Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the "lab-on-a-chip" paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results.

(De)colonization through topophilia: Marjorie Kinnan Rawlings’s life and work in Florida

(De)colonization Through Topophilia: Marjorie Kinnan Rawlings’s Life and Work in Florida attempts to reveal the author’s intimate connection to and mental growth through her place, namely the Cross Creek environs, and its subsequent effect on her writing. In 1928, Marjorie Kinnan Rawlings and her first husband Charles Rawlings came to Cross Creek, Florida. They bought the shabby farmhouse on Cross Creek Road, trying to be both, writers and farmers. However, while Charles Rawlings was unable to write in the backwoods of the Florida Interior, Rawlings found her literary voice and entered a symbiotic, reciprocal relationship with the natural world of the Cracker frontier. Her biographical preconditions – a childhood spent in the rural area of Rock Creek, outside of Washington D. C. - and a father who had instilled in her a sense of place or topophilia, enabled her to overcome severe marriage tensions and the hostile climate women writers faced during the Depression era. Nature as a helping ally and as an “undomesticated”(1) space/place is a recurrent motif throughout most of Rawlings’s Florida literature. At a time when writing the American landscape/documentary and the extraction of the self from texts was the prevalent literary genre, Marjorie Kinnan Rawlings inscribed herself into her texts. However, she knew that the American public was not yet ready for a ‘feminist revolt’, but was receptive of the longtime ‘inaudible’ voices from America’s regions, especially with regard to urban poverty and a homeward yearning during the Depression years. Fusing with the dynamic eco-consciousness of her Cracker friends and neighbors, Rawlings wrote in the literary category of regionalism enabling her to pursue three of her major aims: an individuated self, a self that assimilated with the ‘master narratives’ of her time and the recognition of the Florida Cracker and Scrub region. The first part of this dissertation briefly introduces the largely unknown and underestimated writer Marjorie Kinnan Rawlings, providing background information on her younger years, the relationship toward her family and other influential persons in her life. Furthermore, it takes a closer look at the literary category of regionalism and Rawlings’s use of ‘place’ in her writings. The second part is concerned with the ‘region’ itself, the state of Florida. It focuses on the natural peculiarities of the state’s Interior, the scrub and hammock land around her Cracker hamlet as well as the unique culture of the Florida Cracker. Part IV is concerned with the analysis of her four Florida books. The author is still widely related to the ever-popular novel The Yearling (1938). South Moon Under (1933) and Golden Apples (1935), her first two novels, have not been frequently republished and have subsequently fallen into oblivion. Cross Creek (1942), Rawlings’s last Florida book, however, has recently gained renewed popularity through its use in classes on nature writers and the non-fiction essay but it requires and is here re-evaluated as the author’s (relational) autobiography. The analysis through place is brought to completion in this work and seems to intentionally close the circle of Rawlings’s Florida writings. It exemplifies once more that detachment from place is impossible for Rawlings and that the intermingling of life and place in literature, is essential for the (re)creation of her identity. Cross Creek is therefore not only one of Rawlings’s greatest achievements; it is more importantly the key to understanding the author’s self and her fiction. Through the ‘natural’ interrelationship of place and self and by looking “mutually outward and inward,”(2) Marjorie Kinnan Rawlings finds her literary voice, a home and ‘a room of her own’ in which to write and come to consciousness. Her Florida literature is not only product but also medium and process in her assessment of her identity and self. _____________ (1) Alaimo, Stacy. Undomesticated Ground: Recasting Nature as Feminist Space (Ithaca: Cornell UP, 2000) 23. (2) Libby, Brooke. “Nature Writing as Refuge: Autobiography in the Natural World” Reading Under the Sign of Nature. New Essays in Ecocriticism. Ed. John Tallmadge and Henry Harrington. (Salt Lake City: The U of Utah P, 2000) 200.

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.