Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model

Laboratory experiments simulating gravity-driven coastal surface currents produced by estuarine fresh-water discharges into the ocean are discussed. The currents are generated inside a rotating tank filled with salt water by the continuous release of buoyant fresh water from a small source at the fluid surface. The height, the width and the length of the currents are studied as a function of the background rotation rate, the volumetric discharge rate and the density difference at the source. Two complementary experimental data sets are discussed and compared with each other. One set of experiments was carried out in a tank of diameter 1 m on a small-scale rotating turntable. The second set of experiments was conducted at the large-scale Coriolis Facility (LEGI, Grenoble) which has a tank of diameter 13 m. A simple geostrophic model predicting the current height, width and propagation velocity is developed. The experiments and the model are compared with each other in terms of a set of non-dimensional parameters identified in the theoretical analysis of the problem. These parameters enable the corresponding data of the large-scale and the small-scale experiments to be collapsed onto a single line. Good agreement between the model and the experiments is found

Localization and its consequences for quantum walk algorithms and quantum communication

The exponential speed-up of quantum walks on certain graphs, relative to classical particles diffusing on the same graph, is a striking observation. It has suggested the possibility of new fast quantum algorithms. We point out here that quantum mechanics can also lead, through the phenomenon of localization, to exponential suppression of motion on these graphs (even in the absence of decoherence). In fact, for physical embodiments of graphs, this will be the generic behaviour. It also has implications for proposals for using spin networks, including spin chains, as quantum communication channels.Comment: 4 pages, 1 eps figure. Updated references and cosmetic changes for v

Buoyancy-driven exchange flows in inclined ducts

Buoyancy-driven exchange flows arise in the natural and built environment wherever bodies of fluids at different densities are connected by a narrow constriction. In this paper we study these flows in the laboratory using the canonical stratified inclined duct experiment, which sustains an exchange flow in an inclined duct of rectangular cross-section over long time periods (Meyer & Linden, J. Fluid Mech., vol. 753, 2014). We study the behaviour of these sustained stratified shear flows by focusing on three dependent variables of particular interest: the qualitative flow regime (laminar, wavy, intermittently turbulent, or fully turbulent), the mass flux (net transport of buoyancy between reservoirs), and the interfacial thickness (thickness of the layer of intermediate density between the two counter-flowing layers). Dimensional analysis reveals five non-dimensional independent input parameters: the duct aspect ratios in the longitudinal direction $A$ and spanwise direction $B$, the tilt angle $\theta$, the Reynolds number $Re$ (based on the initial buoyancy difference driving the flow), and the Prandtl number $Pr$ (we consider both salt and temperature stratifications). After reviewing the literature and open questions on the scaling of regimes, mass flux, and interfacial thickness with $A,B,\theta,Re,Pr$, we present the first extensive, unified set of experimental data where we varied systematically all five input parameters and measured all three output variables with the same methodology. Our results in the $(\theta,Re)$ plane for five sets of $(A,B,Pr)$ reveal a variety of scaling laws, and a non-trivial dependence of all three variables on all five parameters, in addition to a sixth elusive parameter. We further develop three classes of candidate models to explain the observed scaling laws: ..

Stability of a buoyancy-driven coastal current at the shelf break

Author Posting. © Cambridge University Press, 2002. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 452 (2002): 97-121, doi:10.1017/S0022112001006668.Buoyancy-driven surface currents were generated in the laboratory by releasing buoyant fluid from a source adjacent to a vertical boundary in a rotating container. Different bottom topographies that simulate both a continental slope and a continental ridge were introduced in the container. The topography modified the flow in comparison with the at bottom case where the current grew in width and depth until it became unstable once to non-axisymmetric disturbances. However, when topography was introduced a second instability of the buoyancy-driven current was observed. The most important parameter describing the flow is the ratio of continental shelf width W to the width L* of the current at the onset of the instability. The values of L* for the first instability, and L*[minus sign]W for the second instability were not influenced by the topography and were 2–6 times the Rossby radius. Thus, the parameter describing the flow can be expressed as the ratio of the width of the continental shelf to the Rossby radius. When this ratio is larger than 2–6 the second instability was observed on the current front. A continental ridge allowed the disturbance to grow to larger amplitude with formation of eddies and fronts, while a gentle continental slope reduced the growth rate and amplitude of the most unstable mode, when compared to the continental ridge topography. When present, eddies did not separate from the main current, and remained near the shelf break. On the other hand, for the largest values of the Rossby radius the first instability was suppressed and the flow was observed to remain stable. A small but significant variation was found in the wavelength of the first instability, which was smaller for a current over topography than over a flat bottom.Partial support for C.C. was provided by a TMR fellowship, MAS3-CT96-5017

Unbounded Human Learning: Optimal Scheduling for Spaced Repetition

In the study of human learning, there is broad evidence that our ability to retain information improves with repeated exposure and decays with delay since last exposure. This plays a crucial role in the design of educational software, leading to a trade-off between teaching new material and reviewing what has already been taught. A common way to balance this trade-off is spaced repetition, which uses periodic review of content to improve long-term retention. Though spaced repetition is widely used in practice, e.g., in electronic flashcard software, there is little formal understanding of the design of these systems. Our paper addresses this gap in three ways. First, we mine log data from spaced repetition software to establish the functional dependence of retention on reinforcement and delay. Second, we use this memory model to develop a stochastic model for spaced repetition systems. We propose a queueing network model of the Leitner system for reviewing flashcards, along with a heuristic approximation that admits a tractable optimization problem for review scheduling. Finally, we empirically evaluate our queueing model through a Mechanical Turk experiment, verifying a key qualitative prediction of our model: the existence of a sharp phase transition in learning outcomes upon increasing the rate of new item introductions.Comment: Accepted to the ACM SIGKDD Conference on Knowledge Discovery and Data Mining 201

Quasi-Particle Degrees of Freedom versus the Perfect Fluid as Descriptors of the Quark-Gluon Plasma

The hot nuclear matter created at the Relativistic Heavy Ion Collider (RHIC) has been characterized by near-perfect fluid behavior. We demonstrate that this stands in contradiction to the identification of QCD quasi-particles with the thermodynamic degrees of freedom in the early (fluid) stage of heavy ion collisions. The empirical observation of constituent quark ``$n_q$'' scaling of elliptic flow is juxtaposed with the lack of such scaling behavior in hydrodynamic fluid calculations followed by Cooper-Frye freeze-out to hadrons. A ``quasi-particle transport'' time stage after viscous effects break down the hydrodynamic fluid stage, but prior to hadronization, is proposed to reconcile these apparent contradictions. However, without a detailed understanding of the transitions between these stages, the ``$n_q$'' scaling is not a necessary consequence of this prescription. Also, if the duration of this stage is too short, it may not support well defined quasi-particles. By comparing and contrasting the coalescence of quarks into hadrons with the similar process of producing light nuclei from nucleons, it is shown that the observation of ``$n_{q}$'' scaling in the final state does not necessarily imply that the constituent degrees of freedom were the relevant ones in the initial state.Comment: 9 pages, 7 figures, Updated text and figure

A New Method to Determine Tooth Positions and Dental Arch Dimensions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66726/2/10.1177_00220345720510042301.pd