Experimental analysis of thermo-physical processes in acoustically levitated heated droplets

An experimental setup using radiative heating has been used to understand the thermo-physical phenomena and chemical transformations inside acoustically levitated cerium nitrate precursor droplets. In this transformation process, through infrared thermography and high speed imaging, events such as vaporization, precipitation and chemical reaction have been recorded at high temporal resolution, leading to nanoceria formation with a porous morphology. The cerium nitrate droplet undergoes phase and shape changes throughout the vaporization process. Four distinct stages were delineated during the entire vaporization process namely pure evaporation, evaporation with precipitate formation, chemical reaction with phase change and formation of final porous precipitate. The composition was examined using scanning and transmission electron microscopy that revealed nanostructures and confirmed highly porous morphology with trapped gas pockets. Transmission electron microscopy (TEM) and high speed imaging of the final precipitate revealed the presence of trapped gases in the form of bubbles. TEM also showed the presence of nanoceria crystalline structures at 70 degrees C. The current study also looked into the effect of different heating powers on the process. At higher power, each phase is sustained for smaller duration and higher maximum temperature. In addition, the porosity of the final precipitate increased with power. A non-dimensional time scale is proposed to correlate the effect of laser intensity and vaporization rate of the solvent (water). The effect of acoustic levitation was also studied. Due to acoustic streaming, the solute selectively gets transported to the bottom portion of the droplet due to strong circulation, providing it rigidity and allows it become bowl shaped. (C) 2010 Elsevier Ltd. All rights reserved.

Descriptions of operators in quantum mechanics

The problem of expressing a general dynamical variable in quantum mechanics as a function of a primitive set of operators is studied from several points of view. In the context of the Heisenberg commutation relation, the Weyl representation for operators and a new Fourier-Mellin representation are related to the Heisenberg group and the groupSL(2,R) respectively. The description of unitary transformations via generating functions is analysed in detail. The relation between functions and ordered functions of noncommuting operators is discussed, and results closely paralleling classical results are obtained.

Minimal three-component SU(2) gadget for polarization optics

Two identities involving quarter-wave plates and half-wave plates are established. These are used to improve on an earlier gadget involving four wave plates leading to a new gadget involving just three plates, a half-wave plate and two quarter-wave plates, which can realize all SU(2) polarization transformations. This gadget is shown to involve the minimum number of quarter-wave and half-wave plates. The analysis leads to a decomposition theorem for SU (2) matrices in terms of factors which are symmetric fourth and eighth roots of the identity.

Effect of altering endogenous gonadotrophin concentrations on the kinetics of testicular germ cell turnover in the bonnet monkey (Macaca radiata)

The role of FSH and diurnal testosterone rhythms in specific germ cell transformations during spermatogenesis were investigated using DNA flow cytometry and morphometry of the seminiferous epithelium of the adult male bonnet monkey (Macaca radiata), the endogenous hormone levels of which were altered by two different protocols. (1) Active immunization of five monkeys for 290 days using ovine FSH adsorbed on Alhydrogel resulted in the neutralization of endogenous FSH, leaving the LH and diurnal testosterone rhythms normal. (2) Desensitization of the pituitary gonadotrophs of ten monkeys by chronically infusing gonadotrophin-releasing hormone analogue, buserelin (50 micrograms/day release rate), via an Alzet pump implant (s.c.) led to a 60-80% reduction in LH and FSH as well as total abolition of testosterone rhythms. The basal testosterone level (3.3 +/- 2.0 micrograms/l), however, was maintained in this group by way of an s.c. testosterone silicone elastomer implant. Both of the treatments caused significant (P < 0.01) nearly identical reduction in testicular biopsy scores, mitotic indices and daily sperm production rates compared with respective controls. The germ cell DNA flow cytometric profiles of the two treatment groups, however, were fundamentally different from each other. The pituitary-desensitized group exhibited a significant (P < 0.001) increase in 2C (spermatogonial) and decrease in 1C (round spermatid) populations while S-phase (preleptotene spermatocytes) and 4C (primary spermatocytes) populations were normal, indicating an arrest in meiosis caused presumably by the lack of increment in nocturnal serum testosterone. In contrast, in the FSH-immunized group, at day 80 when the FSH deprivation was total, the primary block appeared to be at the conversion of spermatogonia (2C) to cells in S-phase and primary spermatocytes (4C reduced by > 90%). In addition, at this time, although the round spermatid (1C) population was reduced by 65% (P < 0.01) the elongate spermatid (HC) population showed an increase of 52% (P < 0.05). This, taken together with the fact that sperm output in the ejaculate is reduced by 80%, suggests a blockade in spermiogenesis and spermiation. Administration of booster injections of oFSH at time-points at which the antibody titre was markedly low (at days 84 and 180) resulted in a transient resurgence in spermatogenesis (at day 180 and 228), and this again was blocked by day 290 when the FSH antibody titre increased.

Formal total synthesis of (+)-didemniserinolipid B

The formal total synthesis of (+)-didemniserinolipid B, a marine tunicate possessing a 6,8-dioxabicyclo3.2.1]octane framework, was accomplished starting from L-(+)-tartaric acid. The key transformations in the synthesis include the elaboration of a gamma-hydroxy-amide readily obtained by desymmetrization of tartaric acid bis-amide via the controlled addition of a Grignard reagent followed by stereoselective reduction of the resulting ketone. (C) 2010 Elsevier Ltd. All rights reserved.

Experimental Test of the Quantum No-Hiding Theorem

The no-hiding theorem says that if any physical process leads to bleaching of quantum information from the original system, then it must reside in the rest of the Universe with no information being hidden in the correlation between these two subsystems. Here, we report an experimental test of the no-hiding theorem with the technique of nuclear magnetic resonance. We use the quantum state randomization of a qubit as one example of the bleaching process and show that the missing information can be fully recovered up to local unitary transformations in the ancilla qubits.

Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.

Characterization of lysozyme crystals with unusually low solvent content

Studies on the low-humidity (88%) forms of tetragonal and monoclinic lysozyme, resulting from water-mediated transformations, have provided a wealth of information on the variability in protein hydration, its structural consequences and the water structure associated with proteins, in addition to facilitating the delineation of the rigid and the flexible regions in the protein molecule and the invariant features in its hydration shell. Surprisingly, monoclinic lysozyme continues to diffract even when the environmental humidity is drastically reduced, thus permitting the structural study of the enzyme at different levels of hydration. As part of a study in this direction, three very low humidity forms, two of them occuring at a nominal relative humidity of 38% and the other at 5% relative humidity, have been characterized. These have unprecedented low solvent contents of 16.9, 17.6 and 9.4%, respectively, as determined by the Matthews method.

Photochemistry of benzylidene-d,l-piperitones in solution and the melt phase

The solution- and melt-phase photochemistry of four trans-benzylidene-d,l-piperitones (1) has been investigated under a variety of conditions. The 1 undergo trans reversible cis isomerization to establish a quasi photostationary state. Further irradiation leads to 2 via oxidative ring closure. Conspicuously absent are dimers (obtained upon irradiation of the neat crystals) and the plausible Norrish Type II photoproducts, 3. Although 1c yields 2c, no evidence for the alternative cyclization route to 2a (requiring loss of HCl) has been observed. Rationalizations for the transformations are presented. The structure of 2b has been determined unambiguously from X-ray crystallographic analysis.

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.

Stability analysis of stochastically parametered nonconservative columns

Nonconservatively loaded columns. which have stochastically distributed material property values and stochastic loadings in space are considered. Young's modulus and mass density are treated to constitute random fields. The support stiffness coefficient and tip follower load are considered to be random variables. The fluctuations of external and distributed loadings are considered to constitute a random field. The variational formulation is adopted to get the differential equation and boundary conditions. The non self-adjoint operators are used at the boundary of the regularity domain. The statistics of vibration frequencies and modes are obtained using the standard perturbation method, by treating the fluctuations to be stochastic perturbations. Linear dependence of vibration and stability parameters over property value fluctuations and loading fluctuations are assumed. Bounds for the statistics of vibration frequencies are obtained. The critical load is first evaluated for the averaged problem and the corresponding eigenvalue statistics are sought. Then, the frequency equation is employed to transform the eigenvalue statistics to critical load statistics. Specialization of the general procedure to Beck, Leipholz and Pfluger columns is carried out. For Pfluger column, nonlinear transformations are avoided by directly expressing the critical load statistics in terms of input variable statistics.

Electron microscopy and diffraction of ordering in Ni---W alloys

Electron microscopy and diffraction studies of ordering in stoichiometric Ni-20%W and off-stoichiometric Ni-15%W alloys have been carried out. The specimens of Ni-20%W were first disordered at 1398 K for 4 h and then quenched rapidly into water. Short range order (SRO) spots were observed at {1 1/2 0}* positions. Two hitherto unknown metastable phases: D-2h(25)-Ni2W and DO22-Ni3W were observed in the diffraction patterns. Long range order (LRO) transformations were studied at 1103 and 1213 K. Kinetics and mechanism of transformations have been identified. Ni-15%W specimens were solution treated at 1523 K for 1 h followed by quenching in water. SRO spots similar to those found in Ni-20%W were observed in this alloy as well. The transition to LRO was studied at 1093 K. Distinct Ni4W precipitates could be observed after 5 h of annealing at this temperature. After 100 h of annealing precipitates were found to grow into faceted shape coherent with the disordered matrix. After prolonged annealing for over 150 h the Ni4W precipitates began to lose coherency by the generation of misfit dislocations. The microstructural observations have been compared for the stoichiometric and off-stoichiometric alloys.

On the decomposition of ? phase in some rapidly quenched titanium-eutectoid alloys

The decomposition of the beta phase in rapidly quenched Ti-2.8 at. pet Co, Ti-5.4 at. pet Ni, Ti-4.5 at. pet, and 5.5 at. pet Cu alloys has been investigated by electron microscopy. During rapid quenching, two competitive phase transformations, namely martensitic and eutectoid transformation, have occurred, and the region of eutectoid transformation is extended due to the high cooling rates involved. The beta phase decomposed into nonlamellar eutectoid product (bainite) having a globular morphology in Ti-2.8 pet Co and Ti-4.5 pet Cu (hypoeutectoid) alloys. In the near-eutectoid Ti-5.5 pet Cu alloy, the decomposition occurred by a lamellar (pearlite) type, whereas in Ti-5.4 pct Ni (hypereutectoid), both morphologies were observed. The interfaces between the proeutectoid alpha and the intermetallic compound in the nonlamellar type as well as between the proeutectoid alpha and the pearlite were often found to be partially coherent. These findings are in agreement with the Lee and Aaronson model proposed recently for the evolution of bainite and pearlite structures during the solid-state transformations of some titanium-eutectoid alloys. The evolution of the Ti2Cu phase during rapid quenching involved the formation of a metastable phase closely related to an ''omega-type'' phase before the equilibrium phase formed. Further, the lamellar intermetallic compound Ti2Cu was found to evolve by a sympathetic nucleation process. Evidence is established for the sympathetic nucleation of the proeutectoid alpha crystals formed during rapid quenching.

Plate-shaped transformation products in zirconium-base alloys

Plate-shaped products resulting from martensitic, diffusional, and mixed mode transformations in zirconium-base alloys are compared. in the present study. These alloys are particularly suitable for the comparison in view of the fact that the lattice correspondence between the parent beta (bcc) and the product alpha (hcp) or gamma-hydride (fct) phases are remarkably similar for different types of transformations. Crystallographic features such as orientation relations, habit planes, and interface structures associated with these transformations have been compared:, with a view toward examining whether the transformation mechanisms have characteristic imprints on these experimental observables. Martensites exhibiting dislocated lath, internally twinned plate, and self-accommodating three-plate cluster morphologies have been encountered in Zr-2.5Nb alloy. Habit planes corresponding to all these morphologies have been found to be consistent with the predictions based on the invariant plane strain (IFS) criterion. Different morphologies have been found to reflect the manner in which the neighboring martensite variants are assembled. Lattice-invariant shears (LISs) for all these cases have been identified to be either {10 (1) over bar 1}(alpha) ((1) over bar 123)(alpha) slip or twinning on (10 (1) over bar 1)(alpha) planes. Widmanstatten alpha precipitates, forming in a step-quenching treatment, have been shown to have a lath morphology, the alpha/beta interface being decorated with a periodic array of (c + a) dislocations at a spacing of 8 to 10 nm. The line vectors of these dislocations are nearly parallel to the invariant lines. The alpha precipitates, forming in the retained beta phase on aging, exhibit an internally twinned structure with a zigzag habit plane. Average habit planes for the morphologies have been found to lie near the {103}(beta) - {113}(beta) poles, which are close to the specific variant of the {112}(beta) plane, which transforms into a prismatic plane of the type {1 (1) over bar 00}(alpha). The crystallography of the formation of the gamma-hydride phase (fct) from both the alpha and beta phases is seen to match the IFS predictions. While the beta-gamma transformation can be treated approximately as a simple shear on the basal plane involving a change in the stacking sequence, the alpha-gamma transformation call be conceptually broken into a alpha --> beta transformation following the Burgers correspondence and the simple beta-gamma shear process. The active eutectoid decomposition in the Zr-Cu system, beta --> alpha + beta', has been described in terms of cooperative growth of the alpha phase from the beta phase through the Burgers correspondence and of the partially ordered beta' (structurally similar to the equilibrium Zr2Cu phase) through an ordering process. Similarities and differences in crystallographic features of these transformations have been discussed. and the importance of the invariant line vector in deciding the geometry of the corresponding habit planes has been pointed out.

Similarity solution of unsteady boundary layer equations with a magnetic field

The unsteady laminar incompressible boundary layer flow of an electrically conducting fluid in the stagnation region of two-dimensional and axisymmetric bodies with an applied magnetic field has been studied. The boundary layer equations which are parabolic partial differential equations with three independent variables have been reduced to a system of ordinary differential equations by using suitable transformations and then solved numerically using a shooting method. Here, we have obtained new solutions which are solutions of both the boundary layer and Navier-Stokes equations.