A class of one-dimensional steady-state flows in radiation-gas-dynamics

The study of steady-state flows in radiation-gas-dynamics, when radiation pressure is negligible in comparison with gas pressure, can be reduced to the study of a single first-order ordinary differential equation in particle velocity and radiation pressure. The class of steady flows, determined by the fact that the velocities in two uniform states are real, i.e. the Rankine-Hugoniot points are real, has been discussed in detail in a previous paper by one of us, when the Mach number M of the flow in one of the uniform states (at x=+∞) is greater than one and the flow direction is in the negative direction of the x-axis. In this paper we have discussed the case when M is less than or equal to one and the flow direction is still in the negative direction of the x-axis. We have drawn the various phase planes and the integral curves in each phase plane give various steady flows. We have also discussed the appearance of discontinuities in these flows.

On the unreasonable effectiveness of Gutzmer's formula

In this article we plan to demonstrate the usefulness of `Gutzmer's formula' in the study of various problems related to the Segal-Bargmann transform. Gutzmer's formula is known in several contexts: compact Lie groups, symmetric spaces of compact and noncompact type, Heisenberg groups and Hermite expansions. We apply Gutzmer's formula to study holomorphic Sobolev spaces, local Peter-Weyl theorems, Paley-Wiener theorems and Poisson semigroups.

Metabolism of a monoterpene ketone, R-(+)-pulegone—a hepatotoxin in rat

R-(+)-Pulegone was administered orally to rats and the urinary metabolites were investigated. Six metabolites were isolated and purified using column and thin layer chromatographic techniques. Metabolites were identified by i.r., n.m.r. and mass spectral analyses.The neutral metabolites isolated from urine of rats treated with pulegone (I) were: pulegol (II), 2-hydroxy-2(1'-hydroxy-1'-methylethyl)-5-methylcyclohexanone (III), 3,6-dimethyl-7a-hydroxy-5,6,7,7a-tetrahydro-2(4H)-benzofuranone (V) and menthofuran (VII). Metabolites II and III were also excreted in conjugated form.Acidic metabolites isolated from urine of rats treated with pulegone (I) were: 5-methyl-2(1'-methyl-1'-carboxyethylidene)cyclohexanone (IV) and 5-methyl-5-hydroxy-2(1'hydroxy-'-carboxyethyl)cyclohexanone (VI).

Methyl ethyl ketone plus water plus secondary butyl alcohol: A potential system for the exploration of a quadruple critical point

We report preliminary experiments on the ternary-liquid mixture, methyl ethyl ketone (MEK)+water (W)+secondary butyl alcohol (sBA)-a promising system for the realization of the quadruple critical point (QCP). The unusual tunnel-shaped phase diagram shown by this system is characterized and visualized by us in the form of a prismatic phase diagram. Light-scattering experiments reveal that (MEK+W+sBA) shows near three-dimensional-Ising type of critical behavior near the lower critical solution temperatures, with the susceptibility exponent (gamma) in the range of 1.217 <=gamma <= 1.246. The correlation length amplitudes (xi(o)) and the critical exponent (nu) of the correlation length (xi) are in the ranges of 3.536 <=xi(o)<= 4.611 A and 0.619 <=nu <= 0.633, respectively. An analysis in terms of the effective susceptibility exponent (gamma(eff)) shows that the critical behavior is of the Ising type for MEK concentrations in the ranges of 0.1000 <= X <= 0.1250 and X >= 0.3000. But, for the intermediate range of 0.1750 <= X < 0.3000, the system shows a tendency towards mean-field type of critical behavior. The advantages of the system (MEK+W+sBA) over the system (3-methylpyridine+water+heavy water+potassium Iodide) for the realization of a QCP are outlined.

Splittings of free groups, normal forms and partitions of ends

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x S (1). These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in pi (2)(M) can be represented by an embedded sphere.

Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.

Electron Donor-Acceptor Complexes of the Fullerenes C60 and C70 with Amines

Based on electronic absorption spectroscopy, C60 is found to form complexes with aromatic amines with an enthalpy of association in the range 9-16 kJ mol-1. Interaction of C70 with the amines is negligible. Cyclic voltammetric measurements confirm these observations.

DNA Compaction by a Dendrimer

At physiological pH, a PAMAM dendrimer is positively charged and can effectively bind negatively charged DNA. Currently, there has been great interest in understanding this complexation reaction both for fundamental (as a model for complex biological reactions) as well as for practical (as a gene delivery material and probe for sensing DNA sequence) reasons. Here, we have studied the complexation between double-stranded DNA (dsDNA) and various generations of PAMAM dendrimers (G3-05) through atomistic molecular dynamics simulations in the presence of water and ions. We report the compaction of DNA on a nanosecond time scale. This is remarkable, given the fact that such a short DNA duplex with a length close to 13 nm is otherwise thought to be a rigid rod. Using several nanoseconds long MD simulations, we have observed various binding modes of dsDNA and dendrimers for various generations of PAMAM dendrimers at varying charge ratios, and it confirms some of the binding modes proposed earlier. The binding is driven by the electrostatic interaction, and the larger the dendrimer charge, the stronger the binding affinity. As DNA wraps/binds to the dendrimer, counterions originally condensed onto DNA (Na+) and the dendrimer (Cl-) get released. We calculate the entropy of counterions and show that there is gain in entropy due to counterion release during the complexation. MD simulations demonstrate that, when the charge ratio is greater than 1 (as in the case of the G5 dendrimer), the optimal wrapping of DNA is observed. Calculated binding energies of the complexation follow the trend G5 > 04 > 03, in accordance with the experimental data. For a lower-generation dendrimer, such as G3, and, to some extent, for G4 also, we see considerable deformation in the dendrimer structure due to their flexible nature. We have also calculated the various helicoidal parameters of DNA to study the effect of dendrimer binding on the structure of DNA. The B form of the DNA is well preserved in the complex, as is evident from various helical parameters, justifying the use of the PAMAM dendrimer as a suitable delivery vehicle.

Surface acoustic wave distribution and acousto-optic interaction in proton exchanged LiNbO3 waveguides

The efficiency of acoustooptic (AO) interaction in YZ-cut proton exchanged (PE) LiNbO3 waveguides is theoretically analysed by determining the overlap between the optical and acoustic field distributions. The present analysis takes into account the perturbed SAW field distribution due to the presence of the PE layer on the LiNbO3 substrate determined by the rigorous layered medium approach. The overlap is found to be significant upto very high acoustic frequencies of the order of 5 GHz, whereas in the earlier analysis by vonHelmolt and Schaffer [6] for diffused waveguides, it was shown that the overlap integral rolls down to nearly zero at this high frequency range.

Data compression by linear prediction for storage and transmission of EEG signals

The EEG time series has been subjected to various formalisms of analysis to extract meaningful information regarding the underlying neural events. In this paper the linear prediction (LP) method has been used for analysis and presentation of spectral array data for the better visualisation of background EEG activity. It has also been used for signal generation, efficient data storage and transmission of EEG. The LP method is compared with the standard Fourier method of compressed spectral array (CSA) of the multichannel EEG data. The autocorrelation autoregressive (AR) technique is used for obtaining the LP coefficients with a model order of 15. While the Fourier method reduces the data only by half, the LP method just requires the storage of signal variance and LP coefficients. The signal generated using white Gaussian noise as the input to the LP filter has a high correlation coefficient of 0.97 with that of original signal, thus making LP as a useful tool for storage and transmission of EEG. The biological significance of Fourier method and the LP method in respect to the microstructure of neuronal events in the generation of EEG is discussed.

Rectilinear Path Following in 3D Space

This paper addresses the problem of determining an optimal (shortest) path in three dimensional space for a constant speed and turn-rate constrained aerial vehicle, that would enable the vehicle to converge to a rectilinear path, starting from any arbitrary initial position and orientation. Based on 3D geometry, we propose an optimal and also a suboptimal path planning approach. Unlike the existing numerical methods which are computationally intensive, this optimal geometrical method generates an optimal solution in lesser time. The suboptimal solution approach is comparatively more efficient and gives a solution that is very close to the optimal one. Due to its simplicity and low computational requirements this approach can be implemented on an aerial vehicle with constrained turn radius to reach a straight line with a prescribed orientation as required in several applications. But, if the distance between the initial point and the straight line to be followed along the vertical axis is high, then the generated path may not be flyable for an aerial vehicle with limited range of flight path angle and we resort to a numerical method for obtaining the optimal solution. The numerical method used here for simulation is based on multiple shooting and is found to be comparatively more efficient than other methods for solving such two point boundary value problem.

Kinematics of the Cometary Globules in the Gum Nebula

We report a study of the kinematics of the cometary globules in the Gum Nebula using the J = 1 yields 0 transition line of (CO-12)O. A morphological center for the system with which 60 percent of the globules are associated is identified. It is shown that the observed radial velocities of the heads of the globules are consistent with an expansion of the system. Systematic velocity gradients are present along some of the tails. The estimated expansion age and the tail stretching age are both about a few million years, suggesting a common origin for the expansion and the formation of the tails. The presence of young stars of similar ages in some of the globules points to star formation triggered by the same cause. Possible scenarios are briefly discussed.