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Nanoparticle-Filled Thermoplastics and Thermoplastic Elastomer: Structure-Property Relationships
(2012)

The present work focuses on the structure-property relationships of
particulate-filled thermoplastics and thermoplastic elastomer (TPE). In this work
two thermoplastics and one TPE were used as polymer matrices, i.e. amorphous
bisphenol-A polycarbonate (PC), semi-crystalline isotactic polypropylene (iPP),
and a block copolymer poly(butylene terephthalate)-block-poly(tetramethylene
glycol) TPE(PBT-PTMG). For PC, a selected type of various Aerosil® nano-SiO2
types was used as filler to improve the thermal and mechanical properties by
maintaining the transparency of PC matrix. Different types of SiO2 and TiO2
nanoparticles with different surface polarity were used for iPP. The goal was to
examine the influence of surface polarity and chemical nature of nanoparticles on
the thermal, mechanical and morphological properties of iPP composites. For
TPE(PBT-PTMG), three TiO2 particles were used, i.e. one grade with hydroxyl
groups on the particle surface and the other two grades are surface-modified with
metal and metal oxides, respectively. The influence of primary size and dispersion
quality of TiO2 particles on the properties of TPE(PBT-PTMG)/TiO2 composites
were determined and discussed.
All polymer composites were produced by direct melt blending in a twin-screw
extruder via masterbatch technique. The dispersion of particles was examined by
using scanning electron microscopy (SEM) and micro-computerized tomography
(μCT). The thermal and crystalline properties of polymer composites were characterized by using thermogravimetric analysis (TGA) and differential
scanning calorimetry (DSC). The mechanical and thermomechanical properties
were determined by using mechanical tensile testing, compact tension and
Charpy impact as well as dynamic-mechanical thermal analysis (DMTA).
The SEM results show that the unpolar-surface modified nanoparticles are better
dispersed in polymer matrices as iPP than polar-surface nanoparticles, especially
in case of using Aeroxide® TiO2 nanoparticles. The Aeroxide® TiO2 nanoparticles
with a polar surface due to Ti-OH groups result in a very high degree of
agglomeration in both iPP and TPE matrices because of strong van der Waals
interactions among particles (hydrogen bonding). Compared to unmodified
Aeroxide® TiO2 nanoparticles, the other grades of surface modified TiO2 particles
are very homogenously dispersed in used iPP and TPE(PBT-PTMG). The
incorporation of SiO2 nanoparticles into bisphenol-A PC significantly increases
the mechanical properties of PC/SiO2 nanocomposites, particularly the resistance
against environmental stress crazing (ESC). However, the transparency of
PC/SiO2 nanocomposites decreases with increasing nanoparticle content and
size due to a mismatch of infractive indices of PC and SiO2 particles. The different
surface polarity of nanoparticles in iPP shows evident influence on properties of
iPP composites. Among iPP/SiO2 nanocomposites, the nanocomposite
containing SiO2 nanoparticles with a higher degree of hydrophobicity shows
improved fracture and impact toughness compared to the other iPP/SiO2
composites. The TPE(PBT-PTMG)/TiO2 composites show much better thermal and mechanical properties than neat TPE(PBT-PTMG) due to strong chemical
interactions between polymer matrix and TiO2 particles. In addition, better
dispersion quality of TiO2 particles in used TPE(PBT-PTMG) leads to dramatically
improved mechanical properties of TPE(PBT-PTMG)/TiO2 composites.

Granular systems in solid-like state exhibit properties like stiffness
dependence on stress, dilatancy, yield or incremental non-linearity
that can be described within the continuum mechanical framework.
Different constitutive models have been proposed in the literature either based on relations between some components of the stress tensor or on a quasi-elastic description. After a brief description of these
models, the hyperelastic law recently proposed by Jiang and Liu [1]
will be investigated. In this framework, the stress-strain relation is
derived from an elastic strain energy density where the stable proper-
ties are linked to a Drucker-Prager yield criteria. Further, a numerical method based on the finite element discretization and Newton-
Raphson iterations is presented to solve the force balance equation.
The 2D numerical examples presented in this work show that the stress
distributions can be computed not only for triangular domains, as previoulsy done in the literature, but also for more complex geometries.
If the slope of the heap is greater than a critical value, numerical instabilities appear and no elastic solution can be found, as predicted by
the theory. As main result, the dependence of the material parameter
Xi on the maximum angle of repose is established.

The safety of embedded systems is becoming more and more important nowadays. Fault Tree Analysis (FTA) is a widely used technique for analyzing the safety of embedded systems. A standardized tree-like structure called a Fault Tree (FT) models the failures of the systems. The Component Fault Tree (CFT) provides an advanced modeling concept for adapting the traditional FTs to the hierarchical architecture model in system design. Minimal Cut Set (MCS) analysis is a method that works for qualitative analysis based on the FTs. Each MCS represents a minimal combination of component failures of a system called basic events, which may together cause the top-level system failure. The ordinary representations of MCSs consist of plain text and data tables with little additional supporting visual and interactive information. Importance analysis based on FTs or CFTs estimates the contribution of each potential basic event to a top-level system failure. The resulting importance values of basic events are typically represented in summary views, e.g., data tables and histograms. There is little visual integration between these forms and the FT (or CFT) structure. The safety of a system can be improved using an iterative process, called the safety improvement process, based on FTs taking relevant constraints into account, e.g., cost. Typically, relevant data regarding the safety improvement process are presented across multiple views with few interactive associations. In short, the ordinary representation concepts cannot effectively facilitate these analyses.
We propose a set of visualization approaches for addressing the issues above mentioned in order to facilitate those analyses in terms of the representations.
Contribution:
1. To support the MCS analysis, we propose a matrix-based visualization that allows detailed data of the MCSs of interest to be viewed while maintaining a satisfactory overview of a large number of MCSs for effective navigation and pattern analysis. Engineers can also intuitively analyze the influence of MCSs of a CFT.
2. To facilitate the importance analysis based on the CFT, we propose a hybrid visualization approach that combines the icicle-layout-style architectural views with the CFT structure. This approach facilitates to identify the vulnerable components taking the hierarchies of system architecture into account and investigate the logical failure propagation of the important basic events.
3. We propose a visual safety improvement process that integrates an enhanced decision tree with a scatter plot. This approach allows one to visually investigate the detailed data related to individual steps of the process while maintaining the overview of the process. The approach facilitates to construct and analyze improvement solutions of the safety of a system.
Using our visualization approaches, the MCS analysis, the importance analysis, and the safety improvement process based on the CFT can be facilitated.

Recently, a new Quicksort variant due to Yaroslavskiy was chosen as standard sorting
method for Oracle's Java 7 runtime library. The decision for the change was based on
empirical studies showing that on average, the new algorithm is faster than the formerly
used classic Quicksort. Surprisingly, the improvement was achieved by using a dual pivot
approach — an idea that was considered not promising by several theoretical studies in the
past. In this thesis, I try to find the reason for this unexpected success.
My focus is on the precise and detailed average case analysis, aiming at the flavor of
Knuth's series “The Art of Computer Programming”. In particular, I go beyond abstract
measures like counting key comparisons, and try to understand the efficiency of the
algorithms at different levels of abstraction. Whenever possible, precise expected values are
preferred to asymptotic approximations. This rigor ensures that (a) the sorting methods
discussed here are actually usable in practice and (b) that the analysis results contribute to
a sound comparison of the Quicksort variants.

In the presented work, we make use of the strong reciprocity between kinematics and geometry to build a geometrically nonlinear, shearable low order discrete shell model of Cosserat type defined on triangular meshes, from which we deduce a rotation–free Kirchhoff type model with the triangle vertex positions as degrees of freedom. Both models behave physically plausible already on very coarse meshes, and show good
convergence properties on regular meshes. Moreover, from the theoretical side, this deduction provides a
common geometric framework for several existing models.

Today, polygonal models occur everywhere in graphical applications, since they are easy
to render and to compute and a very huge set of tools are existing for generation and
manipulation of polygonal data. But modern scanning devices that allow a high quality
and large scale acquisition of complex real world models often deliver a large set of
points as resulting data structure of the scanned surface. A direct triangulation of those
point clouds does not always result in good models. They often contain problems like
holes, self-intersections and non manifold structures. Also one often looses important
surface structures like sharp corners and edges during a usual surface reconstruction.
So it is suitable to stay a little longer in the point based world to analyze the point cloud
data with respect to such features and apply a surface reconstruction method afterwards
that is known to construct continuous and smooth surfaces and extend it to reconstruct
sharp features.

Worldwide the installed capacity of renewable technologies for electricity production is
rising tremendously. The German market is particularly progressive and its regulatory
rules imply that production from renewables is decoupled from market prices and electricity
demand. Conventional generation technologies are to cover the residual demand
(defined as total demand minus production from renewables) but set the price at the
exchange. Existing electricity price models do not account for the new risks introduced
by the volatile production of renewables and their effects on the conventional demand
curve. A model for residual demand is proposed, which is used as an extension of
supply/demand electricity price models to account for renewable infeed in the market.
Infeed from wind and solar (photovoltaics) is modeled explicitly and withdrawn from
total demand. The methodology separates the impact of weather and capacity. Efficiency
is transformed on the real line using the logit-transformation and modeled as a stochastic process. Installed capacity is assumed a deterministic function of time. In a case study the residual demand model is applied to the German day-ahead market
using a supply/demand model with a deterministic supply-side representation. Price trajectories are simulated and the results are compared to market future and option
prices. The trajectories show typical features seen in market prices in recent years and the model is able to closely reproduce the structure and magnitude of market prices.
Using the simulated prices it is found that renewable infeed increases the volatility of forward prices in times of low demand, but can reduce volatility in peak hours. Prices
for different scenarios of installed wind and solar capacity are compared and the meritorder effect of increased wind and solar capacity is calculated. It is found that wind
has a stronger overall effect than solar, but both are even in peak hours.

We consider the maximum flow problem with minimum quantities (MFPMQ), which is a variant of the maximum flow problem where
the flow on each arc in the network is restricted to be either zero or above a given lower bound (a minimum quantity), which
may depend on the arc. This problem has recently been shown to be weakly NP-complete even on series-parallel graphs.
In this paper, we provide further complexity and approximability results for MFPMQ and several special cases.
We first show that it is strongly NP-hard to approximate MFPMQ on general graphs (and even bipartite graphs) within any positive factor.
On series-parallel graphs, however, we present a pseudo-polynomial time dynamic programming algorithm for the problem.
We then study the case that the minimum quantity is the same for each arc in the network and show that, under this restriction, the problem is still
weakly NP-complete on general graphs, but can be solved in strongly polynomial time on series-parallel graphs.
On general graphs, we present a \((2 - 1/\lambda) \)-approximation algorithm for this case, where \(\lambda\) denotes the common minimum quantity of all arcs.

This papers deals with the minimization of seminorms \(\|L\cdot\|\) on \(\mathbb R^n\) under the constraint of a bounded I-divergence \(D(b,H\cdot)\). The I-divergence is also known as Kullback-Leibler divergence and appears in many models in imaging science, in particular when dealing with Poisson data. Typically, \(H\) represents here, e.g., a linear blur operator and \(L\) is some discrete derivative operator. Our preference for the constrained approach over
the corresponding penalized version is based on the fact that the I-divergence of data
corrupted, e.g., by Poisson noise or multiplicative Gamma noise can be estimated by statistical methods. Our minimization technique rests upon relations between constrained and penalized convex problems and resembles the idea of Morozov's discrepancy principle.
More precisely, we propose first-order primal-dual algorithms which reduce the problem to the solution of certain proximal minimization problems in each iteration step. The most interesting of these proximal minimization problems is an I-divergence constrained least squares problem. We solve this problem by connecting it to the corresponding I-divergence
penalized least squares problem with an appropriately chosen regularization parameter. Therefore, our algorithm produces not only a sequence of vectors which converges to a minimizer of the constrained problem but also a sequence of parameters which convergences to a regularization parameter so that the penalized problem has the same solution as our constrained one. In other words, the solution of this penalized problem fulfills the I-divergence constraint. We provide the proofs which are necessary to understand
our approach and demonstrate the performance of our algorithms for different
image restoration examples.

Image restoration and enhancement methods that respect important features such as edges play a fundamental role in digital image processing. In the last decades a large
variety of methods have been proposed. Nevertheless, the correct restoration and
preservation of, e.g., sharp corners, crossings or texture in images is still a challenge, in particular in the presence of severe distortions. Moreover, in the context of image denoising many methods are designed for the removal of additive Gaussian noise and their adaptation for other types of noise occurring in practice requires usually additional efforts.
The aim of this thesis is to contribute to these topics and to develop and analyze new
methods for restoring images corrupted by different types of noise:
First, we present variational models and diffusion methods which are particularly well
suited for the restoration of sharp corners and X junctions in images corrupted by
strong additive Gaussian noise. For their deduction we present and analyze different
tensor based methods for locally estimating orientations in images and show how to
successfully incorporate the obtained information in the denoising process. The advantageous
properties of the obtained methods are shown theoretically as well as by
numerical experiments. Moreover, the potential of the proposed methods is demonstrated
for applications beyond image denoising.
Afterwards, we focus on variational methods for the restoration of images corrupted
by Poisson and multiplicative Gamma noise. Here, different methods from the literature
are compared and the surprising equivalence between a standard model for
the removal of Poisson noise and a recently introduced approach for multiplicative
Gamma noise is proven. Since this Poisson model has not been considered for multiplicative
Gamma noise before, we investigate its properties further for more general
regularizers including also nonlocal ones. Moreover, an efficient algorithm for solving
the involved minimization problems is proposed, which can also handle an additional
linear transformation of the data. The good performance of this algorithm is demonstrated
experimentally and different examples with images corrupted by Poisson and
multiplicative Gamma noise are presented.
In the final part of this thesis new nonlocal filters for images corrupted by multiplicative
noise are presented. These filters are deduced in a weighted maximum likelihood
estimation framework and for the definition of the involved weights a new similarity measure for the comparison of data corrupted by multiplicative noise is applied. The
advantageous properties of the new measure are demonstrated theoretically and by
numerical examples. Besides, denoising results for images corrupted by multiplicative
Gamma and Rayleigh noise show the very good performance of the new filters.