Shock waves and drag in the numerical calculation of isentropic transonic flow

Properties of the shock relations for steady, irrotational, transonic flow are discussed and compared for the full and approximate governing potential in common use. Results from numerical experiments are presented to show that the use of proper finite difference schemes provide realistic solutions and do not introduce spurious shock waves. Analysis also shows that realistic drags can be computed from shock waves that occur in isentropic flow. In analogy to the Oswatitsch drag equation, which relates the drag to entropy production in shock waves, a formula is derived for isentropic flow that relates drag to the momentum gain through an isentropic shock. A more accurate formula for drag, based on entropy production, is also derived, and examples of wave drag evaluation based on these formulas are given and comparisons are made with experimental results

Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs

Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi's elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi's sn or cn functions. Examples illustrate key steps of the algorithms. The new algorithms are implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope, limitations, and future extensions of the software are addressed. A survey is given of related algorithms and symbolic software to compute exact solutions of nonlinear differential equations.Comment: 39 pages. Software available from Willy Hereman's home page at http://www.mines.edu/fs_home/whereman

Evidence for a ν=5/2\nu=5/2 Fractional Quantum Hall Nematic State in Parallel Magnetic Fields

We report magneto-transport measurements for the fractional quantum Hall state at filling factor $\nu=$ 5/2 as a function of applied parallel magnetic field ($B_{||}$). As $B_{||}$ is increased, the 5/2 state becomes increasingly anisotropic, with the in-plane resistance along the direction of $B_{||}$ becoming more than 30 times larger than in the perpendicular direction. Remarkably, the resistance anisotropy ratio remains constant over a relatively large temperature range, yielding an energy gap which is the same for both directions. Our data are qualitatively consistent with a fractional quantum Hall \textit{nematic} phase

Observation of An Anisotropic Wigner Crystal

We report a new correlated phase of two-dimensional charged carriers in high magnetic fields, manifested by an anisotropic insulating behavior at low temperatures. It appears near Landau level filling factor $\nu=1/2$ in hole systems confined to wide GaAs quantum wells when the sample is tilted in magnetic field to an intermediate angle. The parallel field component ($B_{||}$) leads to a crossing of the lowest two Landau levels, and an elongated hole wavefunction in the direction of $B_{||}$. Under these conditions, the in-plane resistance exhibits an insulating behavior, with the resistance along $B_{||}$ more than 10 times smaller than the resistance perpendicular to $B_{||}$. We interpret this anisotropic insulating phase as a two-component, striped Wigner crystal

A site-specific standard for comparing dynamic solar ultraviolet protection characteristics of established tree canopies

A standardised procedure for making fair and comparable assessments of the ultraviolet protection of an established tree canopy that takes into account canopy movement and the changing position of the sun is presented for use by government, planning, and environmental health authorities. The technique utilises video image capture and replaces the need for measurement by ultraviolet radiometers for surveying shade quality characteristics of trees growing in public parks, playgrounds and urban settings. The technique improves upon tree shade assessments that may be based upon single measurements of the ultraviolet irradiance observed from a fixed point of view. The presented technique demonstrates how intelligent shade audits can be conducted without the need for specialist equipment, enabling the calculation of the Shade Protection Index (SPI) and Ultraviolet Protection Factor (UPF) for any discreet time interval and over a full calendar year

Inheritance of Black Hair Patterns in Cattle Lacking the Extension Factor for Black (E.). IV, Partitioning Phenotypes by Castration

Author Institution: Department of Dairy Science, Ohio Agricultural Experiment Station, Wooste

Multicomponent fractional quantum Hall states with subband and spin degrees of freedom

In wide GaAs quantum wells where two electric subbands are occupied we apply a parallel magnetic field or increase the electron density to cause a crossing of the two $N=0$ Landau levels of these subbands and with opposite spins. Near the crossing, the fractional quantum Hall states in the filling factor range $1<\nu<3$ exhibit a remarkable sequence of pseudospin polarization transitions resulting from the interplay between the spin and subband degrees of freedom. The field positions of the transitions yield a new and quantitative measure of the composite Fermions' discrete energy level separations. Surprisingly, the separations are smaller when the electrons have higher spin-polarization

Even-denominator Fractional Quantum Hall Effect at a Landau Level Crossing

The fractional quantum Hall effect (FQHE), observed in two-dimensional (2D) charged particles at high magnetic fields, is one of the most fascinating, macroscopic manifestations of a many-body state stabilized by the strong Coulomb interaction. It occurs when the filling factor ($\nu$) of the quantized Landau levels (LLs) is a fraction which, with very few exceptions, has an odd denominator. In 2D systems with additional degrees of freedom it is possible to cause a crossing of the LLs at the Fermi level. At and near these crossings, the FQHE states are often weakened or destroyed. Here we report the observation of an unusual crossing of the two \emph{lowest-energy} LLs in high-mobility GaAs 2D $hole$ systems which brings to life a new \emph{even-denominator} FQHE at $\nu=1/2$