Numerical simulation of steady supersonic flow

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques

Investigation of the utility of mean square approximation systems and in system response predictions

A method is presented for estimating the variability of a system's natural frequencies arising from the variability of the system's parameters. The only information required to obtain the estimates is the member variability, in the form of second order properties, and the natural frequencies and mode shapes of the mean system. Several examples are worked out in detail to illustrate how the method is applied

Application of CFD techniques toward the validation of nonlinear aerodynamic models

Applications of Computational fluid dynamics (CFD) methods to determine the regimes of applicability of nonlinear models describing the unsteady aerodynamic responses to aircraft flight motions are described. The potential advantages of computational methods over experimental methods are discussed and the concepts underlying mathematical modeling are reviewed. The economic and conceptual advantages of the modeling procedure over coupled, simultaneous solutions of the gasdynamic equations and the vehicle's kinematic equations of motion are discussed. The modeling approach, when valid, eliminates the need for costly repetitive computation of flow field solutions. For the test cases considered, the aerodynamic modeling approach is shown to be valid

Journal Staff

Half of the world's forest is in boreal and sub-boreal ecozones, containing large carbon stores and fluxes. Carbon lost from headwater streams in these forests is underestimated. We apply a simple stable carbon isotope idea for quantifying the CO2 loss from these small streams; it is based only on in-stream samples and integrates over a significant distance upstream. We demonstrate that conventional methods of determining CO2 loss from streams necessarily underestimate the CO2 loss with results from two catchments. Dissolved carbon export from headwater catchments is similar to CO2 loss from stream surfaces. Most of the CO2 originating in high CO2 groundwaters has been lost before typical in-stream sampling occurs. In the Harp Lake catchment in Canada, headwater streams account for 10% of catchment net CO2 uptake. In the Krycklan catchment in Sweden, this more than doubles the CO2 loss from the catchment. Thus, even when corrected for aquatic CO2 loss measured by conventional methods, boreal and sub-boreal forest carbon budgets currently overestimate carbon sequestration on the landscape

Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check

We show that when the Hornberger--Sipe calculation of collisional decoherence is carried out with the squared delta function a delta of energy instead of a delta of the absolute value of momentum, following a method introduced by Di\'osi, the corrected formula for the decoherence rate is simply obtained. The results of Hornberger and Sipe and of Di\'osi are shown to be in agreement. As an independent cross-check, we calculate the mean squared coordinate diffusion of a hard sphere implied by the corrected decoherence master equation, and show that it agrees precisely with the same quantity as calculated by a classical Brownian motion analysis.Comment: Tex: 14 pages 7/30/06: revisions to introduction, and references added 9/29/06: further minor revisions and references adde

The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals

We have observed the production of strings (disclination lines and loops) via the Kibble mechanism of domain (bubble) formation in the isotropic to nematic phase transition of a sample of uniaxial nematic liquid crystal. The probablity of string formation per bubble is measured to be $0.33 \pm 0.01$. This is in good agreement with the theoretical value $1/ \pi$ expected in two dimensions for the order parameter space $S^2/{\bf Z}_2$ of a simple uniaxial nematic liquid crystal.Comment: 17 pages, in TEX, 2 figures (not included, available on request

Contraction of broken symmetries via Kac-Moody formalism

I investigate contractions via Kac-Moody formalism. In particular, I show how the symmetry algebra of the standard 2-D Kepler system, which was identified by Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was denoted by ${\mathbb H}_2$, gets reduced by the symmetry breaking term, defined by the Hamiltonian $$H(\beta)= \frac 1 {2m} (p_1^2+p_2^2)- \frac \alpha r - \beta r^{-1/2} \cos ((\phi-\gamma)/2).$$ For this $H (\beta)$ I define two symmetry loop algebras ${\mathfrak L}_{i}(\beta), i=1,2$, by choosing the `basic generators' differently. These ${\mathfrak L}_{i}(\beta)$ can be mapped isomorphically onto subalgebras of ${\mathbb H}_2$, of codimension 2 or 3, revealing the reduction of symmetry. Both factor algebras ${\mathfrak L}_i(\beta)/I_i(E,\beta)$, relative to the corresponding energy-dependent ideals $I_i(E,\beta)$, are isomorphic to ${\mathfrak so}(3)$ and ${\mathfrak so}(2,1)$ for $E0$, respectively, just as for the pure Kepler case. However, they yield two different non-standard contractions as $E \to 0$, namely to the Heisenberg-Weyl algebra ${\mathfrak h}_3={\mathfrak w}_1$ or to an abelian Lie algebra, instead of the Euclidean algebra ${\mathfrak e}(2)$ for the pure Kepler case. The above example suggests a general procedure for defining generalized contractions, and also illustrates the {\em `deformation contraction hysteresis'}, where contraction which involve two contraction parameters can yield different contracted algebras, if the limits are carried out in different order.Comment: 21 pages, 1 figur

Atom cooling by non-adiabatic expansion

Motivated by the recent discovery that a reflecting wall moving with a square-root in time trajectory behaves as a universal stopper of classical particles regardless of their initial velocities, we compare linear in time and square-root in time expansions of a box to achieve efficient atom cooling. For the quantum single-atom wavefunctions studied the square-root in time expansion presents important advantages: asymptotically it leads to zero average energy whereas any linear in time (constant box-wall velocity) expansion leaves a non-zero residual energy, except in the limit of an infinitely slow expansion. For finite final times and box lengths we set a number of bounds and cooling principles which again confirm the superior performance of the square-root in time expansion, even more clearly for increasing excitation of the initial state. Breakdown of adiabaticity is generally fatal for cooling with the linear expansion but not so with the square-root expansion.Comment: 4 pages, 4 figure

Proton-Antiproton Annihilation in Baryonium

A possible interpretation of the near-threshold enhancement in the $(p\bar{p})$-mass spectrum in $J/\psi{\to}\gamma p{\bar p}$ is the of existence of a narrow baryonium resonance X(1860). Mesonic decays of the $(p\bar{p})$-bound state X(1860) due to the nucleon-antinucleon annihilation are investigated in this paper. Mesonic coherent states with fixed $G$-parity and $P$-parity have been constructed . The Amado-Cannata-Dedoder-Locher-Shao formulation(Phys Rev Lett. {\bf 72}, 970 (1994)) is extended to the decays of the X(1860). By this method, the branch-fraction ratios of $Br(X\to \eta 4\pi)$, $Br(X\to \eta 2\pi)$ and $Br(X\to 3\eta)$ are calculated. It is shown that if the X(1860) is a bound state of $(p\bar{p})$, the decay channel ($X\to \eta 4\pi)$ is favored over $(X\to \eta 2\pi)$. In this way, we develop criteria for distinguishing the baryonium interpretation for the near-threshold enhancement effects in $(p\bar{p})$-mass spectrum in $J/\psi{\to}\gamma p{\bar p}$ from other possibilities. Experimental checks are expected. An intuitive picture for our results is discussed.Comment: 19 pages, 3 figure

B\"acklund Transformations of MKdV and Painlev\'e Equations

For $N\ge 3$ there are $S_N$ and $D_N$ actions on the space of solutions of the first nontrivial equation in the $SL(N) MKdV hierarchy, generalizing the two$Z_2$ actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painlev\'e equations.Comment: 8 pages, plain te