Numerical Analysis and Computation Commons^™

Morphological Evolution Of Single-Crystal Ultrathin Solid Films, Mikhail Khenner

Mathematics Faculty Publications

An introduction to mathematical modeling of ultrathin solid films and the role of such modeling in nanotechnologies: Educational/Research presentation for senior physics majors

Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O Bi, where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.

Oscillatory And Monotonic Modes Of Long-Wave Marangoni Convection In A Thin Film, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O Bi, where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mathematics Faculty Publications

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mathematics Faculty Publications

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

Singular Superposition/Boundary Element Method For Reconstruction Of Multi-Dimensional Heat Flux Distributions With Application To Film Cooling Holes, Mahmood Silieti, Eduardo Divo, Alain J. Kassab

Publications

A hybrid singularity superposition/boundary element-based inverse problem method for the reconstruction of multi-dimensional heat flux distributions is developed. Cauchy conditions are imposed at exposed surfaces that are readily reached for measurements while convective boundary conditions are unknown at surfaces that are not amenable to measurements such as the walls of the cooling holes. The purpose of the inverse analysis is to determine the heat flux distribution along cooling hole surfaces. This is accomplished in an iterative process by distributing a set of singularities (sinks) inside the physical boundaries of the cooling hole (usually along cooling hole centerline) with a given …

An H-Adaptive Finite-Element Technique For Constructing 3d Wind Fields, Darrell Pepper, Xiuling Wang

Mechanical Engineering Faculty Research

An h-adaptive, mass-consistent finite-element model (FEM) has been developed for constructing 3D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by an a posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with smooth flow regions and small errors; small element sizes are attributed to fast-changing flow regions and large errors. The adaptive procedure employed in this model uses mesh refinement–unrefinement to satisfy error criteria. Results are presented for wind fields using sparse data obtained from two regions …

Study Of Multibody Dynamics Using Matlab, Kalyani Soman

Mechanical & Aerospace Engineering Theses & Dissertations

Research in computational dynamics has gained importance in the past few years because of the demand for analysis and simulation of various multi-body systems in the growing mechanical and aerospace industry. These multi-body systems are made of individual bodies that are interconnected via mechanical joints. Mathematically, these joints that connect the bodies can be described as constraint equations imposed upon the motions of the involved free bodies. This process will result in an equation of motion expressed in the form of a differential-algebraic equation. It is the main objective of this thesis to develop a solution algorithm that can take …

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mathematics Faculty Publications

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Mikhail Khenner

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Enhanced Stability Of A Dewetting Thin Liquid Film In A Single-Frequency Vibration Field, Sergey Shklyaev, Mikhail Khenner, Alexei Alabuzhev

Mathematics Faculty Publications

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description …

Morphologies And Kinetics Of A Dewetting Ultrathin Solid Film, Mikhail Khenner

Mathematics Faculty Publications

The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a …

Socio-Economic Impacts Of Computer Viruses In Tanzania, M Victor

Tanzania Journal of Engineering and Technology (TJET)

This paper reports on a research project conducted with an objective of identifying and assessing various approaches used by different computer users (Management, System Administrators and end users) in Tanzania to combat computer viruses (CVs), and to assess users' awareness level on CVs. Specifically, the study aimed at assessing the awareness level on CVs to the Tanzanian business community; analyze the socio -economic impact caused by CVs in Tanzania and; assess existing methods, capacity and limitations on controlling CVs in Tanzania. Data was collected using both questionnaires and interview from financial institutions such as NBC and BOT, and telecommunications sector …

Investigation And Applications Of Latin Hypercube Sampling Methods, Prashant K. Patel

Mechanical & Aerospace Engineering Theses & Dissertations

The Latin hypercube sampling method, sometimes called the stratified sampling method, is a commonly used variance reduction method. Recently, the optimal Latin hypercube sampling method (OLH) and the modified optimal Latin hypercube sampling method (MOLH) are introduced in the literature, which use the genetic algorithm to adjust the distance between sampled points.

This paper will compare the basic Latin hypercube, the optimal Latin hypercube and the modified optimal Latin hypercube methods for generating the sample points for statistical application and curve fitting, in te1ms of accuracy and efficiency. Analytical and structural examples are used in this thesis to facilitate the …

Transient Non-Linear Heat Conduction Solution By A Dual Reciprocity Boundary Element Method With An Effective Posteriori Error Estimator, Eduardo Divo, Alain J. Kassab

Publications

A Dual Reciprocity Boundary Element Method is formulated to solve non-linear heat conduction problems. The approach is based on using the Kirchhoff transform along with lagging of the effective non-linear thermal diffusivity. A posteriori error estimate is used to provide effective estimates of the temporal and spatial error. A numerical example is used to demonstrate the approach.

Application Of Meshless Methods For Thermal Analysis, Darrell Pepper, Bozidar Sarler

Mechanical Engineering Faculty Research

Many numerical and analytical schemes exist for solving heat transfer problems. The meshless method is a particularly attractive method that is receiving attention in the engineering and scientific modeling communities. The meshless method is simple, accurate, and requires no polygonalisation. In this study, we focus on the application of meshless methods using radial basis functions (RBFs) — which are simple to implement — for thermal problems. Radial basis functions are the natural generalization of univariate polynomial splines to a multivariate setting that work for arbitrary geometry with high dimensions. RBF functions depend only on the distance from some center point. …

Review Of The Product Development Process And Information Flow In The Manufacturing Industry: Problems And A Possible Wav Forward, E Opiyo

Tanzania Journal of Engineering and Technology (TJET)

No abstract provided.

Application Of Vibrational Techniques In Determination Of Dynamic Properties Of Agricultural Products-State Of The Arton Of Vibrational Techniques In Determination Of Dynamic Properties Of Agricultural Products-State Of The Art, Silas Kajuna

Tanzania Journal of Engineering and Technology (TJET)

Vibration is one of the techniques employed in the determination of dynamic properties of fruits and vegetables. It entails generation of a mechanical or acoustic vibrational signal which is propagated through the flesh of the agricultural material. A transducer is either attached or held close to the specimen to monitor the propagation of the signal through the specimen. The manner in which the signal is transmitted through the material is analyzed, and the dynamic properties of the specimen which relate to its firmness or its internal being are derived. The technique has been around for the past 30 years or …

Correlation Of Finite Element Prediction And Experimental Measurements Of Aircraft Panel Structural Vibration, Olaf L. Storaasli

Mechanical & Aerospace Engineering Theses & Dissertations

With the rapid development of computational capabilities and the implementation of complex tools for commercial finite element programs, predicting structural dynamics and related acoustics of complex structures is presently achievable. Structural finite element modeling is a design tool widely utilized for analysis of problems of all kinds. However, high frequency vibration of complex structures, such as the reinforced aircraft panel used for this study, currently does not correlate well with experimental measurements using conventional modeling methods. An investigation into the commonly used modeling techniques as well as the new tools of commercial finite element analysis packages for the prediction of …

Droplet Evaporation And Deformations In An Amplitude Modulated Ultrasonic Field, Nihad E. Daidzic, Rene Stadler, Adrian Melling

Aviation Department Publications

The aim of the report presented is the measurements of droplet oscillations.

Msda A Machinery Selection Decision Aid For Stubble Management Practices, Linda Leonard, Andrew Green

Grain and other field crops published reports

MSDA is a user friendly program developed to help farmers predict stubble outcomes before acting on their management practice. This manual is an accompaniment to a computer program designed on Micorsoft Excel-macros. Its aim is to help farmers assess their current machinery and stubble handling ability and view options that may be adopted as best practice for their properties.

The program is designed with the complete season in mind. Information is gathered on the full complement of machinery used from harvest through to seeding, to allow farmers to see all choices available and enable them to choose the best system …

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …

Grid Generation And Flow Computation About A Martian Entry Vehicle, John Edward Stewart

Mechanical & Aerospace Engineering Theses & Dissertations

A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results have been obtained for this vehicle in 1968. These results show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed here to verify the earlier results and to further describe the flight characteristics of this vehicle.

An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using an algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are …

Numerical Investigation Of A Non-Newtonian Material Through A Sudden Pipe Expansion, V. G. Masanja

Tanzania Journal of Engineering and Technology (TJET)

A numerical method for solving two dimensional elliptic boundary-value problems of fourth order is used for finding stationary solutions of the equations of motion for a laminar flow through a sudden pipe expansion of an incompressible non-Newtonian fluid with a constitutive equation of the Reiner-Rivlin (R-R) type. Results for the Newtonian fluid, which is a special case, are in excellent agreement with those by previous investigators and they demonstrate the reliability, superiority and accuracy of the method. Results for the non-Newtonian cases could be of value for fixing ideas about visco-elastic behaviour although the R-R fluid allows only inelasticity: this …