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There is growing international concern about the necessity to re-think the university so that it might remain relevant in a modern society. In the traditional task division at universities, knowledge is the main resource. Universities make use of both the cognitive and the informational approach. It was expected that universities use each approach to improve overall university performance. To effectively use the informational approach, universities should apply the tools from knowledge management. To effectively use the cognitive approach, universities must update their teaching-learning strategies to incorporate some of the recent advances in neuroscience and biology of knowledge, specifically from neurobiology and autopoiesis. With this frame, the main contribution of this work is the result of merging pedagogy and biology, towards an ideal future university. This goal was achieved through an exploratory study conducted to identify opportunities and difficulties in improving the teaching-learning process for the future of higher education in Honduras. The Delphi Study was used as a predictive method. Nineteen Honduran experts participated in this study, and two rounds were necessary to achieve consensus.
The multi-disciplinary approach of this research addresses three different fields whose core element is knowledge. First, input from the present field of higher education is used to speak about the future. Second, input is taken from the biology of knowledge, and its contributions from neurobiology and autopoiesis that allow modifying and completing the already existing learning theories with a biological basis. Third, input is taken from the knowledge process, which is traditionally used as an organizational tool and know is translated to the individual level. The exploration shows that experts are concerned about all the missions and responsibilities of universities, but they agree that changes should primarily take place in the teaching dimension. Even though they are not aware of the possible contributions of biology, they suggest new forms of teaching that more favor skills development, promotes values, pertinent knowledge, and personal development over short-term contents. The resulting BRAIN Model encompasses the ideal future of higher education regarding teaching and learning, according to experts’ answers. It provides a useful guide that any reform in teaching should take into account for a holistic, integral, and therefore more efficient learning task.

Fluid extraction is a typical chemical process where two types of fluids are mixed together. The high complexity of this process which involves droplet coalescence, breakup, mass transfer, and counter-current flow often makes design difficult. The industrial design of these processes is still based on expensive mini-plant and pilot plant experiments. Therefore, there is a strong need for research into the stimulation of fluid-fluid interaction processes using computational fluid dynamics (CFD).
Previous multi-phase fluid simulations have focused on the development of models that couple mass and momentum using the Navier-Stokes equation. Recent population balance models (PBM) have proved to be important methods for analyzing droplet breakage and collisions. A combination of CFD and PBM facilitates the simulation of flow property by solving coupling equations, and the calculation of the droplet size and numbers. In our study, we successfully coupled an Euler-Euler CFD model with the breakup and coalescence models proposed by Luo and Svendsen (59).
The simulation output of extraction columns provides a mathematical understand- ing of how fluids are mixed inside a mixing device. This mixing process shows that the dispersed phase of a flow generates large blobs and bubbles. Current mathemati- cal simulation results often fail to provide an intuitive representation of how well two different types of fluid interact, so intuitive and physically plausible visualization tech- niques are in high demand to help chemical engineers to explore and analyze bubble column simulation data. In chapter 3, we present the visualization tools we developed for extraction column data.
Fluid interfaces and free surfaces are topics of growing interest in the field of multi- phase computational fluid dynamics. However, the analysis of the flow field relative to the material interface shape and topology is a challenging task. In chapter 5, we present a technique that facilitates the visualization and analysis of complex material interface behaviors over time. To achieve this, we track the surface parameterization of time-varying material interfaces and identify locations where there are interactions between the material interfaces and fluid particles. Splatting and surface visualization techniques produce an intuitive representation of the derived interface stability. Our results demonstrate that the interaction of a flow field with a material interface can be understood using appropriate extraction and visualization techniques, and that our techniques can help the analysis of mixing and material interface consistency.
In addition to texture-based methods for surface analysis, the interface of two- phase fluid can be considered as an implicit function of the density or volume fraction values. High-level visualization techniques such as topology-based methods can re- veal the hidden structure underlying simple simulation data, which will enhance and advance our understanding of multi-fluid simulation data. Recent feature-based vi- sualization approaches have explored the possibility of using Reeb graphs to analyze scalar field topologies(19, 107). In chapter 6, we present a novel interpolation scheme for interpolating point-based volume fraction data and we further explore the implicit fluid interface using a topology-based method.

Efficient time integration and nonlinear model reduction for incompressible hyperelastic materials
(2013)

This thesis deals with the time integration and nonlinear model reduction of nearly incompressible materials that have been discretized in space by mixed finite elements. We analyze the structure of the equations of motion and show that a differential-algebraic system of index 1 with a singular perturbation term needs to be solved. In the limit case the index may jump to index 3 and thus renders the time integration into a difficult problem. For the time integration we apply Rosenbrock methods and study their convergence behavior for a test problem, which highlights the importance of the well-known Scholz conditions for this problem class. Numerical tests demonstrate that such linear-implicit methods are an attractive alternative to established time integration methods in structural dynamics. In the second part we combine the simulation of nonlinear materials with a model reduction step. We use the method of proper orthogonal decomposition and apply it to the discretized system of second order. For a nonlinear model reduction to be efficient we approximate the nonlinearity by following the lookup approach. In a practical example we show that large CPU time savings can achieved. This work is in order to prepare the ground for including such finite element structures as components in complex vehicle dynamics applications.

This thesis is separated into three main parts: Development of Gaussian and White Noise Analysis, Hamiltonian Path Integrals as White Noise Distributions, Numerical methods for polymers driven by fractional Brownian motion.
Throughout this thesis the Donsker's delta function plays a key role. We investigate this generalized function also in Chapter 2. Moreover we show by giving a counterexample, that the general definition for complex kernels is not true.
In Chapter 3 we take a closer look to generalized Gauss kernels and generalize these concepts to the case of vector-valued White Noise. These results are the basis for Hamiltonian path integrals of quadratic type. The core result of this chapter gives conditions under which pointwise products of generalized Gauss kernels and certain Hida distributions have a mathematical rigorous meaning as distributions in the Hida space.
In Chapter 4 we discuss operators which are related to applications for Feynman Integrals as differential operators, scaling, translation and projection. We show the relation of these operators to differential operators, which leads to the well-known notion of so called convolution operators. We generalize the central homomorphy theorem to regular generalized functions.
We generalize the concept of complex scaling to scaling with bounded operators and discuss the relation to generalized Radon-Nikodym derivatives. With the help of this we consider products of generalized functions in chapter 5. We show that the projection operator from the Wick formula for products with Donsker's deltais not closable on the square-integrable functions..
In Chapter 5 we discuss products of generalized functions. Moreover the Wick formula is revisited. We investigate under which conditions and on which spaces the Wick formula can be generalized to. At the end of the chapter we consider the products of Donsker's delta function with a generalized function with help of a measure transformation. Here also problems as measurability are concerned.
In Chapter 6 we characterize Hamiltonian path integrands for the free particle, the harmonic oscillator and the charged particle in a constant magnetic field as Hida distributions. This is done in terms of the T-transform and with the help of the results from chapter 3. For the free particle and the harmonic oscillator we also investigate the momentum space propagators. At the same time, the $T$-transform of the constructed Feynman integrands provides us with their generating functional. In Chapter 7, we can show that the generalized expectation (generating functional at zero) gives the Greens function to the corresponding Schrödinger equation.
Moreover, with help of the generating functional we can show that the canonical commutation relations for the free particle and the harmonic oscillator in phase space are fulfilled. This confirms on a mathematical rigorous level the heuristics developed by Feynman and Hibbs.
In Chapter 8 we give an outlook, how the scaling approach which is successfully applied in the Feynman integral setting can be transferred to the phase space setting. We give a mathematical rigorous meaning to an analogue construction to the scaled Feynman-Kac kernel. It is open if the expression solves the Schrödinger equation. At least for quadratic potentials we can get the right physics.
In the last chapter, we focus on the numerical analysis of polymer chains driven by fractional Brownian motion. Instead of complicated lattice algorithms, our discretization is based on the correlation matrix. Using fBm one can achieve a long-range dependence of the interaction of the monomers inside a polymer chain. Here a Metropolis algorithm is used to create the paths of a polymer driven by fBm taking the excluded volume effect in account.

Many real life problems have multiple spatial scales. In addition to the multiscale nature one has to take uncertainty into account. In this work we consider multiscale problems with stochastic coefficients.
We combine multiscale methods, e.g., mixed multiscale finite elements or homogenization, which are used for deterministic problems with stochastic methods, such as multi-level Monte Carlo or polynomial chaos methods.
The work is divided into three parts.
In the first two parts we study homogenization with different stochastic methods. Therefore we consider elliptic stationary diffusion equations with stochastic coefficients.
The last part is devoted to the study of mixed multiscale finite elements in combination with multi-level Monte Carlo methods. In the third part we consider multi-phase flow and transport equations.

The automatic analysis and retrieval of technical line drawings is hindered by many challenges such as: the large amount of contextual clutter around the symbols within the drawings, degradation, transformations on the symbols in drawings, large databases of drawings
and large alphabets of symbols. The core tasks required for the analysis of technical line
drawings are: symbol recognition, spotting and retrieval. The current systems for performing these tasks have poor performance due to the mentioned challenges. This dissertation
presents a number of methods that address these challenges. These methods achieve both
accurate and efficient symbol spotting and retrieval in technical line drawings, and perform
significantly better than state-of-the-art methods on the same problems. An overview of
the key contributions of this dissertation is given in the following.
First, this dissertation presents a geometric matching-based method for symbol recognition
and spotting. The method performs recognition in the presence of large amounts of contextual clutter, and provides precise localization of the recognized symbols. On standard
databases such as GREC-2005 and GREC-2011, the method achieves up to 10% higher
recall and up to 28% higher precision than state-of-the-art methods on the spotting task,
and achieves up to 7% higher recognition accuracy on the isolated recognition task. The
method is based on a geometric matching approach, which is flexible enough to incorporate
improvements on the matching strategy, feature types and information on the features. The
method also includes an adaptive preprocessing algorithm that deals with a wide variety
of noise types.
In order to improve the performance of the spotting method when dealing with degraded
drawings, two novel methods are presented in this dissertation. Both methods are based on
combining geometric matching with machine learning techniques. The geometric matching
is used to automatically generate training data that contain information on how well the
features of the queries are matched in both the true and the false matches found by the
spotting method. The first method learns the feature weights of the different query symbols
by linear discriminant analysis (LDA). The weighted query features are used in the spotting
method and result in 27% higher average precision than the original method, with a speedup
factor of 2. The second method uses SVM classification as a post-spotting step to distinguish
the true from the false matches in the spotting method. The use of the classification step
further improves the average precision of the spotting method by 20.6%.
This dissertation also presents methods for content analysis of line drawings. First, a
method for accurate and consistent detection (95.8%) of regions of interest (ROIs) is presented. The method is based on statistical feature grouping. The ROI-finding method is
identified as an important part of a symbol retrieval system: the better the detected ROIs,the higher the performance of a retrieval system. The ROI-finding method is also used to
improve the performance of the geometric-based spotting system.
Second, a symbol clustering method for building a compact and accurate representation of
a large database of technical drawings is presented. This method uses the output from the
ROI-finding method as input, and uses geometric matching as a similarity measure. The
method achieves high accuracy (90.1% recall, 94.3% precision) in forming clusters of symbols. The representatives of the clusters (34 symbols) are used as key entries to a symbol
index, which is identified as the outcome of an off-line stage of a symbol retrieval system.
Finally, an efficient and high performing large scale symbol retrieval system is presented
in this dissertation. The system follows the bag of visual words (BoVW) model, but with
using methods that are suitable to line drawings. The system uses the symbol index to
represent a database of drawings. During the on-line query retrieval stage, the query is
analyzed by the ROI-finding method, matched with the key entries of the symbol index via
geometric matching, and finally, a spatial verification step is performed on the retrieved
matches. The system achieves a query lookup time that is independent of the size of the
database, and is instead dependent on the size of the symbol index. The system achieves up
to 10% higher recall and up to 28% higher precision than state-of-the-art spotting systems
on similar databases.
Overall, these contributions are major advancements in the research of graphics recognition.
The hope is that, such contributions provide the basis for the development of reliable and
accurate performing applications for browsing, querying or classification of line drawings
for the benefit of end users.