Limits to phase resolution in matter-wave interferometry

We study the quantum dynamics of a two-mode Bose-Einstein condensate in a time-dependent symmetric double-well potential using analytical and numerical methods. The effects of internal degrees of freedom on the visibility of interference fringes during a stage of ballistic expansion are investigated varying particle number, nonlinear interaction sign and strength, as well as tunneling coupling. Expressions for the phase resolution are derived and the possible enhancement due to squeezing is discussed. In particular, the role of the superfluid-Mott insulator crossover and its analog for attractive interactions is recognized.

Verdi's Settings of Shakespeare : from Play to Liberetto to Opera

As a Senior Scholar pursuing the topic, Verdi's Settings of Shakespeare: From Play to Libretto to Opera, I have endeavoured to study a project relevant to my majors, Music and English. During first semester, I carefully analysed Shakespeare's plays, Macbeth, Othello and Falstaff. The highlight of my project was in January when I travelled to New York City and spent the day working with the Metropolitan Opera Guild. I was also able to see a performance of Verdi's Othello with Jon Vickers in the lead role. During the second semester, I studied the musical aspects of the compositions. I spent time analysing musical passages and relating them to the plays and the operas. I was also able to continue my study of Italian, which I find extremely beneficial while studying Verdi's libretti. On Monday, 13th May, 1974, I gave a lecture presentation of my project. At this time, I showed slides of Metropolitan productions of the operas, presented my own rendition of five arias (in costume) and talked about comparisions between the plays and the operas. I applied for a Rotary Fellowship to take my project to Europe and am presently waiting to hear the results. If I do receive the fellowship, I am planning to spend a year studying the plays and operas in England and Italy. Afterwards, I hope to publish a paper explaining my findings. The paper is divided into six sections. The first section is an introduction which explains the period of Romanticism and its relationship to Shakespeare and Verdi. The second section is devoted to discussing the librettist for Macbeth, Francesco Piave. Following this section the opera Macbeth is discussed. Arrigo Boito, the librettist for Otello and Falstaff is discussed in the fourth section. The last two sections deal with Otello and Falstaff. I have also included a number of musical selections to better explain certain passages. My project has been invaluable to me. My Senior Scholar project has allowed me the freedom of independent study as well as a means of tying my majors together.

Be the Change You Wish to See: National Attiudes and Climate Change Policy

A multitude of views characterize what should or should not be done about climate change, and in the past decades, nations have acted very differently in the face of climate change. This study explores factors that affect individuals' attitudes and concerns towards the environment and how those attitudes ultimately affect climate change policy. One model investigates the link between individual attitudes and countries' actions on climate change, and the results show that attitudes indeed matter in the implementation of policy. Different measures of democracy such as freedom of the press also prove to be important as channels for these attitudes. A second model identifies a number of political, socioeconomic and demographic characteristics that matter for people's attitudes towards climate change.

An exploratory study on how to improve the economy of American Samoa

Deep in the South Pacific region about 2,300 miles southwest of the Hawaiian islands1 lies a United States territory that many Americans have never heard of nor known anything about. However, some famous Americans such as Troy Polamalu of the Pittsburgh Steelers, semi retired professional wrestler Dwayne “The Rock” Johnson, and Hawaii Congresswoman Tulsi Gabbard have genealogical roots there. More importantly, many of the Territory’s sons and daughters have served and lost their lives for the United States flag and the cause of freedom around the world. This place is called American Samoa, a collection of seven islands that if glued together would have a total landmass of approximately 76 square miles, just a tad bigger than the capital city of the United States. According to the United States Census Bureau, there were 55,519 residents of American Samoa in 2010.1 The majority of them are ethnic Samoans, a Polynesian sect that traces its history back to early migrants from Southeast Asia who settled the islands around 1500 B.C.2 3 The climate is warm all year long and the forests along the mountains are ripe with vegetation. The main island is Tutuila with its beautiful and coveted landlocked harbor that was used as a coaling station by the United States naval ships during World War II. In fact, it was the Pago Pago Harbor that diminished the impact of the 2009 Tsunami that devastated the Samoan islands by channeling the waters of the Pacific Ocean towards the end of the harbor instead of flooding many other villages surrounding the Pago Pago Bay area. Lives and property were destroyed near the end of the Harbor but it could have been worse for the entire Bay area. Locally grown foods include coconut, taro, banana, guava, sugar cane, papaya, yam, pineapple, and breadfruit. It is completely surrounded by the Pacific Ocean from which the locals obtain a variety of seafood. There is a popular saying in Samoa that goes, “In Samoa, it is impossible to starve 1 American Samoa Department of Commerce, 2012 Statistical Yearbook, http://www.doc.as/wpcontent/uploads/2011/06/2012-Statistical-Yearbook-1.pdf 2 U.S. Census Bureau News, U.S. Census Bureau Releases 2010 Census Population Counts for American Samoa, http://www.census.gov/2010census/news/releases/operations/cb11-cn177.html (Aug. 24, 2011). 3 3 J. Robert Shaffer, American Samoa: 100 Years Under the United States Flag (Honolulu, Hawaii: Island Heritage Publishing, 2000), 34. 4 because people live off of the land’s and the ocean’s abundant resources.” To the west of American Samoa lies a larger group of four islands that make up the Sovereign State of Samoa, which became independent from New Zealand in 1962. Samoa and American Samoa share the same language, culture, and religion but are divided by government and political systems. The focus of this study will be on American Samoa, which became a United States territory in 1900 when the principal chiefs of Tutuila (the largest island in American Samoa) ceded the islands to the United States.

BEM Formulations Based on Kirchhoff's Hypoyhesis to Perform Linear Bending Analysis of Plates Reinforced by Beams

In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoffs hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a stab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. on these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degrees of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration. [DOI: 10.1115/1.4005010]

A simple method for choosing the parameters of a two degree-of-freedom tuned vibration absorber

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Ability of different restorative materials to prevent in situ secondary caries: analysis by polarized light-microscopy and energy-dispersive X-ray

Secondary caries is the main cause of direct restoration replacement. The purpose of this study was to analyze enamel adjacent to different restorative materials after in situ cariogenic challenge using polarized-light microscopy (PLM), scanning electron microscopy (SEM) and energy-dispersive X-ray analysis (EDS). Twelve volunteers, with a low level of dental plaque, a low level of mutans streptococci, and normal salivary flow, wore removable palatal acrylic appliances containing enamel specimens restored with Z250 composite, Freedom composite, Fuji IX glass-ionomer cement, or Vitremer resin-modified glass-ionomer for 14 days. Volunteers dripped one drop of 20% sucrose solution (n = 10) or distilled water (control group) onto each specimen 8 times per day. Specimens were removed from the appliances and submitted to PLM for examination of the lesion area (in mm(2)), followed by dehydration, gold-sputtering, and submission to SEM and EDS. The calcium (Ca) and phosphorus (P) contents were evaluated in weight per cent (%wt). Differences were found between Z250 and Vitremer, and between Z250 and FujiIX, when analyzed using PLM. Energy-dispersive X-ray analysis results showed differences between the studied materials regarding Ca %wt. In conclusion, enamel adjacent to glass-ionomer cement presented a higher Ca %wt, but this material did not completely prevent enamel secondary caries under in situ cariogenic challenge.

Infrared degrees of freedom of Yang-Mills theory in the Schrodinger representation

We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schrodinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.

Chiral corrections to baryon properties with composite pions

A calculational scheme is developed to evaluate chiral corrections to properties of composite baryons with composite pions. The composite baryons and pions are bound states derived from a microscopic chiral quark model. The model is amenable to standard many-body techniques such as the BCS and random phase approximation formalisms. An effective chiral model involving only hadronic degrees of freedom is derived from the macroscopic quark model by projection onto hadron states. Chiral loops are calculated using the effective hadronic Hamiltonian. A simple microscopic confining interaction is used to illustrate the derivation of the pion-nucleon form factor and the calculation of picnic self-energy corrections to the nucleon and Delta (1232) masses.

The generator coordinate method for a reaction coordinate coupled to a harmonic oscillator bath

This paper investigates the usefulness of the generator coordinate method (GCM) for treating the dynamics of a reaction coordinate coupled to a bath of harmonic degrees of freedom. Models for the unimolecular dissociation and isomerization process (proton transfer) are analyzed. The GCM results, presented in analytical form, provide a very good description and are compared to other methods Like the basis set method and multiconfiguration time dependent self-consistent field. (C) 1998 American Institute of Physics. [S0021-9606(98)50934-8].

Dynamics of two satellites in the 2/1 Mean-Motion resonance: application to the case of Enceladus and Dione

The dynamics of a pair of satellites similar to Enceladus-Dione is investigated with a two-degrees-of-freedom model written in the domain of the planar general three-body problem. Using surfaces of section and spectral analysis methods, we study the phase space of the system in terms of several parameters, including the most recent data. A detailed study of the main possible regimes of motion is presented, and in particular we show that, besides the two separated resonances, the phase space is replete of secondary resonances.

On homoclinic chaos and a control chaos strategy applied to a free-joint nonholonomic manipulator

In this work, the occurrence of chaos (homoclinic scene) is verified in a robotic system with two degrees of freedom by using Poincare-Mel'nikov method. The studied problem was based on experimental results of a two-joint planar manipulator-first joint actuated and the second joint free-that resides in a horizontal plane. This is the simplest model of nonholonomic free-joint manipulators. The purpose of the present study is to verify analytically those results and to suggest a control strategy.

Dynamics of two planets in the 3/2 mean-motion resonance: Application to the planetary system of the pulsar PSR B1257+12

This paper considers the dynamics of two planets, as the planets B and C of the pulsar PSR B1257+12, near a 3/2 mean-motion resonance. A two-degrees-of-freedom model, in the framework of the general three-body planar problem, is used and the solutions are analyzed through surfaces of section and Fourier techniques in the full phase space of the system.

Disappearance of squeezed back-to-back correlations: a new signal of hadron freeze-out from a supercooled quark gluon plasma

We briefly discuss four different possible types of transitions from quark to hadronic matter and their characteristic signatures in terms of correlations. We also highlight the effects arising from mass modification of hadrons in hot and dense hadronic matter, as well as their quantum statistical consequences: the appearance of squeezed quantum states and the associated experimental signatures, i.e., the back-to-back correlations of particle-antiparticle pairs. We briefly review the theoretical results of these squeezed quanta, generated by in-medium modified masses, starting from the first indication of the existence of surprising particle-antiparticle correlations, and ending by considering the effects of chiral dynamics on these correlation patterns. Nevertheless, a prerequisite for such a signature is the experimental verification of its observability. Therefore, the experimental observation of back-to-back correlations in high energy heavy ion reactions would be a unique signature, proving the existence of in-medium mass modification of hadronic states. on the other hand, their disappearance at some threshold centrality or collision energy would indicate that the hadron formation mechanism would have qualitatively changed: asymptotic hadrons above such a threshold are not formed from medium modified hadrons anymore, but rather by new degrees of freedom characterizing the medium. Furthermore, the disappearance of the squeezed BBC could also serve as a signature of a sudden, non-equilibrium hadronization scenario from a supercooled quark-gluon plasma phase.