Fourier Analysis of the BTZ Black Hole

In this paper we extend our previous work regarding the role of the Fourier transformation in bulk to boundary mappings to include the BTZ black hole. We follow standard procedures for modifying Fourier Transformations to accommodate quotient spaces and arrive at a bulk to boundary mapping in a black hole background. We show that this mapping is consistent with known results and lends a new insight into the AdS/CFT duality. We find that the micro-states corresponding to the entropy of a bulk scalar field are the Fourier coefficients on the boundary, which transform under the principal series representation of $SL(2,R)$. Building upon this we present a toy model to analyze the implications of this for the origin of black hole entropy. We find that the black hole micro-states live on the boundary and correspond to the possible emission modes of the black holeComment: 12 page

Do difficulties in mentalizing correlate with severity of borderline personality disorder?

Borderline personality disorder (BPD) is a severe and complex disorder, historically believed to be ‘untreatable’. This view has been challenged through the success of various therapies in enabling individuals with this diagnosis to create ‘a life worth living’. However despite this progress little is known about how or why these treatments work. This thesis aims to contribute to this understanding through exploring the role of mentalization in BPD. Part 1 is a literature review which critically assesses studies investigating the processes that potentially underlie therapeutic change in BPD treatments. It reveals a lack of any research meeting the criteria for concluding a component of therapy a mechanism of change, but finds evidence for a link between therapeutic alliance and clinical outcome. One suggested explanation for this finding is the development of mentalization within a secure therapeutic relationship. Part 2 is an empirical research paper which further explores the contribution of mentalization to BPD. It investigates whether symptom severity in BPD is associated with performance on a battery of tasks measuring different dimensions of mentalizing ability. It also explores whether the current sample share similar impairments in mentalizing to participants in a previous study (Newbury-Helps,2011) with a diagnosis of antisocial personality disorder (ASPD). The results contradicted hypotheses, finding no evidence for a relationship between BPD severity and mentalizing impairments, and revealing significant differences between mentalizing in BPD and ASPD samples. Possible reasons for these findings are discussed, along with their implications for future clinical practice and research. This study was conducted as part of a joint project (Perera, 2012). Part 3 critically appraises this work. The experience of developing and conducting the thesis is examined and retrospective improvements to the study are suggested, along with ideas for future research, in light of the practical and personal challenges encountered throughout the process

The Importance of Radial Migration to Spiral Galaxy Evolution

Spiral galaxy evolution is frequently considered in the context of environment, but internal processes may also play an important role. One such process, called \lq\lq radial migration", rearranges the angular momentum distribution of the disk without causing kinematic heating. Should radial migration be efficient, it could cause a substantial fraction of disk stars to move large radial distances over the lifetime of the disk, thus having significant impact on its kinematic, structural and chemical evolution. However, clues to its efficiency from observational and simulated data are inconclusive and insight from analytic studies is limited. We here aim to build an analytic framework for understanding the physics important to the efficiency of radial migration. In order for a star to migrate radially, it must first be in a “trapped” orbit (a family of orbits that occurs near corotation) due to a transient spiral pattern. The efficiency of radial migration depends on both the duty cycle for transient patterns and the RMS change in orbital angular momentum from each pattern, ^(1/2). This work focuses on the physics that determines the magnitude of ^(1/2), which increases with increasing fraction of and radial excursions for stars in trapped orbits. In this work, we derive both an expression for the maximum radial excursion of a trapped orbit and an analytic “capture criterion” that predicts whether or not a disk star with finite random orbital energy is in a trapped orbit. We then use the capture criterion, in a series of disk galaxy models, to find the fraction of stars in trapped orbits. We show it is primarily a star's orbital angular momentum that determines whether or not it is in a trapped orbit. For an ensemble of stars, the trapped fraction decreases with increasing radial velocity dispersion as e^(-sigma_R^2). Further, the maximum radial excursions for trapped orbits is smaller than excursions expected from the random motions of stars in MW-like spirals. We conclude that radial migration may play a role in the evolution of disk galaxies, but it is not important enough to form major structural components

Phase diagram for morphological transitions of wetting films on chemically structured substrates

Using an interface displacement model we calculate the shapes of thin liquidlike films adsorbed on flat substrates containing a chemical stripe. We determine the entire phase diagram of morphological phase transitions in these films as function of temperature, undersaturation, and stripe widthComment: 15 pages, RevTeX, 7 Figure

Correlation functions near Modulated and Rough Surfaces

In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near surface correlations can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in the deformations in height from a flat surface. Detailed results are given for a regularly patterned surface, as well as for a self-affinely rough surface with roughness exponent $\zeta$. By combining this perturbative calculation in height deformations with the field-theoretic renormalization group approach, we also estimate the values of critical exponents governing the behavior of the decay of correlation functions near a self-affinely rough surface. We find that for the interacting theory, a large enough $\zeta$ can lead to novel surface critical behavior. We also provide scaling relations between roughness induced critical exponents for thermodynamic surface quantities.Comment: 31 pages, 2 figure

Wetting films on chemically heterogeneous substrates

Based on a microscopic density functional theory we investigate the morphology of thin liquidlike wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical step and on a single stripe. In view of applications in microfluidics the accuracy of guiding liquids by chemical microchannels is discussed. Finally we give a general prescription of how to investigate theoretically the wetting properties of substrates with arbitrary chemical structures.Comment: 56 pages, RevTeX, 20 Figure

Critical adsorption near edges

Symmetry breaking surface fields give rise to nontrivial and long-ranged order parameter profiles for critical systems such as fluids, alloys or magnets confined to wedges. We discuss the properties of the corresponding universal scaling functions of the order parameter profile and the two-point correlation function and determine the critical exponents eta_parallel and eta_perpendicular for the so-called normal transition.Comment: 22 pages, 5 figures, accepted for publication in PR