The Flow of Gases in Narrow Channels

Measurements were made of the flow of gases through various narrow channels a few microns wide at average pressures from 0.00003 to 40 cm. Hg. The flow rate, defined as the product of pressure and volume rate of flow at unit pressure difference, first decreased linearly with decrease in mean pressure in the channel, in agreement with laminar-flow theory, reached a minimum when the mean path length was approximately equal to the channel width, and then increased to a constant value. The product of flow rate and square root of molecular number was approximately the same function of mean path length for all gases for a given channel

Single wall carbon nanotube double quantum dot

We report on two top-gate defined, coupled quantum dots in a semiconducting single wall carbon nanotube, constituting a tunable double quantum dot system. The single wall carbon nanotubes are contacted by titanium electrodes, and gated by three narrow top-gate electrodes as well as a back-gate. We show that a bias spectroscopy plot on just one of the two quantum dots can be used to extract the addition energy of both quantum dots. Furthermore, honeycomb charge stability diagrams are analyzed by an electrostatic capacitor model that includes cross capacitances, and we extract the coupling energy of the double quantum dot.Comment: Published in Applied Physics Letters 4 December 2006. http://link.aip.org/link/?APL/89/23211

Meteorological application of Apollo photography Final report

Development of meteorological information and parameters based on cloud photographs taken during Apollo 9 fligh

Treatment of compound tibia fracture with microvascular latissimus dorsi flap and the Ilizarov technique : A cross-sectional study of long-term outcomes

Background: Extensive compound tibial fractures present reconstructive challenges. The present study aimed to assess the outcomes of microvascular latissimus dorsi (LD) flap combined with the Ilizarov technique for extensive compound tibial fractures with bone loss and bone healing complications. Methods: Patient records were reviewed retrospectively. The Lower Extremity Functional Scale (LEFS), the Disabilities of the Arm, Hand and Shoulder (DASH), and the 15D health-related quality of life (HRQoL) instrument were applied. Results: Between 1989 and 2014, 16 patients underwent reconstruction with a microvascular LD flap and bone transport (11/16) or late bone lengthening (5/16). The mean clinical follow-up time was 6.6 (standard deviation (SD): 6.5) years. Three patients had minor complications requiring reoperation. Partial necrosis of one flap required late flap reconstruction in one case. Late bone grafting was used to enhance union in eight of 16 cases. The mean new bone gain was 3.8 cm (SD: 2.5). Overall, 11 patients completed the questionnaires in a mean of 22.3 years (SD: 2.4) after surgery. The main findings revealed a relatively good function of the reconstructed limb and good shoulder function. The mean HRQoL was comparable to that of an age-standardized sample of the general population. Conclusion: Segmental tibia transport and lengthening to correct limb length discrepancy do not compromise the microvascular muscle flap. Combined microvascular LD flap reconstruction and the Ilizarov technique can be used in treating acute compound tibial defects, pseudoarthrosis, and osteitis, all associated with significant amputation risk. Fair long-term functional outcomes and HRQoL are achieved when these combined techniques are used. (C) 2016 British Association of Plastic, Reconstructive and Aesthetic Surgeons. Published by Elsevier Ltd. All rights reserved.Peer reviewe

The flow of plasma in the solar terrestrial environment

The overall goal of our NASA Theory Program was to study the coupling, time delays, and feedback mechanisms between the various regions of the solar-terrestrial system in a self-consistent, quantitative manner. To accomplish this goal, it will eventually be necessary to have time-dependent macroscopic models of the different regions of the solar-terrestrial system and we are continually working toward this goal. However, with the funding from this NASA program, we concentrated on the near-earth plasma environment, including the ionosphere, the plasmasphere, and the polar wind. In this area, we developed unique global models that allowed us to study the coupling between the different regions. These results are highlighted in the next section. Another important aspect of our NASA Theory Program concerned the effect that localized 'structure' had on the macroscopic flow in the ionosphere, plasmasphere, thermosphere, and polar wind. The localized structure can be created by structured magnetospheric inputs (i.e., structured plasma convection, particle precipitation or Birkland current patterns) or time variations in these input due to storms and substorms. Also, some of the plasma flows that we predicted with our macroscopic models could be unstable, and another one of our goals was to examine the stability of our predicted flows. Because time-dependent, three-dimensional numerical models of the solar-terrestrial environment generally require extensive computer resources, they are usually based on relatively simple mathematical formulations (i.e., simple MHD or hydrodynamic formulations). Therefore, another goal of our NASA Theory Program was to study the conditions under which various mathematical formulations can be applied to specific solar-terrestrial regions. This could involve a detailed comparison of kinetic, semi-kinetic, and hydrodynamic predictions for a given polar wind scenario or it could involve the comparison of a small-scale particle-in-cell (PIC) simulation of a plasma expansion event with a similar macroscopic expansion event. The different mathematical formulations have different strengths and weaknesses and a careful comparison of model predictions for similar geophysical situations provides insight into when the various models can be used with confidence

Stellar Oscillations Network Group

Stellar Oscillations Network Group (SONG) is an initiative aimed at designing and building a network of 1m-class telescopes dedicated to asteroseismology and planet hunting. SONG will have 8 identical telescope nodes each equipped with a high-resolution spectrograph and an iodine cell for obtaining precision radial velocities and a CCD camera for guiding and imaging purposes. The main asteroseismology targets for the network are the brightest (V<6) stars. In order to improve performance and reduce maintenance costs the instrumentation will only have very few modes of operation. In this contribution we describe the motivations for establishing a network, the basic outline of SONG and the expected performance.Comment: Proc. Vienna Workshop on the Future of Asteroseismology, 20 - 22 September 2006. Comm. in Asteroseismology, Vol. 150, in the pres

Solvable Critical Dense Polymers

A lattice model of critical dense polymers is solved exactly for finite strips. The model is the first member of the principal series of the recently introduced logarithmic minimal models. The key to the solution is a functional equation in the form of an inversion identity satisfied by the commuting double-row transfer matrices. This is established directly in the planar Temperley-Lieb algebra and holds independently of the space of link states on which the transfer matrices act. Different sectors are obtained by acting on link states with s-1 defects where s=1,2,3,... is an extended Kac label. The bulk and boundary free energies and finite-size corrections are obtained from the Euler-Maclaurin formula. The eigenvalues of the transfer matrix are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields a selection rule for the physically relevant solutions to the inversion identity and explicit finitized characters for the associated quasi-rational representations. In particular, in the scaling limit, we confirm the central charge c=-2 and conformal weights Delta_s=((2-s)^2-1)/8 for s=1,2,3,.... We also discuss a diagrammatic implementation of fusion and show with examples how indecomposable representations arise. We examine the structure of these representations and present a conjecture for the general fusion rules within our framework.Comment: 35 pages, v2: comments and references adde

On dimension reduction in Gaussian filters

A priori dimension reduction is a widely adopted technique for reducing the computational complexity of stationary inverse problems. In this setting, the solution of an inverse problem is parameterized by a low-dimensional basis that is often obtained from the truncated Karhunen-Loeve expansion of the prior distribution. For high-dimensional inverse problems equipped with smoothing priors, this technique can lead to drastic reductions in parameter dimension and significant computational savings. In this paper, we extend the concept of a priori dimension reduction to non-stationary inverse problems, in which the goal is to sequentially infer the state of a dynamical system. Our approach proceeds in an offline-online fashion. We first identify a low-dimensional subspace in the state space before solving the inverse problem (the offline phase), using either the method of "snapshots" or regularized covariance estimation. Then this subspace is used to reduce the computational complexity of various filtering algorithms - including the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within a novel subspace-constrained Bayesian prediction-and-update procedure (the online phase). We demonstrate the performance of our new dimension reduction approach on various numerical examples. In some test cases, our approach reduces the dimensionality of the original problem by orders of magnitude and yields up to two orders of magnitude in computational savings

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed