Dynamical Hartree-Fock-Bogoliubov Theory of Vortices in Bose-Einstein Condensates at Finite Temperature

We present a method utilizing the continuity equation for the condensate density to make predictions of the precessional frequency of single off-axis vortices and of vortex arrays in Bose-Einstein condensates at finite temperature. We also present an orthogonalized Hartree-Fock-Bogoliubov (HFB) formalism. We solve the continuity equation for the condensate density self-consistently with the orthogonalized HFB equations, and find stationary solutions in the frame rotating at this frequency. As an example of the utility of this formalism we obtain time-independent solutions for quasi-two-dimensional rotating systems in the co-rotating frame. We compare these results with time-dependent predictions where we simulate stirring of the condensate.Comment: 13 pages, 11 figures, 1 tabl

Modeling the buckling and delamination of thin films

I study numerically the problem of delamination of a thin film elastically attached to a rigid substrate. A nominally flat elastic thin film is modeled using a two-dimensional triangular mesh. Both compression and bending rigidities are included to simulate compression and bending of the film. The film can buckle (i.e., abandon its flat configuration) when enough compressive strain is applied. The possible buckled configurations of a piece of film with stripe geometry are investigated as a function of the compressive strain. It is found that the stable configuration depends strongly on the applied strain and the Poisson ratio of the film. Next, the film is considered to be attached to a rigid substrate by springs that can break when the detaching force exceeds a threshold value, producing the partial delamination of the film. Delamination is induced by a mismatch of the relaxed configurations of film and substrate. The morphology of the delaminated film can be followed and compared with available experimental results as a function of model parameters. `Telephone-cord', polygonal, and `brain-like' patterns qualitatively similar to experimentally observed configurations are obtained in different parameter regions. The main control parameters that select the different patterns are the mismatch between film and substrate and the degree of in-plane relaxation within the unbuckled regions.Comment: 8 pages, 10 figure

Quantifying Finite Temperature Effects in Atom Chip Interferometry of Bose-Einstein Condensates

We quantify the effect of phase fluctuations on atom chip interferometry of Bose-Einstein condensates. At very low temperatures, we observe small phase fluctuations, created by mean-field depletion, and a resonant production of vortices when the two clouds are initially in anti-phase. At higher temperatures, we show that the thermal occupation of Bogoliubov modes makes vortex production vary smoothly with the initial relative phase difference between the two atom clouds. We also propose a technique to observe vortex formation directly by creating a weak link between the two clouds. The position and direction of circulation of the vortices is subsequently revealed by kinks in the interference fringes produced when the two clouds expand into one another. This procedure may be exploited for precise force measurement or motion detection.Comment: 7 pages, 5 figure

TB91: The Effect of Acidity, Organic Matter, and Sesquioxide Polymers on the Permanet Charge and pH-Dependent Cation Exchange Capacity of the Caribou Loam Soil.

In this study the components of cation exchange capacity (CEC) were measured in an acid spodosol to determine (1) the increase in KC1-CEC in the whole soil when limed, (2) the contribution of the organic fraction to CEC, and (3) the magnitude of CEC reduction by Al and Fe polymers.https://digitalcommons.library.umaine.edu/aes_techbulletin/1098/thumbnail.jp

Effects of temperature upon the collapse of a Bose-Einstein condensate in a gas with attractive interactions

We present a study of the effects of temperature upon the excitation frequencies of a Bose-Einstein condensate formed within a dilute gas with a weak attractive effective interaction between the atoms. We use the self-consistent Hartree-Fock Bogoliubov treatment within the Popov approximation and compare our results to previous zero temperature and Hartree-Fock calculations The metastability of the condensate is monitored by means of the $l=0$ excitation frequency. As the number of atoms in the condensate is increased, with $T$ held constant, this frequency goes to zero, signalling a phase transition to a dense collapsed state. The critical number for collapse is found to decrease as a function of temperature, the rate of decrease being greater than that obtained in previous Hartree-Fock calculations.Comment: 4 pages LaTeX, 3 eps figures. To appear as a letter in J. Phys.

The impact of mutation and gene conversion on the local diversification of antigen genes in African trypanosomes

Patterns of genetic diversity in parasite antigen gene families hold important information about their potential to generate antigenic variation within and between hosts. The evolution of such gene families is typically driven by gene duplication, followed by point mutation and gene conversion. There is great interest in estimating the rates of these processes from molecular sequences for understanding the evolution of the pathogen and its significance for infection processes. In this study, a series of models are constructed to investigate hypotheses about the nucleotide diversity patterns between closely related gene sequences from the antigen gene archive of the African trypanosome, the protozoan parasite causative of human sleeping sickness in Equatorial Africa. We use a hidden Markov model approach to identify two scales of diversification: clustering of sequence mismatches, a putative indicator of gene conversion events with other lower-identity donor genes in the archive, and at a sparser scale, isolated mismatches, likely arising from independent point mutations. In addition to quantifying the respective probabilities of occurrence of these two processes, our approach yields estimates for the gene conversion tract length distribution and the average diversity contributed locally by conversion events. Model fitting is conducted using a Bayesian framework. We find that diversifying gene conversion events with lower-identity partners occur at least five times less frequently than point mutations on variant surface glycoprotein (VSG) pairs, and the average imported conversion tract is between 14 and 25 nucleotides long. However, because of the high diversity introduced by gene conversion, the two processes have almost equal impact on the per-nucleotide rate of sequence diversification between VSG subfamily members. We are able to disentangle the most likely locations of point mutations and conversions on each aligned gene pair

Gapless finite-TT theory of collective modes of a trapped gas

We present predictions for the frequencies of collective modes of trapped Bose-condensed $^{87}$Rb atoms at finite temperature. Our treatment includes a self-consistent treatment of the mean-field from finite-$T$ excitations and the anomolous average. This is the first gapless calculation of this type for a trapped Bose-Einstein condensed gas. The corrections quantitatively account for the downward shift in the $m=2$ excitation frequencies observed in recent experiments as the critical temperature is approached.Comment: 4 pages Latex and 2 postscript figure

Regional Stratigraphic Framework of Surficial Sediments and Bedrock Beneath Lake Ontario

Approximately 2550 km of single-channel high-resolution seismic reflection profiles have been interpreted and calibrated with lithological and geochronological information from four representative piston cores and one grab sample to provide a regional stratigraphie framework for the subbottom deposits of Lake Ontario. Five units overlying Paleozoic bedrock were identified and mapped. These are classified as informal units and represent, from oldest to youngest: (A) subglacial till (?) deposited by the Port Huron ice at the end of the Wisconsin glaciation; (B) an ice-marginal (?) unit confined to the western part of the lake that was probably deposited during retreat of the Port Huron ice shortly after 13 ka; (C) a regionally extensive unit of laminated glacio-lacustrine clay that accumulated until about 11 ka; (D) a weakly laminated to more massive lake clay deposited during a period of reduced water supply and rising water levels after the drawdown of the high-level glacial lakes (Iroquois and successors); and (E) modern lake clay less than 10 m thick that began accumulating around 6-8 ka with the subsequent return of upper Great Lakes drainage through the Ontario basin. Seismic reflections also define the configuration of the bedrock surface and pre-glacial stream valleys incised in the bedrock surface. Several anomalous bottom and subbottom features in the surficial sediments are mapped, such as discontinuous and offset reflections, furrows, gas pockets, and areas of large subbottom relief. None of these features appear to be spatially correlative with the diffuse seismicity that characterizes the lake area or with deeper structures such as Paleozoic bedrock faults or crustal-penetrating faults in the Precambrian basement.On a interprété et étalonné environ 2550 km de profils de sismique réflexion monocanal à haute résolution selon les données lithologiques et géochronologique de quatre sondages représentatifs faits par carottier à piston et un échantillon prélevé avec une benne afin d'établir le cadre stratigraphique des dépôts accumulés sous le fond du lac Ontario. Cinq unités recouvrant le substratum paiéozoïque ont été identifées et cartographiées. Ces unités informelles, de la plus ancienne à la plus jeune, sont : (A) un till sous-glaciaire (?) déposé par les glaces de Port Huron à la fin de la glaciation wisconsienne; (B) une unité de limite glaciaire (?) confinée à la partie ouest du lac et qui a probablement été déposée pendant le retrait des glaces de Port Huron, peu après 13 ka; (C) une unité d'étendue régionale d'argile glaciolacustre feuilletée qui s'est accumulée jusqu'à environ 11 ka; (D) une argile lacustre, de faiblement feuilletée à massive, mise en place au cours d'une période où il y eut approvisionnement en eau réduit et hausse du niveau de l'eau après l'abaissement des lacs glaciaires (Iroquois et ultérieurs); et (E) une argile lacustre moderne de moins de 10 m d'épaisseur qui a commencé à s'accumuler à partir de 6-8 ka après la reprise du drainage des Grands Lacs par le bassin Ontario. La sismique réflexion a aussi permis de délimiter la configuration de la surface du socle et des vallées pré-glaciaires qui y sont entaillées. Plusieurs éléments des sédiments de surface du fond du lac et sous le fond ont été cartographies, comme des réflexions de discontinuités et de décalages, des rainures, des poches de gaz et des zones de grandes formes enfouies. Aucun de ces éléments ne semble correspondre spatialement à la sis-micité diffuse qui caractérise la région du lac ou aux structures profondes comme les failles de substratum paiéozoïque ou celle du socle précambrien.Ungefàhr 2550 km seismischer Reflexionsprofile wurden interpretiert und kalibiriert mit lithologischen und geochronologischen Informationen von vier repràsentativen Kolbenbohrkernen und einer ausges-chùrften Probe, um den regionalen stratigraphischen Rahmen fur die unter dem Bett des Ontariosees gelegenen Ablagerungen zu erhalten. Man hat fùnf Einheiten, die das anstehende Gestein aus dem Palàozoikum ùberlagern, identifiziert und kartographiert: (A) eine subglaziale Grundmoràne (?), die durch das Eis von Port Huron am Ende der Wisconsin-Vereisung abgelagert wurde; (B) eine auf den westlichen Teil des Sees begrenzte Eisrand (?)-Einheit, die wahrs-cheinlich wàhrend des Rùckzugs des Port Huron-Eises kurz nach 13ka abgelagert wurde; (C) eine regional ausgedehnte Einheit von blâttrigem glaziallimnischem Lehm, die sien bis etwa 11 ka ansammelte, (D) ein schwachbis massivblàttriger Seelehm, der wàhrend einer Période verminderter Wasserzufuhr und steigenden Wasserspiegeln sich ansammelte; und (E) moderner Seelehm von weniger als 10 m Dicke, der sich um etwa 6-8 ka anzusammeln begann, mit der Rùckkehr der Drainage der oberen GroRen Seen durch das Ontariobecken. Seismische Reflexionen las-sen auch die Konfiguration der Sockeloberflàche und der pràglazialen in die Sockeloberflàche eingeschnittenen FluBtàler erkennen. Mehrere unregelmàfîige Grundund Untergrunderscheinungen der Oberflàchensedimente wurden kartographiert, wie Diskontinuitàt und Hôhenunschiede der Reflexionen, Mulden, Gastaschen und Gebiete mit breitem Untergrundrelief. Keine dieser Erscheinungen scheint ràumlich mit der fur das Seen-Gebiet charakteristischen Seismik zu korrelieren oder mit tieferen Strukturen, wie die Verwerfungen des anstehenden Gestems aus dem Palàozoikum order durch die Kruste dringende Verwergungen im pràkambrischen Untergrund