Poisson Density Research Articles

Microstructure characterization and SCG of newly engineered dental ceramics

ObjectivesThe aim of this study was to characterize the microstructure of four dental CAD-CAM ceramics and evaluate their susceptibility to stress corrosion. MethodsSEM and EDS were performed for microstructural characterization. For evaluation of the pattern of crystallization of the ceramics and the molecular composition, XRD and FTIR, respectively, were used. Elastic modulus, Poisson's ratio, density and fracture toughness were also measured. The specimens were subjected to biaxial flexure under five stress rates (0.006, 0.06, 0.6, 6 and 60MPa/s) to determine the subcritical crack growth parameters (n and D). Twenty-five specimens were further tested in mineral oil for determination of Weibull parameters. Two hundred forty ceramic discs (12mm diameter and 1.2mm thick) were made from four ceramics: feldspathic ceramic – FEL (Vita Mark II, Vita Zahnfabrik), ceramic-infiltrated polymer – PIC (Vita Enamic, Vita Zahnfabrik), lithium disilicate – LD (IPS e.max CAD, Ivoclar Vivadent) and zirconia-reinforced lithium silicate – LS (Vita Suprinity, Vita Zahnfabrik). ResultsPIC discs presented organic and inorganic phases (n=29.1±7.7) and Weibull modulus (m) of 8.96. The FEL discs showed n=36.6±6.8 and m=8.02. The LD discs showed a structure with needle-like disilicate grains in a glassy matrix and had the lowest value of n (8.4±0.8) and m=6.19. The ZLS discs showed similar rod-like grains, n=11.2±1.4 and m=9.98. SignificanceThe FEL and PIC discs showed the lowest susceptibility to slow crack growth (SCG), whereas the LD and ZLS discs presented the highest. PIC presented the lowest elastic modulus and no crystals in its composition, while ZLS presented tetragonal zirconia. The overall strength and SCG of the new materials did not benefit from the additional phase or microconstituents present in them.

Theoretical Study on Vibration of Non-homogeneous Tapered Visco-Elastic Rectangular Plate

A temperature-thickness coupling problem of non-homogeneous rectangular plate is analyzed. Here authors considered bi-parabolic variation in temperature i.e. parabolic in x-direction and parabolic in y-direction while variation in plate’s thickness is assumed bi-linear i.e. linear in x-direction and linear in y-direction. To characterize the non-homogeneity present in plate’s material, authors considered that poisson ratio and density of the plate’s material vary exponentially and linearly in one direction respectively. Along with, material of the plate is considered isotropic and visco-elastic. Rayleigh Ritz approach has been applied to find the time period and deflection for first two modes of vibration for diverse values of non-homogeneity constant, taper constant, density parameter, aspect ratio and thermal gradient. Results for both modes of vibration are shown in tabular form.

The thermo-mechanical properties estimation of fullerene-reinforced resin epoxy composites by molecular dynamics simulation – A comparative study

A comparative study was conducted to determine the effects of fullerene on the thermo-mechanical properties of Araldite LY 5052/Aradur HY 5052 cross-linked resin epoxy by molecular dynamics simulations. Different from ordinary epoxy resins, Araldite LY 5052/Aradur HY 5052 cross-linked resin epoxy is composed of four compounds that provide different thermal and mechanical properties. The thermo-mechanical properties of three different Araldite LY 5052/Aradur HY 5052 cross-linked resin epoxies, of which one has no fullerene and two have weight fractions of 8.64% (LY/HY/C60 (1) epoxy system) and 15.9% (LY/HY/C60 (2) epoxy system), were comparatively studied. Simulation results indicated that the glass transition temperature (Tg) has slight variations for different fullerene-containing epoxy systems and that the coefficients of thermal expansions decrease by adding fullerene to the resin epoxy system. Furthermore, mechanical properties such as Young's, bulk, and shear moduli, as well as Poisson's ratio and density, show considerable improvements after the addition of fullerene to the epoxy systems. The best mechanical properties were obtained for the weight fractions of 8.64%; this result was in agreement with the experimental results. For example, the Young's modulus of the LY/HY epoxy system increases by 19.5% and 7.5% in the LY/HY/C60 (1) epoxy system and LY/HY/C60 (2) epoxy system, respectively. The evolution of the local structures of the different fullerene-containing epoxy systems were also investigated by studying the radial distribution functions.

Production-inventory analysis of single-station parallel machine make-to-stock/make-to-order system with random demands and lead times

Hybrid Make-To-Stock (MTS)/ Make-To-Order (MTO) production systems have captivated the attention of academic and practical societies due to their high levels of flexibility and profits of stock-based systems. This paper addresses a single-station production system including two parallel machines with two production modes; one of machines is allowed to process MTO (specific) products, whilst both machines might process these products in the other mode. In the considered system, it is assumed that demands and lead times follow Poisson and exponential density functions, respectively. In this regard, a queueing model is developed upon which extensive numerical analyses are conducted with respect to the exclusive performance measures for MTS and MTO products. The defined measures comprise fill rate, average number of finished products, and average number of orders for MTS products, and average number of specific orders in the system, expected response time, and on-time delivery rate for MTO products. Additionally, sensitivity analyses are performed.

Relaxed Poisson cure rate models.

The purpose of this article is to make the standard promotion cure rate model (Yakovlev and Tsodikov, ) more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution (Laskin, ). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, ) is a simple way to obtain a new cure rate model that is a compromise between the promotion and geometric cure rate models allowing for superdispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter, but a competitor to negative-binomial cure rate models (Rodrigues etal., ). Some mathematical properties of a proper relaxed Poisson density are explored. A simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are finally presented.

Effect of Thermal Gradient on Vibration of Non-uniform Visco-elastic Rectangular Plate

Here, a theoretical model is presented to analyze the effect of bilinear temperature variations on vibration of non-homogeneous visco-elastic rectangular plate with non-uniform thickness. Non-uniformity in thickness of the plate is assumed linear in one direction. Since plate’s material is considered as non-homogeneous, authors characterized non-homogeneity in poisson ratio and density of the plate’s material exponentially in x-direction. Plate is supposed to be clamped at the ends. Deflection for first two modes of vibration is calculated by using Rayleigh–Ritz technique and tabulated for various values of plate’s parameters i.e. taper constant, aspect ratio, non-homogeneity constants and thermal gradient. Comparison of present findings with existing literature is also provided in tabular and graphical manner.

Phase transitions of NbHx (1 ≤ x ≤ 2) from first principles calculation

First-principles calculation reveals that the face-centered cubic (FCC) structure of NbH1 and NbH1.25 is energetically unstable and will automatically transform to the face-centered tetragonal (FCT) structure, and that the intrinsic composition range of the FCT → FCC transition of NbHx phases is 1.5 ≤ x < 2.0. Calculations also show that FCC is the most stable structure of NbHx under high pressure, and that the face-centered orthorhombic (FCO) and FCT structures of each NbH1 and NbH1.25 as well as FCT and FCC of each NbH1.5 and NbH1.75 are very close to each other in terms of the behaviors of phase transition and electronic structure. In addition, Poisson's ratio and density of states are discussed, respectively, to provide a fundamental understanding of various phase transitions in NbHx (1 ≤ x ≤ 2) phases.

Elastic seismic inversion and reservoir characterization in the Llanos Basin, Colombia

The contribution of seismic inversion to lithology and fluid characterization in oil reservoirs is geology and data dependent. Several studies of reservoir characterization based on elastic seismic inversion in the Llanos Basin in Colombia have proved to be successful for accurate description of the siliciclastic lithology of lower members of the Carbonera Formation. Mass density estimated from the inversion has been an important lithology discriminator because of compaction of shale, which exhibits larger densities than sand. In the analysis of properties calculated from well-log data, the separation in property space of oil sands and brine sands is moderate to small. Oil sands likely are distributed toward the zones of lower VP/VS ratio, Poisson's ratio, density, and bulk modulus, compared with other lithofluid types. The theoretical effect of fluid substitution in elastic rock parameters and density, although small because of the proximity of heavy-oil density to water density, is nevertheless present in these reservoirs. Successful exploitation of the seismic information associated with the discrimination of oil-bearing and brine-bearing sands has been achieved via fine calibration of the elastic inversion and derived reservoir indicators and by combining this information with relative two-way time (TWT) location of the strata to interpreted horizons. With statistical analysis and direct analysis over crossplots, indicators for oil sands have been formulated that are consistent with information available from wells, although slightly less accurate than lithologic (Vshale) estimation. After lithology estimation is performed from the seismic-inversion results, further improvement of the lithology description is achieved by combining the seismic-derived lithology with the localized well-log lithology profiles using geostatistical methods.

A Bayesian Approach for the Cox Proportional Hazards Model with Covariates Subject to Detection Limit.

The research on biomarkers has been limited in its effectiveness because biomarker levels can only be measured within the thresholds of assays and laboratory instruments, a challenge referred to as a detection limit (DL) problem. In this paper, we propose a Bayesian approach to the Cox proportional hazards model with explanatory variables subject to lower, upper, or interval DLs. We demonstrate that by formulating the time-to-event outcome using the Poisson density with counting process notation, implementing the proposed approach in the OpenBUGS and JAGS is straightforward. We have conducted extensive simulations to compare the proposed Bayesian approach to the other four commonly used methods and to evaluate its robustness with respect to the distribution assumption of the biomarkers. The proposed Bayesian approach and other methods were applied to an acute lung injury study, in which a panel of cytokine biomarkers was studied for the biomarkers’ association with ventilation-free survival.

Vibration Characteristics of Multi-walled Carbon Nanotubes/epoxy Composites Beam

Composites are composed of matrix and reinforcement. Generally the matrix is a polymer material. Carbon nanotubes have excellent mechanical properties, electrical and thermal properties and can be used as a reinforcement. In this study, multi-walled carbon nanotubes (MWNTs)/epoxy specimens was prepared with different MWNTs wt% to explore the vibration characteristics of composites beam. Vibration characteristics including mode shapes and natural frequencies. We measured the Young's modulus, Poisson's ratio and density of the specimens, used as the parameters in finite element analysis to obtain the mode shape and natural frequency of cantilever composite beams. The experiment and simulation results showed that adding MWNTs had some influence on the resonant frequency.

Computing the noncentral gamma distribution, its inverse and the noncentrality parameter

The noncentral gamma distribution can be viewed as a generalization of the noncentral chi-squared distribution and it can be expressed as a mixture of a Poisson density function with a incomplete g...

Finite Element Analysis: A Maxillofacial Surgeon’s Perspective

The science of finite element analysis (FEA) is purely a mathematical way of solving complex problems in the universe. In medical field, this is an innovation in biomedical research and development, as it gives easier mathematical solution to biological problems. This article deals with the understanding of various basic material properties of bone like Young's modulus, yield strength, Bulk modulus, shear modulus, Poisson's ratio and density from a maxillofacial surgeon's perspective. Basic concepts in FEA, its application, advantages, disadvantages, and limitations in the field of maxillofacial surgery have been discussed. The importance of surgical fraternity to be in coordination with evolving technologies has been emphasized for the future of evidence based practice of oral and maxillofacial surgery.

On the dynamic response of a half-space subjected to a moving mass

The dynamic response of a homogeneous, isotropic elastic half-space under a moving time-varying inertial load with subsonic speed is investigated. The surface of the half-space, which is under the action of the moving load, is a thin frictionless layer. In order to study the influences of the inertia of loads, the problem was first solved for a moving load and, then, the procedure was extended to include the inertial effects. The Navier equations of motion for the two-dimensional half-space were transformed to a system of wave-type partial differential equations using the Stokes–Helmholtz resolution. A new moving coordinate system was used and a modified system of equation was derived. The solutions of the modified system are obtained by utilizing a concurrent two-sided and one-sided Laplace transformation. The transformed dynamic responses and stresses were inverted by the Cagniard–de Hoop method. The effects of the inertia of the moving load were included using a numerical procedure to obtain the vertical surface displacement. Numerical examples for a landing traversing object on a half-space are presented to illustrate the methodology for finding the dynamic stresses and displacements in the half-space for moving load and mass cases. The final results revealed the influences of the inertia of moving loads on the dynamic stresses and displacements in the half-space. A parametric study was carried out to clarify the effects of the magnitude of the load, the Poisson ratio, density and shear moduli of the half-space on the results.

Kinetics of Myosin Node Aggregation into a Contractile Ring

We study a stochastic aggregation model for the assembly of the contractile ring from a broad band of nodes during cytokinesis in fission yeast. We found that bands of nodes condense into rings when the range of node interactions is larger than the width of the band. Wide bands are unstable to clump formation due to Poisson density fluctuations. We derive expressions for node kinetics and times for ring vs clump formation and test them using numerical simulations. These results suggest clump formation mechanisms in mutant cells.

Massively Multicore Parallelization of Kohn-Sham Theory.

A multicore parallelization of Kohn-Sham density functional theory is described, using an accelerator technology made by ClearSpeed Technology. Efficiently scaling parallelization over 2304 cores is achieved. To deliver this degree of parallelism, the Coulomb problem is reformulated to use Poisson density fitting with numerical quadrature of the required three-index integrals; extensive testing reveals negligible errors from the additional approximations.

Multiscale Poisson Intensity and Density Estimation

The nonparametric Poisson intensity and density estimation methods studied in this paper offer near minimax convergence rates for broad classes of densities and intensities with arbitrary levels of smoothness. The methods and theory presented here share many of the desirable features associated with wavelet-based estimators: computational speed, spatial adaptivity, and the capability of detecting discontinuities and singularities with high resolution. Unlike traditional wavelet-based approaches, which impose an upper bound on the degree of smoothness to which they can adapt, the estimators studied here guarantee nonnegativity and do not require any a priori knowledge of the underlying signal's smoothness to guarantee near-optimal performance. At the heart of these methods lie multiscale decompositions based on free-knot, free-degree piecewise-polynomial functions and penalized likelihood estimation. The degrees as well as the locations of the polynomial pieces can be adapted to the observed data, resulting in near-minimax optimal convergence rates. For piecewise-analytic signals, in particular, the error of this estimator converges at nearly the parametric rate. These methods can be further refined in two dimensions, and it is demonstrated that platelet-based estimators in two dimensions exhibit similar near-optimal error convergence rates for images consisting of smooth surfaces separated by smooth boundaries.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites.

The free vibration analysis and optimal design of an adhesively bonded functionally graded single lap joint

In this study, three-dimensional free vibration and stress analyses of an adhesively bonded functionally graded single lap joint were carried. The effects of the adhesive material properties, such as modulus of elasticity, Poisson's ratio and density were found to be negligible on the first ten natural frequencies and mode shapes of the adhesive joint. Both the finite element method and the back-propagation artificial neural network (ANN) method were used to investigate the effects of the geometrical parameters, such as overlap length, plate thickness and adhesive thickness; and the material composition variation through the plate thickness on the natural frequencies, mode shapes and modal strain energy of the adhesive joint. The suitable ANN models were trained successfully using a series of free vibration and stress analyses for various random geometrical parameters and compositional gradient exponents. The ANN models showed that the support length, the plate thickness and the compositional gradient exponent played important role on the natural frequencies, mode shapes and modal strain energies of the adhesive joint whereas the adhesive thickness had a minor effect. In addition, the optimal joint dimensions and compositional gradient exponent were determined using genetic algorithm and ANN models so that the maximum natural frequency and the minimum modal strain energy conditions are satisfied for each natural frequency of the adhesively bonded functionally graded single lap joint.

Borehole‐guided AVO analysis of P‐P and P‐S reflections: Quantifying uncertainty on density estimates

ABSTRACTSeismic properties of isotropic elastic formations are characterized by the three parameters: acoustic impedance, Poisson's ratio and density. Whilst the first two are usually well estimated by analysing the amplitude variation with angle (AVA) of reflected P‐P waves, density is known to be poorly resolved. However, density estimates would be useful in many situations encountered in oil and gas exploration, in particular, for minimizing risks in looking ahead while drilling. We design a borehole seismic experiment to investigate the reliability of AVA extracted density. Receivers are located downhole near the targeted reflectors and record reflected P‐P and converted P‐S waves. A non‐linear, wide‐angle‐based Bayesian inversion is then used to access the a posteriori probability distributions associated with the estimation of the three isotropic elastic parameters. The analysis of these distributions suggests that the angular variation of reflected P‐S amplitudes provides additional substantial information for estimating density, thus reducing the estimate uncertainty variance by more than one order of magnitude, compared to using only reflected P‐waves.

Optimal design of an adhesively-bonded corner joint with single support based on the free vibration analysis

This study investigates the three-dimensional free vibration behaviour of an adhesively-bonded corner joint with single support. The modulus of elasticity, Poisson's ratio and density of adhesive were found to have negligible effects on the first 10 natural frequencies and mode shapes of the corner joint. The effects of the geometrical parameters, such as support length, plate thickness, adhesive thickness and joint length, on the natural frequencies, mode shapes and modal strain energies of the adhesive joint were also investigated using both the finite element method and the back-propagation artificial neural network (ANN) method. The free vibration and stress analyses were carried out for the corner joints with various random geometrical parameters so that a suitable ANN model could be trained successfully. The support length, plate thickness and joint length all played important roles in the natural frequencies, mode shapes and modal strain energies of the corner joint, whereas the adhesive thickness for the range of adhesive thickness studied had only a minor effect. The Genetic Algorithm was also combined with the present ANN models in order to determine the optimum geometrical dimensions which satisfied the maximum natural frequency and minimum modal strain energy conditions for each natural frequency and mode shape of the adhesively-bonded corner joint.