The Hamilton-Jacobi equation revisited

A new analysis of the nature of the solutions of the Hamilton-Jacobi equation of classical dynamics is presented based on Caratheodory’s theorem concerning canonical transformations. The special role of a principal set of solutions is stressed, and the existence of analogous results in quantum mechanics is outlined.

Characteristics of Proportional Weirs

A theorem termed the Geometrical Continuity Theorem is enunciated and proven. This theorem throws light on the aspects of the continuity of the proportional portion with the base weir portion. These two portions constitute the profile of a proportional weir. A weir of this type with circular bottom is designed. The theorem is used to establish the continuity at the junction of the proportional and the base weir portions of this weir. The coordinates of the weir profile are obtained by numerical methods and are furnished in tabular form for ready use by designers. The discharge passing through the weir is a linear function of the head. The verification of the assumed linear discharge-head relation is furnished for one of the three weirs with which experiments were conducted. The coefficient of discharge for this typical weir is found to be a constant with a value of 0.59.

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.

The Electronic Structure of Graphite from Compton Profile Measurements

Compton profile data are used to investigate the ground state wavefunction of graphite. The results of two new $\gamma$-ray measurements are reported and compared with the results of earlier $\gamma$-ray and electron scattering measurements. A tight-binding calculation has been carried out and the results of earlier calculations based on a molecular model and a pseudo-potential wavefunction are considered. The analysis, in terms of the reciprocal form factor, shows that none of the calculations gives an adequate description of the data in the basal plane although the pseudo-potential calculation describes the anisotropy in the plane reasonably well. In the basal plane the zero-crossing theorem appears to be violated and this problem must be resolved before more accurate models can be derived. In the c-axis direction the molecular model and the tight binding calculation give better agreement with the experimental data than does the pseudopotential calculation.

Prospects of riboflavin carrier protein (RCP) as an antifertility vaccine in male and female mammals

Riboflavin carrier protein (RCP) is obligatorily involved in yolk deposition of the vitamin, riboflavin, in the developing oocyte of the hen. The production of this protein is inducible by oestrogen. It is evolutionarily conserved in terms of its physicochemical, immunological and functional characteristics. It is the prime mediator of vitamin supply to the developing fetus in mammals, including primates. Passive immunoneutralization of the protein terminates pregnancy in rats. Active immunization of rats and bonnet monkeys with avian RCP prevents pregnancy without causing any adverse physiological effects of the mother in terms of her vitamin status, reproductive cycles or reproductive-endocrine profile. Denatured, linearized RCP is more effective in eliciting neutralizing antibodies capable of interfering with embryonic viability either before or during peri-implantation stages. Two defined stretches of sequential epitopes, one located at the N-terminus and the other at the C-terminus of the protein have been identified. Active immunization with either of these epitopes conjugated with diptheria toxoid curtails pregnancy in rats and monkeys. Immunohistochemical localization of RCP on ovulated oocytes and early embryos shows that the antibodies cause degeneration only of early embryos. RCP is produced intra-testicularly and becomes localized on acrosomal surface of mammalian spermatozoa. Active immunization of male rats and monkeys with denatured RCP markedly reduces fertility by impairing the fertilizing potential of spermatozoa. These findings suggest that RCP, or its defined fragments, could be a novel, first generation vaccine for regulating fertility in both the sexes.

Algebraic Cryptanalysis of CTRU Cryptosystem

CTRU, a public key cryptosystem was proposed by Gaborit, Ohler and Sole. It is analogue of NTRU, the ring of integers replaced by the ring of polynomials $\mathbb{F}_2[T]$ . It attracted attention as the attacks based on either LLL algorithm or the Chinese Remainder Theorem are avoided on it, which is most common on NTRU. In this paper we presents a polynomial-time algorithm that breaks CTRU for all recommended parameter choices that were derived to make CTRU secure against popov normal form attack. The paper shows if we ascertain the constraints for perfect decryption then either plaintext or private key can be achieved by polynomial time linear algebra attack.

Constitutive equation for elevated temperature flow behavior of plain carbon steels using dimensional analysis

Dimensional analysis using π-theorem is applied to the variables associated with plastic deformation. The dimensionless groups thus obtained are then related and rewritten to obtain the constitutive equation. The constants in the constitutive equation are obtained using published flow stress data for carbon steels. The validity of the constitutive equation is tested for steels with up to 1.54 wt%C at temperatures: 850–1200 °C and strain rates: 6 × 10−6–2 × 10−2 s−1. The calculated flow stress agrees favorably with experimental data.

A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test oil a standard rectangular rigid tank partially filled with liquid The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements. and the obtained results are compared with available results in the published literature (C) 2009 Elsevier Inc All rights reserved

Influence of magnetic clusters on electrical and magnetic properties of In1-xMnxSb/GaAs dilute magnetic semiconductor grown by liquid phase epitaxy

In1-xMnxSb films have been grown with different Mn doping concentrations (x = 0.0085, 0.018, 0.029 and 0.04) beyond the equilibrium 14 solubility limit by liquid phase epitaxy. We have studied temperature dependent resistivity, the Hall effect, magnetoresistance and magnetization for all compositions. Saturation in magnetization observed even at room temperature suggests the existence of ferromagnetic clusters in the film which has been verified by scanning electron microscopy studies. The anomalous Hall coefficient is found to be negative. Remnant field present on the surface of the clusters seems to affect the anomalous Hall effect at very low fields (below 350 Gauss). In the zero field resistivity, a variable-range hopping conduction mechanism dominates below 3.5 K for all samples above which activated behavior is predominant. The temperature dependence of the magnetization measurement shows a magnetic ordering below 10 K which is consistent with electrical measurements. (c) 2007 Elsevier Ltd. All rights reserved.

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.

Eddy diffusivity: A single dispersion analysis of high resolution drifters in a tidal shallow estuary

In an estuary, mixing and dispersion resulting from turbulence and small scale fluctuation has strong spatio-temporal variability which cannot be resolved in conventional hydrodynamic models while some models employs parameterizations large water bodies. This paper presents small scale diffusivity estimates from high resolution drifters sampled at 10 Hz for periods of about 4 hours to resolve turbulence and shear diffusivity within a tidal shallow estuary (depth < 3 m). Taylor's diffusion theorem forms the basis of a first order estimate for the diffusivity scale. Diffusivity varied between 0.001 – 0.02 m2/s during the flood tide experiment. The diffusivity showed strong dependence (R2 > 0.9) on the horizontal mean velocity within the channel. Enhanced diffusivity caused by shear dispersion resulting from the interaction of large scale flow with the boundary geometries was observed. Turbulence within the shallow channel showed some similarities with the boundary layer flow which include consistency with slope of 5/3 predicted by Kolmogorov's similarity hypothesis within the inertial subrange. The diffusivities scale locally by 4/3 power law following Okubo's scaling and the length scale scales as 3/2 power law of the time scale. The diffusivity scaling herein suggests that the modelling of small scale mixing within tidal shallow estuaries can be approached from classical turbulence scaling upon identifying pertinent parameters.

Non-Gaussianities and Preheating from N-flation and Magnetogenesis via rotating cosmic string loops

In this thesis we examine multi-field inflationary models of the early Universe. Since non-Gaussianities may allow for the possibility to discriminate between models of inflation, we compute deviations from a Gaussian spectrum of primordial perturbations by extending the delta-N formalism. We use N-flation as a concrete model; our findings show that these models are generically indistinguishable as long as the slow roll approximation is still valid. Besides computing non-Guassinities, we also investigate Preheating after multi-field inflation. Within the framework of N-flation, we find that preheating via parametric resonance is suppressed, an indication that it is the old theory of preheating that is applicable. In addition to studying non-Gaussianities and preheatng in multi-field inflationary models, we study magnetogenesis in the early universe. To this aim, we propose a mechanism to generate primordial magnetic fields via rotating cosmic string loops. Magnetic fields in the micro-Gauss range have been observed in galaxies and clusters, but their origin has remained elusive. We consider a network of strings and find that rotating cosmic string loops, which are continuously produced in such networks, are viable candidates for magnetogenesis with relevant strength and length scales, provided we use a high string tension and an efficient dynamo.

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).

Gonadotropin inhibitory substances

A FSH inhibitor from the urine of bonnet monkeys has been isolated and some of its physicochemical, biological, and immunochemical properties have been described. One of the likely sources of the inhibitor in the monkey seems to be the kidney. This inhibitor has been used in delineating the role of FSH in follicular development in the ovary of the female rat. A method has been described for isolating human LH inhibitor in a fairly pure state.