Stewart K. Kurtz

Properties of a three-dimensional Poisson-Voronoi tesselation: A Monte Carlo study

A complete statistical description of the properties of a cellular microstructure generated by a three-dimensional Poisson-Voronoi tesselation has been obtained by a rigorous computer simulation involving several hundred thousand cells. A two-parameter gamma distribution is found to be a good fit to the cells face, volume, and surface area distributions. For a sample size of several thousand cells or less, a lognormal distribution can also be used to approximate these distributions. The individual face, area, and edge length distributions are also obtained.

Three coordinate phosphorus and boron as π-donor and π-acceptor moieties respectively, in conjugated organic molecules for nonlinear optics: crystal and molecular structures of E-Ph–CHCH–B(mes)2, E-4-MeO–C6H4–CHCH-B(mes)2, and E-Ph2P–CHCH–B(mes)2[mes = 2,4,6-Me3C6H2]

Hydroboration of π-donor substituted alkynes D–CC–H [D = Ph2P, 4-X–C6H4-(X = H, MeS, MeO, H2N), and (η5-C5H5)Fe(η5-C5H4-)] with dimesitylborane {[(mes)2BH]2, mes = 2,4,6-Me3C6H2} yields air-stable ‘push–pull’E-alkenes of the form E-D–CHCH–B(mes)2, which possess large molecular hyperpolarizabilities, β, as shown by electric-field induced second-harmonic generation (EFISH) experiments at 1.91 µm; single crystal X-ray diffraction studies indicate that E-Ph–CHCH–B(mes)2 and E-4-MeO–C6H4–CHCH–B(mes)2 crystallise in centrosymmetric space groups, whereas E-Ph2P–CHCH–B(mes)2 crystallises in the acentric space group P212121 and exhibits powder SHG of 1.064 µm laser light.

Sol-gel processing of PbTiO 3 and Pb(Zr 0.52 Ti 0.48 )O 3 fibers

Homogeneous and stoichiometric PbTiO 3 and PbZr 0.52 Ti 0.48 O 3 gel fibers were drawn from viscous solutions prepared by sol-gel processing of alkoxide precursors. The fibrous gels on heating at 450 and 600 °C, respectively, formed the well-crystallized phases of PbTiO 3 and PbZr 0.52 Ti 0.48 O 3 . Fibers heat treated at 700 °C are a few centimeters long and 50 to 150 μm in diameter. PbZr 0.52 Ti 0.48 O 3 fibers subjected to heat treatment at 700 °C for 1 h consisted of fully dense submicron grains (0.15 to 0.2 μm). However, PbTiO 3 fibers under analogous conditions showed a few micropores with grains of ∼0.1 μm. Dielectric constants of these PbTiO 3 and PbZr 0.52 Ti 0.48 O 3 fibers were approximately 300 and 800, respectively.

A New Approach to the Challenge of Machinery Prognostics

Current generation mechanical diagnostic equipment is designed to identify individual events or trends in the output of sensors mounted on a mechanical component, subsystem, or system. Such equipment can provide a useful indication that a failure condition may be developing, but it cannot provide reliable prediction of the remaining safe or operational life. Typically, these diagnostic systems simply compare the output of individual sensors against a priori thresholds to establish a measure of the systems health. Two problems result from this approach: (1) There is no advantage taken of possible synergy among the sensors, i.e., the determination of health is one dimensional; and (2) the diagnosis provides only a statement regarding the current equipment health, but does not provide a prediction of the time remaining to failure. This often leads to an operational environment in which diagnostic equipment outputs are either ignored because of frequent false alarms or frequent (and costly) time-based preventive maintenance is performed to avoid hazardous failures. This paper describes a new approach to the development of a more robuts diagnosis and prognostic capability. It is based on the fusion of sensor-based and model-based information. Sensor-based information is the essence of current diagnostic systems. Model-based information combines dynamic models of individual components with micromechanical models of relevant failure mechanisms, such as fracture and crack propagation. These micromechanical models must account for initial flaw size ditribution and other microstructural parameters describing initial component condition. A specific application of this approach is addressed, the diagnosis of mechanical failure in meshing gears. Four specific issues are considered: (a) how to couple a validated numerical simulation of gear transmission error (due to tooth spacing irregularity, or material inhomogeneity) with physically and empirically based descriptions of fatigue crack grawth to predict a failure precursor signature at the component level; (b) how to predict the manifestation of this signature at the subsystem or system level where sensors are located; (c) how to fuse this model-based information with the corresponding sensor-based information to predict remaining safe or operational life of a gear; and (d) issues associated with extending this methodology to bearings and other rotating machinery components

Properties of a two-dimensional Poisson-Voronoi tesselation: A Monte-Carlo study

Abstract On the basis of simulation of 2 × 10 6 polygons, the distribution of the topological parameter (number of sides) as well as the distributions of area, perimeter, and edge length of the two-dimensional (2D) Poisson-Voronoi polygons have been accurately determined. A two-parameter gamma distribution has been found to be a good fit to both the topological and the area distributions. For sample sizes less than 5000 polygons, the two-parameter lognormal distribution can also be used to accurately describe these distributions. The area, perimeter, and edge length distributions for polygons having a fixed number of edges have also been obtained. The 2D cross section of a three-dimensional Voronoi tesselation has also been studied. The side and area distributions for these cross sections have been found to be significantly different from those in the case of pure 2D Voronoi tesselation. For the former case, our results for the mean number of sides of the neighboring cells of an n -sided cell are in agreement with Aboavs rule as well as his experimental results for the 2D cross section of magnesium oxide grains.

Simulation of material microstructure using a 3D voronoi tesselation: Calculation of effective thermal expansion coefficient of polycrystalline materials

Abstract The three-dimensional Poisson-Voronoi model is used to simulate a topologically equivalent material microstructure. A finite element package has been written to use this model to calculate the effective thermal expansion coefficient of the polycrystalline aggregate using the single crystal thermoelastic properties. The results have been found to be close to the experimental values and the values calculated from the Hashins exact equation for hexagonal, tetragonal and trigonal materials.

Structural phase transitions, ferroelectricity and high temperature superconductivity

Abstract Calculations based on a local double well potential show the near coincidence of a ferroelectric transition and a high temperature superconducting phase transition. Using double well parameters consistent with the Abrahams-Kurtz-Jamieson (AKJ) relation for ferroelectric phase transitions in oxide perovskite ferroelectrics we find that the superconducting transition temperature falls above or below the ferroelectrics transition temperature depending on modest changes in the height of the unrenormalized double well barrier. For the ReBa2Cu3O7-δ superconductors, this ferroelectric transition appears to fall above the superconducting transition temperature. The shallowness of the double-well in this case is consistent with our previous suggestion that the ReBa2Cu3O7-δ are relaxor ferroelectrics with a ferroelectric transition temperature that depends on the specific rare earth and a more or less constant superconducting transition temperature in the 90–100°K region. This result has important implicat...

Monte-Carlo study of angular and edge length distributions in a three-dimensional Poisson-Voronoi tesselation

Abstract Several hundred thousand three-dimensional Poisson-Voronoi cells have been simulated to study accurately the distributions of the dihedral angles (angles between adjacent faces), bond angles (angles between adjacent edges), total edge length of a face and total edge length of a cell. The mean values of the dihedral angle and the bond angle are found to be very close to those required by the equilibrium surface tension criterion for the polycrystalline grains. A two-parameter gamma distribution can be used to describe the total edge length distribution of a cell. For a sample size of less than few thousand cells, a twoparameter lognormal distribution can also be used to describe the total edge length distribution of the cell.

A Monte Carlo Study of Size and Angular Properties of a Three-Dimensional Poisson-Delaunay Cell

On the basis of simulation of 1.2×106 three-dimensional Poisson-Delaunay cells, the statistical properties of their size and angular parameters have been studied. The moments of the volume, face area, and edge length distributions are found to be equal to those obtained from the exact expressions of Miles and of Moller. The volume, surface area, and face area distributions can be described by the two-parameter gamma distribution. The normal distribution can be used to describe the distributions of the total edge length of a cell and the perimeter of a face. The edge length distribution has also been studied. The distribution of the angle in a face is found to be in accordance with its theoretical distribution.

Resonance enhanced Raman scatter in liquid benzene at vapor-phase absorption peaks

The resonance enhanced Raman spectra in the 1B2u mode of the forbidden benzene electronic transition band, ~230-270 nm, has been investigated. Resonance enhanced Raman scattering in both liquid benzene and liquid toluene exhibit the greatest enhancement when the wavelength of excitation is tuned to the vapor-phase absorption peaks; even though the sample volume is in a liquid state. Raman signals for the symmetric breathing mode of the carbon ring are found to be resonantly enhanced by several orders of magnitude (>500X) with deep UV excitation compared to non-resonant visible excitation. Since the benzene absorbs near this resonant wavelength, its effect on the sampled volume cannot be neglected in determining the resonance gain, as we discuss in detail. Large resonant gains correspond with excitation at the 247, 253, and 259 nm absorption peaks in the benzene vapor spectrum. The narrow region of resonance gain is investigated in detail around the absorption peak located at 259 nm using 0.25 nm steps in the excitation wavelength. We observe the resonance gain tracking the vapor phase absorption peaks and valleys within this narrow range. Results are interpreted in terms of the coherence forced by the use of a forbidden transition for resonance excitation.