Filling a box with translates of two bricks

We give a new proof of the following interesting fact recently proved by Bower and Michael: if a d-dimensional rectangular box can be tiled using translates of two types of rectangular bricks, then it can also be tiled in the following way. We can cut the box across one of its sides into two boxes, one of which can be tiled with the first brick only and the other one with the second brick. Our proof relies on the Fourier Transform. We also show that no such result is true for three, or more, types of bricks

Minority Versus Mainstream: Sir Samuel Ferguson, James Clarence Mangan, and the Anglo-Irish Literary Canon

Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej nauk

BFT2_2: a General Class of 2d2d N=(0,2)\mathcal{N}=(0,2) Theories, 3-Manifolds and Toric Geometry

We introduce and initiate the study of a general class of $2d$ $\mathcal{N}=(0,2)$ quiver gauge theories, defined in terms of certain 2-dimensional CW complexes on oriented 3-manifolds. We refer to this class of theories as BFT$_2$\mbox{'}s. They are natural generalizations of Brane Brick Models, which capture the gauge theories on D1-branes probing toric Calabi-Yau 4-folds. The dynamics and triality of the gauge theories translates into simple transformation of the underlying CW complexes. We introduce various combinatorial tools for analyzing these theories and investigate their connections to toric Calabi-Yau manifolds, which arise as their master and moduli spaces. Invariance of the moduli space is indeed a powerful criterion for identifying theories in the same triality class. We also investigate the reducibility of these theories.Comment: 44 pages, 32 figure

Brick Collage

bricolage: construction or creation from a diverse range of available things I create abstracted modular sculptures, assemblages, and collages that playfully reference utility, using salvaged materials and carefully fabricated objects. My sculptures are considerately composed, elevating the materials with a determined focus on how each disparate part connects to the next to become a meaningful whole. I have a reverence for all of the objects and materials I use, no matter their origin, and thoroughly consider how each of their forms, textures, colors, weights and other formal and physical qualities integrate into a whole. With the use of recognizable utilitarian objects or components the sculptures take on an implied function. The work creates a space for the viewer to pay attention, and to consider what they are seeing. The positions of the ragpicker, the djobbeur, and the bricoleur as tropes of reclamation resonate deeply with me. These figures take action with urgency in the face of adversity. They are driven by imagination. I understand these figures as timeless, their responses to reality perpetually relevant in our world and my own as an individual with consistent experiences of trauma, and adversity. I do see myself as a bricoleur, though I know that I do not live with the level of deprivation that these historical figures did. Advisor: Peter Pinnel

Optical studies of crystal phase heterostructures

III-V semiconductors are commonly used for a variety of optical applications, such as LED based lights and solar sells. Most III-V semiconductors, such as GaAs and InP, exhibit the zinc-blende (zb) crystal structure, but in the form of nanowires it is also possible to create them in the wurtzite (wz) crystal structure. This allows for the creation of novel heterostructures consisting of the same compound, but different crystal structures, so called crystal phase orpolytype heterostructures. Unlike material heterostructures, these polytype heterostructures have atomically sharp interfaces with minimal strain. This could make them ideal candidates for a number of applications, such as single photon sources, and as an environment to study interesting physical phenomena such as electron crystals and quantum dots (Q-dots).In this work I have used photoluminescence (PL) spectroscopy and photoluminescence excitation (PLE) spectroscopy to investigate a number of InP and GaAs polytype heterostructures. PL and PLE are non-invasive optical techniques that use absorption and emission of photons to gain information about a number of semiconductor properties, such as bandgap, band structure and the energy of impurity levels. The PL and PLE measurements of single, nanowires are combined with electron microscopy. This allows for the correlation of the morphology and crystal structure quality with the optical properties of the polytype heterostructures. Finally, the measured optical properties are correlated to numerical calculations of electronic structure.This thesis consists of three papers. In paper I it is shown that the Fermi-level pinning at the semiconductor-air surface influences the perceived valence band offset between the wz and zb crystal structure in GaAs nanowires. In paper II the existence of a two dimensional electron gas at the wz-zb interface in modulation doped InP nanowires is demonstrated. Finally, paper III explores zb-GaAs Q-dots in narrow wz-GaAs nanowires. The existence of multiple Q-dot states is confirmed trough PLE, whose energies correlate with numerical calculations of the Q-dot energy levels. The results in this thesis pave the way towards the use of polytype heterostructures for the study of physical phenomena, such as electron crystals

The Panchromatic Hubble Andromeda Treasury XI: The Spatially-Resolved Recent Star Formation History of M31

We measure the recent star formation history (SFH) across M31 using optical images taken with the \texit{Hubble Space Telescope} as part of the Panchromatic Hubble Andromeda Treasury (PHAT). We fit the color-magnitude diagrams in ~9000 regions that are ~100 pc $\times$ 100 pc in projected size, covering a 0.5 square degree area (~380 kpc$^2$, deprojected) in the NE quadrant of M31. We show that the SFHs vary significantly on these small spatial scales but that there are also coherent galaxy-wide fluctuations in the SFH back to ~500 Myr, most notably in M31's 10-kpc star-forming ring. We find that the 10-kpc ring is at least 400 Myr old, showing ongoing star formation over the past ~500 Myr. This indicates the presence of molecular gas in the ring over at least 2 dynamical times at this radius. We also find that the ring's position is constant throughout this time, and is stationary at the level of 1 km/s, although there is evidence for broadening of the ring due to diffusion of stars into the disk. Based on existing models of M31's ring features, the lack of evolution in the ring's position makes a purely collisional ring origin highly unlikely. We find that the global SFR has been fairly constant over the last ~500 Myr, though it does show a small increase at 50 Myr that is 1.3 times the average SFR over the past 100 Myr. During the last ~500 Myr, ~60% of all SF occurs in the 10-kpc ring. Finally, we find that in the past 100 Myr, the average SFR over the PHAT survey area is $0.28\pm0.03$ M$_\odot$ yr$^{-1}$ with an average deprojected intensity of $7.3 \times 10^{-4}$ M$_\odot$ yr$^{-1}$ kpc$^{-2}$, which yields a total SFR of ~0.7 M$_\odot$ yr$^{-1}$ when extrapolated to the entire area of M31's disk. This SFR is consistent with measurements from broadband estimates. [abridged]Comment: 23 pages, 17 figures, 2 tables, accepted for publication in Ap

Brief historical review of Earthen Architecture in the World with a focus on Spain and South Korea

Although modern progress relegated earth construction to countries with low level of industrial development due to more modern and resistant materials such as concrete, actually, this is awakening a great interest due to its low energy and recyclability properties are positioning it as a sustainable material. The earth as a material presents many advantages; by one hand, loam is able to absorb and desorb humidity faster, in a greater extent than other materials allowing a balance indoor climate