Theorems on the functional limits of derivatives of a function at infinity

Proceedings - Mathematical Sciences -     

"Pump-probe" atom-centered density matrix propagation studies to gauge anharmonicity and energy repartitioning in atmospheric reactive adducts: case study of the OH + isoprene and OH + butadiene reaction intermediates

Time-resolved "pump-probe" ab initio molecular dynamics studies are constructed to probe the stability of reaction intermediates, the mechanism of energy transfer, and energy repartitioning, for moieties involved during the interaction of volatile organic compunds with hydroxyl radical. These systems are of prime importance in the atmosphere. Specifically, the stability of reaction intermediates of hydroxyl radical adducts to isoprene and butadiene molecules is used as a case study to develop novel computational techniques involving "pump-probe" ab initio molecular dynamics. Starting with the various possible hydroxyl radical adducts to isoprene and butadiene, select vibrational modes of each of the adducts are populated with excess energy to mimic the initial conditions of an experiment. The flow of energy into the remaining modes is then probed by subjecting the excited adducts to ab initio molecular dynamics simulations. It is found that the stability of the adducts arises directly due to the anhormonically driven coupling of the modes to facilitate repartitioning of the excess vibrational energy. This kind of vibrational repartitioning has a critical influence on the energy density.     

Gas chromatographic determination of polysaccharide gums in foods after hydrolysis and derivatization

A gas chromatographic method was evaluated for the determination of food grade gums in dairy products, salad dressings and meat sauces. The gums studied were tragacanth, karaya, ghatti, carob, guar, arabic and xanthan gum. The extraction method included removal of fat followed by starch degradation then precipitation of protein. The isolated gums were hydrolysed with trifluoroacetic acid and the resulting neutral monosaccharides converted to their aldonitrile acetate derivatives for determination by gas chromatography. Recoveries from thirteen different commodities averaged 85%. However, the recovery of guar gum from ice cream and cold pack cheese was 42 and 50%, respectively. In a comparison of enzyme hydrolysis and iodine complexation for the removal of starch the former was simpler and provided cleaner extracts than the iodine treatment. Both gave similar results.     

Experimental and ab initio dynamical investigations of the kinetics and intramolecular energy transfer mechanisms for the OH + 1,3-butadiene reaction between 263 and 423 K at low pressure

The rate constants for the reaction of the OH radical with 1,3-butadiene and its deuterated isotopomer has been measured at 1-6 Torr total pressure over the temperature range of 263-423 K using the discharge flow system coupled with resonance fluorescence/laser-induced fluorescence detection of OH. The measured rate constants for the OH + 1,3-butadiene and OH + 1,3-butadiene- d 6 reactions at room temperature were found to be (6.98 +/- 0.28) x 10 (-11) and (6.94 +/- 0.38) x 10 (-11) cm (3) molecule (-1) s (-1), respectively, in good agreement with previous measurements at higher pressures. An Arrhenius expression for this reaction was determined to be k 1 (II)( T) = (7.23 +/- 1.2) x10 (-11)exp[(664 +/- 49)/ T] cm (3) molecule (-1) s (-1) at 263-423 K. The reaction was found to be independent of pressure between 1 and 6 Torr and over the temperature range of 262- 423 K, in contrast to previous results for the OH + isoprene reaction under similar conditions. To help interpret these results, ab initio molecular dynamics results are presented where the intramolecular energy redistribution is analyzed for the product adducts formed in the OH + isoprene and OH + butadiene reactions.     

Alpha decay of isobaric analogue states in24Mg and28Si

Theα-decay of isobaric analogue states (which are forbidden by isospin selection rules) excited in²⁴Mg and²⁸Si through preton capture by²³Na atE _p=677 and 739 keV and by²⁷Al atE _p=295, 327 and 405 keV, respectively, have been studied using solid state track detectors. The ratio ofα-decay widths of the two resonance states in²⁴Mg to the state at 1.632 MeV (2⁺) in²⁰Ne yields the value 0.065 for the mixing parameterε and the value 4.01 keV for the Coulomb matrix element responsible for the isospin mixing in²⁴Mg. In²⁸Si the measurement of theα-decay widths of the three resonance states resulted in the determination of the proton, gamma and alpha partial widths which comprise the total width of the resonance states. Limits have been set for the value of the two mixing parameters involved in this case. Upper limits of 16 and 39 keV have been obtained for the Coulomb matrix elements responsible for the isospin mixing in²⁸Si.     

Long range correlation in earthquake precursory signals

Research on earthquake prediction has drawn serious attention of the geophysicist, geologist and investigators in different fields of science across the globe for many decades. Researchers around the world are actively working on recording pre-earthquake changes in non-seismic parameters through a variety of methods that include anomalous changes in geochemical parameters of the Earth’s crust, geophysical properties of the lithosphere as well as ionosphere etc. Several works also have been done in India to detect earthquake precursor signals using geochemical and geophysical methods. However, very few works have been done so far in India in this field through the application of nonlinear techniques to the recorded geophysical and geochemical precursory signals for earthquakes. The present paper deals with a short review of the early works on geochemical precursors that have been carried out in India as yet. With a view to detect earthquake precursory signals by means of gas-geochemical method we developed a network of seismo-geochemical monitoring observatories in India in hot springs and mud volcano crater. In the last few years we detected several geochemical anomalies and those were observed prior to some major earthquakes that occurred within a radius of 1500?km from the test sites. In the present paper we have applied nonlinear techniques to the long term, real-time and natural data sets of radon-222 and associated gamma originated out of the terrestrial degassing process of the earth. The results reveal a clear signature of the long range correlation present in the geochemical time series. This approach appears to be a potential tool to explore intrinsic information hidden within the earthquake precursory signals.     

Run up flow of an incompressible micropolar fluid between parallel plates – A state space approach

In this paper, we study the run up flow of an incompressible micropolar fluid between two horizontal infinitely long parallel plates. Initially a flow of the fluid is induced by a constant pressure gradient until steady state is reached. After the steady state is reached, the pressure gradient is suddenly withdrawn while the two plates are impulsively started with different velocities in their own plane. Using the Laplace transform technique and adopting the state space approach, we obtain the velocity and microrotation components in Laplace transform domain. A standard numerical inversion procedure is used to find the velocity and microrotation in space-time domain for various values of time, distance, material parameters and pressure gradient. The variation of velocity and microrotation components is studied and the results are illustrated through graphs. It is observed that the micropolarity parameter has a decreasing effect on velocity component. It is also found that as the gyration parameter increases there is a decrease in microrotation component and an increase in velocity component.     

Vibration of rectangular orthotropic plates

Summary An approximate analytical procedure has been given to solve the problem of a vibrating rectangular orthotropic plate, with various combinations of simply supported and clamped boundary conditions. Numerical results have been given for the case of a clamped square plate.Nomenclature 2a, 2b sides of the rectangular plate - h plate thickness - E _x , E _y , E, G elastic constants of te orthotropic material - D _x E _x h ³/12 - D _y E _y h ³/12 - H _xy Eh ³/12+Gh ³/6 D _x , D _y and H _xy are rigidity constants of the orthotropic plate - mass of the plate per unit area - Poisson's ratio - W deflection of the plate - p circular frequency - b/a ratio - X _m , Y _n characteristic functions of the vibrating beam problem - p ² a ² b ²/H _xy the frequency parameter.     

Multiscale theory of collective and quasiparticle modes in quantum nanosystems

A quantum nanosystem (such as a quantum dot, nanowire, superconducting nanoparticle, or superfluid nanodroplet) involves widely separated characteristic lengths. These lengths range from the average nearest-neighbor distance between the constituent fermions or bosons, or the lattice spacing for a conducting metal, to the overall size of the quantum nanosystem (QN). This suggests the wave function has related distinct dependencies on the positions of the constituent fermions and bosons. We show how the separation of scales can be used to generate a multiscale perturbation scheme for solving the wave equation. Results for electrons or other fermions show that, to lowest order, the wave function factorizes into an antisymmetric (fermion) part and a symmetric (bosonlike) part. The former manifests the short-range/exclusion-principle behavior, while the latter corresponds to collective behaviors, such as plasmons, which have a boson character. When the constituents are bosons, multiscale analysis shows that, to lowest order, the wave function can also factorize into short- and long-scale parts. However, to ensure that the product wave function has overall symmetric particle label exchange behavior, there could, in principle, be states of the boson nanosystem where both the short- and long-scale factors are either boson- or fermionlike; the latter "dual fermion" states are, due to their exclusion-principle-like character, of high energy (i.e., single particle states cannot be multiply occupied). The multiscale perturbation analysis is used to argue for the existence of a coarse-grained wave equation for bosonlike collective behaviors. Quasiparticles, with effective mass and interactions, emerge naturally as consequences of the long-scale dynamics of the constituent particles. The multiscale framework holds promise for facilitating QN computer simulations and novel approximation schemes.