Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Long-lived giant number fluctuations in a swarming granular nematic

Coherently moving flocks of birds, beasts, or bacteria are examples of living matter with spontaneous orientational order. How do these systems differ from thermal equilibrium systems with such liquid crystalline order? Working with a fluidized monolayer of macroscopic rods in the nematic liquid crystalline phase, we find giant number fluctuations consistent with a standard deviation growing linearly with the mean, in contrast to any situation where the central limit theorem applies. These fluctuations are long-lived, decaying only as a logarithmic function of time. This shows that flocking, coherent motion, and large-scale inhomogeneity can appear in a system in which particles do not communicate except by contact.

3-Benzyl-6-benzylamino-1-methyl-5-nitro-1,2,3,4-tetrahydropyrimidine

In the title compound, C19H22N4O2, the tetrahydropyrimidine ring adopts an envelope conformation (with the N atom connected to the benzyl group representing the flap). This benzyl group occupies a quasi-axial position. The two benzyl groups lie over the tetrahydropyridimidine ring. The amino group is a hydrogen-bond donor to the nitro group.

Formation of ω-Al7Cu2Fe phase during laser processing of quasicrystal-forming Al-Cu-Fe alloy

The formation of an ω-Al7Cu2Fe phase during laser cladding of quasicrystal-forming Al65Cu23.3Fe11.7 alloy on a pure aluminium substrate is reported. This phase is found to nucleate at the periphery of primary icosahedral-phase particles. A large number of ω-phase particles form an envelope around the icosahedral phase. On the outer side, they form an interface with an agr-Al solid solution. Detailed transmission electron microscopic observations show that the ω phase exhibits an orientation relationship with the icosahedral phase. Analysis of experimental results suggests that the ω phase forms by precipitation on an icosahedral phase by heterogeneous nucleation and grows into the aluminium-rich melt until supersaturation is exhausted. The microstructural observations are explained in terms of available models of phase transformations.

Influence of surfactant and annealing temperature on optical properties of sol-gel derived nano-crystalline TiO2 thin films

Titanium dioxide thin films have been synthesized by sol-gel spin coating technique on glass and silicon substrates with and without surfactant polyethylene glycol (PEG). XRD and SEM results confirm the presence of nano-crystalline (anatase) phase at an annealing temperature of 300 degrees C. The influence of surfactant and annealing temperature on optical properties of TiO2 thin films has been studied. Optical constants and film thickness were estimated by Swanepoel's (envelope) method and by ellipsometric measurements in the visible spectral range. The optical transmittance and reflectance were found to decrease with an increase in PEG percentage. Refractive index of the films decreased and film thickness increased with the increase in percentage of surfactant. The refractive index of the un-doped TiO2 films was estimated at different annealing temperatures and it has increased with the increasing annealing temperature. The optical band gap of pure TiO2 films was estimated by Tauc's method at different annealing temperature. (C) 2010 Elsevier B.V. All rights reserved.

Structural Ordering of Disordered Ligand-Binding Loops of Biotin Protein Ligase into Active Conformations as a Consequence of Dehydration

Mycobacterium tuberculosis (Mtb), a dreaded pathogen, has a unique cell envelope composed of high fatty acid content that plays a crucial role in its pathogenesis. Acetyl Coenzyme A Carboxylase (ACC), an important enzyme that catalyzes the first reaction of fatty acid biosynthesis, is biotinylated by biotin acetyl-CoA carboxylase ligase (BirA). The ligand-binding loops in all known apo BirAs to date are disordered and attain an ordered structure only after undergoing a conformational change upon ligand-binding. Here, we report that dehydration of Mtb-BirA crystals traps both the apo and active conformations in its asymmetric unit, and for the first time provides structural evidence of such transformation. Recombinant Mtb-BirA was crystallized at room temperature, and diffraction data was collected at 295 K as well as at 120 K. Transfer of crystals to paraffin and paratone-N oil (cryoprotectants) prior to flash-freezing induced lattice shrinkage and enhancement in the resolution of the X-ray diffraction data. Intriguingly, the crystal lattice rearrangement due to shrinkage in the dehydrated Mtb-BirA crystals ensued structural order of otherwise flexible ligand-binding loops L4 and L8 in apo BirA. In addition, crystal dehydration resulted in a shift of similar to 3.5 angstrom in the flexible loop L6, a proline-rich loop unique to Mtb complex as well as around the L11 region. The shift in loop L11 in the C-terminal domain on dehydration emulates the action responsible for the complex formation with its protein ligand biotin carboxyl carrier protein (BCCP) domain of ACCA3. This is contrary to the involvement of loop L14 observed in Pyrococcus horikoshii BirA-BCCP complex. Another interesting feature that emerges from this dehydrated structure is that the two subunits A and B, though related by a noncrystallographic twofold symmetry, assemble into an asymmetric dimer representing the ligand-bound and ligand-free states of the protein, respectively. In-depth analyses of the sequence and the structure also provide answers to the reported lower affinities of Mtb-BirA toward ATP and biotin substrates. This dehydrated crystal structure not only provides key leads to the understanding of the structure/function relationships in the protein in the absence of any ligand-bound structure, but also demonstrates the merit of dehydration of crystals as an inimitable technique to have a glance at proteins in action.

L-p Wiener-Tauberian theorems for M(2)

We prove two sided and one sided analogues of the Wiener-Tauberian theorem for the Euclidean motion group, M(2).

On the design of quadratic weirs

This paper considers the problem of the design of the quadratic weir notch, which finds application in the proportionate method of flow measurement in a by-pass, such that the discharge through it is proportional to the square root of the head measured above a certain datum. The weir notch consists of a bottom in the form of a rectangular weir of width 2W and depth a over which a designed curve is fitted. A theorem concerning the flow through compound weirs called the “slope discharge continuity theorem” is discussed and proved. Using this, the problem is reduced to the determination of an exact solution to Volterra's integral equation in Abel's form. It is shown that in the case of a quadratic weir notch, the discharge is proportional to the square root of the head measured above a datum Image a above the crest of the weir. Further, it is observed that the function defining the shape of the weir is rapidly convergent and its value almost approximates to zero at distances of 3a and above from the crest of the weir. This interesting and significant behaviour of the function incidentally provides a very good approximate solution to a particular Fredholm integral equation of the first kind, transforming the notch into a device called a “proportional-orifice”. A new concept of a “notch-orifice” capable of passing a discharge proportional to the square root of the head (above a particular datum) while acting both as a notch, and as an orifice, is given. A typical experiment with one such notch-orifice, having A = 4 in., and W = 6 in., shows a remarkable agreement with the theory and is found to have a constant coefficient of discharge of 0.61 in the ranges of both notch and orifice.

Note on the locally product and almost locally product structures

This paper is concerned with a study of some of the properties of locally product and almost locally product structures on a differentiable manifold X n of class C k . Every locally product space has certain almost locally product structures which transform the local tangent space to X n at an arbitrary point P in a set fashion: this is studied in Theorem (2.2). Theorem (2.3) considers the nature of transformations that exist between two co-ordinate systems at a point whenever an almost locally product structure has the same local representation in each of these co-ordinate systems. A necessary and sufficient condition for X n to be a locally product manifold is obtained in terms of the pseudo-group of co-ordinate transformations on X n and the subpseudo-groups [cf., Theoren (2.1)]. Section 3 is entirely devoted to the study of integrable almost locally product structures.

Reciprocity relation in scattering by media subjected to an external magnetic field

Krishnan's reciprocity theorem in colloid optics, ρ{variant}u=1+l/ρ{variant}h/1+1/ρ{variant}v is generalised for the case when the scattering medium is subjected to an external orienting field. It is shown theoretically that a general relation of the type IBA=I′AB results in this case, where IBA is the intensity of the component of the scattered light having its electric vector inclined at an angle B to the vertical with the incident light polarised at an angle A to the vertical, the external field direction being parallel to the incident beam. I′AB is the corresponding intensity with the magnetic field parallel of the scattered ray. Experimental verification of the above generalisation is also given.

A fast time-domain algorithm for the assessment of tissue blood flow in laser-Doppler flowmetry

In this study, we derive a fast, novel time-domain algorithm to compute the nth-order moment of the power spectral density of the photoelectric current as measured in laser-Doppler flowmetry (LDF). It is well established that in the LDF literature these moments are closely related to fundamental physiological parameters, i.e. concentration of moving erythrocytes and blood flow. In particular, we take advantage of the link between moments in the Fourier domain and fractional derivatives in the temporal domain. Using Parseval's theorem, we establish an exact analytical equivalence between the time-domain expression and the conventional frequency-domain counterpart. Moreover, we demonstrate the appropriateness of estimating the zeroth-, first- and second-order moments using Monte Carlo simulations. Finally, we briefly discuss the feasibility of implementing the proposed algorithm in hardware.

Characterization of viral proteins ofOryctes baculovirus and comparison between two geographical isolates

BacilliformOryctes baculovirus particles have been visualized in electron micrographs of midgut sections from virus infectedOryctes rhinoceros beetles. Morphologically the Indian isolate (Oryctes baculovirus, KI) resembled the previously reportedOryctes baculovirus, isolate PV505. The constituent proteins of baculovirus KI have been analysed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and by Western blots using polyclonal antibodies raised against the complete viral particles, as probes. A total of forty eight viral proteins have been identified. Fourteen viral proteins were located on the viral envelope. Among the proteins constituting the nucleocapsid, three were located internally within the capsid. A 23.5 kDa protein was tightly associated with viral DNA in the nucleocapsid core. Two envelope and seven capsid proteins stained positive for glycosylation. Comparison between the viral proteins of KI and PV505 revealed differences in SDS-PAGE profiles and glycosylation patterns. Immunoblotting of KI and PV505 proteins with anti KI antiserum demonstrated antigenic differences between the two viral isolates.

Robust fixed order lateral H-2 controller for micro air vehicle

This paper presents a robust fixed order H-2 controller design using Strengthened discrete optimal projection equations, which approximate the first order necessary optimality condition. The novelty of this work is the application of the robust H-2 controller to a micro aerial vehicle named Sarika2 developed in house. The controller is designed in discrete domain for the lateral dynamics of Sarika2 in the presence of low frequency atmospheric turbulence (gust) and high frequency sensor noise. The design specification includes simultaneous stabilization, disturbance rejection and noise attenuation over the entire flight envelope of the vehicle. The resulting controller performance is comprehensively analyzed by means of simulation.

Undamped Oscillations of Collisionless Stellar Systems: Spheres,Spheroids and Discs.

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.