Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Pentoxifylline induces hyperactivation and acrosome reaction in spermatozoa of golden hamsters: changes in motility kinematics

Pentoxifylline (PF) is used to enhance motility of spermatozoa from infertile human subjects. We have previously shown that 0.45 mM PF improved capacitation of spermatozoa and fertilization of oocytes in vitro in hamsters. The present study was carried out to assess PF- induced changes in motility kinematics of hamster spermatozoa by a computer-aided sperm analyser (CASA) and determine the timing of onset of hyperactivation (HA) and acrosome reaction (AR) in PF-treated spermatozoa. Motility kinematics were analysed by CASA for 0-8 h in the absence or presence of 0.45 mM PF in Tyrode's medium supplemented with lactate, pyruvate and polyvinyl alcohol (TLP-PVA) or in TLP-PVA with bovine serum albumin (TALP-PVA). Conventional assessment was also made on the percentage of motility and quality of motility of spermatozoa; values were expressed as sperm motility index (SMI). Both in TALP-PVA and TLP-PVA, PF markedly increased SMI, especially the quality of motility (P < 0.02) by 2-3 h which was sustained up to 6 h. The motility kinematic data of PF-treated spermatozoa in TALP-PVA showed that average path velocity, curvilinear velocity and amplitude of lateral head displacement significantly (P < 0.05) increased as early as 2 h, with the expected decrease in straightness (STR) and linearity (LIN). Similar changes were also observed with PF-treated spermatozoa in TLP-PVA. Moreover, the percentage of hyperactivated spermatozoa in PF-treated samples was significantly (P < 0.001) higher than the untreated control at 2 h. To determine whether PF could induce AR, independent of bovine serum albumin, quantitative AR was assessed by observing the presence or absence of acrosomal cap on viable spermatozoa. PF significantly (P < 0.001) increased the percentage of AR as early as 2 h, reaching maximum at 4 h both in TALP-PVA (P < 0.05) and in TLP-PVA (P < 0.001). These results show that, in hamsters, PF induces early onset (by 2 h) of HA and AR and increases the proportion of spermatozoa undergoing physiological maturation.

The dielectric coated conducting sphere - modal and near field characteristics.

A modal analysis and near-field study for a dielectric-coated conducting sphere excited by a delta function electric field source has been made. The structure can support an infinite number of modes theoretically. For equatorial excitation only odd order modes are excited, whereas for non-equatorial excitation both even and odd order modes are excited. The variation of the amplitude coefficients both internal and external exhibit a different nature of variation with respect to the various structure parameters for different modes. The field distributions both in the r and theta directions for non-equatorial excitation show good agreement between theory and experiment for the strongest mode.

The hydrogen bond: a molecular beam microwave spectroscopist's view with a universal appeal

In this manuscript, we propose a criterion for a weakly bound complex formed in a supersonic beam to be characterized as a `hydrogen bonded complex'. For a `hydrogen bonded complex', the zero point energy along any large amplitude vibrational coordinate that destroys the orientational preference for the hydrogen bond should be significantly below the barrier along that coordinate so that there is at least one bound level. These are vibrational modes that do not lead to the breakdown of the complex as a whole. If the zero point level is higher than the barrier, the `hydrogen bond' would not be able to stabilize the orientation which favors it and it is no longer sensible to characterize a complex as hydrogen bonded. Four complexes, Ar-2-H2O, Ar-2-H2S, C2H4-H2O and C2H4-H2S, were chosen for investigations. Zero point energies and barriers for large amplitude motions were calculated at a reasonable level of calculation, MP2(full)/aug-cc-pVTZ, for all these complexes. Atoms in molecules (AIM) theoretical analyses of these complexes were carried out as well. All these complexes would be considered hydrogen bonded according to the AIM theoretical criteria suggested by Koch and Popelier for C-H center dot center dot center dot O hydrogen bonds (U. Koch and P. L. A. Popelier, J. Phys. Chem., 1995, 99, 9747), which has been widely and, at times, incorrectly used for all types of contacts involving H. It is shown that, according to the criterion proposed here, the Ar-2-H2O/H2S complexes are not hydrogen bonded even at zero kelvin and C2H4-H2O/H2S complexes are. This analysis can naturally be extended to all temperatures. It can explain the recent experimental observations on crystal structures of H2S at various conditions and the crossed beam scattering studies on rare gases with H2O and H2S.

Voltage gated Na+ channels contribute to membrane voltage fluctuation in \alpha T3-1 pituitary gonadotroph cells

\alpha T3-1 cells showed a slope resistance of 1.8 G\omega. The cell membrane surface was not smooth and a scanning electron micrograph showed a complex structure with blebs and microvilli like projections. The cells showed spontaneous fluctuations at zero current resting membrane potential and hyperpolarization increased the amplitude of membrane potential fluctuations. The amplitude of membrane potential fluctuations at hyperpolarized membrane potential was attenuated on application of TTX to the bath solution. The potential at which half steady state inactivation of isolated sodium current occurred, was at a very hyperpolarized potential (-95.4 mV). The study presented in this paper shows that the voltage gated sodium channels contribute to the increase in the amplitude of electrical noise with hyperpolarization in \alpha T3-1 cells.

On Multi-Dimensional Packets of Surface Waves

By using the method of operators of multiple scales, two coupled nonlinear equations are derived, which govern the slow amplitude modulation of surface gravity waves in two space dimensions. The equations of Davey and Stewartson, which also govern the two-dimensional modulation of the amplitude of gravity waves, are derived as a special case of our equations. For a fully dispersed wave, symmetric about a point which moves with the group velocity, the coupled equations reduce to a nonlinear Schrödinger equation with extra terms representing the effect of the curvature of the wavefront.

A note on fractal dimensions of biomedical waveforms

In this paper, we study performance of Katz method of computing fractal dimension of waveforms, and its estimation accuracy is compared with Higuchi's method. The study is performed on four synthetic parametric fractal waveforms for which true fractal dimensions can be calculated, and real sleep electroencephalogram. The dependence of Katz's fractal dimension on amplitude, frequency and sampling frequency of waveforms is noted. Even though the Higuchi's method has given more accurate estimation of fractal dimensions, the study suggests that the results of Katz's based fractal dimension analysis of biomedical waveforms have to be carefully interpreted.

Electrophysiological correlates of hanseniasis

Sensory nerve action potentials (SNAPs) and compound nerve action potentials (CNAPs) were recorded from 25 normal subjects and 21 hanseniasis patients following electrical stimulation of the median nerve at the wrist. The various nerve conduction parameters from the affected nerves of the patients were compared with those from the clinically normal nerves of patients as well as data from healthy individuals. Analysis of the data and clinical correlation studies indicate the suitability of amplitudes of the SNAPs and CNAPs rather than the nerve conduction velocities in better characterizing the neuropathy of the patients. Significantly reduced amplitudes of responses from clinically unaffected nerves of patients indicate an early stage of neuropathy, thus being of predictive value. Further, a discriminant classifier, trained on data from clinically affected nerves of patients, classified most of the data from clinically unaffected nerves of patients as abnormal. This indicates that clinical neurophysiological studies can reveal leprous neuropathy much before it becomes clinically evident by means of sensory or motor loss. A discriminant score involving only the parameters of motor threshold, amplitude of digit potential and palm nerve conduction velocity is able to classify almost all of the normal and abnormal responses. The authors hope that further confirmative studies might ultimately lead to the use of the study of distal sensory conduction in the upper limbs in possible screening of a population exposed to Mycobacterium leprae. On the other hand, misclassification of a normal person occurred and suggests that further refinement of the methods is necessary in order to facilitate wider use of the methods under held conditions.

Post-liquefaction undrained monotonic behaviour of sands: experiments and DEM simulations

This paper presents the results of a series of servo-controlled cyclic triaxial tests and numerical simulations using the three- dimensional discrete element method (DEM) on post-liquefaction undrained monotonic strength of granular materials. In a first test series,undrained monotonic tests were carried out after dissipating the excess pore water pressure developed during liquefaction. The influence of different parameters such as amplitude of axial strain,relative density and confining pressure prior to liquefaction on the post-liquefaction undrained response have been investigated.The results obtained highlight an insignificant influence of amplitude of axial strain, confining pressure and a significant influence of relative density on the post-liquefaction undrained monotonic stress-strain response.In the second series, undrained monotonic tests were carried out on similar triaxial samples without dissipating the excess pore water pressure developed during liquefaction. The results highlight that the amplitude of axial strain prior to liquefaction has a significant influence on the post-liquefaction undrained monotonic response.In addition,DEM simulations have been carried out on an assembly of spheres to simulate post-liquefaction behaviour.The simulations were very similar to the experiments with an objective to understand the behaviour of monotonic strength of liquefied samples from the grain scale. The numerical simulations using DEM have captured qualitatively all the features of the post-liquefaction undrained monotonic response in a manner similar to that of the experiments.In addition,a detailed study on the evolution of micromechanical parameters such as the average coordination number and induced anisotropic coefficients has been reported during the post-liquefaction undrained monotonic loading.

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control chemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Studies on the assessment of the adequacy of anesthesia

Several hypnosis monitoring systems based on the processed electroencephalogram (EEG) have been developed for use during general anesthesia. The assessment of the analgesic component (antinociception) of general anesthesia is an emerging field of research. This study investigated the interaction of hypnosis and antinociception, the association of several physiological variables with the degree of intraoperative nociception, and aspects of EEG Bispectral Index Scale (BIS) monitoring during general anesthesia. In addition, EEG features and heart rate (HR) responses during desflurane and sevoflurane anesthesia were compared. A propofol bolus of 0.7 mg/kg was more effective than an alfentanil bolus of 0.5 mg in preventing the recurrence of movement responses during uterine dilatation and curettage (D C) after a propofol-alfentanil induction, combined with nitrous oxide (N2O). HR and several HR variability-, frontal electromyography (fEMG)-, pulse plethysmography (PPG)-, and EEG-derived variables were associated with surgery-induced movement responses. Movers were discriminated from non-movers mostly by the post-stimulus values per se or normalized with respect to the pre-stimulus values. In logistic regression analysis, the best classification performance was achieved with the combination of normalized fEMG power and HR during D C (overall accuracy 81%, sensitivity 53%, specificity 95%), and with the combination of normalized fEMG-related response entropy, electrocardiography (ECG) R-to-R interval (RRI), and PPG dicrotic notch amplitude during sevoflurane anesthesia (overall accuracy 96%, sensitivity 90%, specificity 100%). ECG electrode impedances after alcohol swab skin pretreatment alone were higher than impedances of designated EEG electrodes. The BIS values registered with ECG electrodes were higher than those registered simultaneously with EEG electrodes. No significant difference in the time to home-readiness after isoflurane-N2O or sevoflurane-N2O anesthesia was found, when the administration of the volatile agent was guided by BIS monitoring. All other early and intermediate recovery parameters were also similar. Transient epileptiform EEG activity was detected in eight of 15 sevoflurane patients during a rapid increase in the inspired volatile concentration, and in none of the 16 desflurane patients. The observed transient EEG changes did not adversely affect the recovery of the patients. Following the rapid increase in the inhaled desflurane concentration, HR increased transiently, reaching its maximum in two minutes. In the sevoflurane group, the increase was slower and more subtle. In conclusion, desflurane may be a safer volatile agent than sevoflurane in patients with a lowered seizure threshold. The tachycardia induced by a rapid increase in the inspired desflurane concentration may present a risk for patients with heart disease. Designated EEG electrodes may be superior to ECG electrodes in EEG BIS monitoring. When the administration of isoflurane or sevoflurane is adjusted to maintain BIS values at 50-60 in healthy ambulatory surgery patients, the speed and quality of recovery are similar after both isoflurane-N2O and sevoflurane-N2O anesthesia. When anesthesia is maintained by the inhalation of N2O and bolus doses of propofol and alfentanil in healthy unparalyzed patients, movement responses may be best avoided by ensuring a relatively deep hypnotic level with propofol. HR/RRI, fEMG, and PPG dicrotic notch amplitude are potential indicators of nociception during anesthesia, but their performance needs to be validated in future studies. Combining information from different sources may improve the discrimination of the level of nociception.

A model of the polarization position-angle swings in BL Lacertae objects

The polarization position-angle swings that have been measured in a number of BL Lacertae objects and highly variable quasars are interpreted in terms of shock waves which illuminate (by enhanced synchrotron radiation) successive transverse cross sections of a magnetized, relativistic jet. The jet is assumed to have a nonaxisymmetric magnetic field configuration of the type discussed in the companion paper on the equilibria of force-free jets. For a jet that is viewed at a small angle to the axis, the passage of a shock will give rise to an apparent rotation of the polarization position angle whose amplitude can be substantially larger than 180 deg. The effects of freely propagating shocks are compared with those of bow shocks which form in front of dense obstacles in the jet, and specific applications to 0727 - 115 and BL Lacertae are considered. In the case of 0727 - 115, it is pointed out that the nonuniformity of the swing rate and the apparent oscillations of the degree of polarization could be a consequence of relativistic aberration.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

6,8-Dibromo-5-hydroxy-4-oxo-2-phenyl-4H-chromen-7-yl acetate

In the title compound, C17H10Br2O5, the chromene ring is almost planar with minimal puckering [total puckering amplitude = 0.067 (4) angstrom]. The dihedral angle between chromeme ring system and phenyl ring is 3.7 (2)degrees. The crystal structure is stabilized by intermolecular C-H center dot center dot center dot O interactions and an intramolecular O-H center dot center dot center dot O hydrogen bond also occurs.

Therapeutic hypothermia after cardiac arrest : Studies on neurological and cardiological outcome and prediction of outcome in hypothermia-treated patients resuscitated from out-of-hospital cardiac arrest

The outcome of the successfully resuscitated patient is mainly determined by the extent of hypoxic-ischemic cerebral injury, and hypothermia has multiple mechanisms of action in mitigating such injury. The present study was undertaken from 1997 to 2001 in Helsinki as a part of the European multicenter study Hypothermia after cardiac arrest (HACA) to test the neuroprotective effect of therapeutic hypothermia in patients resuscitated from out-of-hospital ventricular fibrillation (VF) cardiac arrest (CA). The aim of this substudy was to examine the neurological and cardiological outcome of these patients, and especially to study and develop methods for prediction of outcome in the hypothermia-treated patients. A total of 275 patients were randomized to the HACA trial in Europe. In Helsinki, 70 patients were enrolled in the study according to the inclusion criteria. Those randomized to hypothermia were actively cooled externally to a core temperature 33 ± 1ºC for 24 hours with a cooling device. Serum markers of ischemic neuronal injury, NSE and S-100B, were sampled at 24, 36, and 48 hours after CA. Somatosensory and brain stem auditory evoked potentials (SEPs and BAEPs) were recorded 24 to 28 hours after CA; 24-hour ambulatory electrocardiography recordings were performed three times during the first two weeks and arrhythmias and heart rate variability (HRV) were analyzed from the tapes. The clinical outcome was assessed 3 and 6 months after CA. Neuropsychological examinations were performed on the conscious survivors 3 months after the CA. Quantitative electroencephalography (Q-EEG) and auditory P300 event-related potentials were studied at the same time-point. Therapeutic hypothermia of 33ºC for 24 hours led to an increased chance of good neurological outcome and survival after out-of-hospital VF CA. In the HACA study, 55% of hypothermia-treated patients and 39% of normothermia-treated patients reached a good neurological outcome (p=0.009) at 6 months after CA. Use of therapeutic hypothermia was not associated with any increase in clinically significant arrhythmias. The levels of serum NSE, but not the levels of S-100B, were lower in hypothermia- than in normothermia-treated patients. A decrease in NSE values between 24 and 48 hours was associated with good outcome at 6 months after CA. Decreasing levels of serum NSE but not of S-100B over time may indicate selective attenuation of delayed neuronal death by therapeutic hypothermia, and the time-course of serum NSE between 24 and 48 hours after CA may help in clinical decision-making. In SEP recordings bilaterally absent N20 responses predicted permanent coma with a specificity of 100% in both treatment arms. Recording of BAEPs provided no additional benefit in outcome prediction. Preserved 24- to 48-hour HRV may be a predictor of favorable outcome in CA patients treated with hypothermia. At 3 months after CA, no differences appeared in any cognitive functions between the two groups: 67% of patients in the hypothermia and 44% patients in the normothermia group were cognitively intact or had only very mild impairment. No significant differences emerged in any of the Q-EEG parameters between the two groups. The amplitude of P300 potential was significantly higher in the hypothermia-treated group. These results give further support to the use of therapeutic hypothermia in patients with sudden out-of-hospital CA.