Browsing by Author "Boisen, Monte B. Jr."
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- Bond length and bonded radii variations in nitride molecules and crystalsButerakos, Lewis A. (Virginia Tech, 1990-08-09)Molecular Orbital calculations on 31 H3:e_mxm+N:e hydronitride molecules containing 3-, 4-, and 6-coordinate X-cations from rows 1-4 of the periodic table yield minimum energy bond lengths, Rt(XN), which reproduce observed bond lengths, Ro(XN), in crystalline nitrides to within o.O₃A, on average. A linear regression analysis of In[Rt(XN)] vs. In(p) with p = air, where a is the Pauling bond strength and r is the row number of the X -cation in the periodic table, gives the equation R(XN) = 1.47p-O.2\ which is shown to reproduce the observed XN bond lengths of Baur (1987) to within o.o9A, on average. This equation is statistically identical to the equation R( XN) 1.49p-O.22, derived from a linear regression analysis ofln[Ro{XN)] vs. In(p), and is similar in form to those obtained for the oxides (R(XO) = 1.39p-O.22) and the sulfides (R(XS) = 1.83p-O.21).
- Bonding properties of coordinated polyhedra in molecules and crystalsHill, Frances Cull (Virginia Tech, 1995-12-05)Force constants and electron density distributions in coordination polyhedra in molecules and crystals are modeled using Hartree-Fock molecular orbital methods. Model bond-stretching force constants calculated for coordination polyhedra in a series of nitride, oxide and sulfide molecules are ~ 10-20% larger than obtained with spectroscopic methods. Well-developed correlations obtain between the force constants and minimum energy bond lengths, effective nuclear charges and polyhedral compressibilities of molecules and crystals. Model electron density distributions calculated for a large number of molecules with MOn (n = 1, 2,3,4 or 6) coordination polyhedra show that the MO bonds of a given type vary in a regular way with the value of the electron density at bond critical points, bonded radii and the curvatures of the electron density. The bonded interactions in the polyhedra are examined in terms of criteria set forth by Bader and Essen (1984) and Cremer and Kraka (1984).
- Cell design in a cellular system using guard channels, call queueing and channel borrowingJain, Nikhil (Virginia Tech, 1993-12-05)This dissertation develops an analytic framework to undertake cell design in a cellular system. The cell is modeled in a broader sense than ever done before. In our analytical model, we incorporated the use of guard channels, queueing of new calls, and hybrid channel allocation. A numerically stable and efficient solution to a queueing system with two arrival streams having reserved and borrowable servers has been developed. This queueing system is used to model the cell behavior. The model provides valuable insights into the behavior of the cell, and this in turn has been used to devise an efficient stochastic optimization algorithm for determining the minimum number of channels required by the cell. Our techniques are stable, easy to implement for practical systems and produce optimized solutions quickly. This is particularly useful because we expect that future designs of cellular systems may execute such algorithms on cell-site processors.
- Computational Alchemy: The Rational Design of New Superhard MaterialsTeter, David Michael (Virginia Tech, 1998-06-29)First--principles electronic structure calculations have been performed to help identify and direct the synthesis of new superhard compounds. An improved figure of merit for hardness is identified and used to show that carbon nitrides are not likely to be harder than diamond.
- The Creation of Algorithms Designed for Analyzing Periodic Surfaces of Crystals and Mineralogically Important Sites in Molecular Models of Crystals: Understanding the Electron Density Function Through Visual Examinations of the Curvature and Shape of the Equi-Value Laplacian SurfacesBeverly, Lesa Lynn (Virginia Tech, 2000-07-21)The goals of the research presented in this dissertation were to create algorithms that produce images of complex phenomena, to study the efficacy of the algorithms, and to apply these algorithms to important mineralogical problems. The algorithms that were created include the Sphere Projection method, the Chicken Wire method, and methods for calculating the curvature at any point on a surface. The Sphere Projection method is best applied to roughly spherical surfaces. A theorem about the "fit" to a sphere determines the accuracy of the model in this special case and gives some insight into the limitations of this method. The Chicken Wire method was developed to model those surfaces for which the Sphere Projection method was ineffective. The effectiveness of the Chicken Wire method was also determined. The algorithms were used to produce images of equi-value surfaces of the Laplacian of the electron density function in selected molecules. The water molecule, H2O, was studied to demonstrate that these new methods are capable of reproducing known features. The disiloxane molecule, H6Si2O7, was studied because it serves as a model for bonding in quartz and other important silicates. Lastly, the molecule NaLi2Si2OF9 was examined as a molecular model for low albite. A new discovery suggests that these algorithms will be an important tool in mineralogy.
- The electronic structure of galena and hematite surfaces: applications to the interpretations of STM images, XPS spectra and heterogeneous surface reactionsBecker, Udo (Virginia Tech, 1995-11-07)Scanning tunneling microscopy (STM) images and scanning tunneling spectroscopy (STS) spectra of galena (PbS) and hematite (a-Fe203) were calculated using ab-initio methods in order to interpret experimental images and spectra that were taken in previous studies. These calculations have helped to understand which states of the mineral surfaces were imaged depending on the bias voltage and tip-sample separation. The computational results also gave insight in electron transfer processes that take place during surface adsorption/oxidation/reduction processes. In this context, different oxidation (using O₂ and ferric iron as oxidants) and gold adsorption/reduction mechanisms on galena were evaluated at an atomic level. On hematite, the main emphasis was determining the differences in the local electronic structure of specific sites above the surface and the electronic structure of the bulk. Hereby, step sites turned out to have an increased local density of states at certain electron binding energies that are absent on flat surfaces. states can explain the highly increased reactivity of step sites as compared to terraces. X-ray photoelectron spectra (XPS) were calculated to compare the photoelectron peaks of the calculated specific surface structures (that do not have a bulk equivalent) with experimentally obtained XPS spectra. Most of the calculated peak chemical shifts coincided with those that were found in experiments and that were previously interpreted in terms of known bulk structures. Therefore, it can be inferred that the conventional way of interpreting XPS spectra might be incomplete if specific surface structures are neglected. In order to understand step velocities on a gypsum (010) surface, step energies of different step directions were calculated using an ab-initio approach. An approximately linear relationship was found between the calculated step energies and the experimentally determined step velocities.
- The Exit Time Distribution for Small Random Perturbations of Dynamical Systems with a Repulsive Type Stationary PointButerakos, Lewis Allen (Virginia Tech, 2003-08-04)We consider a stochastic differential equation on a domain D in n-dimensional real space, where the associated dynamical system is linear, and D contains a repulsive type stationary point at the origin O. We obtain an exit law for the first exit time of the solution process from a ball of arbitrary radius centered at the origin, which involves additive scaling as in Day (1995). The form of the scaling constant is worked out and shown to depend on the structure of the Jordan form of the linear drift. We then obtain an extension of this exit law to the first exit time of the solution process from the general domain D by considering the exit in two stages: first from the origin O to the boundary of the ball, for which the aforementioned exit law applies, and then from the boundary of the ball to the boundary of D. In this way we are able to determine for which Jordan forms we can obtain a limiting distribution for the first exit time to the boundary of D as the noise approaches 0. In particular, we observe there are cases for which the exit time distribution diverges as the noise approaches 0.
- First-principles study of several hypothetical silica framework structuresTeter, D. M.; Gibbs, Gerald V.; Boisen, Monte B. Jr.; Allan, D. C.; Teter, M. P. (American Physical Society, 1995-09-15)Several hypothetical silica structures have been generated using a simulated-annealing strategy with an ab initio based covalent-bonding potential. First-principles total-energy pseudopotential methods have been used to examine several. promising hypothetical structures and to compare their structural parameters, cohesive energies, and bulk moduli with those of low quartz;, low cristobalite, silica sodalite, and stishovite. The cohesive energies of these hypothetical structure types are found to be equivalent to those of low quartz, low cristobalite, and silica sodalite, and significantly lower than that of stishovite.
- Groups, Graphs, and Symmetry-BreakingPotanka, Karen Sue (Virginia Tech, 1998-04-16)A labeling of a graph G is said to be r-distinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an r-distinguishing labeling on G is called the distinguishing number of G. The distinguishing set of a group Gamma, D(Gamma), is the set of distinguishing numbers of graphs G in which Aut(G) = Gamma. It is shown that D(Gamma) is non-empty for any finite group Gamma. In particular, D(Dn) is found where Dn is the dihedral group with 2n elements. From there, the generalized Petersen graphs, GP(n,k), are defined and the automorphism groups and distinguishing numbers of such graphs are given.
- Librational displacements of silicate tetrahedra in response to temperature and pressureDowns, Robert T. (Virginia Tech, 1992-12-05)Recently it has been concluded that the SiO₄ silicate tetrahedra in crystals behave as rigid bodies. This conclusion is based on analyses of the atomic displacement factors of Si and O atoms obtained from single crystal diffraction experiments wherein the amplitudes of atomic vibrations are ascribed to translational, librational and screw-correlated modes of motion for the entire SiO₄ group. If the displacement ellipsoids are considered to represent time averaged quadratic surfaces of equal configurational potential energy about the mean position of an atom, then an analysis of the these displacements should provide detailed information about the SiO₄ group and the crystal. The apparent SiO bond lengths recorded for silicates over a range of temperatures are typically either invariant or exhibit a contraction with increasing temperature. A rigid-body thermal analysis was completed for the tetrahedra in nine silicates whose structures have been determined over a range of temperatures from 15 K to 1250 K and whose tetrahedra seem to behave as rigid units. The coordinates provided by the analysis yield bond lengths and polyhedral volumes corrected for the librational motion of each silicate tetrahedron. The bond lengths and volumes estimated for tetrahedra with four bridging oxygens seem to increase with temperature at a faster rate than those with four nonbridging oxygen atoms. Those for tetrahedra with two or three nonbridging oxygen atoms tend to increase at an intermediate rate. An analysis of the rigid-body motion of coordinated polyhedra yields a simple but accurate expression for correcting bond lengths for thermal vibrations. Observed anisotropic displacement parameters for Si and O atoms indicate that the SiO₄ tetrahedra in quartz behave as rigid bodies. A configurational potential energy curve, constructed from the librational components of the rigid body motion of the tetrahedra, shows a double well for α quartz and a single well for β quartz when plotted as a function of the displacement of the O atom with temperature. The configurational energetics of α and β quartz are examined with a theoretical potential energy function based on parameters obtained from molecular orbital calculations. The calculations indicate that the temperature behavior of a quartz is governed by the energetics of the SiOSi angle, in contrast to β quartz which is governed by the energetics of the SiO bond. The mechanism of the α ⇌ β transition is examined in terms of the experimental and modeled configurational potential energy curves. Evidence for the proposal that π bonding is the driving mechanism for the transition is lacking. Structural and volume compressibility data for α-cristobalite were determined by single crystal X-ray diffraction methods for pressures up to ~1.6 GPa, where cristobalite undergoes a reversible phase transition. The bulk modulus was determined to be 11.5(7) GPa with a pressure derivative of 9(2). The SiOSi angle shows a greater decrease than observed for quartz and coesite while the SiO bond lengths and the OSiO angles remain essentially unchanged. The responses of V/V₀ and SiOSi angle to pressure for the silica polymorphs are compared and it is found that the percentage decrease in the volume is linearly correlated with the percentage decrease in the SiOSi angle, regardless of the framework structure type. A mathematical modeling of the energies of the structural changes that are induced by pressure suggests that the contribution to the total energy ascribed to Si0Si angle bending terms is the same in quartz and cristobalite.
- Mathematical Models of the Alpha-Beta Phase Transition of QuartzMoss, George W. (Virginia Tech, 1999-07-27)We examine discrete models with hexagonal symmetry to compare the sequence of transitions with the alpha-inc-beta phase transition of quartz. We examine a model by Parlinski which employs interactions of nearest and next-nearest neighbor atoms. We numerically determine the configurations which lead to minimum energy for a range of parameters. We then use Golubitsky's results on systems with hexagonal symmetry to derive the bifurcation diagram for Parlinski's model. Finally, we study a large class of modifications to Parlinski's model and show that all such modifications have the same bifurcation picture as the original model.
- Minimal PMU placement for graph observability: a decomposition approachBrueni, Dennis J. (Virginia Tech, 1993-12-06)This thesis explores the PMU placement problem, that is, the placement of a minimal number of Phase Measurement Units (PMUs) on the nodes of a power system graph such that the entire graph is observed. The NP-completeness of PMU placement for planar bipartite graphs is shown. PMU placement algorithms are developed for graphs of bounded tree width, such as trees and outer planar graphs. Graph decompositions are used to develop efficient algorithms that produce minimal PMU covers. These algorithms are developed, analyzed, and compared theoretically. Algorithm animations were used in the study to develop insight into the problem and to understand algorithm behavior.
- Modeling reconfiguration algorithms for regular architectureDeBrunner, Linda Sumners (Virginia Tech, 1991-07-05)Three models are proposed to evaluate and design distributed reconfigurable systems for fault tolerant, highly reliable applications. These models serve as valuable tools for developing fault tolerant systems. In each model, cells work together in parallel to change the global structure through a series of separate actions. In the Local Supervisor Model (LSM), selected cells guide the reconfiguration process. In the Tessellation Automata Model (TAM), each cell determines its next state based on its state and its neighbors' states, and communicates its state information to its neighbors. In the Interconnected Finite State Machine Model (IFS:MM:), each cell determines its next state and outputs based on its state and its inputs. The hierarchical nature of the TAM and IFSMM provides advantages in evaluating, comparing, and designing systems. The use of each of these models in describing systems is demonstrated. The IFSMM: is emphasized since it is the most versatile of the three models. The IFSMM: is used to identify algorithm weaknesses and improvements, compare existing algorithms, and develop a novel design for a reconfigurable hypercube.
- Modeling the properties of silicatesBartelmehs, Kurt Lane (Virginia Tech, 1993-02-18)Assuming a simple force field involving only short range Non-Coulombic molecular energy terms along with P1 symmetry, a variation of the SQLOO model (Boisen and Gibbs, 1993) successfully generates the structure types of both α and β1 quartz along with at least five alternative structure types of silica not yet observed to our knowledge. These structure types are identified by the existence of symmetry elements represented in the optimized atomic coordinates and cell parameters that define a minimizer in the model. A family of minimizers is discovered through the combined use of Monte Carlo simulated annealing followed by quasi-Newton minimization techniques. The results are in contrast with the assertion made by Tse et al. (1992) that new structure types of SiO₂ can only be arrived at by Molecular Dynamic methods. By varying the parameters used in the minimization process, different families of structure types are discovered. Several structure types were found to have high symmetries. These results are in contrast with the findings by Kramer et aL (1991) that the stability of high symmetry structures of silica are stabilized in part by ionicity. The results reported here are for calculations involving Z = 3 and 6 formula units. This strategy may be useful in the prediction of possible high silica zeolite structure types. An examination of the atomic displacement parameters (ADPs) obtained for TO₄ tetrahedra (T = Si, Al) suggest rigid TO bonds are more common in non-framework than in framework silicates. Correlated motion is found among the ADPs that is consistent with TLS rigid body motion. For these data, the translational motion is represented by the ADPs of the central T atom while both the librational and translational motion is contained in those of the surrounding O atoms. The libration angle for rigid tetrahedra is linearly dependent on the difference between the isotropic equivalent displacement parameter of the T and O atoms, B(T) and B(O), respectively. The value of B(O) is on average twice that of B(T) with a maximum value of ~ 2.0Ų. Variations in the SiO bond lengths of rigid tetrahedra in the silica polymorphs is related only to fs(O). Rigid TO and OO bonds are a necessary but not sufficient condition for rigid body motion. Nonrigid tetrahedra may represent crystals containing disorder or problems with the refinement. The computer program EXCALIBR (Bloss and Riess, 1973; Bloss, 1981, p. 202) has been rewritten and markedly improved. Like EXCALIBR, EXCALIBR II solves optical extinction data, as determined with a spindle stage, and determines the optic axial angle 2V and the orientation of the crystal’s optical indicatrix. EXCALIBR II uses a modification to Joel’s equation as a means of obtaining the optic axes of a crystal. Furthermore, EXCALIBR II successfully solves extinction data where one optic axis of a biaxial crystal is 90° to the spindle axis, an orientation that had thwarted its predecessor. EXCALIBR II also accurately determines the optical indicatrix orientation for uniaxial crystals. After solving extinction data for several different wavelengths and/or temperatures, EXCALIBR II calculates the angular change of each optic direction with wavelength and/or temperature along with the error on the angle. Using a simple t-test, it then computes a p-value to aid in the decision as to whether the optical direction truly exhibits dispersion. This is a more valid and sensitive procedure than the χ² test used by EXCALIBR, particularly because the covariance in each optic vector’s coefficients are taken into consideration and the results are invariant to the vector’s orientation.
- An object-oriented database system for efficient information retrieval applicationsChen, QiFan (Virginia Tech, 1992-03-16)This dissertation deals with the application of object-oriented database techniques to the problem of storage and access of information retrieval (IR) data, especially data that can be organized as a graph, such as a thesaurus encoded in semantic networks, or hypertext collections. Even traditional IR models can use graph representations of documents and concepts. This dissertation reports the development of an object-oriented model called the LEND (Large External object-oriented Network Database) model. This model contains not only features found in a typical object-oriented model but also those that specifically are designed for graph-structured data. A query language is provided facilitating the specification of graph-oriented queries. A prototype LEND system has been implemented to test the model on realistic graph-structured data. It adopts an open system architecture and design, and is easily extensible, like the LEND model itself. The research result of suitable data structures and algorithms (a class of minimal perfect hashing functions) for the efficient implementation of the LEND model is also reported. These data structures and algorithms enable retrieval of a node or a set of nodes in an optimal fashion. Placement of a large graph on a disk is studied as well. The method developed permits efficient traversal of graphs.
- Real-time phasor measurements for improved monitoring and control of power system stabilityBaldwin, Thomas L. (Virginia Tech, 1993-05-06)This thesis investigates the use of real-time phasor measurements for voltage and transient stability monitoring and control. Taking advantage of the ability of a Phasor Measurement Unit (PMU) placed at a bus to sample at a fast rate the voltage and current phasors of that bus) various schemes for placing PMU's are considered and evaluated. These schemes include coherency based methods and pilot point placement techniques for system controllability. A novel scheme is proposed which places a minimal set of PMU's so as to make the system measurement model observable, and thereby linear. This placement scheme is derived from the topological observability theory. It concerns the building of a spanning measurement sub-graph across the system with actual or pseudo-measurement assigned to each of its branches. The minimal PMU set is found through a dual search algorithm which uses both a modified bisecting search and a simulated annealing-based method. The former fixes the number of PMU's while the latter look for a placement set that leads to an observable network. In order to accelerate the procedure, an initial PMU placement is provided by a graph-theoretic procedure which builds a spanning measurement sub-graph according to a depth-first search. From computer simulation results performed on various test systems, it appears that only one fourth of the system buses need to be provided with PMU's in order to make the system observable. In an effort to reduce the computing time of transient stability assessment, a dynamic equivalent is presented, which results from the elimination of the load buses provided with voltage--dependent loads. The elimination is performed through a new version of the Ward equivalencing method. In this approach, the equivalent current injections are expressed in terms of the retained bus angles and a sensitivity matrix. The non-linearity of the load flow model is accounted for through piecewise linear approximations by updating the sensitivity matrix whenever the operating point moves beyond the validity of the linearization. The expressions of the incremental changes in the generator electric power is derived. The study also investigates the possibility of using the telemetered data provided by the PMU's during pre-fault and post-fault operating conditions in conjunction with a. new version of the Extended Equal Area Criterion (EEAC) method. The latter is able to handle complex loads through the dynamic Ward equivalencing method. The performance of the approach is illustrated on three test systems which have been reduced to the internal generator nodes.
- The response of polyhedra in close packed structures to temperature and pressureBrown, Stephen A. (Virginia Tech, 1993-07-03)The mean quadratic elongation, < A >, is used to measure the distortions of close packed arrays of anions in crystals. It is also used to trace how such distortions vary with temperature (T) and pressure (P). A calculation of < ..\ > for arrays of anions in materials that adopt the rutile and olivine structure-types shows that the arrays exhibit increased distortions with increasing P whereas those in materials that adopt the dolomite structure-type exhibit a decrease in distortion. On the other hand, the close packed arrays in the dolomite and calcite structure-types become more distorted with increasing T. The array of oxide anions in rutile show an increased distortion while those in stishovite show a decreased distortion with increasing T. An analysis of apparent bulk moduli and linear thermal expansion coefficients calculated for the constituent polyhedra shows that the distortion of a material with a close packed structure is governed by its unoccupied as well as its occupied polyhedra. It also indicates that the rearrangement of the anions in such materials induced by an increase in P is governed by the apparent bulk moduli of its constituent polyhedra rather than by a tendency of the anions to adopt a more perfect close packed array.
- The Structure of the 2-Sylow Subgroups of the Ideal Class Groups of Imaginary Bicyclic Biquadratic FieldsRanalli, Ramona Renee (Virginia Tech, 1997-11-18)In this dissertation class groups of imaginary bicyclic biquadratic fields are considered. In chapter 1 we develop a method for determining the structure of the 2-class group of K. In chapters 3, 4, and 5 this method is applied to determine all imaginary bicyclic biquadratic extensions of Q with class number 4, 8, and 16, as well as to determine the specific structure of each.
- A study of the mean-square displacement amplitudes of T and O atoms in framework silicates and aluminosilicates: evidence for rigid TO bonds, order, disorder, twinning and stacking faults in crystalsDowns, Robert T. (Virginia Tech, 1989-12-05)The mean-square displacement amplitudes (MSDA) of the tetrahedral cations Si and Al are compared to the MSDA of their coordinated O atoms in framework silica polymorphs and aluminosilicate structures. Criteria are established which indicate order, structural disorder or substitutional disorder in a framework crystal.
- A study of the promolecule radius of nitrides, oxides and sulfides and of the bond critical point properties of the electron density distribution in nitridesFeth, Shari (Virginia Tech, 1996-12-05)"We cannot afford the luxury any longer of ignoring the nature of the bonding in these interesting compounds .... " P.E.D. Morgan, (1974). An understanding of bonding is paramount to furthering our understanding of materials (Morgan, 1974). The properties of materials are governed by the interactions between atoms. These interactions are governed by the nature of the bonds. In this study, two methods are explored which provide insight into chemical interactions. First, promolecule radii, calculated for nitride, oxide, and sulfide coordinated polyhedra with bond lengths fixed at the sums of effective ionic and crystal radii, are analyzed. Radii calculated for transition and non-transition cations for the first four rows of the periodic table are highly correlated with crystal radii derived for oxide and sulfide crystals and with ionic radii derived for nitride crystals. Promolecule radii calculated for the coordination polyhedra match experimentally determined bonded radii to within ~0.02Å, on average. Calculated radii anions tend to match ionic radii when bonded to highly electropositive cations and atomic radii when bonded to highly electronegative cations. In the second study, molecular orbital calculations were completed on a series of small molecules containing the nitride anion. Bond type can be characterized by studying the systematics of parameters derived from the bond critical point properties of the electron density distributions. A set of criteria is established to suggest how covalent or ionic a bond is. This criteria is based on bond critical point properties such as the Laplacian of the electron density distribution evaluated at the bond critical point, the electron density distribution at the critical point, the local energy density at the critical point, the relative electronegativity of the cation, the curvatures of the electron density distribution, and the distance from the nucleus of the nitride anion to the bond critical point, (the bonded radius of the nitrogen atom). Parameters computed for promolecule data indicate that these easily obtained results offer a method of calculating bond critical properties which are close in value to the more extensive results derived from molecular orbital calculations.