Filtered density function for large eddy simulation of turbulent reacting flows

A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Itô-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD) in a temporally developing mixing layer and a spatially developing planar jet under both non-reacting and reacting conditions. In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results. © 1998 American Institute of Physics.

Simulation of RNA silencing pathway for time-dependent transgene transcription rate

The synthesis of dsRNA is analyzed using a pathway model with amplifications caused by the aberrant RNAs. The transgene influx rate is assumed time-decaying considering the fact that the number of transgenes can not be infinite. The dynamics of the transgene induced RNA silencing is investigated using a system of coupled nonautonomous ordinary nonlinear differential equations which describe the model phenomenologically. The silencing phenomena are detected after a period of transcription. Important contributions of certain parameters are discussed with several numerical examples.

Real-time Computer Simulation of Three Dimensional Elastostatics using the Finite Point Method

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

Stochastic Algorithms for Discrete Parameter Simulation Optimization

We present two efficient discrete parameter simulation optimization (DPSO) algorithms for the long-run average cost objective. One of these algorithms uses the smoothed functional approximation (SFA) procedure, while the other is based on simultaneous perturbation stochastic approximation (SPSA). The use of SFA for DPSO had not been proposed previously in the literature. Further, both algorithms adopt an interesting technique of random projections that we present here for the first time. We give a proof of convergence of our algorithms. Next, we present detailed numerical experiments on a problem of admission control with dependent service times. We consider two different settings involving parameter sets that have moderate and large sizes, respectively. On the first setting, we also show performance comparisons with the well-studied optimal computing budget allocation (OCBA) algorithm and also the equal allocation algorithm. Note to Practitioners-Even though SPSA and SFA have been devised in the literature for continuous optimization problems, our results indicate that they can be powerful techniques even when they are adapted to discrete optimization settings. OCBA is widely recognized as one of the most powerful methods for discrete optimization when the parameter sets are of small or moderate size. On a setting involving a parameter set of size 100, we observe that when the computing budget is small, both SPSA and OCBA show similar performance and are better in comparison to SFA, however, as the computing budget is increased, SPSA and SFA show better performance than OCBA. Both our algorithms also show good performance when the parameter set has a size of 10(8). SFA is seen to show the best overall performance. Unlike most other DPSO algorithms in the literature, an advantage with our algorithms is that they are easily implementable regardless of the size of the parameter sets and show good performance in both scenarios.

Recent Advances in Low CTE and High Density System-on-a-Package (SOP) Substrate with Thin Film Component Integration

The Packaging Research Center has been developing next generation system-on-a-package (SOP) technology with digital, RF, optical, and sensor functions integrated in a single package/module. The goal of this effort is to develop a platform substrate technology providing very high wiring density and embedded thin film passive and active components using PWB compatible materials and processes. The latest SOP baseline process test vehicle has been fabricated on novel Si-matched CTE, high modulus C-SiC composite core substrates using 10mum thick BCB dielectric films with loss tangent of 0.0008 and dielectric constant of 2.65. A semi-additive plating process has been developed for multilayer microvia build-up using BCB without the use of any vacuum deposition or polishing/CMP processes. PWB and package substrate compatible processes such as plasma surface treatment/desmear and electroless/electrolytic pulse reverse plating was used. The smallest line width and space demonstrated in this paper is 6mum with microvia diameters in the 15-30mum range. This build-up process has also been developed on medium CTE organic laminates including MCL-E-679F from Hitachi Chemical and PTFE laminates with Cu-Invar-Cu core. Embedded decoupling capacitors with capacitance density of >500nF/cm2 have been integrated into the build-up layers using sol-gel synthesized BaTiO3 thin films (200-300nm film thickness) deposited on copper foils and integrated using vacuum lamination and subtractive etch processes. Thin metal alloy resistor films have been integrated into the SOP substrate using two methods: (a) NiCrAlSi thin films (25ohms per square) deposited on copper foils (Gould Electronics) laminated on the build-up layers and two step etch process for resistor definition, and (b) electroless plated Ni-W-P thin films (70 ohms to few Kohms per square) on the BCB dielectric by plasma surface treatment and activation. The electrical design and build-up layer structure along- - with key materials and processes used in the fabrication of the SOP4 test vehicle were presented in this paper. Initial results from the high density wiring and embedded thin film components were also presented. The focus of this paper is on integration of materials, processes and structures in a single package substrate for system-on-a-package (SOP) implementation