College of Science (COS)

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Resolving Land Use Conflicts
Tideman, Nicolaus (Farm Foundation, 1972)
Physical interaction of nitrogen with Pyrex, stainless-steel, and nickel at very low-pressure
Outlaw, R. A.; Brock, F. J.; Wightman, James P. (American Institute of Physics, 1974)
The physical adsorption of nitrogen on the surfaces of Pyrex, 347 stainless steel, and polycrystallinenickel was investigated over the pressure range 1×10−12–3×10−7 Torr and for the temperatures 77.4 and 87.4 °K. The metal surfaces were prepared by vacuum firing, by chemical cleaning, and, following bakeout, by electron impact desorption (EID). Work function measurements were used to indicate changes in the surface condition following electron bombardment, and a mass spectrometer was used to monitor gas composition. The isotherms revealed that the stainless surface was very heterogeneous and that the Pyrex surface area had a roughness factor of 1.7. Nitrogen isotherms were also taken on the metal surfaces after they had been exposed to oxygen. Very little change in physical adsorption on the nickel was detected, presumably because the chemisorbed oxygen was incorporated into the bulk. The chemical adsorption of N2 on nickel at room temperature and below was not observed.
Scatterings initiated by two coherent beams
Li, M. C. (American Physical Society, 1974-04)
A theory, which exhibits the characteristic features of scatterings initiated by two coherent beams, is discussed in the present paper. We show that the imaginary part of the scattering amplitude is an experimentally measurable quantity. To know the imaginary part of the amplitude is quite important for certain aspects of quantum mechanics, for example, the dispersion relation for a fixed momentum transfer. This relation has not yet been experimentally verified.
Spheroidal analysis of Coulomb scattering
Li, M. C. (AIP Publishing, 1974-05)
In studying the spheroidal problem of a charged particle scattered by two charged centers, we have had to deal with a differential equation. Its solution was complicated. In this paper, we study a very similar differential equation, which appears in the Coulomb problem. The solution for this equation, however, can be put in a simple form. For completeness the spheroidal analysis of the Coulomb scattering amplitude is also discussed.
An improved laser-schlieren system for measurement of shock-wave velocity
Bander, J. A.; Sanzone, G. (AIP Publishing, 1974-07)
An improved laser_schlieren system for the measurement of shock_wave velocities has been developed which employs a single detector.Calibration of multiple detectors has been obviated. The system has been shown to yield, in addition to the shock_wave velocity, additional information on the arrival time of the contact surface. Shock_tube performance is compared to the predictions of Mirels' theories.
Expansion-free electromagnetic solutions of Kerr-Schild class
Debney, G. (AIP Publishing, 1974-07)
Starting with the general Kerr_Schild form of the metric tensor,d s2=_+l_l (where l is null and _ is flat space_time), a study is made for those solutions of the Einstein_Maxwell equations in which l is geodesic, shear_free, and expansion_free. It is shown that all resulting solutions must be of Petrov type [4] or type [_] and the Maxwell field must be null. Because of the expansion_free assumption there exist flat and conformally flat gauge conditions on all metrics in this class; i.e., there exist metrics of this Kerr_Schild form which are flat (or conformally flat) but are not Lorentz_related. A method is given for obtaining meaningful solutions to the field equations with the latter gauge equivalence class removed. A simple example of a radiative field of type [4] along a line singularity exhibits how solutions in this class may be generated.
Dynamic nuclear polarization in samarium-doped lanthanum magnesium nitrate
Byvik, C. E.; Wollan, D. S. (American Physical Society, 1974-08)
We report theoretical and experimental investigations of the dynamic nuclear polarization (DNP) and nuclear spin-lattice relaxation of protons in single crystals of lanthanum magnesium nitrate (LMN) weakly doped (≅0.1-1.1-mole%) with samarium ions (LMN:Sm) at 9.1 GHz and liquid-helium temperatures. Theoretical expressions for DNP and nuclear relaxation are given for a homogeneously broadened ESR line in the high-temperature limit. DNP effects due to the electron dipole-dipole reservoir (EDDR) are predicted for the case of well-resolved satellites. Our DNP experiments on LMN:Sm are in general agreement with the conventional theory, but no evidence for direct EDDR effects on DNP with well-resolved satellites is seen, despite suggestive nuclear-relaxation data. Various explanations for this disagreement are proposed. We suggest that these EDDR effects may be seen in crystals of ≅3-5-mole% LMN:Sm or in equivalent systems.
Scattering of two coherent beams by multiple centers
Li, M. C. (American Physical Society, 1974-09)
This is a continuation in the theoretical study of scattering initiated by two coherent beams. Here the scattering by multiple independent centers is discussed. The presence of these centers involves some problems, which are not present in scattering with a single beam. I show how these problems may be overcome, thus allowing the phase of the scattering amplitude to be determined experimentally.
On the spectrum of linear transport operator
Larsen, E. W.; Zweifel, Paul F. (AIP Publishing, 1974-11)
In this paper, spectral properties of the time_independent linear transport operator A are studied. This operator is defined in its natural Banach space L 1(D _ V), where D is the bounded space domain and V is the velocity domain. The collision operator K accounts for elastic and inelastic slowing down, fission, and low energy elastic and inelastic scattering. The various cross sections in K and the total cross section are piecewise continuous functions of position and speed. The two cases _0>0 and _0=0 are treated, where _0 is the minimum neutron speed. For _0=0, it is shown that _(A) consists of a full half_plane plus, in an adjoining strip, point eigenvalues and curves. For _0>0, _(A) consists just of point eigenvalues and curves in a certain half_space. In both cases, the curves are due to purely elastic ``Bragg'' scattering and are absent if this scattering does not occur. Finally the spectral differences between the two cases _0>0 and _0=0 are discussed briefly, and it is proved that A is the infinitesimal generator of a strongly continuous semigroup of operators.
Power statistics for wave propagation in one-dimension and comparison with radiative transport theory. II
Kohler, Werner E.; Papanico.G.C. (AIP Publishing, 1974-12)
We consider the one_dimensional problem of a slab having a random index of refraction and illuminated from within by a point source. We compute the expected value and the fluctuations of both the total power and power flux. These quantities, which are functions of the slab width, source location, and observation point, are determined in the limit of weak refractive index fluctuations and large slab thickness. We compare the expected values of total intensity and flux with the predictions of radiative transport theory. We also compare the results of both theories with numerical simulations.
Bearing estimation using a large towed array
Hinich, Melvin J.; Rule, William (Acoustical Society of America, 1975)
When a towed array of hydrophones is significantly nonlinear due to bending, ordinary linear array beamforming gives a biased estimate of the true source bearing. By processing the array as a sequence of smaller aperture subarrays and then computing the mean of the subarray bearings, the variation due to bending is reduced and a reasonably precise estimate is obtained if the average bending angle with respect to the nominal axis is small. The median and mean subarray bearings are analyzed for a theoreticalstatistical model and are tested using artificial data for various sinusoidal array geometries.
Generalized optical theorem in coherent scattering
Li, M. C. (American Physical Society, 1975-03)
It is shown that the generalized optical theorem in quantum mechanics is a useful theorem in the scattering of two coherent beams.
Extension of Case formulas to L_p. Application to half and full space problems
Larsen, E. W.; Sancaktar, Selim; Zweifel, Paul F. (AIP Publishing, 1975-05)
The singular eigenfunction expansions originally applied by Case to solutions of the transport equation are extended from the space of Hölder‐continuous functions to the function spaces X p = {f‖μf (μ) ‐ L p }, where the expansions are now to be interpreted in the X p norm. The spectral family for the transport operator is then obtained explicitly, and is used to solve transport problems with X p sources and incident distributions.
The conditional entropy in the microcanonical ensemble
Dietz, D.; Greenberg, William (AIP Publishing, 1975-08)
The existence of the configurational microcanonical conditional entropy in classical statistical mechanics is proved in the thermodynamic limit for a class of long_range multiparticle observables. This result generalizes a theorem of Lanford for finite range observables.
Crystal scattering of two coherent neutron beams
Li, M. C. (American Physical Society, 1975-10)
The crystal scattering of two coherent neutron beams is discussed. It is found that the conventional pair correlation function used in single-beam scattering is insufficient to describe the scattering of two coherent neutron beams. A generalized pair correlation function with unequal momentum transfer is introduced. It is found that the energy exchange between vibrational quanta of the crystal and incident neutrons leads to a modification of the scattering amplitude. Through the scattering of two coherent neutron beams one is able to measure directly the phase of the scattering amplitude.
Multigroup neutron transport. I. Full range
Bowden, Robert L.; Sancaktar, Selim; Zweifel, Paul F. (AIP Publishing, 1976-01)
A functional analytic approach to the N_group, isotropic scattering, particle transport problem is presented. A full_range eigenfunction expansion is found in a particularly compact way, and the stage is set for the determination of the half_range expansion, which is discussed in a companion paper. The method is an extension of the work of Larsen and Habetler for the one_group case.
Multigroup neutron transport. II. Half range
Bowden, Robert L.; Sancaktar, Selim; Zweifel, Paul F. (AIP Publishing, 1976-01)
This paper accompanies a preceding one in which a functional analytic method was used to obtain the full_range expansion in multigoup neutron transport. In the present paper the analysis is extended to obtain the half_range expansion. The method used is an extension of the work of Larsen and Habetler for the one_group case. The results are given in terms of certain matrices which are solutions of coupled integral equations and which factor the dispersion matrix.
Water-pollution monitoring using matched spatial filters
Almeida, S. P.; Eu, J. K. T. (Optical Society of America, 1976-02)
Presented are some results obtained from the application of matched spatial filtering techniques to the identification of biological specimens called diatoms (i.e., water algae). A prototype semiautomatic optical processor has been developed that utilizes the Vander Lugt type complex spatial filters. We describe the optical filter averaging technique employed and discuss our semi in situ developing method for the filters. The advantage of this method with regards to the critical position requirements for time sharing optical filters is also presented. The filter holder is mounted on X, Y stages and precision positioned under the control of a PDP-11-40 computer.
Case eigenfunction expansion for a conservative medium
Greenberg, William; Zweifel, Paul F. (AIP Publishing, 1976-02)
By using the resolvent integration technique introduced by Larsen and Habetler, the one‐speed, isotropic scattering,neutron transport equation is treated in the infinite and semi‐infinite media. It is seen that the results previously obtained by Case’s ’’singular eigenfunction’’ approach are in agreement with those obtained by resolvent integration.
Functional calculus for symmetric multigroup transport operator
Greenberg, William (AIP Publishing, 1976-02)
A rigorous treatment of the symmetric multigroup transport equation is given by developing the functional calculus for the transport operator. Von Neumann spectral theory is applied to nonorthogonal cyclic subspaces, and the isometries onto C (N) are explicitly evaluated.

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