Some experiences with the viscous-inviscid interaction approach

Methods for simulating compressible viscous flow using the viscid-inviscid interaction approach are described. The formulations presented range from the more familiar full-potential/boundary-layer interaction schemes to a method for coupling Euler/Navier-Stokes and boundary-layer algorithms. An effort is made to describe the advantages and disadvantages of each formulation. Sample results are presented which illustrate the applicability of the methods

Inductive Algebras for Finite Heisenberg Groups

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups.Comment: 5 page

Geodynamo and mantle convection simulations on the Earth Simulator using the Yin-Yang grid

We have developed finite difference codes based on the Yin-Yang grid for the geodynamo simulation and the mantle convection simulation. The Yin-Yang grid is a kind of spherical overset grid that is composed of two identical component grids. The intrinsic simplicity of the mesh configuration of the Yin-Yang grid enables us to develop highly optimized simulation codes on massively parallel supercomputers. The Yin-Yang geodynamo code has achieved 15.2 Tflops with 4096 processors on the Earth Simulator. This represents 46% of the theoretical peak performance. The Yin-Yang mantle code has enabled us to carry out mantle convection simulations in realistic regimes with a Rayleigh number of $10^7$ including strongly temperature-dependent viscosity with spatial contrast up to $10^6$.Comment: Plenary talk at SciDAC 200

A formulation for the boundary-layer equations in general coordinates

This is a working paper in which a formulation is given for solving the boundary-layer equations in general body-fitted curvilinear coordinates while retaining the original Cartesian dependent variables. The solution procedure does not require that any of the coordinates be orthogonal, and much of the software developed for many Navier-Stokes schemes can be readily used. A limited number of calculations has been undertaken to validate the approach

Classification of lower extremity movement patterns based on visual assessment: reliability and correlation with 2-dimensional video analysis

CONTEXT: Abnormal movement patterns have been implicated in lower extremity injury. Reliable, valid, and easily implemented assessment methods are needed to examine existing musculoskeletal disorders and investigate predictive factors for lower extremity injury. OBJECTIVE: To determine the reliability of experienced and novice testers in making visual assessments of lower extremity movement patterns and to characterize the construct validity of the visual assessments. DESIGN: Cross-sectional study. SETTING: University athletic department and research laboratory. PATIENTS OR OTHER PARTICIPANTS: Convenience sample of 30 undergraduate and graduate students who regularly participate in athletics (age = 19.3 ± 4.5 years). Testers were 2 experienced physical therapists and 1 novice postdoctoral fellow (nonclinician). MAIN OUTCOME MEASURE(S): We took videos of 30 athletes performing the single-legged squat. Three testers observed the videos on 2 occasions and classified the lower extremity movement as dynamic valgus, no change, or dynamic varus. The classification was based on the estimated change in frontal-plane projection angle (FPPA) of the knee from single-legged stance to maximum single-legged squat depth. The actual FPPA change was measured quantitatively. We used percentage agreement and weighted κ to examine tester reliability and to determine construct validity of the visual assessment. RESULTS: The κ values for intratester and intertester reliability ranged from 0.75 to 0.90, indicating substantial to excellent reliability. Percentage agreement between the visual assessment and the quantitative FPPA change category was 90%, with a κ value of 0.85. CONCLUSIONS: Visual assessments were made reliably by experienced and novice testers. Additionally, movement-pattern categories based on visual assessments were in excellent agreement with objective methods to measure FPPA change. Therefore, visual assessments can be used in the clinic to assess movement patterns associated with musculoskeletal disorders and in large epidemiologic studies to assess the association between lower extremity movement patterns and musculoskeletal injury

Inductive algebras and homogeneous shifts

Inductive algebras for the irreducible unitary representations of the universal cover of the group of unimodular two by two matrices are classified. The classification of homogeneous shift operators is obtained as a direct consequence. This gives a new approach to the results of Bagchi and Misra

Superlinear Increase of Photocurrent due to Stimulated Scattering into a Polariton Condensate

We show that when a monopolar current is passed through an n-i-n structure, superlinear photocurrent response occurs when there is a polariton condensate. This is in sharp contrast to the previously observed behavior for a standard semiconductor laser. Theoretical modeling shows that this is due to a stimulated exciton-exciton scattering process in which one exciton relaxes into the condensate, while another one dissociates into an electron-hole pair.Comment: 17 pages with 10 figure

Quantum capacitance mediated carbon nanotube optomechanics

Cavity optomechanics allows the characterization of a vibration mode, its cooling and quantum manipulation using electromagnetic fields. Regarding nanomechanical as well as electronic properties, single wall carbon nanotubes are a prototypical experimental system. At cryogenic temperatures, as high quality factor vibrational resonators, they display strong interaction between motion and single-electron tunneling. Here, we demonstrate large optomechanical coupling of a suspended carbon nanotube quantum dot and a microwave cavity, amplified by several orders of magnitude via the nonlinearity of Coulomb blockade. From an optomechanically induced transparency (OMIT) experiment, we obtain a single photon coupling of up to g(0) = 2 . 95 Hz. This indicates that normal mode splitting and full optomechanical control of the carbon nanotube vibration in the quantum limit is reachable in the near future. Mechanical manipulation and characterization via the microwave field can be complemented by the manifold physics of quantum-confined single electron devices