Construction of exactly solvable quantum models of Calogero and Sutherland type with translation invariant four-particle interactions

We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.Comment: 14 pages, no figures, 1 table, replaced and enlarged version, a note adde

An exactly solvable model of the Calogero type for the icosahedral group

We construct a quantum mechanical model of the Calogero type for the icosahedral group as the structural group. Exact solvability is proved and the spectrum is derived explicitly.Comment: 13 pages, no figures, latex 2epsilo

The construction of trigonometric invariants for Weyl groups and the derivation of corresponding exactly solvable Sutherland models

Trigonometric invariants are defined for each Weyl group orbit on the root lattice. They are real and periodic on the coroot lattice. Their polynomial algebra is spanned by a basis which is calculated by means of an algorithm. The invariants of the basis can be used as coordinates in any cell of the coroot space and lead to an exactly solvable model of Sutherland type. We apply this construction to the $F_4$ caseComment: 13 pages, no figures, latex 2epsilon, corrected versio

Exactly solvable dynamical systems in the neighborhood of the Calogero model

The Hamiltonian of the $N$-particle Calogero model can be expressed in terms of generators of a Lie algebra for a definite class of representations. Maintaining this Lie algebra, its representations, and the flatness of the Riemannian metric belonging to the second order differential operator, the set of all possible quadratic Lie algebra forms is investigated. For N=3 and N=4 such forms are constructed explicitly and shown to correspond to exactly solvable Sutherland models. The results can be carried over easily to all $N$.Comment: 23 pages, 2 figures, replaced and enlarged versio

Is it possible to construct exactly solvable models?

We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite matrices. These eigenvectors are transcribed into eigenfunctions of a selfadjoint Schr\"odinger operator. We prove the feasibility of our method by constructing a new "$AG_3$ model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the $B_3$ model. In order to better understand features of our construction we exhibit the $F_4$ rational model with our method.Comment: 22 pages, 2 eps figures, latex 2epsilon, usepackage epsfi

Development of an intelligent object for grasp and manipulation research

Kõiva R, Haschke R, Ritter H. Development of an intelligent object for grasp and manipulation research. Presented at the ICAR 2011, Tallinn, Estonia.In this paper we introduce a novel device, called iObject, which is equipped with tactile and motion tracking sensors that allow for the evaluation of human and robot grasping and manipulation actions. Contact location and contact force, object acceleration in space (6D) and orientation relative to the earth (3D magnetometer) are measured and transmitted wirelessly over a Bluetooth connection. By allowing human-human, human-robot and robot-robot comparisons to be made, iObject is a versatile tool for studying manual interaction. To demonstrate the efficiency and flexibility of iObject for the study of bimanual interactions, we report on a physiological experiment and evaluate the main parameters of the considered dual-handed manipulation task

Three dimensional maps of the Magellanic Clouds using RR Lyrae Stars and Cepheids II. The Small Magellanic Cloud

We use data on variable stars from the Optical Gravitational Lensing Experiment (OGLE III) survey to determine the three-dimensional structure of the Small Magellanic Cloud (SMC). Deriving individual distances to RR Lyrae stars and Cepheids we investigate the distribution of these tracers of the old and young population in the SMC. Photometrically estimated metallicities are used to determine the distances to 1494 RR Lyrae stars, which have typical ages greater than 9 Gyr. For 2522 Cepheids, with ages of a few tens to a few hundred Myr, distances are calculated using their period-luminosity relation. Individual reddening estimates from the intrinsic color of each star are used to obtain high precision three-dimensional maps. The distances of RR Lyrae stars and Cepheids are in very good agreement with each other. The median distance of the RR Lyrae stars is found to be 61.5 +/- 3.4 kpc. For the Cepheids a median distance of 63.1 +/- 3.0 kpc is obtained. Both populations show an extended scale height, with 2.0 +/- 0.4 kpc for the RR Lyrae stars and 2.7 +/- 0.3 kpc for the Cepheids. This confirms the large depth of the SMC suggested by a number of earlier studies. The young population is very differently oriented than the old stars. While we find an inclination angle of 7{\deg} +/- 15{\deg} and a position angle of 83{\deg} +/- 21{\deg} for the RR Lyrae stars, for the Cepheids an inclination of 74{\deg} +/- 9{\deg} and a position angle of 66{\deg} +/- 15{\deg} is obtained. The RR Lyrae stars show a fairly homogeneous distribution, while the Cepheids follow roughly the distribution of the bar with their northeastern part being closer to us than the southwestern part of the bar. Interactions between the SMC, LMC, and Milky Way are presumably responsible for the tilted, elongated structure of the young population of the SMC.Comment: 13 pages, 6 figures, 4 tables, published in A

Evaporation processes of microdrops: modelling, simulation and data analysis

Die vorliegende Arbeit entstand an der Universität Siegen innerhalb der Forschergruppe „Physikalische und chemische Grundlagen, Komponenten und Systeme für die Lab-on-Microchip Technologie“ in einem Teilprojekt mit dem Schwerpunkt auf der Untersuchung von Verdunstungsprozessen von Mikrotropfen. In enger Kopplung an die am Mainzer Max-Planck-Institut für Polymerforschung durchgeführten Experimente wurden neue Erkenntnisse im Hinblick auf das komplexe Zusammenspiel physikalisch-chemischer Prozesse bei Tropfenverdunstungsprozessen auf der Mikro- und Nanometerskala gewonnen. Dies gelang durch die Entwicklung neuer Modellierungsansätze, den zielgerichteten Einsatz von Simulationen und der anschließenden Datenanalyse. Ziel der vorliegenden Arbeit ist es, die durchgeführten experimentellen Arbeiten zu unterstützen, indem - neue experimentelle Methoden validiert werden - bestimmte Effekte und Phänomene untersucht werden, die (noch) nicht experimentell untersucht werden konnten - aus den Simulationsergebnissen abgeleitete Vorschläge für einen verbesserten experimentellen Aufbau gegeben werden. Im ersten Teil der Arbeit „Cantilever“ werden einerseits die durch den Verdunstungsprozess von Mikrotropfen hervorgerufenen elastischen Deformationen eines AFM-Cantilevers mit Hilfe eines neuentwickelten 3D-Simulationsmodells untersucht. Andererseits wird die experimentelle Erweiterung der sogenannten Cleveland-Methode zur Kalibrierung von AFM-Cantilevern durch automatisierte Finite Elemente Simulationen validiert. In beiden Fällen sind Ergebnisse erzielt worden, die im Bereich der angenommenen Fehlertoleranz der etablierten Methoden liegen. Der zweite Teil der Arbeit stellt ein Werkzeug zur Profilanalyse regelmäßig strukturierter Oberflächen (Mikrokrater) vor, wie sie z. B. durch den Verdunstungsprozess von Toluol-Tropfen auf Polystyrol-Substraten entstehen (s. dritter Teil der Arbeit). Das Werkzeug beschreibt die Originalkrater durch einen gemittelten Rotationsellipsoid, der durch einen B-Spline definiert wird. Die „Form“ des B-Splines wird durch die Minimierung einer Fehlerquadratsumme mit Hilfe eines Genetischen Algorithmus „optimal“ an die Rohdaten angepasst. Aus den Parametern des B-Splines werden abschließend globale geometrische Parameter abgeleitet, die eine automatische statistische Analyse ermöglichen. Der Verdunstungsprozess von Toluol-Tropfen auf Polystyrol-Substraten wird im dritten Teil der Arbeit beschrieben. Dazu wurde ein neuer, auf einem bereits bestehenden Modell aufbauender Modellierungsansatz zur Beschreibung des Verdunstungsprozesses von mikrometer-großen Toluol-Tropfen auf einem Polystyrol-Substrat entwickelt. Eine Verbesserung gegenüber dem Vorgängermodell wird vor allem durch eine konsequente Formulierung des Modells in Form partieller Differentialgleichungen und der Implementierung in der adaptiven Finite Elemente Bibliothek DEAL erzielt. Auf diese Weise wurde in erster Linie die numerische Genauigkeit erhöht. Zusätzlich wird der Einfluss von einigen wichtigen Systemparametern auf das resultierende Kraterprofil mit dem bestehenden Simulator im Rahmen von Sensitivitätsanalysen untersucht. Im vierten Teil der Arbeit werden die erzielten Ergebnisse der drei ersten, für sich abgeschlossenen Teile zueinander in Relation gesetzt, um so neue Erkenntnisse zu gewinnen. Abschließend erfolgen eine kapitelübergreifende Diskussion und ein Ausblick auf mögliche Anknüpfungspunkte für weitere wissenschaftliche Arbeiten

I Married You for Fun: A New Translation and Adaptation of Natalia Ginzburg’s Ti Ho Sposato per Allegria

Senior Project submitted to The Division of Arts and The Division of Languages and Literature of Bard College

Mobile Mindfulness: There\u27s an App for That!

Previous research indicates that practicing mindfulness-based strategies over an extended period of time may positively impact individuals’ well-being, such as improved mood and cognitive performance (Chambers, Lo, & Allen, 2008; Kabat-Zinn, 1990; Kabat-Zinn, 2003; Mrazek, Franklin, Phillips, Baird, & Schooler, 2013). This research also indicates there may be immediate benefits to practicing mindfulness strategies; however, a majority of the existing literature on this topic has focused primarily on extended mindfulness-practices over several weeks with an in-person guide or trained researcher. The purpose of the current study was two-fold. First, how practicing one of two mindfulness-based strategies for a short period of time (e.g., less than two minutes per day over a one week period) influenced several psychological variables of interest (i.e., attention and awareness, depression, anxiety, stress, mood, and cognitive performance) was assessed. Second, the short mindfulness-based strategies were guided by a mobile-phone application; thus, the effectiveness of practicing mindfulness without the physical presence of a guide or researcher trained in meditation was assessed. Participants came to an initial lab session (Time 1) and completed self-report measures assessing the variables of interest along with a cognitive task to test their working memory capability. Participants either learned and practiced one mindfulness-based strategy (mindful breathing or a body scan) or engaged in a no-strategy (control) condition. After the initial lab session, participants in the mindfulness strategy conditions were instructed to practice the strategy on their own for three days using a mobile-phone application. Participants returned to the lab for a final lab session (Time 2) and once ii again practice the assigned mindfulness strategy, answered the self-report questionnaires, and completed the cognitive task. Based on previous research, it was hypothesized that participants in the mindful breathing and body scan conditions compared to the control condition would show increases in attention and awareness, positive affect, and cognitive performance from the initial lab session (Time 1) to the final lab session (Time 2). It was also hypothesized that participants in the mindful breathing and body scan conditions compared to the control condition would show decreases in depression, anxiety, stress, and negative affect from Time 1 to Time 2. Seventy-four participants completed all parts of the current study; there were not significant differences across conditions and time on most of the self-report measures. However, there was a significant main effect of time on negative affect and performance on the cognitive task. Exploratory analyses were conducted to further probe the data for relationships between the variables of interest. A negative correlation between self-reported mindfulness, attention, and awareness was found in relation to depression, anxiety, stress, and negative affect. Although not significant, a positive correlation between self-reported mindfulness, attention, and awareness was found in relation to positive affect and cognitive performance. The results suggest that more research is needed on the effect of brief mindfulness practices guided by a mobile-phone application. Contributions of the current study, as well as future research and limitations, are discussed