Some exact results basic to the linearized Boltzmann equations for a binary mixture of rigid spheres

Six exact solutions (related to the conservation of number, energy and momentum) of the linearized Boltzmann equations for a binary mixture of rigid spheres, for the case of isotropic scattering in the center-of-mass system, are reported. The verification of the reported exact solutions (collisional invariants) is based on a recently reported explicit formulation of the linearized Boltzmann equation for a binary mixture of rigid spheres. Elementary analysis is used also to establish a basic flow condition.     

Rotational isomerism in 3-chloro-1-propanol from the microwave spectrum

The rotational spectra of two conformations of 3-chloro-propanol were observed for the four possible $\text{Cl(35)}\text{Cl(37)}$ and $\text{H}\text{D}$ isotopic species. For both conformations the oxygen atom is gauche with respect to the C₂C₃ bond and the hydroxyl hydrogen is trans with respect to the C₂C₁ bond. In one conformation (T) the chlorine is trans with respect to C₁C₂ and it is gauche in the other form (G). The ground state of the G form is about 0.7 kcal/mole more stable than that of the T form. A discussion is given about the failure to observe the H bond species. The most likely reason is the too close approach of Cl and O in this hypothetical configuration. The quadrupole coupling constants were obtained for the G form. The rotational spectra of five excited states of the T form and of one excited state of the G species were measured. Partial r₀ and r_s structures are given.     

Effect of manifold design and firing order on the short term spectrum

Separation by homomorphic filtering of the engine speed dependent harmonics from the remaining components of a vehicle's acoustic emission involves selection of the optimum quefrency for the filter. This requires an understanding of the formation, on the short term log power spectrum, of harmonics of both the fundamental frequency from successive cylinder firings and also the frequency from firings of the same cylinder. It is shown that these harmonics depend on the combination of the design of the engine's exhaust manifold and on the cylinder firing order. Comparisons are made between the engine harmonics displayed from segments of time series containing different numbers of crankshaft rotations. Finally graphs are included where meaningful comparison can be made between homomorphed spectra of two different vehicles of the same type. As a result of this investigation an explanation is offered which resolves the problems encountered by workers analysing engine related harmonics.     

A numerical evaluation of an analytical representation of the components in a Fourier decomposition of the phase matrix for the scattering of polarized light

An analytical representation of the components in a Fourier decomposition of the phase matrix for a theory of multiple light scattering that includes the effects of polarization is evaluated, and selected numerical results are given for several particular scattering models.     

Thermodynamic binding parameters evaluated by using phase-resolved fluorescence spectrometry

Equilibrium binding constants as a function of temperature were determined for the binding of 4-amino-N-methylphthalimide (4-AMP) to β-cyclodextrin and to human and bovine serum albumins, and for 6-propionyl-2-(dimethylamino)naphthalene (PRODAN) to β-cyclodextrin, by using phase-resolved fluorimetry to eliminate errors from the significant fluorescence contribution from the free 4-AMP or PRODAN. Enthalpy and entropy values were also calculated from these experimental data.     

Radiative transfer in finite inhomogeneous plane-parallel atmospheres

The F_N method is used to deduce accurate numerical results for the exit distributions of radiation relevant to a finite, plane-parallel atmosphere with an exponentially varying albedo for single scattering.     

One-speed transport theory for spherical media with internal sources and incident radiation

The time-independent one-speed neutron transport equation for media with spherically symmetric invariance properties and an isotropic scattering law is discussed. The analysis allows for isotropic internal emission, and emphasis is placed on the treatment of neutrons incident on the free surface of a finite spherical medium.

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Zusammenfassung Gegenstand diese Artikels ist eine zeitunabhängige, monoenergetische Neutronentransportgleichung für Medien mit sphärisch symmetrischen Invarianzeigenschaften und isotropem Streugesetz. Die Analysis erlaubt isotrope interne Emission und behandelt das Problem des Neutroneneinfalls auf eine freie Oberfläche eines endlichen sphärischen Mediums.

     

Free energy of conformational changes in vapors from low resolution microwave spectroscopic intensities

An analysis of the factors controlling the relative intensities of low resolution microwave spectroscopic bands of conformers leads to a formula for ΔG, the free energy difference between two conformers, in terms of the relative intensities of two bands of the same rotational quantum number J. Estimates of the a dipole moment component, and the rotational constants A, B, C, for the two conformers also occur in the formula. A partial experimental test is discussed, which compares two isotopic forms rather than two conformers.     

TheF N method for radiative transfer problems without azimuthal symmetry

The formalism required to solve by theF _N method radiative transfer problems lacking azimuthal symmetry is developed, and numerical results are given.

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Zusammenfassung Es wird der Formalismus entwickelt der zur Lösung von Strahlungsproblemen mit derF _N -Methode benötigt wird, falls keine azimutale Symmetrie vorliegt. Numerische Ergebnisse werden gegeben.

     

An exact analytical solution of x coth x = α x2 + 1

The theory of complex variables is used to develop exact closed-form solutions of the transcendental equation x coth x = α x² + 1. The parameter α is considered to be real, and the reported analysis yields analytical expressions, in terms of elementary quadratures, for the real solutions x, as they depend on prescribed values of α.