Light guiding light: Nonlinear refraction in rubidium vapor

Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions. (C) 2001 Published by Elsevier Science B.V.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

The relation between the transversus abdominis muscles, sacroilac joint mechanics, and low back pain

Study Design. Two abdominal muscle patterns were tested in the same group of individuals, and their effects were compared in relation to sacroiliac joint laxity. One pattern was contraction of the transversus abdominis, Independently of the other abdominals; the other was a bracing action that used all the lateral abdominal muscles. Objectives. To demonstrate the biomechanical effect of the exercise for the transversus abdominis known to be effective in low back pain. Summary of Background Data. Drawing in the abdominal wall is a specific exercise for the transversus abdominis muscle (in cocontraction with the multifidus), which is used in the treatment of back pain. Clinical effectiveness has been demonstrated to be a reduction of 3-year recurrence from 75% to 35%. To the authors' best knowledge, there is not yet in vivo proof of the biomechanical effect of this specific exercise. This study of a biomechanical model on the mechanics of the sacroiliac joint, however, predicted a significant effect of transversus abdominis muscle force. Methods. Thirteen healthy individuals who could perform the test patterns were included. Sacroiliac joint laxity values were recorded with study participants in the prone position during the two abdominal muscle patterns. The values were recorded by means of Doppler Imaging of vibrations. Simultaneous electromyographic recordings and ultrasound imaging were used to verify the two muscle patterns. Results. The range of sacroiliac joint laxity values observed in this study was comparable with levels found in earlier studies of healthy individuals. These values decreased significantly in all individuals during both muscle patterns (P < 0.001). The independent transversus abdominis contraction decreased sacroiliac joint laxity (or rather increased sacroiliac joint stiffness) to a significantly greater degree than the general abdominal exercise pat-tern (P < 0.0260). Conclusions. Contraction of the transversus abdominis significantly decreases the laxity of the sacroiliac joint. This decrease in laxity is larger than that caused by a bracing action using all the lateral abdominal muscles. These findings are in line with the authors' biomechanical model predictions and support the use of independent transversus abdominis contractions for the treatment of low back pain.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Probing the time course of nonlinear discriminations during human electrodermal conditioning

Animal-based theories of Pavlovian conditioning propose that patterning discriminations are solved using unique cues or immediate configuring. Recent studies with humans, however, provided evidence that in positive and negative patterning two different rules are utilized. The present experiment was designed to provide further support for this proposal by tracking the time course of the allocation of cognitive resources. One group was trained in a positive patterning; schedule (A-, B-, AB+) and a second in a negative patterning schedule (A+, B+, AB-). Electrodermal responses and secondary task probe reaction time were measured. In negative patterning, reaction times were slower during reinforced stimuli than during non-reinforced stimuli at both probe positions while there were no differences in positive patterning. These results support the assumption that negative patterning is solved using a rule that is more complex and requires more resources than does the rule employed to solve positive patterning. (C) 2001 Elsevier Science (USA).

Numerical investigations of flow and energy fields near a thermoacoustic couple

The flow field and the energy transport near thermoacoustic couples are simulated using a 2D full Navier-Stokes solver. The thermoacoustic couple plate is maintained at a constant temperature; plate lengths, which are short and long compared with the particle displacement lengths of the acoustic standing waves, are tested. Also investigated are the effects of plate spacing and the amplitude of the standing wave. Results are examined in the form of energy vectors, particle paths, and overall entropy generation rates. These show that a net heat-pumping effect appears only near the edges of thermoacoustic couple plates, within about a particle displacement distance from the ends. A heat-pumping effect can be seen even on the shortest plates tested when the plate spacing exceeds the thermal penetration depth. It is observed that energy dissipation near the plate increases quadratically as the plate spacing is reduced. The results also indicate that there may be a larger scale vortical motion outside the plates which disappears as the plate spacing is reduced. (C) 2002 Acoustical Society of America.

Effect of manual hyperinflation on hemodynamics, gas exchange, and respiratory mechanics in ventilated patients

The authors investigated the effect of manual hyperinflation (MHI) with set parameters applied to patients on mechanical ventilation on hemodynamics, respiratory mechanics, and gas exchange. Sixteen critically ill patients post-septic shock, with acute lung injury, were studied. Heart rate, arterial pressure, and mean pulmonary artery pressure were recorded every minute. pulmonary artery occlusion pressure, cardiac output, arterial blood gases, and dynamic compliance (C-dyn) were recorded pre- and post-MHI. From this, systemic vascular resistance index (SVRI), cardiac index, oxygen delivery, and partial pressure of oxygen:fraction of inspired oxygen (PaO2:FiO(2)) ratio were calculated. There were significant increases in SVRI (P < 0.05) post-MHI and diastolic arterial pressure (P < 0.01)during MHI. C-dyn increased post-MHI (P < 0.01) and was sustained at 20 minutes post-MHI (P < 0.01). Subjects with an intrapulmonary cause of lung disease had a significant decrease (P = 0.02) in PaO2:FiO(2), and those with extrapulmonary causes of lung disease had a significant increase (P < 0.001) in PaO2:FiO(2) post-MHI. In critically ill patients, MHI resulted in an improvement in lung mechanics and an improvement in gas exchange in patients with lung disease due to extrapulmonary events and did not result in impairment of the cardiovascular system.

Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates

This paper presents a large amplitude vibration analysis of pre-stressed functionally graded material (FGM) laminated plates that are composed of a shear deformable functionally graded layer and two surface-mounted piezoelectric actuator layers. Nonlinear governing equations of motion are derived within the context of Reddy's higher-order shear deformation plate theory to account for transverse shear strain and rotary inertia. Due to the bending and stretching coupling effect, a nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the plate that is subjected to uniform temperature change, in-plane forces and applied actuator voltage. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed FGM laminated plates are derived. A semi-analytical method that is based on one-dimensional differential quadrature and Galerkin technique is proposed to predict the large amplitude vibration behavior of the laminated rectangular plates with two opposite clamped edges. Linear vibration frequencies and nonlinear normalized frequencies are presented in both tabular and graphical forms, showing that the normalized frequency of the FGM laminated plate is very sensitive to vibration amplitude, out-of-plane boundary support, temperature change, in-plane compression and the side-to-thickness ratio. The CSCF and CFCF plates even change the inherent hard-spring characteristic to soft-spring behavior at large vibration amplitudes. (C) 2003 Elsevier B.V. All rights reserved.