resonant cavities become the favored RF ''coil'' type and may be built using streamline elements to reduce the inductance of the system. In modeling such systems, the quasi-static approach of assuming that current flows evenly in all conductor cross sections and that adjacent conductors do not affect each other becomes less reasonable. The proximity of RF conductors in resonators typically causes RF eddy currents to flow, whereby the current density in each rung is altered by the RF fields generated by nearby conductors. The proper understanding and prediction of how resonators will perform require a model of the current densities flowing in conducting sections, including all RF eddy current effects. Very few models of this type have been presented in the literature. This article presents an overview of one such model and of how it may be applied to a variety of resonators, both shielded and unshielded, circular, and elliptical, in cross section. Results are presented from a shielded head coil operating at 2 tesla. (C) 1997 John Wiley & Sons, Inc.

Direct visualisation of B-1 inhomogeneity by flip angle dependency

Inhomogeneities in the spatial distribution of the excitatory Radio Frequency (RF) field, are still a dominant source of artifacts and loss of signal to noise ratio in MR imaging experiments, A number of strategies have been proposed to quantify this distribution, However, in this technical note we present a relatively simple MR imaging procedure which can be used to visualise RF inhomogeneities directly either by means of the magnitude or the phase of an image. To visualise the RF field distribution in both the inner and outer volumes of the coil, we have performed experiments in which the entire coil is submerged in a non-conducting fluid, To the best of our knowledge this strategy has not been used previously in order to evaluate coil performance, Finally, we demonstrate that the method is sensitive enough to reveal the effects of the sample properties on the effective RF wavelength of the transmitted field. (C) 1997 Elsevier Science Inc.

Pulsed quadrature-phase squeezing of solitary waves in chi((2)) parametric waveguides

It is shown that coherent quantum simultons (simultaneous solitary waves at two different frequencies) can undergo quadrature-phase squeezing as they propagate through a dispersive chi((2)) waveguide. This requires a treatment of the coupled quantized fields including a quantized depleted pump field. A technique involving nonlinear stochastic parabolic partial differential equations using a nondiagonal coherent state representation in combination with an exact Wigner representation on a reduced phase space is outlined. We explicitly demonstrate that group-velocity matched chi((2)) waveguides which exhibit collinear propagation can produce quadrature-phase squeezed simultons. Quasi-phase-matched KTP waveguides, even with their large group-velocity mismatch between fundamental and second harmonic at 425 nm, can produce 3 dB squeezed bright pulses at 850 nm in the large phase-mismatch regime. This can be improved to more than 6 dB by using group-velocity matched waveguides.

Maternal smoking during pregnancy: Impact on otoacoustic emissions in neonates

Objectives: To determine the effect of maternal smoking during pregnancy on transient evoked otoacoustic emissions levels in neonates. Methods: This was a cross-sectional study investigating neonates in the maternity ward of a university hospital in the city of Sao Paulo, Brazil. A total of 418 term neonates without prenatal or perinatal complications were evaluated. The neonates were divided into two groups: a study group, which comprised 98 neonates born to mothers who had smoked during pregnancy; and a control group, which comprised 320 neonates born to mothers who had not. In order to compare the two ears and the two groups in terms of the mean overall response and the mean transient evoked otoacoustic emissions in response to acoustic stimuli delivered at different frequencies, we used analysis of variance with repeated measures. Results: The mean overall response and the mean frequency-specific response levels were lower in the neonates in the study group (p < 0.001). The mean difference between the groups was 2.47 dB sound pressure level (95% confidence interval: 1.47-3.48). Conclusions: Maternal smoking during pregnancy had a negative effect on cochlear function, as determined by otoacoustic emissions testing. Therefore, pregnant women should be warned of this additional hazard of smoking. It is important that smoking control be viewed as a public health priority and that strategies for treating tobacco dependence be devised. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Late Auditory evoked potentials in individuals with tinnitus

Long latency auditory evoked potentials (LLAEP) alterations in individuals with tinnitus are suggestive of dysfunction in the central auditory pathways at a cortical level. Aim: to characterize the LLAEP in individuals with and without tinnitus exposed to occupational noise. Method: Cross-sectional contemporary cohort, prospective study. Sixty subjects exposed to occupational noise, ranging in age from 29 to 50 years underwent LLAEP assessment; 30 of them had tinnitus complaint and 30 did not have tinnitus. Results: we observed significant statistical difference regarding the mean values of latencies of waves N1 (p<0.001), P2 (p=0.002) and P300 (p=0.039) when we compared individuals with and without tinnitus. In individuals with tinnitus we also noticed a greater number of altered results concerning components N1 (60%) and P2 (66.7%), although only component P2 presented significant statistical difference (p=0.010). For the LLAEP, the latency increase was the only type of alteration found (p=1.000). We found a greater association between bilateral tinnitus and bilateral alteration for all components N1(73%), P2(73%) and P300(50%). Conclusion: It is relevant to study LLAEP in individuals with tinnitus exposed to high occupational sound pressure levels.

Influence of Cochlear Function on Auditory Temporal Resolution in Tinnitus Patients

Our aim was to analyze the influence of subtle cochlear damage on temporal auditory resolution in tinnitus patients. Forty-eight subjects (hearing threshold <= 25 dB HL) were assigned to one of two experimental groups: 28 without auditory complaints (mean age, 28.8 years) and 20 with tinnitus (mean age, 33.5 years). We analyzed distortion product otoacoustic emission growth functions (by threshold, slope, and estimated amplitude), extended high-frequency thresholds, and the Gaps-in-Noise test. There were differences between the groups, principally in the extended high-frequency thresholds and the Gaps-in-Noise test results. Our findings suggest that subtle peripheral hearing impairment affects temporal resolution in tinnitus, even when pure-tone thresholds as conventionally measured appear normal. Copyright (C) 2010 S. Karger AG, Basel