Effect of reactive and nonreactive surface modifications and compatibilizer use on mechanical and flame-retardant properties of linear low-density polyethylene filled with huntite and hydromagnesite mineral

Journal of Thermal Analysis and Calorimetry - In the current study, huntite and hydromagnesite (HH) was used as flame-retardant additive in linear low-density polyethylene (LLDPE). The effect of HH...     

Multichannel quantization for molecular systems. III. Complex rotation of coordinates

Multichannel quantization is performed with a complex rotation of the coordinates for both bound states and resonances. Two examples are considered: (a models corresponding to overlapping resonances with two harmonic potentials and a linear potential, for which analytical solutions can be formulated; ( photodissociation of a linear triatomic system. The purpose of these studies is two-fold (i) illustrating that the localization of the resonance wavefu upon rotation allows for the use of boundary conditions identical to those prevailing for a bound state. Our numerical experiments show that complex ro does provide a simple solution for the initialization for large interparticle distance and that closely lying resonant energies can be accurately deter (ii) examining two versions of the complex rotation method when there is more than one coordinate. One may either rotate all coordinates in the startin hamiltonian and derive coupled equations from this transformed hamiltonian, or rotate the coordinate in the coupled equations derived from the untransf hamiltonian. We observe, and demonstrate numerically, that the first version, in the case of a bound state, can only provide a real energy after conver results are obtained. The photodissociation rates obtained in the two versions of the method are shown to agree well with those obtained with a coupled approach with real coordinates. However, the occurrence of spurious widths due to truncation in the number of channels or inaccuracies in the numerical may prevent the study of narrow resonances.     

Semiclassical model for accidental predissociation in diatomic molecules

After a short review of possible quantum treatments, the uniform semiclassical theory of Child (J. Mol. Spectrosc.53, 280 (1974)) is applied to the problem of accidental predissociation in a diatomic molecule where a bound state dissociates into a continuum via a coupling with a near-degenerate second bound state. A complete connection diagram and an analytical expression for the lineshape is provided. This expression is used in the diabatic limit to derive the widths and shifts of the resonances. Checks are made for two test cases for which a simplified quantum model leads to analytical formulas. The familiar case in which each resonance shares the initial width of the perturbing state according to its weight in the configuration interaction wavefunction is verified. In the opposite coupling scheme, the “resonance narrowing” phenomenon predicted by the quantum model is also obtained.     

Angular distributions using the artificial channel method: Application to 4HeD+ infrared photodissociation

The Shapiro's artificial channel method is used to obtain angular distributions and total dissociation cross sections as a function of enemy in the infrared photofragmentation of ⁴HeD⁺     

Development of flow in the entrance region of a converging channel

An approximate solution for the laminar flow of an incompressible viscous fluid in the entrance region of a converging channel is obtained. The radial velocity distribution at the entrance of the channel is taken to be a symmetric but otherwise arbitrary function of the angular position. Expressions for the velocity components and pressure are given. The case of the uniformly distributed entrance velocity is considered as an example.     

Multichannel quantization and the static stark effect

A coupled channel formulation for the static Stark effect on the hydrogen atom is used to obtain directly the complex resonance energies through an iterative matching procedure. The formulation makes use of a complex coordinate. This solves the initialization problem in a very simple way, since the boundary conditions can be those used for bound states. A comparison is made with the results of Reinhardt and collaborators who expand the complex rotated resonance wave function in a basis of integrable functions.     

Oscillatory flow near the entry of a circular tube

Zusammenfassung Die periodische laminare Strömung einer zähen inkompressiblen Flüssigkeit in der Eintrittspartie eines zylindrischen Rohres wird auf Grund der linearisierten Gleichungen vonNavier undStokes berechnet. Es wird dabei angenommen, dass im Eintrittsquerschnitt in jedem Zeitpunkt eine über den Querschnitt konstante Geschwindigkeit herrsche, die jedoch eine Funktion der Zeit ist. Formeln für den Druckgradienten und die Geschwindigkeitskomponenten in Richtung längs der Rohrachse werden erhalten. Ebenso wird die Einlaufstrecke berechnet.

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Sommaire On étudie l'écoulement laminaire oscillatoire d'un fluide incompressible visqueux près de l'entrée d'un tube circulaire sur la base des équations linéairisées Navier-Stokes. On suppose que la vitesse du fluide soit uniforme à l'entrée et qu'elle soit une fonction de temps connue périodique arbitraire. On obtient des formules pour les composantes longitudinales de la vitesse et le gradient de pression et on calcule la longueur d'entrée.

     

Development of flow in the inlet length of a circular tube starting from rest

Zusammenfassung Auf der Grundlage linearisierter Navier-Stokes-Gleichungen wird die instationäre laminare Strömung einer reibungsbehafteten, inkompressiblen Flüssigkeit im Einlaufbereich eines kreisförmigen Rohres behandelt. Es wird angenommen, dass sich die Flüssigkeit zum Anfangszeitpunkt im Ruhezustand befindet und dass die Geschwindigkeitsverteilung im Einlaufquerschnitt eine bekannte Funktion der Zeit und des Radius ist. Es werden Formeln für die Längskomponente der Geschwindigkeit sowie für den Druckgradienten angegeben.     

Exceptional points in multichannel resonance quantization

We derive from the quantization condition of a multichannel resonance problem the behaviour of resonance energies close to an exceptional point (EP) where two resonance energies coalesce. The formalism is applied to a one-dimensional model of the molecular ion H₂ ⁺. Although the approach does not use a matrix diagonalization procedure, all known results about exceptional points are present, including the transfer from one resonance to another when following a loop encircling the EP. We study how the resonance wave functions behave along loops around the EP, as well as the associated geometric phases.     

Reduced-diabatic vibrational close coupled treatment of molecular dissociation dynamics

A close coupled treatment in a vibrational adiabatic representation is applied to the study of molecular photodissociation dynamics. The procedure which is developed here involves three steps: transformation from a diabatic to an adiabatic basis set, truncation of the adiabatic basis set, back transformation to a reduced–diabatic basis set. In the two model cases which are studied, dissociation spectra show complicated peaks and dips, patterns interpreted in terms of shape and Feshbach resonances associated to vibrational predissociation with a relatively high potential barrier in the excited state. An important reduction in the number of channels required for a given final accuracy can be reached by using the reduced–diabatic basis set instead of the usual diabatic one. This is very promising for studying energy partitioning in molecular systems with several internal degrees of freedom taking part in the dynamics.