In the recent years, researchers have discovered a multitude of applications using nanofibers in fields like composites, biotechnology, environmental engineering, defense, optics and electronics. This increase in nanofiber applications needs a higher rate of nanofiber production. Electrospinning has proven to be the best nanofiber manufacturing process because of simplicity and material compatibility. Study of effects of various electrospinning parameters is important to improve the rate of nanofiber processing. In addition, several applications demand well-oriented nanofibers. Researchers have experimentally tried to control the nanofibers using secondary external electric field. In the first study, the electrospinning process is modeled and the bending instability of a viscoelastic jet is simulated. For this, the existing discrete bead model is modified and the results are compared, qualitatively, with previous works in literature. In this study, an attempt is also made to simulate the effect of secondary electric field on electrospinning process and whipping instability. It is observed that the external secondary field unwinds the jet spirals, reduces the whipping instability and increases the tension in the fiber. Lattice Boltzmann method (LBM) has gained popularity in the past decade as the method is easy implement and can also be parallelized. In the second part of this thesis, a hybrid numerical scheme which couples lattice Boltzmann method with finite difference method for a Oldroyd-B viscoelastic solution is proposed. In this scheme, the polymer viscoelastic stress tensor is included in the equilibrium distribution function and the distribution function is updated using SRT-LBE model. Then, the local velocities from the distribution function are evaluated. These local velocities are used to evaluate local velocity gradients using a central difference method in space. Next, a forward difference scheme in time is used on the Maxwell Upper Convected model and the viscoelastic stress tensor is updated. Finally, using the proposed numerical method start-up Couette flow problem for Re = 0.5 and We = 1.1, is simulated. The velocity and stress results from these simulations agree very well with the analytical solutions.

Studying dynamics of magnetization relaxation in excited magnetic materials is important both for understanding the rates and pathways of magnetization relaxation and for the potential use in spin-based electronics and data storage devices in the future. Previous studies have demonstrated that the size of nanocrystals is an important factor for energy relaxation in quantum dots and metal nanoparticles. Since magnetization relaxation is one of energy relaxation pathways, the size of nanocrystals may be also an important factor for magnetization relaxation in nanoscale magnetic materials. The goal of this study is to have a better understanding of magnetization relaxation in nanoscale magnetic materials. In particular, we focused on the correlation between the nanocrystal size and the rates of spin-lattice relaxation (SLR), a magnetization relaxation pathway, in magnetic nanocrystals. The size-dependent magnetization relaxation rate after optically induced demagnetization in colloidal Fe3O4 nanocrystals was measured by using time-resolved Faraday rotation (FR). Fe3O4 nanocrystals were chosen as the model system to study the correlation between the size of nanocrystals and the rates of SLR due to the wellestablished synthetic procedure of making nanocrystals with various sizes and narrow size dispersion. Faster SLR rates were observed in smaller Fe3O4 nanocrystals. The results suggested the surface of nanocrystals have higher efficiency of SLR than the interior region by using a simple model to analyze the SLR rates of Fe3O4 nanocrystals with various sizes. Higher efficiency of SLR at the surface may be due to the stronger spin-orbit coupling at the surface relative to the interior region. In addition to magnetization dynamics studies, the effect of oxidation on static FR in iron oxide nanocrystals (between Fe3O4 and y-Fe2O3) was studied. The results indicated FR signal is linearly correlated to the strength of optical transition between Fe2 and Fe3 in Fe3O4 for a given size of nanocrystals.

Functional expression of a protein in life form is decided by its tertiary structure. In the past few decades, a significant number of studies have been made on this subject. However, the folding rules of a protein still stay unsolved. The challenge is to predict the three-dimensional tertiary structure of a protein from its primary amino acid sequence. We propose a hybrid method combining homology model and the folding approach to predict protein three-dimensional structure from amino acid sequence. The previous researches on folding problem mostly take the HP (Hydrophobic-Polar) model, which is not able to simulate the native structure of proteins. We use a more exquisite model, the sliced lattice model, to approximate the native forms. Another essential factor influencing protein structures is disulfide bonds, which are ignored in the HP model. We use the ant colony optimization algorithm to approximate the folding problem with the constrained disulfide bond on the sliced lattice HP model. We show that the prediction results are better than previous methods by the measurement of RMSD(Root Mean Square Deviation).

In general, subset sum problem is strongly believed to be computationally difficult to solve. But in 1983, Lagarias and Odlyzko proposed a probabilistic algorithm for solving subset sum problems of sufficiently low density in polynomial time. In 1991, Coster et. al. improved the Lagarias-Odlyzko algorithm and solved subset sum problems with higher density. Both algorithms reduce subset sum problem to finding shortest non-zero vectors in special lattices. In this thesis, we first proposed a new viewpoint to define the problems which can be solved by this two algorithms and shows the improved algorithm isn't always better than the Lagarias-Odlyzko algorithm. Then we verify this notion by experimentation. Finally, we find that the Lagrias-Odlyzko algorithm can solve the high-density subset sum problems if the weight of solution is higher than 0.7733n or lower than 0.2267n, even the density is close to 1.

Abstract The softening effects of ferromagnetic magnon on some ferromagnetic semiconductors and colossal magnetoresistance manganites have attracted much attention. Such effect can be calculated from the single orbital ferromagnetic Kondo lattice model in proper conducting carrier numbers utilizing the equation of motion method with one magnon excitation and Random Phase approximations. However, if we take into account the Coulomb repulsion and use the Gutzwiller projection method to transfer this repulsion force to conducting bandwidth modulation, the softening effect disappear. This paper describes qualitively the effect of softening on properties of different colossal manganites.

This research develops an extendible framework for reproducing watercolor in a digital environment, with a focus on interactivity using the GPU. The framework uses the lattice Boltzmann method, a relatively new approach to fluid dynamics, and the Kubelka-Munk reflectance model to capture the optical properties of watercolor. The work is demonstrated through several paintings produced using the system.

Systems in which there are strong specific interactions between the polymer and CO₂ are of interest in a number of applications including polymer foaming, coating and impregnation. Unfortunately, experimental data on the phase behavior of such systems are relatively scarce, as are models that explicitly consider specific interactions in such systems. The overall goal of this work was therefore to develop a method for the measurement of specific interactions in polymer + CO₂ systems and to apply such measurements to the development of a thermodynamic model for polymer solutions. This work demonstrates that in situ ATR-FTIR spectroscopy may be used to quantify specific interactions in CO₂ + polymer- systems that incorporate carbonyl, ether, siloxane and sulfone groups. However, carbonyl stretching frequencies cannot be used to quantify such interactions between CO₂ and carbonyl polymers, contrary to what has been suggested in the literature. This is because blue shifts in the carbonyl stretching frequencies were observed in the ATR-FTIR spectra of CO₂ + PVAc, CO₂ + PMMA, CO₂ + PLA, and CO₂ + PLGA85 systems. These CO₂ induced blue shifts can be attributed to dielectric effects, and therefore cannot be used to quantify specific interactions in these systems. We propose the use of the temperature dependence of the CO₂ bending mode to quantify specific interactions in CO₂ + carbonyl polymers. With this method, the enthalpies of association for C=O...CO₂ specific interactions were found to be between -7 and -10 kJ/mol in the order: CO₂ + PVAc > CO₂ + PCL ≈ CO₂ + PLA > CO₂ + PLGA85 > CO₂ + PMMA. The method was also extended to other CO₂ philic polymers, leading to enthalpies of association in the order CO₂ + PEG > CO₂ + PVAc > CO₂ + PSF > CO₂ + PMSSQ >> CO₂ + PVDF&PS. Specific interactions in polymer + CO₂systems were also investigated via NVT molecular dynamics simulations Such interactions were found to decrease in the order: CO₂...C-O-C > CO₂...O=C-O > CO₂...Si-O-Si. In addition, the association distance was identified to be 3.2 Å. Finally, CO₂ accessibility was found to decrease in the order PVAc > PVMK > PLA > PMA. It was also confirmed that 96 % of associated CO₂ molecules interact with one carbonyl group in these systems. A ternary extension of the Compressible Lattice Model (CLM) was developed and the enthalpy of specific interactions obtained from ATR_FTIR spectra was incorporated into the model to correlate and predict phase behavior in polymer + CO₂ + cosolvent systems. This work shows that model parameters obtained from binary data can be used to predict ternary system behavior with average absolute deviations between calculated and experimental values (AAD) less than 10%. The Sanchez-Lacombe lattice-fluid partition function was extended to associated systems by incorporating an association factor obtained from the Compressible Lattice Model. The resulting Associated Sanchez-Lacombe (ASL) EOS has the same form as the SL EOS, but includes the effects of specific interaction in the calculation of lattice energies, and chemical potentials. We demonstrate that ASL model parameters obtained from correlation of sorption equilibria can be used to predict swelling of polymers with AAD less than 10%. In summary, specific interactions between CO₂ and C=O and other CO₂-philic groups have been quantified using in situ ATR-FTIR spectroscopy. The results have been directly incorporated into a lattice model that is able to correlate cloud points, and sorption equilibria, using a single parameter. The model is therefore likely to be beneficial in many applications involving polymer + CO₂ or polymer + CO₂ + cosolvent systems including polymer impregnation, coating, foaming, and polymer membranes for CO₂ capture. An EOS formulation for the model has been derived for the calculation of swelling in these systems.

Recently, Formal Concept Analysis has proven to be an efficient method for the analysis and representation of information. However, the possibility to visualize concept hierarchies is being affected by the difficulty of drawing attractive diagrams automatically. Reducing the number of edge crossings seems to increase the readability of those drawings. This dissertation concerns with a mandatory prerequisite of this constraint, namely the characterization and visual representation of planar lattices. The manifold existing approaches and algorithms are thereby considered under a different point of view. It is well known that exactly the planar lattices (or planar posets) possess an additional order ``from left to right''. Our aim in this work is to define left-relations and left-orders more precisely and to describe several aspects of planar lattices with their help. The three approaches employed structure the work in as many parts: Left-relations on lattices allow a more efficient consideration of conjugate orders since they are uniquely determined by the sorting of the meet-irreducibles. Additionally, the restriction on the meet-irreducibles enables us to achieve an intuitive description of standard contexts of planar lattices similar to the consecutive-one property. With the help of left-relations on diagrams, planar lattices can indeed be drawn without edge crossings in the plane. Thereby, lattice-theoretically found left-orders can be detected in the graphical representation again. Furthermore, we modify the left-right-numbering algorithm in order to obtain attribute-additive and plane drawings of planar lattices. Finally, we will consider left-relations on contexts. They turn out to be fairly similar structures to the Ferrers-graphs. Planar lattices can be characterized by a property of these graphs, namely the bipartiteness. We will constructively prove this result. Subsequently, we can design an efficient algorithm that finds all non-similar plane diagrams of a lattice. / Die Formale Begriffsanalyse hat sich in den letzten Jahren als effizientes Werkzeug zur Datenanalyse und -repräsentation bewährt. Die Möglichkeit der visuellen Darstellung von Begriffshierarchien wird allerdings durch die Schwierigkeit, ansprechende Diagramme automatisch generieren zu können, beeinträchtigt. Offenbar sind Diagramme mit möglichst wenig Kantenkreuzungen für den menschlichen Anwender leichter lesbar. Diese Arbeit beschäftigt sich mit mit einer diesem Kriterium zugrunde liegenden Vorleistung, nämlich der Charakterisierung und Darstellung planarer Verbände. Die schon existierenden vielfältigen Ansätze und Methoden werden dabei unter einem neuen Gesichtspunkt betrachtet. Bekannterweise besitzen genau die planaren Verbände (bzw. planare geordnete Mengen) eine zusätzliche Ordnung "von links nach rechts". Unser Ziel in dieser Arbeit ist es, solche Links-Relationen bzw. Links-Ordnungen genauer zu definieren und verschiedene Aspekte planarer Verbände mit ihrer Hilfe zu beschreiben. Die insgesamt drei auftretenden Sichtweisen gliedern die Arbeit in ebensoviele Teile: Links-Relationen auf Verbänden erlauben eine effizientere Behandlung konjugierter Ordnungen, da sie durch die Anordnung der Schnitt-Irreduziblen schon eindeutig festgelegt sind. Außerdem erlaubt die Beschränkung auf die Schnitt-Irreduziblen eine anschauliche Beschreibung von Standardkontexten planarer Verbände ähnlich der consecutive-one property. Mit Hilfe der Links-Relationen auf Diagrammen können planare Verbände tatsächlich eben gezeichnet werden. Dabei lassen sich verbandstheoretisch ermittelte Links-Ordnungen in der graphischen Darstellung wieder finden. Weiterhin geben wir in eine Modifikation des left-right-numbering an, mit der planare Verbände merkmaladditiv und eben gezeichnet werden können. Schließlich werden wir Links-Relationen auf Kontexten betrachten. Diese stellen sich als sehr ähnlich zu Ferrers-Graphen heraus. Planare Verbände lassen sich durch eine Eigenschaft dieser Graphen, nämlich die Bipartitheit, charakterisieren. Wir werden dieses Ergebnis konstruktiv beweisen und darauf aufbauend einen effizienten Algorithmus angeben, mit dem alle nicht-ähnlichen ebenen Diagramme eines Verbandes bestimmt werden können.

In this Doktorarbeit the Lattice Boltzmann scheme, a heuristic method for the simulation of flows in complicated boundaries, is investigated. Its theory is renewed by emphasizing the entropy maximization principle, and new means for the modelling of geometries (including moving boundaries) and the visual representation of evoluting flows are presented. An object oriented implemen- tation is given with communication between objects realized by an interpreter object and communication from outside realized via interprocess communica- tion. Within the new theoretical apprach the applicability of existing Lattice Boltzmann schemes to model thermal flows for arbitrary temperatures is reex- amined. / In dieser Doktorarbeit wird das Gitter-Boltzmann-Schema, eine heuristische Methode fuer die Simulation von Stroemungen innerhalb komplexer Raender, untersucht. Die zugrundeliegende Theorie wird unter neuen Gesichtspunkten, insbesondere dem Prinzip der Entropiemaximierung, betrachtet. Des weiteren werden neuartige Methoden fuer die Modellierung der Geometrie (einschl. beweglicher Raender) und der visuellen Darstellung aufgezeigt. Eine objektorientierte Implementierung wird vorgestellt, wobei die Kommunikation zwischen den Objekten über Interpreter-Objekte und die Kommunikation mit der Aussenwelt ueber Interprozess-Kommunikation gehandhabt wird. Mit dem neuen theoretischen Ansatz wird die Gueltigkeit bestehender Gitter-Boltzmann-Schemata fuer die Anwendung auf Stroemungen mit nicht konstanter Temperatur untersucht.

The work presented in this thesis was motivated by the large amount of experimental investigations of the phonons in quasicrystals. The generalized vibrational density of states (GVDOS) was measured for many quasicrystalline phases and in some cases at different temperatures [suck et al (1997), Dugain et al (1997)]. The progress achieved in the structure determination of approximants to some quasicrystals was a legitimate motivation for numerical investigations of lattice dynamics in these structures. Two different types of interatomic interactions were used: the spring model and the ab-initio pair potentials. The investigations explained the shape of some experimentally measured GVDOS (d-AlNiCo, o-Al13Co4 and i-ZnMgY) via the calculation of the partial vibrational densities of states. Both calculated and measured GVDOS of the d-AlNiCo phase showed an intensity excess at low energies relatively to the ideal Debye behaviour. This excess was found to be a consequence of the existence of special modes at theses energies which are called ``quasi-localized modes''. These modes seem to be characteristic of the lattice dynamics in the complex Al-TM structures. To calculate the frequency shift due to the shift of the GVDOS through low energies observed experimentally at high temperatures, a new method based on a Monte-Carlo simulation was developed. It was shown that the quasi-localized modes introduce large frequency shifts at low energies. Finally, the vibrational entropy was also investigated, and it was found that it contributes to the stabilization of the complex structures over the relatively simple structures at high temperatures. / Die Arbeit, die in dieser Dissertation präsentiert wird, wurde durch eine Vielzahl von experimentellen Beobachtungen von Phononen in Quasikristallen motiviert. Die verallgemeinerte vibrationelle Zustandsdichte (GVDOS, generalized vibrational density of states) wurde für viele quasikristalline Phasen gemessen und für einige auch bei verschiedener Temperatur [Suck et al. (1997), Dugain et al. (1997)]. Der Fortschritt, der in der Bestimmung von Näherungen für einige Quasikristalle erreicht wurde war eine legitime Motivation für numerische Untersuchungen der Gitterdynamik auf diesen Strukturen. Es wurden zwei unterschiedliche interatomare Wechselwirkungen verwendet: Das Federmodell und die ab-initio Paar Potentiale. Die Untersuchungen erklärten die Form einiger experimenteller GVDOS-Messungen (d-AlNiCo, o-Al13Co4 und i-ZnMgY) mittels der Berechnung der partiellen vibrationellen Zustandsdichte. Beide, berechnete und gemessene, GVDOS der d-AlNiCo Phase zeigten einen Intensitätsanstieg bei kleinen Energien relativ zum idealen Debye Verhalten. Dieser Anstieg stellte sich als Konsequenz der Existenz von besonderen Moden bei diesen Energien heraus, die quasi-lokalisierte Moden genannt werden. Diese Moden scheinen charakteristisch für die Gitterdynamik in den komplexen Al-TM Strukturen zu sein. Um die experimentell beobachtete Frequenzverschiebung aufgrund der Verschiebung der GVDOS durch niedrige Energien zu berechnen, wurde eine neue, auf Monte-Carlo Simulation beruhende, Methode entwickelt. Es wurde gezeigt, daß die quasi-lokalisierten Moden große Frequenzverschiebungen bei kleinen Energien hervorrufen. Letzt-lich wurde auch die vibrationelle Entropie untersucht und es stellte sich heraus, daß sie bei hohen Temperaturen dazu beiträgt die komplexen Strukturen gegenüber den relativ einfachen zu stabilisieren.