An adaptive kernel-split quadrature method for parameter-dependent layer potentials

Direct numerical simulation (DNS) of fluid flow in porous media with many scales is often not feasible, and an effective or homogenized description is more desirable. To construct the homogenized equations, effective properties must be computed. Computation of effective properties for nonperiodic microstructures can be prohibitively expensive, as many local cell problems must be solved for different macroscopic points. In addition, the local problems may also be computationally expensive. When the microstructure varies slowly, we develop an efficient numerical method for two scales that achieves essentially the same accuracy as that for the full resolution solve of every local cell problem. In this method, we build a dense hierarchy of macroscopic grid points and a corresponding nested sequence of approximation spaces. Essentially, solutions computed in high accuracy approximation spaces at select points in the the hierarchy are used as corrections for the error of the lower accuracy approximation spaces at nearby macroscopic points. We give a brief overview of slowly varying media and formal Stokes homogenization in such domains. We present a general outline of the algorithm and list reasonable and easily verifiable assumptions on the PDEs, geometry, and approximation spaces. With these assumptions, we achieve the same accuracy as the full solve. To demonstrate the elements of the proof of the error estimate, we use a hierarchy of macro--grid points in $[0,1]^2$ and finite element (FE) approximation spaces in $[0,1]^2$. We apply this algorithm to Stokes equations in a slowly porous medium where the microstructure is obtained from a reference periodic domain by a known smooth map. Using the arbitrary Lagrange--Eulerian (ALE) formulation of the Stokes equations (cf. [G. P. Galdi and R. Rannacher, Fundamental Trends in Fluid-Structure Interaction, Contemporary Challenges in Mathematical Fluid Dynamics and Its Applications 1, World Scientific, Singapore, 2010]), we obtain modified Stokes equations with varying coefficients in the periodic domain. We show that the algorithm can be utilized in this setting. Finally, we implement the algorithm on the modified Stokes equations, using a simple stretch deformation mapping, and compute the effective permeability. We show that our efficient computation is of the same order as the full solve.

Sedimentation behaviour and colloidal properties of porous, chemically modified silicas in non-aqueous solvents

Converter copper slag can be viewed as an important secondary resource for valuable metals, considering its high commercial value. The current research investigates the recycling of copper by a combination of theoretical and experimental methods. Based on a modified Stokes equation, it was determined that copper droplets in the molten slag exhibited a low terminal settling velocity of 2.140 × 10−6 m/s. The copper particles will collide with each other during settling, resulting in particle growth. The results from high temperature experimentation, scanning electron microscopy, and energy-dispersive spectroscopy confirm that in the absence of reducing agents, copper droplets are encased in magnetite to form composite ‘Cu droplet–magnetite’ particles. Other copper droplets adhere to magnetite particles which are suspended in the slag in a short-range-ordered array. The study also confirms that in the presence of increasing amounts of anthracite as a reducing agent, the magnetite content of the slag is progressively decreased and the recovery of copper from the slag is significantly improved. Based on the findings from this work, a new processing route is proposed to treat copper slag for the recovery of copper.

PageRank is typically computed from the power of transition matrix in a Markov Chain model. It is therefore computationally expensive, and efficient approximation methods to accelerate the computation are necessary, especially when it comes to large graphs. In this paper, we propose two sampling algorithms for PageRank efficient approximation: Direct sampling and Adaptive sampling. Both methods sample the transition matrix and use the sample in PageRank computation. Direct sampling method samples the transition matrix once and uses the sample directly in PageRank computation, whereas adaptive sampling method samples the transition matrix multiple times with an adaptive sample rate which is adjusted iteratively as the computing procedure proceeds. This adaptive sample rate is designed for a good trade-off between accuracy and efficiency for PageRank approximation. We provide detailed theoretical analysis on the error bounds of both methods. We also compare them with several state-of-the-art PageRank approximation methods, including power extrapolation and inner---outer power iteration algorithm. Experimental results on several real-world datasets show that our methods can achieve significantly higher efficiency while attaining comparable accuracy than state-of-the-art methods.

Massively parallel implementation of an explicit CFD algorithm on unstructured grids, II

This thesis aims at developing efficient mathematical methods for solving hierarchical dynamic optimization problems. The main motivation is to model processes in nature, for which there is evidence to assume that they run optimally. We describe models of such processes by optimal control problems (called optimal control models (OCMs)). However, an OCM typically includes unknown parameters that cannot be derived entirely on a theoretical basis, which is in particular the case for the cost function. Therefore, we develop parameter estimation techniques to estimate the unknowns in an OCM from observation data of the process. Mathematically, this leads to a hierarchical dynamic optimization problem with a parameter estimation problem on the upper level and an optimal control problem on the lower level. We focus on multi-stage equality and inequality constrained optimal control problems based on nonlinear ordinary differential equations. The main goal of this thesis is to derive numerically efficient mathematical methods for solving hierarchical dynamic optimization problems, and to use these methods to estimate parameters in high-dimensional OCMs from real-world measurement data. We develop parameter-dependent OCMs for the gait of cerebral palsy patients and able-bodied subjects. The unknown parameters in the OCMs are then estimated from real-world motion capture data provided by the Heidelberg MotionLab of the Orthopedic University Clinic Heidelberg by using the mathematical methods developed within this work. The main novelties and contributions of this thesis to the field of hierarchical dynamic optimization are summarized herein. - We establish a novel mathematical method, a so-called direct all-at-once approach, for solving hierarchical dynamic optimization problems based on the direct multiple shooting method and first-order optimality conditions. - Furthermore, we propose an efficient numerical algorithm for large-scale hierarchical dynamic optimization problems, which fully exploits the structures inherited from both the hierarchical setting and the discretization. - Pontryagin's maximum principle is used to analyze solution properties of hierarchical dynamic optimization problems like second-order optimality conditions of the lower-level problem. - In addition, we propose and discuss alternative methods for hierarchical dynamic optimization that are based on derivative-free optimization and a bundle approach. These methods keep the hierarchical problem setting and do not reformulate the lower-level problem using first-order optimality conditions. - We establish a novel lifting method for regularizing mathematical programs with complementarity constraints, which is discussed and numerically investigated by means of a well-known collection of benchmark problems. - Proofs of regularity and convergence results for sequential quadratic programming methods applied to lifted mathematical programs with complementarity constraints are provided. - Efficient state-of-the-art implementations of all mathematical methods derived in this thesis, as well as a benchmark collection of hierarchical dynamic optimization problems are presented. - High-dimensional optimal control gait models for cerebral palsy patients and able-bodied subjects are developed. The mathematical methods derived in this thesis are used to estimate the unknown model parameters from real-world motion capture data provided by the Heidelberg MotionLab of the Orthopedic University Clinic Heidelberg. The theoretical and practical results presented in this thesis can be considered an initial motivating step towards answering open questions in current medical research in fields like treatment planning, classification of gaits, or the evaluation of surgeries by means of hierarchical dynamic optimization.

Innovative approach to teaching assumes the use of methods and techniques not only for organizing the training process but also for controlling students' knowledge. Thus, the problem of finding and describing interactive, the most efficient students' knowledge control methods arises. The article focuses on various students' knowledge control methods; analyses their opportunities on the basis of teachers' and the students' activity analysis and the mechanism of their interaction; actualization of students' motivational sphere and their need for self-rating and estimation. Intellectual game is reasoned as one of efficient students' knowledge control methods. The technique of using intellectual games for students' knowledge control that is based on the contextual principle, the principle of interlocution and reflexivity is described. The set of rules and the procedures containing a complex of methods which provide the logic of phases for carrying out intellectual games is stated. The elaborated methodology of students' knowledge control is offered for interactive students' knowledge control which is conceptually based on creative potential of students, development of their cognitive abilities, and formation of their abilities for auto analysis and self-rating and estimation. The value of the offered methodology consists in its application that gives the chance to carry out both training, and assessment of knowledge at different stages of the current, intermediate and total control on the unified basis while studying different disciplines.

The aim of this thesis is to explore computational methods for the shape from shading problem as formulated through the image irradiance equation. We seek to develop robust, efficient methods and test our algorithms on synthetic images ranging from simple smooth surfaces to complex digital terrain model data. We consider three different approaches. The first approach revisits the method of characteristic strips with a view to using more stable integration schemes than had been used in earlier works. Stable schemes coupled with projections onto the image irradiance equation are used. Although the effects of noise are thereby reduced, the solution is still deemed unsatisfactory even for very simple surfaces. The second approach considers Horn's variational technique as a basis for producing a fast solver. We devise a discretization scheme coupled with a special continuation multigrid method for this formulation. We also allow for multiple image data and explicit knowledge of the location of discontinuities in surface height and orientation. Given multiple image data, we obtain excellent results even in the presence of discontinuities. The third approach examines a class of solution techniques based on fluid flow which are new to the shape from shading literature. This formulation is ill posed in general, so we propose a regularization of the problem. We observe that the algorithm is prone to producing spurious results. Analysis shows that these are due to the non-random accumulation of errors in the computed solution. Of the three approaches considered, the variational method yields the most promising results. Efficient, good quality reconstructions are obtained, especially when data from more than one image are available.

Linear and nonlinear spectroscopy techniques are widely used to study numerous important chemical and physical processes. However, the interpretation of these experimental spectra often becomes very complicated because a particular spectrum constitutes a mere footprint of a host of various, possibly intertwined, effects. In this spirit, calculations in the time-dependent picture provide a useful tool for decoding such spectra. Nevertheless, the ultimate challenge is to devise a theoretical framework that could yield sufficient efficiency as well as accuracy to describe the molecular system of interest in a satisfactory way. The strategy is relatively straightforward for low dimensional systems that are directly tractable, e.g., with exact quantum dynamics performed on an equidistant grid. Despite the formidable overall exponential scaling, these calculations can be significantly accelerated by using higher-order split-operator propagation schemes. In general however, one is forced to seek an affordable balance between physical accuracy on one hand and computational efficiency on the other by employing, for instance, some of the techniques from the broad family of semiclassical methods based on classical trajectories. To this end, the thawed Gaussian approximation (TGA) is combined with an on-the-fly ab initio scheme (OTF-AI). The resulting OTF-AI-TGA algorithm is efficient enough to treat all vibrational degrees of freedom (DOFs) on an equal footing even in case of larger molecules such as pentathiophene (105 DOFs). Moreover, in sharp contrast to popular approaches based on global harmonic approximation, OTF-AI-TGA reproduces almost perfectly the absorption and photoelectron spectra of ammonia, i.e., spectra with strong dependence on large amplitude motions. In addition to the mere reproduction of experimental spectra, a novel systematic approach is introduced to assess the importance and the dynamical couplings of individual vibrational DOFs. This is in turn used to gain a deeper insight into the associated physical and chemical processes by attributing specific spectral features to the underlying molecular motion. Specifically, in the case of oligothiophenes, this approach was used to assign the dynamical interplay between quinoid and aromatic characters of individual rings to particular spectral patterns and, furthermore, to explain the changes in the vibrational line shape with an increasing number of rings. Furthermore, in systems that are too large to be treated with accurate quantum methods, efficient methods such as OTF-AI-TGA are expected to be useful as a preliminary tool for identification of the subspace of the important DOFs. On this subspace, one can then unleash some of the less efficient yet better-suited methods. In summary, OTF-AI-TGA combined with this novel analysis approach is intended to provide the first crucial step in a hierarchical computational protocol for studying large molecules such as dyes.

Preparation of amino cellulose nanofiber via ε-poly-L-lysine grafting with enhanced mechanical, anti-microbial and food preservation performance

The aim of this paper is to prove global in time existence of weak solutions for a viscoelastic phase separation. We consider the case with singular potentials and degenerate mobilities. Our model couples the diffusive interface model with the Peterlin–Navier–Stokes equations for viscoelastic fluids. To obtain the global in time existence of weak solutions we consider appropriate approximations by solutions of the viscoelastic phase separation with a regular potential and build on the corresponding energy and entropy estimates.

A large part of the data on the World Wide Web resides in the deep web. Executing structured, high-level queries on deep web data sources involves a number of challenges, several of which arise because query execution engines have a very limited access to data. In this paper, we consider the problem of executing aggregation queries involving data enumeration on these data sources, which requires sampling. The existing work in this area (HDSampler and its variants) is based on simple random sampling. We observe that this approach cannot obtain good estimates when the data is skewed. While there has been a lot of work on sampling skewed data, the existing methods are based on prior knowledge of data, and are therefore not applicable to hidden databases.In this paper, we present two prior-knowledge-free sampling algorithms, Adaptive Neighborhood Sampling (ANS) and Two Phase adaptive Sampling (TPS), which allow an aggregation query to be answered with a high accuracy (even when there is a skew), and a low sampling cost. For this purpose, we have developed robust estimators for aggregation functions including AVG, MAX, and MIN.Our experiments show that for data with a moderate or a large skew, ANS and TPS yield more accurate estimates, outperforming HDSampler by a factor of 4 on the average. Even for the cases where data has a small skew, our TPS method has an important advantage, which is that it has only one-third of the sampling costs of HDSampler.

One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

Mitigation approaches and techniques for combustion power plants flue gas emissions: A comprehensive review

Cell-based microfluidic devices have attracted interest for a wide range of applications. While optical cell counting and flow cytometry-type devices have been reported extensively, sensitive and efficient non-optical methods to detect and quantify cells attached over large surface areas within microdevices are generally lacking. We describe an electrical method for counting cells based on the measurement of changes in conductivity of the surrounding medium due to ions released from surface-immobilized cells within a microfluidic channel. Immobilized cells are lysed using a low conductivity, hypotonic media and the resulting change in impedance is measured using surface patterned electrodes to detect and quantify the number of cells. We found that the bulk solution conductance increases linearly with the number of isolated cells contributing to solution ion concentration. The method of cell lysate impedance spectroscopy is sensitive enough to detect 20 cells microL(-1), and offers a simple and efficient method for detecting and enumerating cells within microfluidic devices for many applications including measurement of CD4 cell counts in HIV patients in resource-limited settings. To our knowledge, this is the most sensitive approach using non-optical setups to enumerate immobilized cells. The microfluidic device, capable of isolating specific cell types from a complex bio-fluidic and quantifying cell number, can serve as a single use cartridge for a hand-held instrument to provide simple, fast and affordable cell counting in point-of-care settings.