Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials

The one-body density matrix of weakly interacting, condensed bosons in external potentials is calculated using inhomogeneous Bogoliubov theory. We determine the condensate deformation caused by weak external potentials on the mean-field level. The momentum distribution of quantum fluctuations around the deformed ground state is obtained analytically, and finally the resulting quantum depletion is calculated. The depletion due to the external potential, or potential depletion for short, is a small correction to the homogeneous depletion, validating our inhomogeneous Bogoliubov theory. Analytical results are derived for weak lattices and spatially correlated random potentials, with simple, universal results in the Thomas-Fermi limit of very smooth potentials.Comment: 17 pages, 4 figures. v2: published version, minor change

On the Universality of the Entropy-Area Relation

We present an argument that, for a large class of possible dynamics, a canonical quantization of gravity will satisfy the Bekenstein-Hawking entropy-area relation. This result holds for temperatures low compared to the Planck temperature and for boundaries with areas large compared to Planck area. We also relate our description, in terms of a grand canonical ensemble, to previous geometric entropy calculations using area ensembles.Comment: 6 page

Harmonic Balance and Averaging Techniques for Stick-Slip Limit-Cycle Determination in Mode-Coupling Friction Self-Excited Systems

A minimal model for mode-coupling friction induced instability with Coulomb-type frictional nonlinearity is set up to investigate the applicability and quality of approximative methods to determine the limit cycles of unstable system configurations. It turns out that - due to the multi-degree-of-freedom nature of the mode-coupling instability - harmonic balance approaches yield reasonable results only if applied carefully, i.e. with respect to the special effects of the nonlinearities under consideration. The Krylov-Bogoliubov-Mitropolsky approach yields good results in a straightforward manner, the technique is however formally much more cumbersome

Brighter prospects? Assessing the franchise advantage using census data

This paper uses Census micro data to examine how starting a business as a franchise rather than an independent business affects its survival and growth prospects. We assess factors that influence the decision to become a franchisee and use various empirical approaches to correct for selection bias in our performance analyses. We find that franchised businesses on average exhibit higher survival rates than independent businesses, but importantly, the difference is small compared to claims in the trade press. The effect is also short lived: conditional on surviving a year or two, we no longer find survival (or growth) differences. We then explore two potential sources for this small survival advantage, namely franchisors’ screening process and the benefits arising from the brand and business know-how provided by franchisors. We find evidence that both of the sources contribute to the franchising advantage

Multi-GeV Electron Generation Using Texas Petawatt Laser

We present simulation results and experimental setup for multi-GeV electron generation by a laser plasma wake field accelerator (LWFA) driven by the Texas Petawatt (TPW) laser. Simulations show that, in plasma of density n(e) = 2 - 4 x cm(-3), the TPW laser pulse (1.1 PW, 170 fs) can self-guide over 5 Rayleigh ranges, while electrons self-injected into the LWFA can accelerate up to 7 GeV. Optical diagnostic methods employed to observe the laser beam self-guiding, electron trapping and plasma bubble formation and evolution are discussed. Electron beam diagnostics, including optical transition radiation (OTR) and electron gamma ray shower (EGS) generation, are discussed as well.Physic

Forced instability of core-annular flow in capillary constrictions

Instability of fluid cylinders and jets, a highly nonlinear hydrodynamic phenomenon, has fascinated researchers for nearly 150 years. A subset of the phenomenon is the core-annular flow, in which a non-wetting core fluid and a surrounding wall-wetting annulus flow through a solid channel. The model, for example, represents the flow of oil in petroleum reservoirs. The flow may be forced to break up when passing through a channel’s constriction. Although it has long been observed that the breakup occurs near the neck of the constriction, the exact conditions for the occurrence of the forced breakup and its dynamic theory have not been understood. Here, we test a simple geometric conjecture that the fluid will always break in the constrictions of all channels with sufficiently long wavelengths, regardless of the fluid properties. We also test a theory of the phenomenon. Four constricted glass tubes were fabricated above and below the critical wavelength required for the fluid disintegration. In a direct laboratory experiment, the breakup occurred according to the conjecture: the fluids were continuous in the shorter tubes but disintegrated in the longer tubes. The evolution of the interface to its pinch-off was recorded using high-speed digital photography. The experimentally observed core-annulus interface profiles agreed well with the theory, although the total durations of the process agreed less satisfactorily. Nonetheless, as the theory predicts, the ratio between the experimental and theoretical times of the breakup process tends to one with decreasing capillary number. The breakup condition and the dynamic theory of fluid disintegration in constricted channels can serve as quantitative models of this important natural and technical phenomenon

Software educativo para el aprendizaje colaborativo de geometría

El Juego de la Comunicación es un producto de Software Educativo para el aprendizaje de Geometría en el nivel inicial. Se basa en un trabajo de investigación en Didáctica de la Matemática, relatado en el Capítulo IV de la tesis doctoral de la Dra. Dilma Fregona. Su aplicación está prevista para alumnos de segundo ciclo de la E.G.B. En su concepción original, no informatizada, la red de comunicación entre los alumnos actúa por intermediación del docente, quien se encarga de llevar y traer los mensajes elaborados por alumnos Emisores y alumnos Receptores de un mismo Equipo. Dichos mensajes contribuyen al objetivo de construir figuras geométricas simples (triángulo, cuadrado, rectángulo, rombo y círculo). Los alumnos no están físicamente juntos, de manera que la única posibilidad de comunicarse es a través de los mensajes. El docente tiene la tarea de gestionar la comunicación y además tiene la tarea más importante de supervisar toda la comunicación con el fin de conocer el avance de cada Equipo. El objetivo del desarrollo de esta aplicación fue crear un soporte informático para la experiencia, concebida como un trabajo colaborativo en entorno de red.Eje: Tecnología aplicada en EducaciónRed de Universidades con Carreras en Informática (RedUNCI

Software educativo para el aprendizaje colaborativo de geometría

El Juego de la Comunicación es un producto de Software Educativo para el aprendizaje de Geometría en el nivel inicial. Se basa en un trabajo de investigación en Didáctica de la Matemática, relatado en el Capítulo IV de la tesis doctoral de la Dra. Dilma Fregona. Su aplicación está prevista para alumnos de segundo ciclo de la E.G.B. En su concepción original, no informatizada, la red de comunicación entre los alumnos actúa por intermediación del docente, quien se encarga de llevar y traer los mensajes elaborados por alumnos Emisores y alumnos Receptores de un mismo Equipo. Dichos mensajes contribuyen al objetivo de construir figuras geométricas simples (triángulo, cuadrado, rectángulo, rombo y círculo). Los alumnos no están físicamente juntos, de manera que la única posibilidad de comunicarse es a través de los mensajes. El docente tiene la tarea de gestionar la comunicación y además tiene la tarea más importante de supervisar toda la comunicación con el fin de conocer el avance de cada Equipo. El objetivo del desarrollo de esta aplicación fue crear un soporte informático para la experiencia, concebida como un trabajo colaborativo en entorno de red.Eje: Tecnología aplicada en EducaciónRed de Universidades con Carreras en Informática (RedUNCI