The development of a wax layer on the interior wall of a circular pipe transporting heated oil

In this article we develop a simple model to describe the evolution of a depositional wax layer on the inner surface of a circular pipe transporting heated oil, which contains dissolved wax. When the outer pipe surface is cooled sufficiently, the growth of a wax layer is initiated on the inner pipe wall, and this evolves to a saturated steady state thickness. The model proposed is based on fundamental balances of heat flow from the oil, into the wax layer, and across the pipe wall. We present an analysis of the model, examine a relevant asymptotic limit in which the full details of the solution to the model are available and develop an efficient numerical method (based on the method of fundamental solutions) for producing approximations of the model solution. The mathematical structure of the model is that of a free boundary evolution problem of generalised Stefan type. © The Author, 2014.

Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations

AMS Subj. Classification: 49J15, 49M15

Determination of the Dynamic Contact Angle trough the Meniscus Profile

Станимир Д. Илиев, Нина Хр. Пешева - Представен е хибриден експериментално-числен метод, работещ в реално време, за определяне на макроскопичния динамичен контактен ъгъл, който менискусът на течност в съд формира с вертикална пластина, която се потапя или издърпва с постоянна скорост от съда с течността. Този метод е приложим, когато системата е в стационарно състояние. Методът се базира на пълния хидродинамичен модел на Войнов. Той позволява да се получи числено с висока точност стационарната форма на профила на динамичния менискус (и от там ъгълът на наклон на менискуса) като се използва като гранично условие експериментално определената височина на менискуса на пластината.

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

2000 Mathematics Subject Classification: 65M06, 65M12.

Leak identification in saturated unsteady flow via a Cauchy problem

This work is an initial study of a numerical method for identifying multiple leak zones in saturated unsteady flow. Using the conventional saturated groundwater flow equation, the leak identification problem is modelled as a Cauchy problem for the heat equation and the aim is to find the regions on the boundary of the solution domain where the solution vanishes, since leak zones correspond to null pressure values. This problem is ill-posed and to reconstruct the solution in a stable way, we therefore modify and employ an iterative regularizing method proposed in [1] and [2]. In this method, mixed well-posed problems obtained by changing the boundary conditions are solved for the heat operator as well as for its adjoint, to get a sequence of approximations to the original Cauchy problem. The mixed problems are solved using a Finite element method (FEM), and the numerical results indicate that the leak zones can be identified with the proposed method.

Periodic polymer photonic bandgap structures for on-chip optical cavities

Integrated on-chip optical platforms enable high performance in applications of high-speed all-optical or electro-optical switching, wide-range multi-wavelength on-chip lasing for communication, and lab-on-chip optical sensing. Integrated optical resonators with high quality factor are a fundamental component in these applications. Periodic photonic structures (photonic crystals) exhibit a photonic band gap, which can be used to manipulate photons in a way similar to the control of electrons in semiconductor circuits. This makes it possible to create structures with radically improved optical properties. Compared to silicon, polymers offer a potentially inexpensive material platform with ease of fabrication at low temperatures and a wide range of material properties when doped with nanocrystals and other molecules. In this research work, several polymer periodic photonic structures are proposed and investigated to improve optical confinement and optical sensing. We developed a fast numerical method for calculating the quality factor of a photonic crystal slab (PhCS) cavity. The calculation is implemented via a 2D-FDTD method followed by a post-process for cavity surface energy radiation loss. Computational time is saved and good accuracy is demonstrated compared to other published methods. Also, we proposed a novel concept of slot-PhCS which enhanced the energy density 20 times compared to traditional PhCS. It combines both advantages of the slot waveguide and photonic crystal to localize the high energy density in the low index material. This property could increase the interaction between light and material embedded with nanoparticles like quantum dots for active device development. We also demonstrated a wide range bandgap based on a one dimensional waveguide distributed Bragg reflector with high coupling to optical waveguides enabling it to be easily integrated with other optical components on the chip. A flexible polymer (SU8) grating waveguide is proposed as a force sensor. The proposed sensor can monitor nN range forces through its spectral shift. Finally, quantum dot - doped SU8 polymer structures are demonstrated by optimizing spin coating and UV exposure. Clear patterns with high emission spectra proved the compatibility of the fabrication process for applications in optical amplification and lasing.

Measurement limitations in knife-edge tomographic phase retrieval of focused IR laser beams

An experimental setup to measure the three-dimensional phase-intensity distribution of an infrared laser beam in the focal region has been presented. It is based on the knife-edge method to perform a tomographic reconstruction and on a transport of intensity equation-based numerical method to obtain the propagating wavefront. This experimental approach allows us to characterize a focalized laser beam when the use of image or interferometer arrangements is not possible. Thus, we have recovered intensity and phase of an aberrated beam dominated by astigmatism. The phase evolution is fully consistent with that of the beam intensity along the optical axis. Moreover, this method is based on an expansion on both the irradiance and the phase information in a series of Zernike polynomials. We have described guidelines to choose a proper set of these polynomials depending on the experimental conditions and showed that, by abiding these criteria, numerical errors can be reduced.

Assessment of primary energy conversions of oscillating water columns. II. Power take-off and validations

This is the second part of the assessment of primary energy conversions of oscillating water columns (OWCs) wave energy converters. In the first part of the research work, the hydrodynamic performance of OWC wave energy converter has been extensively examined, targeting on a reliable numerical assessment method. In this part of the research work, the application of the air turbine power take-off (PTO) to the OWC device leads to a coupled model of the hydrodynamics and thermodynamics of the OWC wave energy converters, in a manner that under the wave excitation, the varying air volume due to the internal water surface motion creates a reciprocating chamber pressure (alternative positive and negative chamber pressure), whilst the chamber pressure, in turn, modifies the motions of the device and the internal water surface. To do this, the thermodynamics of the air chamber is first examined and applied by including the air compressibility in the oscillating water columns for different types of the air turbine PTOs. The developed thermodynamics is then coupled with the hydrodynamics of the OWC wave energy converters. This proposed assessment method is then applied to two generic OWC wave energy converters (one bottom fixed and another floating), and the numerical results are compared to the experimental results. From the comparison to the model test data, it can be seen that this numerical method is capable of assessing the primary energy conversion for the oscillating water column wave energy converters.

Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.

Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Modeling of burden distribution in the blast furnace

The blast furnace is the main ironmaking production unit in the world which converts iron ore with coke and hot blast into liquid iron, hot metal, which is used for steelmaking. The furnace acts as a counter-current reactor charged with layers of raw material of very different gas permeability. The arrangement of these layers, or burden distribution, is the most important factor influencing the gas flow conditions inside the furnace, which dictate the efficiency of the heat transfer and reduction processes. For proper control the furnace operators should know the overall conditions in the furnace and be able to predict how control actions affect the state of the furnace. However, due to high temperatures and pressure, hostile atmosphere and mechanical wear it is very difficult to measure internal variables. Instead, the operators have to rely extensively on measurements obtained at the boundaries of the furnace and make their decisions on the basis of heuristic rules and results from mathematical models. It is particularly difficult to understand the distribution of the burden materials because of the complex behavior of the particulate materials during charging. The aim of this doctoral thesis is to clarify some aspects of burden distribution and to develop tools that can aid the decision-making process in the control of the burden and gas distribution in the blast furnace. A relatively simple mathematical model was created for simulation of the distribution of the burden material with a bell-less top charging system. The model developed is fast and it can therefore be used by the operators to gain understanding of the formation of layers for different charging programs. The results were verified by findings from charging experiments using a small-scale charging rig at the laboratory. A basic gas flow model was developed which utilized the results of the burden distribution model to estimate the gas permeability of the upper part of the blast furnace. This combined formulation for gas and burden distribution made it possible to implement a search for the best combination of charging parameters to achieve a target gas temperature distribution. As this mathematical task is discontinuous and non-differentiable, a genetic algorithm was applied to solve the optimization problem. It was demonstrated that the method was able to evolve optimal charging programs that fulfilled the target conditions. Even though the burden distribution model provides information about the layer structure, it neglects some effects which influence the results, such as mixed layer formation and coke collapse. A more accurate numerical method for studying particle mechanics, the Discrete Element Method (DEM), was used to study some aspects of the charging process more closely. Model charging programs were simulated using DEM and compared with the results from small-scale experiments. The mixed layer was defined and the voidage of mixed layers was estimated. The mixed layer was found to have about 12% less voidage than layers of the individual burden components. Finally, a model for predicting the extent of coke collapse when heavier pellets are charged over a layer of lighter coke particles was formulated based on slope stability theory, and was used to update the coke layer distribution after charging in the mathematical model. In designing this revision, results from DEM simulations and charging experiments for some charging programs were used. The findings from the coke collapse analysis can be used to design charging programs with more stable coke layers.

Advanced Adhesion Strength Testing Methods of Thin Film Multilayers in Electronic Packaging Systems

With the continued miniaturization and increasing performance of electronic devices, new technical challenges have arisen. One such issue is delamination occurring at critical interfaces inside the device. This major reliability issue can occur during the manufacturing process or during normal use of the device. Proper evaluation of the adhesion strength of critical interfaces early in the product development cycle can help reduce reliability issues and time-to-market of the product. However, conventional adhesion strength testing is inherently limited in the face of package miniaturization, which brings about further technical challenges to quantify design integrity and reliability. Although there are many different interfaces in today's advanced electronic packages, they can be generalized into two main categories: 1) rigid to rigid connections with a thin flexible polymeric layer in between, or 2) a thin film membrane on a rigid structure. Knowing that every technique has its own advantages and disadvantages, multiple testing methods must be enhanced and developed to be able to accommodate all the interfaces encountered for emerging electronic packaging technologies. For evaluating the adhesion strength of high adhesion strength interfaces in thin multilayer structures a novel adhesion test configuration called “single cantilever adhesion test (SCAT)” is proposed and implemented for an epoxy molding compound (EMC) and photo solder resist (PSR) interface. The test method is then shown to be capable of comparing and selecting the stronger of two potential EMC/PSR material sets. Additionally, a theoretical approach for establishing the applicable testing domain for a four-point bending test method was presented. For evaluating polymeric films on rigid substrates, major testing challenges are encountered for reducing testing scatter and for factoring in the potentially degrading effect of environmental conditioning on the material properties of the film. An advanced blister test with predefined area test method was developed that considers an elasto-plastic analytical solution and implemented for a conformal coating used to prevent tin whisker growth. The advanced blister testing with predefined area test method was then extended by employing a numerical method for evaluating the adhesion strength when the polymer’s film properties are unknown.

PCA-FNN based performance prediction for water injection in oilfields.

In order to solve the problem of uncertain cycle of water injection in the oilfield, this paper proposed a numerical method based on PCA-FNN, so that it can forecast the effective cycle of water injection. PCA is used to reduce the dimension of original data, while FNN is applied to train and test the new data. The correctness of PCA-FNN model is verified by the real injection statistics data from 116 wells of an oilfield, the result shows that the average absolute error and relative error of the test are 1.97 months and 10.75% respectively. The testing accuracy has been greatly improved by PCA-FNN model compare with the FNN which has not been processed by PCA and multiple liner regression method. Therefore, PCA-FNN method is reliable to forecast the effectiveness cycle of water injection and it can be used as an decision-making reference method for the engineers.

Aplicação da metodologia numérica “fast bounds crack” para uma estimativa eficiente da evolução do tamanho de trinca

A significant part of the life of a mechanical component occurs, the crack propagation stage in fatigue. Currently, it is had several mathematical models to describe the crack growth behavior. These models are classified into two categories in terms of stress range amplitude: constant and variable. In general, these propagation models are formulated as an initial value problem, and from this, the evolution curve of the crack is obtained by applying a numerical method. This dissertation presented the application of the methodology "Fast Bounds Crack" for the establishment of upper and lower bounds functions for model evolution of crack size. The performance of this methodology was evaluated by the relative deviation and computational times, in relation to approximate numerical solutions obtained by the Runge-Kutta method of 4th explicit order (RK4). Has been reached a maximum relative deviation of 5.92% and the computational time was, for examples solved, 130,000 times more higher than achieved by the method RK4. Was performed yet an Engineering application in order to obtain an approximate numerical solution, from the arithmetic mean of the upper and lower bounds obtained in the methodology applied in this work, when you don’t know the law of evolution. The maximum relative error found in this application was 2.08% which proves the efficiency of the methodology "Fast Bounds Crack".

COMPREHENSIVE ELECTRICAL/OPTICAL/THERMAL CHARACTERIZATIONS OF HIGH POWER LIGHT EMITTING DIODES AND LASER DIODES

Thermal characterizations of high power light emitting diodes (LEDs) and laser diodes (LDs) are one of the most critical issues to achieve optimal performance such as center wavelength, spectrum, power efficiency, and reliability. Unique electrical/optical/thermal characterizations are proposed to analyze the complex thermal issues of high power LEDs and LDs. First, an advanced inverse approach, based on the transient junction temperature behavior, is proposed and implemented to quantify the resistance of the die-attach thermal interface (DTI) in high power LEDs. A hybrid analytical/numerical model is utilized to determine an approximate transient junction temperature behavior, which is governed predominantly by the resistance of the DTI. Then, an accurate value of the resistance of the DTI is determined inversely from the experimental data over the predetermined transient time domain using numerical modeling. Secondly, the effect of junction temperature on heat dissipation of high power LEDs is investigated. The theoretical aspect of junction temperature dependency of two major parameters – the forward voltage and the radiant flux – on heat dissipation is reviewed. Actual measurements of the heat dissipation over a wide range of junction temperatures are followed to quantify the effect of the parameters using commercially available LEDs. An empirical model of heat dissipation is proposed for applications in practice. Finally, a hybrid experimental/numerical method is proposed to predict the junction temperature distribution of a high power LD bar. A commercial water-cooled LD bar is used to present the proposed method. A unique experimental setup is developed and implemented to measure the average junction temperatures of the LD bar. After measuring the heat dissipation of the LD bar, the effective heat transfer coefficient of the cooling system is determined inversely. The characterized properties are used to predict the junction temperature distribution over the LD bar under high operating currents. The results are presented in conjunction with the wall-plug efficiency and the center wavelength shift.