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We demonstrate that precise solutions of the convective flow equations for a compressible conducting viscous fluid can give degenerate stationary states. That is, two or more completely different stable flows can result for fixed stationary boundary conditions. We characterize these complex flows with finite-difference, smooth-particle methods, and high-order implicit methods. The fluids treated here are viscous conducting gases, enclosed by thermal boundaries in a gravitational field-the "Rayleigh-Benard problem." Degenerate solutions occur in both two-and three-dimensional simulations. This coexistence of solutions is a macroscopic manifestation of the strange attractors seen in atomistic systems far from equilibrium.

Computer simulations of a compressible fluid, convecting heat in two dimensions, suggest that, within a range of Rayleigh numbers, two distinctly different, but stable, time-dependent flow morphologies are possible. The simpler of the flows has two characteristic frequencies: the rotation frequency of the convecting rolls, and the vertical oscillation frequency of the rolls. Observables, such as the heat flux, have a simple-periodic ͑harmonic͒ time dependence. The more complex flow has at least one additional characteristic frequency-the horizontal frequency of the cold, downward-and the warm, upward-flowing plumes. Observables of this latter flow have a broadband frequency distribution. The two flow morphologies, at the same Rayleigh number, have different rates of entropy production and different Lyapunov exponents. The simpler ''harmonic'' flow transports more heat ͑produces entropy at a greater rate͒, whereas the more complex ''chaotic'' flow has a larger maximum Lyapunov exponent ͑corresponding to a larger rate of phase-space information loss͒. A linear combination of these two rates is invariant for the two flow morphologies over the entire range of Rayleigh numbers for which the flows coexist, suggesting a relation between the two rates near the onset of convective turbulence.

Smooth Particle Applied Mechanics provides a novel method for solving the basic equations of continuum mechanics. The method is simple to implement, very stable, and applicable to a variety of far-from-equilibrium situations. It provides an interesting bridge between atomistic and continuum simulations. Here we describe our general explorations of the method, emphasizing recent results for the Rayleigh-Benard problem, a heat conducting flow driven by a convective instability.

Numerical simulations of the fully compressible Navier-Stokes equations are used to study the transition from simple-periodic ''harmonic'' thermal convection to chaotic thermal convection as the Rayleigh number Ra is increased. The simulations suggest that a sharp discontinuity in the relationship between the Nusselt number Nu ͑the ratio of the total heat flux to the Fourier heat flux͒ and the Rayleigh number is associated with this transition in flow morphology. This drop in the Nusselt number is also seen in the data reported in independent experiments involving the convection of two characteristically different fluids-liquid mercury ͓Phys. Rev. E 56, R1302 ͑1997͔͒ ͑a nearly incompressible fluid with Prandtl number Prϭ0.024͒ and gaseous helium ͓Phys. Rev. A 36, 5870 ͑1987͔͒ ͑a compressible fluid with unit Pr͒. The harmonic flow generates a dual-maximum ͑quasiharmonic͒ temperature histogram, while the chaotic flow generates a single-maximum histogram at the center point in the simulated cell. This is consistent with the temperature distributions reported for the convecting mercury before and after the drop in Nu. Our simulations also suggest a hysteresis in the Nu-Ra curve linking the two distinctly different flow morphologies, heat fluxes, and temperature-fluctuation histograms at the same Rayleigh number. ͓S1063-651X͑98͒01909-6͔

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Multispectral imaging can offer many benefits in cost, complexity, resolution, size, weight, and power, relative to hyperspectral imaging. When designing a multispectral system, spectral bandpasses can be selected using optimization algorithms configured to maximally separate target detection scores between target and background regions. A hyperspectral image (HSI) can serve as the source of data from which band groupings can be tested for optimality. The output of an adaptive cosine estimator target detection algorithm is used in an objective function. Three optimization algorithms are compared: particle swarm, dual annealing, and differential evolution. A global optimum is also found using a brute force approach on the Livermore Computing Syrah supercomputer. Three materials are investigated: calcite, gypsum, and limestone. This is done for 3-, 4-, and 5-band systems. The data originate from a longwave infrared HSI of a material display board. The optimization algorithms were run 30 times for every scenario. Performance statistics (maximum, minimum, mean, standard deviation, and median) based on the separation values are given. Additional characterization was performed using receiver operator characteristic (ROC) curves and the area under the ROC curve. While good performance was obtained for the three optimization algorithms, the dual annealing algorithm produced the highest and most consistent detection separation scores on average. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 International License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.