While rheological and microstructural complexities have posed tremendous challenges to researchers in developing first principles models and simulation techniques that can accurately and robustly predict the dynamical behaviour of polymeric flows, the past two decades have offered several significant advances towards accomplishing this goal. These accomplishments include: (1). Stable and accurate formulation of continuum-level viscoelastic constitutive models and their efficient implementation using operator splitting methods to explore steady and transient flows in complex geometries, (2). Prediction of rheology of polymer solutions and melts based on micromechanical models as well as highly parallel self-consistent multiscale simulations of non-homogeneous flows. The main objective of this study is to leverage and build upon the aforementioned advances to develop a quantitative understanding of the flow-micro-structure coupling mechanisms in viscoelastic polymeric fluids and in turn predict, consistent with experiments, their essential macroscopic flow properties e.g. frictional drag, interface shape, etc. To this end, we have performed extensive continuum and multiscale flow simulations in several industrially relevant bulk and free surface flows. The primary motivation for the selection of the specific flow problems is based on their ability to represent different deformation types, and the ability to experimentally verify the simulation results as well as their scientific and industrial significance.

Ultra-wideband systems can be used in indoor wireless personal area network (WPAN) or short-range wireless local area network (WLAN) transmission. Yet owing to the effects of indoor dense multipath, it will cause more power consumption. We usually use Rake receiver to improve system performance. However, we should do some compromise between system performance and the design complexity. Thus, the concept of Selective Rake can be used to substitute for the conventional Rake receiver. Selective Rake receiver uses fewer but more powerful paths instead of using all the paths to raise system performance. Hence, we have to precisely detect the multipath components for best performance. Earlier we use CLEAN algorithm to estimate the multipath components. The CLEAN algorithm can be used in selecting the paths with relatively high energy. But as the impact of frequency selective fading makes the transmitted signal distorted, the CLEAN algorithm no longer applies to this situation. Thus, we use Multiscale CLEAN algorithm instead. Multiscale CLEAN algorithm calculate the value of cross-correlation between the received signal and a set of waveforms, and then choose the higher one as the waveform transmitted. Besides, we use Maximal Ratio Combining to weigh the different paths to get the signal with more power. We represent the signal affected by frequency selective fading by using the second derivatives of Gaussian waveform function with different effective widths of pulse. The waveforms corresponding different effective widths have different spectra which represent the different effects of fading. It is seen that that the multiscale CLEAN has better performance than the CLEAN algorithm with more precise estimation of multipath components. In simulation result, we can figure out path searching using Multiscale CLEAN algorithm is more accurate than using CLEAN algorithm. Even the path with smaller energy gain, using multiscale CLEAN algorithm can search successfully, while CLEAN algorithm cannot do.

The observed multiscale phenomenon of rough surfaces, i.e. the smaller mountains mount on the bigger ones successively, renders the hierarchical structures which are described by the fractal geometry. In this situation, when two rough surfaces are loaded together with a higher load, the smaller asperities will undergo plastic flow and immerge into the bigger asperities below them. In other words, the higher load needs to be supported by the bigger asperities. However, when the GW model was proposed in 1966, its analytical method considered that the length-scale of asperities is fixed, which is independent of load (or surface separation). In such condition, the analytical results for a specific asperity length-scale can only suit the situation of a certain narrow range of load. In this research, a new model, called the multiscale GW model, has been developed, which takes into account the relationship between the load and the asperity length-scale. At first, based on the Nayak¡¦s model the multiscale asperity properties with different surface parameters have been derived, and based on the material yielding theory a criterion for determining the optimal asperity length-scale, which functions as supporting the load, is developed. Then both of the above are integrated into the GW model to build the multiscale GW model. The new model is compared with traditional one qualitatively and quantitatively and show their essential differences. The effects of surface parameters and material parameters are discussed in this model. Finally a comparison with the experiment is made, and reveal the good coincidence.

Over the last two decades, advanced fabrication techniques have enabled the fabrication of materials and devices at sub-micron length scales. For heat conduction, the conventional Fourier model for predicting energy transport has been shown to yield erroneous results on such length scales. In semiconductors and dielectrics, energy transport occurs through phonons, which are quanta of lattice vibrations. When phase coherence effects can be ignored, phonon transport may be modeled using the semi-classical phonon Boltzmann transport equation (BTE). The objective of this thesis is to develop an efficient computational method to solve the BTE, both for single-material and multi-material systems, where transport across heterogeneous interfaces is expected to play a critical role. The resulting solver will find application in the design of microelectronic circuits and thermoelectric devices. The primary source of computational difficulties in solving the phonon BTE lies in the scattering term, which redistributes phonon energies in wave-vector space. In its complete form, the scattering term is non-linear, and is non-zero only when energy and momentum conservation rules are satisfied. To reduce complexity, scattering interactions are often approximated by the single mode relaxation time (SMRT) approximation, which couples different phonon groups to each other through a thermal bath at the equilibrium temperature. The most common methods for solving the BTE in the SMRT approximation employ sequential solution techniques which solve for the spatial distribution of the phonon energy of each phonon group one after another. Coupling between phonons is treated explicitly and updated after all phonon groups have been solved individually. When the domain length is small compared to the phonon mean free path, corresponding to a high Knudsen number ([mathematical equation]), this sequential procedure works well. At low Knudsen number, however, this procedure suffers long convergence times because the coupling between phonon groups is very strong for an explicit treatment of coupling to suffice. In problems of practical interest, such as silicon-based microelectronics, for example, phonon groups have a very large spread in mean free paths, resulting in a combination of high and low Knudsen number; in these problems, it is virtually impossible to obtain solutions using sequential solution techniques. In this thesis, a new computational procedure for solving the non-gray phonon BTE under the SMRT approximation is developed. This procedure, called the coupled ordinates method (COMET), is shown to achieve significant solution acceleration over the sequential solution technique for a wide range of Knudsen numbers. Its success lies in treating phonon-phonon coupling implicitly through a direct solution of all equations in wave vector space at a particular spatial location. To increase coupling in the spatial domain, this procedure is embedded as a relaxation sweep in a geometric multigrid. Due to the heavy computational load at each spatial location, COMET exhibits excellent scaling on parallel platforms using domain decomposition. On serial platforms, COMET is shown to achieve accelerations of 60 times over the sequential procedure for Kn<1.0 for gray phonon transport problems, and accelerations of 233 times for non-gray problems. COMET is then extended to include phonon transport across heterogeneous material interfaces using the diffuse mismatch model (DMM). Here, coupling between phonon groups occurs because of reflection and transmission. Efficient algorithms, based on heuristics, are developed for interface agglomeration in creating coarse multigrid levels. COMET is tested for phonon transport problems with multiple interfaces and shown to outperform the sequential technique. Finally, the utility of COMET is demonstrated by simulating phonon transport in a nanoparticle composite of silicon and germanium. A realistic geometry constructed from x-ray CT scans is employed. This composite is typical of those which are used to reduce lattice thermal conductivity in thermoelectric materials. The effective thermal conductivity of the composite is computed for two different domain sizes over a range of temperatures. It is found that for low temperatures, the thermal conductivity increases with temperature because interface scattering dominates, and is insensitive to temperature; the increase of thermal conductivity is primarily a result of the increase in phonon population with temperature consistent with Bose-Einstein statistics. At higher temperatures, Umklapp scattering begins to take over, causing a peak in thermal conductivity and a subsequent decrease with temperature. However, unlike bulk materials, the peak is shallow, consistent with the strong role of interface scattering. The interaction of phonon mean free path with the particulate length scale is examined. The results also suggest that materials with very dissimilar cutoff frequencies would yield a thermal conductivity which is closest to the lowest possible value for the given geometry. / text

The main aim of this thesis is to design efficient and novel numerical algorithms for a class of deterministic and stochastic dynamical systems with multiple time scales. Classical numerical methods for such problems need temporal resolution to resolve the finest scale and become, therefore, inefficient when the much longer time intervals are of interest. In order to accelerate computations and improve the long time accuracy of numerical schemes, we take advantage of various multiscale structures established from a separation of time scales. This dissertation is organized into four chapters: an introduction followed by three chapters, each based on one of three different papers. The framework of the heterogeneous multiscale method (HMM) is considered as a general strategy both for the design and the analysis of multiscale methods. In Chapter 2, we consider a new class of multiscale methods that use a technique related to the construction of a Poincaré map. The main idea is to construct effective paths in the state space whose projection onto the slow subspace shows the correct dynamics. More precisely, we trace the evolution of the invariant manifold M(t), identified by the level sets of slow variables, by introducing a slowly evolving effective path which crosses M(t). The path is locally constructed through interpolation of neighboring points generated from our developed map. This map is qualitatively similar to a Poincaré map, but its construction is based on the procedure which solves two split equations successively backward and forward in time only over a short period. This algorithm does not require an explicit form of any slow variables. In Chapter 3, we present efficient techniques for numerical averaging over the invariant torus defined by ergodic dynamical systems which may not be mixing. These techniques are necessary, for example, in the numerical approximation of the effective slow behavior of highly oscillatory ordinary differential equations in weak near-resonance. In this case, the torus is embedded in a higher dimensional space and is given implicitly as the intersection of level sets of some slow variables, e.g. action variables. In particular, a parametrization of the torus may not be available. Our method constructs an appropriate coordinate system on lifted copies of the torus and uses an iterated convolution with respect to one-dimensional averaging kernels. Non-uniform invariant measures are approximated using a discretization of the Frobenius-Perron operator. These two numerical averaging strategies play a central role in designing multiscale algorithms for dynamical systems, whose fast dynamics is restricted not to a circle, but to the tori. The efficiency of these methods is illustrated by numerical examples. In Chapter 4, we generalize the classical two-scale averaging theory to multiple time scale problems. When more than two time scales are considered, the effective behavior may be described by the new type of slow variables which do not have formally bounded derivatives. Therefore, it is necessary to develop a theory to understand them. Such theory should be applied in the design of multiscale algorithms. In this context, we develop an iterated averaging theory for highly oscillatory dynamical systems involving three separated time scales. The relevant multiscale algorithm is constructed as a family of multilevel solvers which resolve the different time scales and efficiently computes the effective behavior of the slowest time scale. / text

Many important biomaterials are composed of multiple layers of networked fibers. A prime example is in the field of tissue engineering, in which damaged or diseased native tissues are replaced by artificial tissues that are grown on fibrous polymer networks. For load bearing tissues, it is critical that the mechanical behavior of the engineered tissue be similar to the behavior of the native tissue that it will replace. In the case of soft tissues such as heart valves, the macroscale mechanical behavior is highly anisotropic and nonlinear. This behavior is a result of complex deformations of the collagen and elastin fibers that form the extracellular matrix (ECM). The microstructure of engineered tissues must be properly designed to reproduce this unique macroscopic behavior. While there is a growing interest in modeling and simulation of the mechanical response of this class of biomaterials, a theoretical foundation for such simulations has yet to be firmly established. This work introduces a method for modeling materials that have a layered, fibrous network microstructure. Methods for characterizing the complex network geometry are first established. Then an algorithm is developed for generating realistic network geometry that is a good representation of electrospun tissue scaffolds, which serve as the primary synthetic structure on which engineered tissues are grown. The level of fidelity to the real geometry is a significant improvement on previous representations. This improvement is important, since the scaffold geometry has a strong influence over the macroscopic mechanical behavior of the tissue, cell proliferation and attachment, nutrient and waste flows, and extracellular matrix (ECM) generation. Because of the importance of scaffolds in tissue formation and function, this work focuses on characterizing scaffold network geometry and elucidating the impact of geometry on macroscale mechanics. Simulation plays an important role in developing a detailed understanding of scaffold mechanics. In this work, Cosserat rod theory is used to model individual fibers, which are connected to form a network that is treated as a representative volume element (RVE) of the material. The continuum theory is the basis for a finite element discretization. The nonlinear equations are solved using Newton's method in a parallel implementation that is capable of accurately capturing the large, three-dimensional fiber rotations and large fiber stretches that result from the large macroscopic deformations experienced by these biomaterials in their natural environment. Comparisons of simulation results with existing analytical models of soft tissues show that these models can predict the behavior of scaffold networks with reasonable accuracy, despite the significant differences between soft tissue and scaffold network microstructural geometry. The simulations also reveal how macroscale loading is related to the microscale fiber deformations and the load distribution among the fibers. The effects of different characteristics of the microstructural geometry on macroscopic behavior are explored, and the implications for the design of scaffolds that produce the desired macroscopic behavior are discussed. Overall, the improved modeling of electrospun scaffolds presented in this work is an important step toward designing more functional engineered tissues.

Seismic transitions of the subsurface are typically considered as zero-order singularities (step functions). According to this model, the conventional deconvolution problem aims at recovering the seismic reflectivity as a sparse spike train. However, recent multiscale analysis on sedimentary records revealed the existence of accumulations of varying order singularities in the subsurface, which give rise to fractional-order discontinuities. This observation not only calls for a richer class of seismic reflection waveforms, but it also requires a different methodology to detect and characterize these reflection events. For instance, the assumptions underlying conventional deconvolution no longer hold. Because of the bandwidth limitation of seismic data, multiscale analysis methods based on the decay rate of wavelet coefficients may yield ambiguous results. We avoid this problem by formulating the estimation of the singularity orders by a parametric nonlinear inversion method.

<p>Electronic focal plane arrays (FPA) such as CMOS and CCD sensors have dramatically improved to the point that digital cameras have essentially phased out film (except in very niche applications such as hobby photography and cinema). However, the traditional method of mating a single lens assembly to a single detector plane, as required for film cameras, is still the dominant design used in cameras today. The use of electronic sensors and their ability to capture digital signals that can be processed and manipulated post acquisition offers much more freedom of design at system levels and opens up many interesting possibilities for the next generation of computational imaging systems.</p><p>The AWARE gigapixel scale camera is one such computational imaging system. By utilizing a multiscale optical design, in which a large aperture objective lens is mated with an array of smaller, well corrected relay lenses, we are able to build an optically simple system that is capable of capturing gigapixel scale images via post acquisition stitching of the individual pictures from the array. Properly shaping the array of digital cameras allows us to form an effectively continuous focal surface using off the shelf (OTS) flat sensor technology.</p><p>This dissertation details developments and physical implementations of the AWARE system architecture. It illustrates the optomechanical design principles and system integration strategies we have developed through the course of the project by summarizing the results of the two design phases for AWARE: AWARE-2 and AWARE-10. These systems represent significant advancements in the pursuit of scalable, commercially viable snapshot gigapixel imaging systems and should serve as a foundation for future development of such systems.</p> / Dissertation

No description available.

This thesis centers on the development and analysis of numerical multiscale methods for multiscale problems arising in steady heat conduction, heat transfer and wave propagation in heterogeneous media. In a multiscale problem several scales interact with each other to form a system which has variations over a wide range of scales. A direct numerical simulation of such problems requires resolving the small scales over a computational domain, typically much larger than the microscopic scales. This demands a tremendous computational cost. We develop and analyse multiscale methods based on the heterogeneous multiscale methods (HMM) framework, which captures the macroscopic variations in the solution at a cost much lower than traditional numerical recipes. HMM assumes that there is a macro and a micro model which describes the problem. The micro model is accurate but computationally expensive to solve. The macro model is inexpensive but incomplete as it lacks certain parameter values. These are upscaled by solving the micro model locally in small parts of the domain. The accuracy of the method is then linked to how accurately this upscaling procedure captures the right macroscopic effects. In this thesis we analyse the upscaling error of existing multiscale methods and also propose a micro model which significantly reduces the upscaling error invarious settings. In papers I and IV we give an analysis of a finite difference HMM (FD-HMM) for approximating the effective solutions of multiscale wave equations over long time scales. In particular, we consider time scales T^ε = O(ε−k ), k =1, 2, where ε represents the size of the microstructures in the medium. In this setting, waves exhibit non-trivial behaviour which do not appear over short time scales. We use new analytical tools to prove that the FD-HMM accurately captures the long time effects. We first, in Paper I, consider T^ε =O(ε−2 ) and analyze the accuracy of FD-HMM in a one-dimensional periodicsetting. The core analytical ideas are quasi-polynomial solutions of periodic problems and local time averages of solutions of periodic wave equations.The analysis naturally reveals the role of consistency in HMM for high order approximation of effective quantities over long time scales. Next, in paperIV, we consider T^ε = O(ε−1 ) and use the tools in a multi-dimensional settingto analyze the accuracy of the FD-HMM in locally-periodic media where fast and slow variations are allowed at the same time. Moreover, in papers II and III we propose new multiscale methods which substantially improve the upscaling error in multiscale elliptic, parabolic and hyperbolic partial differential equations. In paper II we first propose a FD-HMM for solving elliptic homogenization problems. The strategy is to use the wave equation as the micro model even if the macro problem is of elliptic type. Next in paper III, we use this idea in a finite element HMM setting and generalize the approach to parabolic and hyperbolic problems. In a spatially fully discrete a priori error analysis we prove that the upscaling error can be made arbitrarily small for periodic media, even if we do not know the exact period of the oscillations in the media. / <p>QC 20150216</p> / Multiscale methods for wave propagation