A bicharacteristic formulation of the ideal MHD equations

On a characteristic surface Omega of a hyperbolic system of first-order equations in multi-dimensions (x, t), there exits a compatibility condition which is in the form of a transport equation along a bicharacteristic on Omega. This result can be interpreted also as a transport equation along rays of the wavefront Omega(t) in x-space associated with Omega. For a system of quasi-linear equations, the ray equations (which has two distinct parts) and the transport equation form a coupled system of underdetermined equations. As an example of this bicharacteristic formulation, we consider two-dimensional unsteady flow of an ideal magnetohydrodynamics gas with a plane aligned magnetic field. For any mode of propagation in this two-dimensional flow, there are three ray equations: two for the spatial coordinates x and y and one for the ray diffraction. In spite of little longer calculations, the final four equations (three ray equations and one transport equation) for the fast magneto-acoustic wave are simple and elegant and cannot be derived in these simple forms by use of a computer program like REDUCE.

DNA Binding, Coprotease, and Strand Exchange Activities of Mycobacterial RecA Proteins: Implications for Functional Diversity among RecA Nucleoprotein Filaments

One of the fundamental questions concerning homologous recombination is how RecA or its homologues recognize several DNA sequences with high affinity and catalyze all the diverse biological activities. In this study, we show that the extent of single-stranded DNA binding and strand exchange (SE) promoted by mycobacterial RecA proteins with DNA substrates having various degrees of GC content was comparable with that observed for Escherichia coli RecA. However, the rate and extent of SE promoted by these recombinases showed a strong negative correlation with increasing amounts of sequence divergence embedded at random across the length of the donor strand. Conversely, a positive correlation was seen between SE efficiency and the degree of sequence divergence in the recipient duplex DNA. The extent of heteroduplex formation was not significantly affected when both the pairing partners contained various degrees of sequence divergence, although there was a moderate decrease in the case of mycobacterial RecA proteins with substrates containing larger amounts of sequence divergence. Whereas a high GC content had no discernible effect on E. coli RecA coprotease activity, a negative correlation was apparent between mycobacterial RecA proteins and GC content. We further show clear differences in the extent of SE promoted by E. coli and mycobacterial RecA proteins in the presence of a wide range of ATP:ADP ratios. Taken together, our findings disclose the existence of functional diversity among E. coli and mycobacterial RecA nucleoprotein filaments, and the milieu of sequence divergence (i.e., in the donor or recipient) exerts differential effects on heteroduplex formation, which has implications for the emergence of new genetic variants.

Glass Transition in the Density Functional Theory of Freezing

A mean-field description of the glass transition in the hard-sphere system is obtained by numerically locating "glassy" minima of a model free-energy functional. These minima, characterized by inhomogeneous but aperiodic density distributions, appear as the average density is increased above the value at which equilibrium crystallization takes place. Investigations of the density distribution and local bond-orientational order at these minima yield results similar to those obtained from simulations.

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.

A Non-contact measurement technique to measure micro surface stress and obtain deformation profiles of the order of 1nm in Micro-cantilever based structures by single image Optical Diffraction method

A new method based on analysis of a single diffraction pattern is proposed to measure deflections in micro-cantilever (MC) based sensor probes, achieving typical deflection resolutions of 1nm and surface stress changes of 50 mu N/m. The proposed method employs a double MC structure where the deflection of one of the micro-cantilevers relative to the other due to surface stress changes results in a linear shift of intensity maxima of the Fraunhofer diffraction pattern of the transilluminated MC. Measurement of such shifts in the intensity maxima of a particular order along the length of the structure can be done to an accuracy of 0.01mm leading to the proposed sensitivity of deflection measurement in a typical microcantilever. This method can overcome the fundamental measurement sensitivity limit set by diffraction and pointing stability of laser beam in the widely used Optical Beam Deflection method (OBDM).

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.

Orientational Order of Liquid-Crystalline 4-Alkyl-N-(p-cyanophenyl)piperidines by 2H and 13C NMR Spectroscopies

The orientational order of nematic 4-alkyl-N-(4-cyanophenyl) piperidines (I) has been determined from H-2 and C-13 NMR spectra. Molecular-order parameters are derived from the carbon-13 chemical shift of the cyano carbon atom in the nematic and the isotropic phases; the sign of the diamagnetic anisotropy is positive. Deuterium quadrupolar splittings from the partially deuterated piperidine ring of I are then related to various C-D bonds.

FIR system identification based on subspaces of a higher order cumulant matrix

A new linear algebraic approach for identification of a nonminimum phase FIR system of known order using only higher order (>2) cumulants of the output process is proposed. It is first shown that a matrix formed from a set of cumulants of arbitrary order can be expressed as a product of structured matrices. The subspaces of this matrix are then used to obtain the parameters of the FIR system using a set of linear equations. Theoretical analysis and numerical simulation studies are presented to characterize the performance of the proposed methods.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

Crystal structures, dynamics and functional implications of molybdenum-cofactor biosynthesis protein MogA from two thermophilic organisms

Molybdenum-cofactor (Moco) biosynthesis is an evolutionarily conserved pathway in almost all kingdoms of life, including humans. Two proteins, MogA and MoeA, catalyze the last step of this pathway in bacteria, whereas a single two-domain protein carries out catalysis in eukaryotes. Here, three crystal structures of the Moco-biosynthesis protein MogA from the two thermophilic organisms Thermus thermophilus (TtMogA; 1.64 angstrom resolution, space group P2(1)) and Aquifex aeolicus (AaMogA; 1.70 angstrom resolution, space group P2(1) and 1.90 angstrom resolution, space group P1) have been determined. The functional roles and the residues involved in oligomerization of the protein molecules have been identified based on a comparative analysis of these structures with those of homologous proteins. Furthermore, functional roles have been proposed for the N- and C-terminal residues. In addition, a possible protein-protein complex of MogA and MoeA has been proposed and the residues involved in protein-protein interactions are discussed. Several invariant water molecules and those present at the subunit interfaces have been identified and their possible structural and/or functional roles are described in brief. In addition, molecular-dynamics and docking studies with several small molecules (including the substrate and the product) have been carried out in order to estimate their binding affinities towards AaMogA and TtMogA. The results obtained are further compared with those obtained for homologous eukaryotic proteins.

First-order hyperpolarizabilities and pKa of weak organic acids in protic solvents are lineraly related

Second-order nonlinearities (beta) of five weak organic acids in protic solvents have been measured by the double-quantum Rayleigh scattering (DRS) technique. beta is found to bear a linear relationship to the pK(a) of these compounds in those solvents. A direct implication of this observation is that the DRS technique can be used to determine the pK(a) of weak organic acids in any solvent.

Mutations in beta ` subunit of Escherichia coli RNA polymerase perturb the activator polymerase functional interaction required for promoter clearance

P>Transcription activator C employs a unique mechanism to activate mom gene of bacteriophage Mu. The activation process involves, facilitating the recruitment of RNA polymerase (RNAP) by altering the topology of the promoter and enhancing the promoter clearance by reducing the abortive transcription. To understand the basis of this multi-step activation mechanism, we investigated the nature of the physical interaction between C and RNAP during the process. A variety of assays revealed that only DNA-bound C contacts the beta' subunit of RNAP. Consistent to these results, we have also isolated RNAP mutants having mutations in the beta' subunit which were compromised in C-mediated activation. Mutant RNAPs show reduced productive transcription and increased abortive initiation specifically at the C-dependent mom promoter. Positive control (pc) mutants of C, defective in interaction with RNAP, retained the property of recruiting RNAP to the promoter but were unable to enhance promoter clearance. These results strongly suggest that the recruitment of RNAP to the mom promoter does not require physical interaction with C, whereas a contact between the beta' subunit and the activator, and the subsequent allosteric changes in the active site of the enzyme are essential for the enhancement of promoter clearance.

Hidden order in serrated flow of metallic glasses

We report results of statistical and dynamic analysis of the serrated stress-time curves obtained from compressive constant strain-rate tests on two metallic glass samples with different ductility levels in an effort to extract hidden information in the seemingly irregular serrations. Two distinct types of dynamics are detected in these two alloy samples. The stress-strain curve corresponding to the less ductile Zr65Cu15Ni10Al10 alloy is shown to exhibit a finite correlation dimension and a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. In contrast, for the more ductile Cu47.5Zr47.5Al5 alloy, the distributions of stress drop magnitudes and their time durations obey a power-law scaling reminiscent of a self-organized critical state. The exponents also satisfy the scaling relation compatible with self-organized criticality. Possible physical mechanisms contributing to the two distinct dynamic regimes are discussed by drawing on the analogy with the serrated yielding of crystalline samples. The analysis, together with some physical reasoning, suggests that plasticity in the less ductile sample can be attributed to stick-slip of a single shear band, while that of the more ductile sample could be attributed to the simultaneous nucleation of a large number of shear bands and their mutual interactions. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.