Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.     

Large-eddy simulations of chevron jet flows with noise predictions

Hybrid large-eddy type simulations for chevron nozzle jet flows are performed at Mach 0.9 and Re = 1.03 × 10⁶. Without using any subgrid scale model (SGS), the numerical approach applied in the present study is essentially implicit large-eddy simulation (ILES). However, a Reynolds-averaged Navier–Stokes (RANS) solution is patched into the near wall region. This makes the overall solution strategy hybrid RANS–ILES. The disparate turbulence length scales, implied by these different modeling approaches, are matched using a Hamilton–Jacobi equation. The complex geometry features of the chevron nozzles are fully meshed. With numerical fidelity in mind, high quality, hexahedral multi-block meshes of 12.5 × 10⁶ cells are used. Despite the modest meshes, the novel RANS–ILES approach shows encouraging performance. Computed mean and second-order fluctuating quantities of the turbulent near field compare favorably with measurements. The radiated far-field sound is predicted using the Ffowcs Williams and Hawkings (FW–H) surface integral method. Encouraging agreement of the predicted far-field sound directivity and spectra with measurements is obtained.     

Measured and modeled enhancement of transition metal emissions in the d.c. plasma jet

Enhancement of sensitive transition metal lines by a sodium matrix is measured in a 3-electrode d.c. plasma jet. Spiking with 0.43 M NaCI causes enhancement by factors of 1.85–2.92 in ionic lines and of 1.22–1.99 in atomic lines for eight of the structurally related analyte elements, but suppresses Zn I and Zn II emissions by about 25 %. Emission response to NaCI of lines within the same spectrum, or between different spectra of like ionization stage, can be simulated to 15 % and 20–25 %, respectively, by approximations linear in energy differences. For ionic lines these differences are the absolute value of the line excitation potential minus the energy of the ion state most readily pumped by Penning ionization by argon. For atomic lines it is the difference between emitting state excitation potential and the first ionization potential. Analyses of the experimental data strongly suggest that: (1) Na acts mainly to pertub radiative transfer rather than collisional redistribution processes; (2) population pumping of excited analyte states is largely driven by Penning ionization; (3) accelerated radiative cooling due to Na is manifested in a lowering of local kinetic temperature; (4) to a first-order of approximation, ambipolar diffusion, analyte-Na collisions of the second kind, and analyte ground state spin, do not influence emission line enhancement by easily ionized elements (EIE). Approximations are developed for predicting transition metal enhancements by arbitrary Na doping concentrations, and means are sketched for extending the method to other analyte group/EIE combinations. Practical implications of the work are noted.     

Special metrics and scales in parabolic geometry

Annals of Global Analysis and Geometry - Given a parabolic geometry, it is sometimes possible to find special metrics characterised by some invariant conditions. In conformal geometry, for example,...