Discrete scale invariance in viscous fingering patterns

We study viscous fingering patterns in a lifting Hele-Shaw cell, where a non-Newtonian fluid (oil paint) is displaced by air. The lengths of the air fingers are measured and their cumulative distribution is seen to follow a power law with log-periodic oscillations indicating the presence of discrete scale invariance. Received 21 May 1999     

Heat transfer for boundary layers with cross flow

An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.     

Generalizations of the Hermite–Biehler theorem: the complex case

The Hermite–Biehler theorem gives necessary and sufficient conditions for the Hurwitz stability of a polynomial in terms of certain interlacing conditions. In this paper, we extend our earlier generalization of the Hermite–Biehler theorem for real, not necessarily Hurwitz polynomials to the domain of polynomials with complex coefficients. This result, which is of interest in its own right, can also be used to analytically solve an important stabilization problem in control theory.     

Discussion on a possible neutrino detector located in India

We have identified some important and worthwhile physics opportunities with a possible neutrino detector located in India. Particular emphasis is placed on the geographical advantage with a stress on the complimentary aspects with respect to other neutrino detectors already in operation.     

Wilson–Sommerfeld quantization rule revisited

A fresh look at the origin of the Wilson–Sommerfeld quantization rule has been pursued to gain new insight. The rule is shown to provide states that satisfy several well‐known theorems of standard quantum mechanics. A few other useful results and scaling relations are also derived. They emerge to act as nice guiding rules of thumb in the course of rigorous computations. Certain features of true excited‐state densities can be understood. Goodness of approximate densities can be assessed. Compressed systems can be studied profitably. A route is also sketched that allows one to retrieve classical trajectories from near‐exact energy eigenfunctions for both bound and resonant states by exploiting this rule. Additionally, a discussion on semiclassical perturbation theory is presented emphasizing the asymptotic behavior. Pilot calculations demonstrate the success of the present endeavor under various circumstances. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 113–125, 2001     

Validation and uncertainty analysis of a multi-residue method for pesticides in grapes using ethyl acetate extraction and liquid chromatography-tandem mass spectrometry

A method was validated for the multi-residue analysis of 82 pesticides in grapes at 相似文献   

Modeling quantum dynamics of photodetachment from closed‐shell anions: Static versus fluctuating well‐depth models

The electronic states of halide ions are modeled by a one‐dimensional Hamiltonian with a potential V(x)=−V₀e. The two parameters V₀ and σ are fixed by requiring V(x) to reproduce the experimentally observed ground‐state ionization potentials of the halide ions concerned. The potentials so generated are shown to support only one bound state in each case. The time‐dependent Fourier grid Hamiltonian method is used to follow the ionization dynamics in monochromatic light of fairly high intensities. The total Hamiltonian, in the most general case, reads H(t)=P/2m−V₀e−ϵ₀s(t)ex sin(ωt). For pulsed fields [s(t)=sin²(πt/t_p)], the computed ionization rate constants are seen to increase with increase in the peak intensity (ϵ₀) of the electric field of light. The possibility of additional transient bound states being generated at the high intensities of light and its possible consequences on the observed ionization rates are explored. The environmental effects on the dynamics are sought to be modeled by allowing the well depth (V₀) to fluctuate randomly [V₀(t)=V₀+ΔVR(t); R(t) randomly fluctuates between +1 and −1 with time, ΔV is fixed]. The ionization rate constants (k_ϵ) are shown to be significantly affected by fluctuations in V₀ and pass through a well‐defined minimum in each case for a certain specified frequency of fluctuation. An alternative model potential V(x)=−V₀e^−σx is also shown to yield similar results. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 469–478, 1999     

On the dynamics of a linear and a nonlinear quantum oscillator with randomly changing harmonic frequency

Numerical experiments with a nonlinear (λχ⁴) oscillator which has its harmonic frequency changing randomly with time reveal certain interesting features of its dynamics of quantum evolution. When λ = 0, the level populations are seen to oscillate. But, as the nonlinear coupling is switched on (λ > 0), a threshold is reached at λ = λ_c when the evolution is seen to be characterized by an abrupt transition dominantly to the highest available state of the unperturbed (initial) oscillator. It is shown that this transition probability is maximized at a particular value of λ. The time threshold for this transition decreases with increasing nonlinear coupling strength. The numerically obtained structures of the underlying quantum-phase spaces of the linear and nonlinear random oscillators are examined. Possible use of these results in a problem of chemical origin is explored. © 1997 John Wiley & Sons, Inc.     

An NHC-Stabilised Phosphinidene for Catalytic Formylation: A DFT-Guided Approach

In recent years, the applications of low-valent main group compounds have gained momentum in the field of catalysis. Owing to the accessibility of two lone pairs of electrons, NHC-stabilised phosphinidenes have been found to be excellent Lewis bases; however, they cannot yet be used as catalysts. Herein, an NHC-stabilised phosphinidene, 1,3-dimethyl-2-(phenylphosphanylidene)-2,3-dihydro-1H imidazole (1), for the activation of CO₂ is reported.A closer inspection of the CO₂ activation process by DFT calculations along with intrinsic bond orbital analysis shows that phosphinidene is associated with phenylsilane through a noncovalent π-π interaction between two phenyl rings which activates the Si−H bond facilitating hydride transfer to the CO₂ molecule. Detailed DFT studies along with spectroscopic experiments were combined to understand the mechanism of CO₂ activation and its catalytic reductive functionalisation leading to the formylation of a range of chemically inert primary amides under mild reaction conditions.