Nonparametric Bayesian Density Modeling with Gaussian Processes

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.

Modeling Nonlinear Peeling of Ductile Thin Films-Critical Assessment of Analytical Bending Models Using FE Simulations

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.

Modeling of Ammonothermal Growth of Nitrides

Bulk single crystals of GaN and AlN can be grown from supercritical fluids using the ammonothermal method, which utilizes ammonia as fluid rather than water as in the hydrothermal process. In this process, a mineralizer such as amide, imide or nitride is used to attack a bulk nitride feedstock at temperatures from 200°C to 500°C and pressures from 1 to 4 kbar. Ammonothermal systems have been modeled here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the fluid flow is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. The effects of particle size on flow pattern and temperature distribution in an autoclave are analyzed.

Two-dimensional Cartesian air-gap element (CAGE) for dynamic finite-element modeling of electrical machines with a flat air gap

This paper extends the air-gap element (AGE) to enable the modeling of flat air gaps. AGE is a macroelement originally proposed by Abdel-Razek et al.for modeling annular air gaps in electrical machines. The paper presents the theory of the new macroelement and explains its implementation within a time-stepped finite-element (FE) code. It validates the solution produced by the new macroelement by comparing it with that obtained by using an FE mesh with a discretized air gap. It then applies the model to determine the open-circuit electromotive force of an axial-flux permanent-magnet machine and compares the results with measurements.

Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Modeling and Simulation of Liquid Pulsed Particulate Fluidized Beds

Pulsed fluidization is of considerable interest in process engineering for improving fluidization quality. Quantitative understanding of the pulsed two-phase flow behaviors is very important for proper design and optimum operation of such contactors. The

Turbulent Modeling of ABL over Wavy Water Surface

A new model accounting for both turbulence and sea state effects has been proposed in this paper to describe momentum, heat and moisture exchanges through air-sea interface. While long wave components mainly change air flow profile, short wave components

Physical modeling of untrenched submarine pipeline instability

Wave-induced instability of untrenched pipeline on sandy seabed is a `wave-soil-pipeline' coupling dynamic problem. To explore the mechanism of the pipeline instability, the hydrodynamic loading with U-shaped oscillatory flow tunnel is adopted, which is quite different from the previous experiment system. Based on dimensional analysis, the critical conditions for pipeline instability are investigated by altering pipeline submerged weight, diameter, soil parameters, etc. Based on the experimental results, different linear relationships between Froude number (Fr) and non-dimensional pipeline weight (G) are obtained for two constraint conditions. Moreover, the effects of loading history on the pipeline stability are also studied. Unlike previous experiments, sand scouring during the process of pipe's losing stability is detected in the present experiments. In addition, the experiment results are compared with the previous experiments, based on Wake II model for the calculation of wave-induced forces upon pipeline. It shows that the results of two kinds of experiments are comparable, but the present experiments provide better physical insight of the wave-soil-pipeline coupling effects.

Modeling Ammonothermal Growth of GaN Single Crystals: The Role of Transport

Single crystal gallium nitride (GaN) is an important technological material used primarily for the manufacture of blue light lasers. An important area of contemporary research is developing a viable growth technique. The ammonothermal technique is an important candidate among many others with promise of commercially viable growth rates and material quality. The GaN growth rates are a complicated function of dissolution kinetics, transport by thermal convection and crystallization kinetics. A complete modeling effort for the growth would involve modeling each of these phenomena and also the coupling between these. As a first step, the crystallization and dissolution kinetics were idealized and the growth rates as determined purely by transport were investigated. The growth rates thus obtained were termed ‘transport determined growth rates’ and in principle are the maximum growth rates that can be obtained for a given configuration of the system. Using this concept, a parametric study was conducted primarily on the geometric and the thermal boundary conditions of the system to optimize the ‘transport determined growth rate’ and determine conditions when transport might be a bottleneck.

Modeling on Runoff Concentration Caused by Rainfall on Hillslopes and Application in Maoping Slope

Based on the fact that the concentration flowlines of overland flow depend on the surface landform of hillslope, a kinematic wave model was developed for simulating runoff generation and flow concentration caused by rainfall on hillslopes. The model-simulated results agree well with experimental observations. Applying the model to the practical case of Maoping slope, we obtained the characteristics of runoff generation and infiltration on the slope. Especially, the simulated results adequately reflected the confluent pattern of surface runoff, which offers a scientific foundation for designing the drainage engineering on the Maoping slope.

Progress In Modeling Of Fluid Flows In Crystal Growth Processes

Modeling of fluid flows in crystal growth processes has become an important research area in theoretical and applied mechanics. Most crystal growth processes involve fluid flows, such as flows in the melt, solution or vapor. Theoretical modeling has played an important role in developing technologies used for growing semiconductor crystals for high performance electronic and optoelectronic devices. The application of devices requires large diameter crystals with a high degree of crystallographic perfection, low defect density and uniform dopant distribution. In this article, the flow models developed in modeling of the crystal growth processes such as Czochralski, ammonothermal and physical vapor transport methods are reviewed. In the Czochralski growth modeling, the flow models for thermocapillary flow, turbulent flow and MHD flow have been developed. In the ammonothermal growth modeling, the buoyancy and porous media flow models have been developed based on a single-domain and continuum approach for the composite fluid-porous layer systems. In the physical vapor transport growth modeling, the Stefan flow model has been proposed based on the flow-kinetics theory for the vapor growth. In addition, perspectives for future studies on crystal growth modeling are proposed. (c) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.