Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

On the truncation of the harmonic oscillator wavepacket

We present an interesting result regarding the implication of truncating the wavepacket of the harmonic oscillator. We show that disregarding the non-significant tails of a function which is the superposition of eigenfunctions of the harmonic oscillator has a remarkable consequence: namely, there exist infinitely many different superpositions giving rise to the same function on the interval. Uniqueness, in the case of a wavepacket, is restored by a postulate of quantum mechanics

Reconstruction of Bandlimited Functions from Unsigned Samples

We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samples are taken at less than twice the Nyquist rate. In the case of uniform samples, we also describe an FFT-based algorithm to perform the reconstruction. We prove that it converges exponentially rapidly in the number of samples used and examine its numerical behavior on some test cases

Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization

We discuss several extensions and applications of the theory of discretely conformally equivalent triangle meshes (two meshes are considered conformally equivalent if corresponding edge lengths are related by scale factors attached to the vertices). We extend the fundamental definitions and variational principles from triangulations to polyhedral surfaces with cyclic faces. The case of quadrilateral meshes is equivalent to the cross ratio system, which provides a link to the theory of integrable systems. The extension to cyclic polygons also brings discrete conformal maps to circle domains within the scope of the theory. We provide results of numerical experiments suggesting that discrete conformal maps converge to smooth conformal maps, with convergence rates depending on the mesh quality. We consider the Fuchsian uniformization of Riemann surfaces represented in different forms: as immersed surfaces in \mathbb {R}^{3}, as hyperelliptic curves, and as \mathbb {CP}^{1} modulo a classical Schottky group, i.e., we convert Schottky to Fuchsian uniformization. Extended examples also demonstrate a geometric characterization of hyperelliptic surfaces due to Schmutz Schaller

A First Search for Cosmogenic Neutrinos with the ARIANNA Hexagonal Radio Array

The ARIANNA experiment seeks to observe the diffuse flux of neutrinos in the 10^8 - 10^10 GeV energy range using a grid of radio detectors at the surface of the Ross Ice Shelf of Antarctica. The detector measures the coherent Cherenkov radiation produced at radio frequencies, from about 100 MHz to 1 GHz, by charged particle showers generated by neutrino interactions in the ice. The ARIANNA Hexagonal Radio Array (HRA) is being constructed as a prototype for the full array. During the 2013-14 austral summer, three HRA stations collected radio data which was wirelessly transmitted off site in nearly real-time. The performance of these stations is described and a simple analysis to search for neutrino signals is presented. The analysis employs a set of three cuts that reject background triggers while preserving 90% of simulated cosmogenic neutrino triggers. No neutrino candidates are found in the data and a model-independent 90% confidence level Neyman upper limit is placed on the all flavor neutrino+antineutrino flux in a sliding decade-wide energy bin. The limit reaches a minimum of 1.9x10^-23 GeV^-1 cm^-2 s^-1 sr^-1 in the 10^8.5 - 10^9.5 GeV energy bin. Simulations of the performance of the full detector are also described. The sensitivity of the full ARIANNA experiment is presented and compared with current neutrino flux models.Comment: 22 pages, 22 figures. Published in Astroparticle Physic

Prospects of e-beam evaporated molybdenum oxide as a hole transport layer for perovskite solar cells

Perovskite solar cells have emerged as one of the most efficient and low cost technology for delivering of solar electricity due to their exceptional optical and electrical properties. Commercialization of the perovskite solar cells is, however, limited because of the higher cost and environmentally sensitive organic hole transport materials such as spiro-OMETAD and PEDOT:PSS. In this study, an empirical simulation was performed using Solar Cell Capacitance Simulator software to explore MoOx thin film as an alternative hole transport material for perovskite solar cells. In the simulation, properties of MoOx thin films deposited by electron beam evaporation technique from high purity (99.99%) MoO3 pellets at different substrate temperatures (room temperature, 100 °C and 200 °C) were used as input parameters. The films were highly transparent (>80%) and have low surface roughness (≤ 2 nm) with bandgap energy ranging between 3.75 eV to 3.45 eV. Device simulation has shown that the MoOx deposited at room temperature can work in both the regular and inverted structures of the perovskite solar cell with a promising efficiency of 18.25%. Manufacturing of the full device is planned in order to utilize the MoOx as an alternative hole transport material for improved performance, good stability and low cost of the perovskite solar cell

Promoting students’ interest through culturally sensitive curricula in higher education

Previous studies have emphasized culturally sensitive curricula in the context of enhancing minoritized students’ education. We examined the relationship between second-year higher education students’ perceptions of the cultural sensitivity of their curriculum and both majoritized and minoritized students’ interest in their course. A total of 286 (228 F) students rated the cultural sensitivity of their curriculum on six scales using a revised version of the Culturally Sensitive Curricula Scales (CSCS-R), the perceived quality of their relationships with teachers, and their interest. The CSCS-R widened the construct with two new scales and showed better reliability. Ethnic minority students (n = 99) perceived their curriculum as less culturally sensitive than White students (n = 182), corroborating previous findings. Black students perceived their curriculum as less culturally sensitive than Asian students. There were no significant differences between ethnic minority and White students on interest or perceived quality of relationships with teachers. Five dimensions of cultural sensitivity (Diversity Represented, Positive Depictions, Challenge Power, Inclusive Classroom Interactions, Culturally Sensitive Assessments) and perceived quality of relationships with teachers predicted interest. Ethnicity did not. Ensuring curricula and assessments represent diversity positively, challenge power and are inclusive may support students’ interest while reflecting an increasingly diverse society