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Lattices

Description: Because lattice theory is so vast, the primary purpose of this paper will be to present some of the general properties of lattices, exhibit examples of lattices, and discuss the properties of distributive and modular lattices.
Date: August 1966
Creator: Rintala, Richard Arne
Partner: UNT Libraries

The crystal structure of neptunium metal

Description: From abstract: "In this paper the number of displaced atoms in equilibrium in a thin cyclotron-bombarded target is estimated as a function of the bombarding particle energy and target temperature."
Date: January 4, 1952
Creator: Zachariasen, William H.
Partner: UNT Libraries Government Documents Department

Flow of Gas Through Turbine Lattices

Description: This report is concerned with fluid mechanics of two-dimensional cascades, particularly turbine cascades. Methods of solving the incompressible ideal flow in cascades are presented. The causes and the order of magnitude of the two-dimensional losses at subsonic velocities are discussed. Methods are presented for estimating the flow and losses at high subsonic velocities. Transonic and supersonic flows in lattices are then analyzed. Some three-dimensional features of the flow in turbines are noted.
Date: May 1956
Creator: Deich, M. E.
Partner: UNT Libraries Government Documents Department

Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices

Description: The notion of uniform countable additivity or uniform absolute continuity is present implicitly in the Lebesgue Dominated Convergence Theorem and explicitly in the Vitali-Hahn-Saks and Nikodym Theorems, respectively. V. M. Dubrovsky studied the connection between uniform countable additivity and uniform absolute continuity in a series of papers, and Bartle, Dunford, and Schwartz established a close relationship between uniform countable additivity in ca(Σ) and operator theory for the classical continuous function spaces C(K). Numerous authors have worked extensively on extending and generalizing the theorems of the preceding authors. Specifically, we mention Bilyeu and Lewis as well as Brooks and Drewnowski, whose efforts molded the direction and focus of this paper. This paper is a study of the techniques used by Bell, Bilyeu, and Lewis in their paper on uniform exhaustivity and Banach lattices to present a Banach lattice version of two important and powerful results in measure theory by Brooks and Drewnowski. In showing that the notions of exhaustivity and continuity take on familiar forms in certain Banach lattices of measures they show that these important measure theory results follow as corollaries of the generalized Banach lattice versions. This work uses their template to generalize results established by Bator, Bilyeu, and Lewis.
Date: August 1999
Creator: Huff, Cheryl Rae
Partner: UNT Libraries

Dually Semimodular Consistent Lattices

Description: A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implies that a covers a ∧ b. L is consistent if for every join-irreducible j and every element x in L, the element x ∨ j is a join-irreducible in the upper interval [x,l]. In this paper, finite dually semimodular consistent lattices are investigated. Examples of these lattices are the lattices of subnormal subgroups of a finite group. In 1954, R. P. Dilworth proved that in a finite modular lattice, the number of elements covering exactly k elements is equal to the number of elements covered by exactly k elements. Here, it is established that if a finite dually semimodular consistent lattice has the same number of join-irreducibles as meet-irreducibles, then it is modular. Hence, a converse of Dilworth's theorem, in the case when k equals 1, is obtained for finite dually semimodular consistent lattices. Several combinatorial results are shown for finite consistent lattices similar to those already established for finite geometric lattices. The reach of an element x in a lattice L is the difference between the rank of x*, the join of x and all the elements covering x, and the rank of x; the maximum reach of all elements in L is the reach of L. Sharp lower bounds for the total number of elements and the number of elements of a given reach in a semimodular consistent lattice given the rank, the reach, and the number of join-irreducibles are found. Extremal lattices attaining these bounds are described. Similar results are then obtained for finite dually semimodular consistent lattices.
Date: May 1988
Creator: Gragg, Karen E. (Karen Elizabeth)
Partner: UNT Libraries

Development of local shear bands and orientation gradients in fcc polycrystals

Description: A finite element formulation which derives constitutive response from crystal plasticity theory is used to examine localized deformation in fcc polycrystals. The polycrystals are simple, idealized arrangements of grains. Localized deformations within individual grains lead to the development of domains that are separated by boundaries of high misorientation. Shear banding is seen to occur on a microscopic scale of grain dimensions. The important consequences of these simulations are that the predicted local inhomogeneities are meeting various requirements which make them possible nucleation sites for recrystallization.
Date: May 1, 1995
Creator: Beaudoin, A. J., Jr.; Mecking, H. & Kocks, U. F.
Partner: UNT Libraries Government Documents Department

Consistency in Lattices

Description: Let L be a lattice. For x ∈ L, we say x is a consistent join-irreducible if x V y is a join-irreducible of the lattice [y,1] for all y in L. We say L is consistent if every join-irreducible of L is consistent. In this dissertation, we study the notion of consistent elements in semimodular lattices.
Date: May 1986
Creator: Race, David M. (David Michael)
Partner: UNT Libraries

A PROCEDURE FOR THE EVALUATION OF NEUTRON-SCATTERING CROSS SECTION IN THE INCOHERENT APPROXIMATION

Description: Calculational procedures oriented toward computer application are preserted to evaluate the neutron inelastic scattering cross section in the incoherent approximation for a simple cubic Bravais lattice. The differential scattering cross section, the scattering law, or inelastic scattering matrices and transport cross sections for multigroup calculations are evaluated using the contributions of 25 phonons. The inelastic scattering cross section for graphite is calculated as an example of polycrystalline media where the phonon-frequency distribution is dependent on the direction of polarization. (H.D.R.)
Date: September 1, 1962
Creator: Jankus, V.Z.
Partner: UNT Libraries Government Documents Department

Theoretical studies of zirconia and defects in zirconia. Final report

Description: Supported by this grant the author has performed total energy electronic structure calculations for cubic, tetragonal, and monoclinic zirconia. The results of these calculations agree with the observed ordering of structures in the phase diagram. He has developed model potentials based on the total energy results. Molecular dynamics calculations using these model potentials give a good description of the phase transitions in and the thermal properties of zirconia.
Date: November 1, 1995
Creator: Jansen, H.J.F.
Partner: UNT Libraries Government Documents Department

Interdiffusion in the Ni-Cr-Co-Mo system at 1300/sup 0/C

Description: Interdiffusion was investigated with solid-solid diffusion couples in the ..cap alpha.. (fcc) region of the quaternary Ni-Cr-Co-Mo system at 1300/sup 0/C for the determination of diffusion paths and diffusional interactions among the components. The concentration profiles for a given couple exhibited a common cross-over composition, Y/sub c/, which reflected the relative depths of diffusion in the terminal alloys. Interdiffusion fluxes were calculated directly from the concentration profiles and the quaternary interdiffusion coefficients were calculated at selected compositions. Ni and Co exhibited up-hill diffusion against their individual concentration gradients in a direction opposite to the interdiffusion of Cr. Quaternary diffusion paths were presented as a set of partial diffusion paths on the basis of relative concentration variables.
Date: January 1, 1985
Creator: Heaney, J.A. III & Dayananda, M.A.
Partner: UNT Libraries Government Documents Department

High energy spin waves in BCC iron

Description: We have studied the dispersion relation of the spin wave excitations in bcc iron by neutron inelastic scattering at the spallation neutron source ISIS. Magnetic intensity was followed up to 550meV along the (100) direction. The general form of the dispersion curve is in qualitative agreement with that calculated from a spin-polarised band model, and in particular we have confirmed the prediction of propagating modes extending above 300meV. 7 refs., 3 figs.
Date: January 1, 1990
Creator: Perring, T.G. (Oxford Univ. (UK). Clarendon Lab.); Boothroyd, A.T.; Paul, D.McK. (Warwick Univ., Coventry (UK). Dept. of Physics); Taylor, A.D.; Osborn, R. (Rutherford Appleton Lab., Chilton (UK)); Newport, R.J. (Kent Univ., Canterbury (UK). Dept. of Physics) et al.
Partner: UNT Libraries Government Documents Department

Experimental studies of cascade phenomena in metals

Description: We review recent ion-irradiation experiments which have been performed to investigate the collapse of displacement cascades to dislocation loops in a range of metals and alloys. Many of the results including the dependencies of the collapse probabilities on irradiation temperature, and ion dose, energy and mass, can be explained within the framework of a thermal spike/cascade melting model which has been suggested by computer molecular dynamics simulations. Other aspects, such as the dependence of collapse propabilities on the crystal structure and the effects of alloying and impurities, are less well understood.
Date: June 1, 1992
Creator: Jenkins, M. L.; Kirk, M. A. & Phythian, W. J.
Partner: UNT Libraries Government Documents Department

Diffuse scattering studies as a tool for characterizing the local order structure and for obtaining pairwise interaction energies

Description: Diffuse scattering is a mature method for characterizing the local order structure of alloy systems. An extension of such structural investigations, for alloys at equilibrium, allows one to obtain pairwise interaction energies. Having experimental pairwise interaction energies for the various coordination shells offers one the potential for more realistic Monte Carlo modelling of alloy systems as they relax toward equilibrium. The diffuse scattering method and the recovery of the interaction energies are reviewed and some preliminary results are used to demonstrate the kinetic {Iota}sing modeling technique.
Date: January 1, 1992
Creator: Epperson, J.E. (Argonne National Lab., IL (United States)); Chen, H. & Anderson, J.P. (Illinois Univ., Urbana, IL (United States). Dept. of Materials Science and Engineering)
Partner: UNT Libraries Government Documents Department

The crystal and molecular structure of azatranes: Azavanadatran (Z=t-Bu), monoazasilatrane (Z=H), azalithatrane (Z=Clo*4*), azaphosphatrane (Z=Me), azagermatrane (Z=t-Bu) and Azaalumatran (Z=nothing)

Description: The crystal and molecular structures of azatranes have been extensively studied for a variety of M atoms. The crystal and molecular structures of six similar cage compounds: (t-Bu)NV(MeNCH{sub 2}CH{sub 2}){sub 3}N, HSi(OCH{sub 2}CH{sub 2}){sub 2}(HNCH{sub 2}CH{sub 2})N, O{sub 4}ClLi(HNCH{sub 2}SH{sub 2}){sub 3}N, MeP(Me{sub 3}NCH{sub 2}CH{sub 2}){sub 3}N, t-BuGe(HNCH{sub 2}CH{sub 2}){sub 3}N, and Al(Me{sub 3}SiNCH{sub 2}CH{sub 2}){sub 3}N were determined by the use of three-dimensional, single crystal x-ray diffraction.
Date: April 23, 1996
Creator: Wang, T.
Partner: UNT Libraries Government Documents Department

Characterizations of Some Combinatorial Geometries

Description: We give several characterizations of partition lattices and projective geometries. Most of these characterizations use characteristic polynomials. A geometry is non—splitting if it cannot be expressed as the union of two of its proper flats. A geometry G is upper homogeneous if for all k, k = 1, 2, ... , r(G), and for every pair x, y of flats of rank k, the contraction G/x is isomorphic to the contraction G/y. Given a signed graph, we define a corresponding signed—graphic geometry. We give a characterization of supersolvable signed graphs. Finally, we give the following characterization of non—splitting supersolvable signed-graphic geometries : If a non-splitting supersolvable ternary geometry does not contain the Reid geometry as a subgeometry, then it is signed—graphic.
Date: August 1992
Creator: Yoon, Young-jin
Partner: UNT Libraries

On Delocalization Effects in Multidimensional Lattices

Description: A cubic lattice with random parameters is reduced to a linear chain by the means of the projection technique. The continued fraction expansion (c.f.e.) approach is herein applied to the density of states. Coefficients of the c.f.e. are obtained numerically by the recursion procedure. Properties of the non-stationary second moments (correlations and dispersions) of their distribution are studied in a connection with the other evidences of transport in a one-dimensional Mori chain. The second moments and the spectral density are computed for the various degrees of disorder in the prototype lattice. The possible directions of the further development are outlined. The physical problem that is addressed in the dissertation is the possibility of the existence of a non-Anderson disorder of a specific type. More precisely, this type of a disorder in the one-dimensional case would result in a positive localization threshold. A specific type of such non-Anderson disorder was obtained by adopting a transformation procedure which assigns to the matrix expressing the physics of the multidimensional crystal a tridiagonal Hamiltonian. This Hamiltonian is then assigned to an equivalent one-dimensional tight-binding model. One of the benefits of this approach is that we are guaranteed to obtain a linear crystal with a positive localization threshold. The reason for this is the existence of a threshold in a prototype sample. The resulting linear model is found to be characterized by a correlated and a nonstationary disorder. The existence of such special disorder is associated with the absence of Anderson localization in specially constructed one-dimensional lattices, when the noise intensity is below the non-zero critical value. This work is an important step towards isolating the general properties of a non-Anderson noise. This gives a basis for understanding of the insulator to metal transition in a linear crystal with a subcritical noise.
Date: May 1998
Creator: Bystrik, Anna
Partner: UNT Libraries

PREFERRED ORIENTATION IN ROLLED AND IN RECRYSTALLIZED HIGH-PURITY URANIUM ROD. Final Report of Metallurgy Program.4.1.17

Description: The preferred orientation of a relatively small piece of high-purity uranium rod, rolled to an 85% reduction at 300 deg C, has been determined in the as-rolled and in the recrystallized conditions. The 12 different charts obtained indicated that the as-rolled texture could be described as a duplex (041) and (352) with the (041) being the major component and with considerable spread about each component. The recrystallized rod showed approximate (041) and (392) components with considerable spread. These texture components for both the as- rolled and the recrystallized rods are not too different from those previously reported for reactor-grade uranium rod. However, it was noted that the texture appeared to be quite sharp for the reduction used, and the maximum intensity on an inverse pole figure was considerably displaced from the periphery of an (001) standard projection for both the rolled and recrystallized rods. (auth)
Date: April 1, 1959
Creator: Mueller, M.H. & Knott, H.W.
Partner: UNT Libraries Government Documents Department

QUANTIZATION OF CRYSTAL VIBRATIONS

Description: Although the Born-von Karman treatment of the dynamics of crystal lattices is superior to that of Debye, the conABSTRACTS tinuum model of Debye is more amenable to computation; therefore the Debye treatment is used to obtain frequencies at a maximum energy. From the classic Hamiltonian of the solid, quantization is carried out by the Schroedinger method. The thermodymamic functions are obtained, and the mean square displacement is derived. (J.S.R.)
Date: July 26, 1957
Creator: DeMarcus, W.C.
Partner: UNT Libraries Government Documents Department