Construction of Stability Multipliers with Prescribed Phase Characteristics: an Improved Value for $\sigma

For a feedback system consisting of a transfer function $G(s)$ in the forward path and a time-varying gain $n(t)(0 \leqq n(t) \leqq k)$ in the feedback loop, a stability multiplier $Z(s)$ has been constructed (and used to prove stability) by Freedman [2] such that $Z(s)(G(s) + {1 / K})$ and $Z(s - \sigma )(0 < \sigma < \sigma _ * )$ are strictly positive real, where $\sigma _ * $ can be computed from a knowledge of the phase-angle characteristic of $G(i\omega ) + {1 / k}$ and the time-varying gain $n(t)$ is restricted by $\sigma _ * $ by means of an integral inequality. In this note it is shown that an improved value for $\sigma _ * $ is possible by making some modifications in his derivation. ©1973 Society for Industrial and Applied Mathematics.

Kinetics of vapour phase oxidation of furfural on vanadium catalyst

Vapour phase oxidation of furfural over vanadium pentoxide catalyst was studied using an isothermal flow reactor in the temperature range of 220–280°C. Maleic anhydride and carbon dioxide are found to be formed from furfural by a parallel reaction scheme. The following rate equation based on the two-stage redox mechanism—the substance to be oxidized reduces the catalyst which in turn is reoxidized by oxygen from the feed—is found to explain the data satisfactorily. The reoxidation of the reduced catalyst was found to be the rate controlling step.

Mechanism of vapour phase oxidation of anthracene over cobalt molybdate catalyst

Vapour phase oxidation of anthracene over cobalt molybdate catalyst was investigated in an isothermal flow reactor in the temperature range of 280—340°C. Fifteen different models based on redox, Langmuir—Hinshelwood and Rideal mechanisms were tested in order to elucidate the mechanism of the above reaction. These models were compared on the basis of three criteria and were finally discriminated employing the non-intrinsic parameter method. Two-stage redox mechanism was found to explain the data satisfactorily.

Separation β-apocarotenals and related compounds by reversed-phase paper and thin-layer chromatography

Abstract is not available.

Condensed phase reactions in solid propellants

The paper investigates the cause for the difference between differential scanning calorimetric results and mass spectrometric studies on polystyrene (PS) ammonium perchlorate (AP) propellants as related to the method of preparation of the propellant and the difference in experimental conditions by the use of mass spectrometry. Sufficient time is given for the product sublimates to interact with each other and attain equilibrium. It is shown that the propellant decomposition is a nonadditive phenomenon and that even a physical mixture of AP and PS does not yield additive decomposition products of its components. Results on the identification of a yellow compound containing chlorine in the bulk of the propellant suggest a condensed phase reaction. The occurrence of the reaction in the porous condensed phase of the propellant may explain the larger exothermicity of the propellant compared to the additive heats of decomposition of its components.

Possibility of a condensed phase of excitons because of phonon induced exciton-exciton pairing

In this paper we study the phonon-induced exciton-exciton interaction. It is found that the interaction can be attractive under certain conditions. Taking into account this attractive interaction, the pairing of excitons with opposite momenta is studied and the excitation spectrum determined. The results are similar to a system of bosons. There appears to be some possibility of superfluid behaviour.

Two-dimensional heat conduction with phase change in a semi-infinite mould

Analytical solution of a 2-dimensional problem of solidification of a superheated liquid in a semi-infinite mould has been studied in this paper. On the boundary, the prescribed temperature is such that the solidification starts simultaneously at all points of the boundary. Results are also given for the 2-dimensional ablation problem. The solution of the heat conduction equation has been obtained in terms of multiple Laplace integrals involving suitable unknown fictitious initial temperatures. These fictitious initial temperatures have interesting physical interpretations. By choosing suitable series expansions for fictitious initial temperatures and moving interface boundary, the unknown quantities can be determined. Solidification thickness has been calculated for short time and effect of parameters on the solidification thickness has been shown with the help of graphs.

Transcriptional events during early phase of germination of rice embryos

GERMINATION transfers a metabolically inert embryo into an active state of growth and development. The presence of conserved mRNAs has been demonstrated in different species of eggs and seeds1–4. In rice embryos, germination was shown to be independent of the synthesis of RNA up to 18–24 h after the start of imbibition5, although RNA synthesis was detected as early as 9 h after the start of imbibition. In this report, the sequence of the transcriptional events taking place during the early phase of the germination of rice embryos are presented.

Monte Carlo simulation of Ising chains showing several phase transitions

A Monte Carlo simulation of Ising chains with competing short-range and infiniterange interactions has been carried out. Results show that whenever the system does not enter a metastable state, variation of temperature brings about phase transitions in the Ising chain. These phase transitions, except for two sets of interaction strengths, are generally of higher order and involve changes in the long-range order while the short-range order remains unaffected.

Liquid phase hydrogenation of aniline in a trickle bed reactor

A rate equation is developed for the liquid phase hydrogenation of aniline over cylindrical catalyst pellets of 30% nickel deposited on clay in a trickle bed reactor. The equation takes into account external and internal diffusional limitations, and describes the experimental data adequately. The hydrogenation reaction is first order with respect to hydrogen and zero order with respect to aniline. Effectiveness factors are in the range 0.003-0.03. Apparent activation energy of the reaction is 12.7 kcal/mol and true activation energy is 39.6 kcal/mol.

Harmonic response of a shock mount employing dual-phase damping

In this note, the application of dual-phase damping to a simple shock mount experiencing a harmonic input is described. The damping ratio is a function of the relative displacement between the foundation and the mounted mass. The purpose of employing such a damping is to reduce the absolute transmissibility over the whole frequency range.

Synthesis of wurtzite-phase ZnS nanocrystal and its optical properties

The wurtzite phase of ZnS nanocrystal has been prepared by annealing in 200-600 degrees C temperature range, its cubic phase of 2-3 nm size. prepared through soft chemical method. Results of isochronal experiments of 2 h at different temperatures indicate that visible transformation to wurtzite from cubic ZnS appears at a temperature of 400 degrees C, which is about three times smaller than that of bulk ZnS phase transition temperature. The phases, nanostructures, and optical absorption characteristics are obtained through X-ray diffraction. transmission electron microscopy, and UV-visible absorption spectroscopy. A stable and green photoluminescence emission peaked at 518 nm is observed from the 600 degrees C annealed samples, under ultraviolet light excitation.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Kinetics of oxidation of pseudocumene in the vapor phase

The kinetics of pseudocumene oxidation in the vapor phase with tin vanadate as catalyst have been studied over the following ranges of the variables: Oxygen concentration, 0.909 to 2.857 mole/m3; pseudocumene concentration, 0.071 to 0.125 mole/m3; temperature, 260 to 320°C; space time, 22.5 to 90 × 104 g. catalyst/mole sec. Oxidation-reduction models have been found to describe the kinetics adequately. The mechanism is found to remain the same throughout the temperature range covered.

Vapor phase oxidation of ethanol over thorium molybdate catalyst

Ethanol oxidation in the vapor phase was studied in an isothermal flow reactor using thorium molybdate catalyst in the temperature range 220–280 °C. Under these conditions the catalyst was highly selective to acetaldehyde formation. The rate data were well represented by a steady state two-stage redox model given by the equation: View the MathML source The parameters of the above model were estimated by linear and nonlinear least squares methods. In the case of nonlinear estimation the sum of the squares of residuals decreased. The activation energies and preexponential factors for the reduction and oxidation steps of the model, estimated by nonlinear least squares technique are: 9.47 kcal/mole, 9.31 g mole/ (sec) (g cat) (atm) and 9.85 kcal/mole, 0.17 g mole/(sec) (g cat) (atm)0.5, respectively. Oxidations of ethanol and methanol over thorium molybdate catalyst were compared under similar conditions.