Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Bioelectrical impedance analysis for the estimation of body composition in rats

Bioelectrical impedance analysis (BIA) was used to assess body composition in rats fed on either standard laboratory diet or on a high-fat diet designed to induce obesity. Bioelectrical impedance analysis predictions of total body water and thus fat-free mass (FFM) for the group mean values were generally within 5% of the measured values by tritiated water ((H2O)-H-3) dilution. The limits of agreement for the procedure were, however, large, approximately +/-25%, limiting the applicability of the technique for measurement of body composition in individual animals.

Evaluation of multifrequency bioelectrical impedance data for predicting lean tissue mass in beef cattle

Multifrequency bioimpedance analysis has the potential to provide a non-invasive technique for determining body composition in live cattle. A bioimpedance meter developed for use in clinical medicine was adapted and evaluated in 2 experiments using a total of 31 cattle. Prediction equations were obtained for total body water, extracellular body water, intracellular body water, carcass water and carcass protein. There were strong correlations between the results obtained through chemical markers and bioimpedance analysis when determined in cattle that had a wide range of liveweights and conditions. The r(2) values obtained were 0.87 and 0.91 for total body water and extracellular body water respectively. Bioimpedance also correlated with carcass water, measured by chemical analysis (r(2) = 0.72), but less well with carcass protein (r(2) = 0.46). These correlations were improved by inclusion of liveweight and sex as variables in multiple regression analysis. However, the resultant equations were poor predictors of protein and water content in the carcasses of a group of small underfed beef cattle, that had a narrow range of liveweights. In this case, although there was no statistical difference between the predicted and measured values overall, bioimpedance analysis did not detect the differences in carcass protein between the 2 groups that were apparent following chemical analysis. Further work is required to determine the sensitivity of the technique in small underfed cattle, and its potential use in heavier well fed cattle close to slaughter weight.

Potential errors in the application of mixture theory to multifrequency bioelectrical impedance analysis

Potential errors in the application of mixture theory to the analysis of multiple-frequency bioelectrical impedance data for the determination of body fluid volumes are assessed. Potential sources of error include: conductive length; tissue fluid resistivity; body density; weight and technical errors of measurement. Inclusion of inaccurate estimates of body density and weight introduce errors of typically < +/-3% but incorrect assumptions regarding conductive length or fluid resistivities may each incur errors of up to 20%.

Prediction of the chemical composition of lamb carcasses from multi-frequency impedance data

Multi-frequency bioimpedance analysis (MFBIA) was used to determine the impedance, reactance and resistance of 103 lamb carcasses (17.1-34.2 kg) immediately after slaughter and evisceration. Carcasses were halved, frozen and one half subsequently homogenized and analysed for water, crude protein and fat content. Three measures of carcass length were obtained. Diagonal length between the electrodes (right side biceps femoris to left side of neck) explained a greater proportion of the variance in water mass than did estimates of spinal length and was selected for use in the index L-2/Z to predict the mass of chemical components in the carcass. Use of impedance (Z) measured at the characteristic frequency (Z(c)) instead of 50 kHz (Z(50)) did not improve the power of the model to predict the mass of water, protein or fat in the carcass. While L-2/Z(50) explained a significant proportion of variation in the masses of body water (r(2) 0.64), protein (r(2) 0.34) and fat (r(2) 0.35), its inclusion in multi-variate indices offered small or no increases in predictive capacity when hot carcass weight (HCW) and a measure of rib fat-depth (GR) were present in the model. Optimized equations were able to account for 65-90 % of the variance observed in the weight of chemical components in the carcass. It is concluded that single frequency impedance data do not provide better prediction of carcass composition than can be obtained from measures of HCW and GR. Indices of intracellular water mass derived from impedance at zero frequency and the characteristic frequency explained a similar proportion of the variance in carcass protein mass as did the index L-2/Z(50).

Electrical impedance particle size method (Coulter Counter) detects the large fat globules in poorly homogenised UHT processed milk

The large fat globules that can be present in UHT milk due to inadequate homogenisation cause a cream layer to form that limits the shelf life of UHT milk. Four different particle size measurement techniques were used to measure the size of fat globules in poorly homogenised UHT milk processed in a UHT pilot plant. The thickness of the cream layer that formed during storage was negatively correlated with homogenisation pressure. It was positively correlated with the mass mean diameter and the percentage volume of particles between 1.5 and 2 mu m diameter, as determined by laser light scattering using the Malvern Mastersizer. Also, the thickness of the cream layer was positively correlated with the volume mode diameter and the percentage volume of particles between 1.5 and 2 mu m diameter, as determined by electrical impedance using the Coulter Counter. The cream layer thickness did not correlate significantly with the Coulter Counter measurements of volume mean diameter, or volume percentages of particles between 2 and 5 mu m or 5 and 10 mu m diameter. Spectroturbidimetry (Emulsion Quality Analyser) and light microscopy analyses were found to be unsuitable for assessing the size of the fat particles. This study suggests that the fat globule size distribution as determined by the electrical impedance method (Coulter Counter) is the most useful for determining the efficiency of homogenisation and therefore for predicting the stability of the fat emulsion in UHT milk during storage.

Data analysis in multiple-frequency bioelectrical impedance analysis

The performance of three analytical methods for multiple-frequency bioelectrical impedance analysis (MFBIA) data was assessed. The methods were the established method of Cole and Cole, the newly proposed method of Siconolfi and co-workers and a modification of this procedure. Method performance was assessed from the adequacy of the curve fitting techniques, as judged by the correlation coefficient and standard error of the estimate, and the accuracy of the different methods in determining the theoretical values of impedance parameters describing a set of model electrical circuits. The experimental data were well fitted by all curve-fitting procedures (r = 0.9 with SEE 0.3 to 3.5% or better for most circuit-procedure combinations). Cole-Cole modelling provided the most accurate estimates of circuit impedance values, generally within 1-2% of the theoretical values, followed by the Siconolfi procedure using a sixth-order polynomial regression (1-6% variation). None of the methods, however, accurately estimated circuit parameters when the measured impedances were low (<20 Omega) reflecting the electronic limits of the impedance meter used. These data suggest that Cole-Cole modelling remains the preferred method for the analysis of MFBIA data.

Bioelectrical impedance analysis predicts outcome in patients with suspected bacteremia

Fluid shifts from intracellular to extracellular water (ICW to ECW) are a feature of sepsis, caused by increased vascular permeability and cell catabolism. Changes in ECW and total body water (TBW) were assessed in a prospective observational study of patients with bacteremia by a bedside technique, and its prognostic impact determined; In 78 hospital patients with fever, the resistance ratio (Rinf/RO) and estimated ECW/TBW ratio from multifrequency bioelectrical impedance analysis, and serum albumin concentration were measured. Rinf/RO and ECW/TBW ratios decreased from day 0 to 2 in patients with significant bacteremia (n = 31), but not in patients with doubtful or negative blood cultures (n = 22 and 25), Increased Rinf/RO at baseline, and further increase of ECW/TBW from day 0 to 2, were associated with lower rate of recovery after 1 week and with higher mortality. Baseline Rinf/RO above the median (0.75) had positive and negative predictive values of 0.31 and 0.95 for death. This prognostic effect was independent of underlying disease and blood culture result in a multivariate model. Hypoalbuminemia at baseline was predictive of outcome, but changes in albumin from day 0 to 2 were unrelated to blood culture results or outcome. In patients with bacteremia,fluid shifts from intracellular to extracellular,vater occur early are rapidly reversible by antibiotic treatment but are associated with adverse prognosis. Bioelectrical impedance deserves further study as a tool for bedside monitoring of patients with bacteremia.

Predicting composition of leg sections with anthropometry and bioelectrical impedance analysis using magnetic resonance imaging as reference

Magnetic resonance imaging (MRI) was used to evaluate and compare with anthropometry a fundamental bioelectrical impedance analysis (BIA) method for predicting muscle and adipose tissue composition in the lower limb. Healthy volunteers (eight men and eight women), aged 41 to 62 years, with mean (S.D.) body mass indices of 28.6 (5.4) kg/m(2) and 25.1 (5.4) kg/m(2) respectively, were subjected to MRI leg scans, from which 20-cm sections of thigh and IO-cm sections of lower leg (calf) were analysed for muscle and adipose tissue content, using specifically developed software. Muscle and adipose tissue were also predicted from anthropometric measurements of circumferences and skinfold thicknesses, and by use of fundamental BIA equations involving section impedance at 50 kHz and tissue-specific resistivities. Anthropometric assessments of circumferences, cross-sectional areas and volumes for total constituent tissues matched closely MRI estimates. Muscle volume was substantially overestimated (bias: thigh, -40%; calf, -18%) and adipose tissue underestimated (bias: thigh, 43%; calf, 8%) by anthropometry, in contrast to generally better predictions by the fundamental BIA approach for muscle (bias:thigh, -12%; calf, 5%) and adipose tissue (bias:thigh, 17%; calf, -28%). However, both methods demonstrated considerable individual variability (95% limits of agreement 20-77%). In general, there was similar reproducibility for anthropometric and fundamental BIA methods in the thigh (inter-observer residual coefficient of variation for muscle 3.5% versus 3.8%), but the latter was better in the calf (inter-observer residual coefficient of variation for muscle 8.2% versus 4.5%). This study suggests that the fundamental BIA method has advantages over anthropometry for measuring lower limb tissue composition in healthy individuals.

Sensitivity of multiple frequency bioelectrical impedance analysis to changes in ion status

Bioelectrical impedance analysis has found extensive application as a simple noninvasive method for the assessment of body fluid volumes, The measured impedance is, however, not only related to the volume of fluid but also to its inherent resistivity. The primary determinant of the resistivities of body fluids is the concentration of ions. The aim of this study was to investigate the sensitivity of bioelectrical impedance analysis to bodily ion status. Whole body impedance over a range of frequencies (4-1012 kHz) of rats was measured during infusion of various concentrations of saline into rats concomitant with measurement of total body and intracellular water by tracer dilution techniques. Extracellular resistance (R-o), intracellular resistance (R-i) and impedance at the characteristic frequency (Z(c)) were calculated. R-o and Z(c) were used to predict extracellular and total body water respectively using previously published formulae. The results showed that whilst R-o and Z(c) decreased proportionately to the amount of NaCl infused, R-i increased only slightly. Impedances at the end of infusion predicted increases iu TBW and ECW of approximately 4-6% despite a volume increase of less than 0.5% in TBW due to the volume of fluid infused. These data are discussed in relation to the assumption of constant resistivity in the prediction of fluid volumes from impedance data.

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.

Assessment of intracellular water by whole body bioelectrical impedance and total body potassium in HIV-positive patients

.:Abstract-Objective: Bioelectrical impedance analysis (BIA) is widely used as bedside assessment of body composition. Body cell mass (BCM) and intracellular water (ICW) are clinically important body compartments. Estimates of ICW obtained from BIA by different calculation approaches were compared to a reference method in male HIV-infected patients. Patients: Representative subsample of clinically stable HIV-infected outpatients, consisting of 42 men with a body mass index of 22.4 +/- 3.8 kg/m(2) (range, 13-31 kg/m(2)). Methods: Total body potassium was assessed in a whole body counter, and compared to 50 kHz mono-frequency BIA and multifrequency bioelectrical impedance spectroscopy. Six different prediction equations for ICW from BIA data were applied. Methods were compared by the Bland-Altman method. Results: BIA-derived ICW estimates explained 58% to 73% of the observed variance in ICW (TBK), but limits of confidence were wide (-16.6 to +18.2% for the best method). BIA overestimated low ICW (TBK) and underestimated high ICW (TBK) when normalized for weight or height. Mono- and multifrequency BIA were not different in precision but population-specific equations tended to narrower confidence limits. Conclusion: BIA is an unreliable method to estimate ICW in this population, in contrast to the better established estimation of total body water and extracellular water. Potassium depletion in severe malnutrition may contribute to this finding but a major part of the residual between methods remains unexplained. (C) 2000 Harcourt Publishers Ltd.