We report numerical simulations of Bénard convection in infinite Prandtl number fluids driven by thermocapillary forces. At high Marangoni numbers a spectrum E(k)∼k−3 of surface temperature fluctuations is estab...
We report numerical simulations of Bénard convection in infinite Prandtl number fluids driven by thermocapillary forces. At high Marangoni numbers a spectrum E(k)∼k−3 of surface temperature fluctuations is established due to the formation of discontinuities of the temperature gradient in the form of thermal ripples between contiguous convective cells. The results support the applicability of Sivashinsky's model equation beyond its mathematical limit of validity.
Direct numerical simulations with up to 10242 resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian ...
Direct numerical simulations with up to 10242 resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian white-in-time noise. The energy spectra for the inverse energy cascade deviate strongly from the expected k−5/3 law and are close (somewhat flatter) to k−3. The reason for the deviation is traced to the emergence of strong vortices distributed over all scales. Statistical properties of the vortices are explored.
Following the ideas of operator product expansion, the velocity v, kinetic energy K=1/2v2, and dissipation rate ε=ν0(∂vi/∂xj)2 are treated as independent dynamical variables, each obeying its own equation of motion....
Following the ideas of operator product expansion, the velocity v, kinetic energy K=1/2v2, and dissipation rate ε=ν0(∂vi/∂xj)2 are treated as independent dynamical variables, each obeying its own equation of motion. The relations Δu(ΔK)2 ∝ r, Δu(Δε)2 ∝ r0, and (Δu)5≊rΔεΔK are derived. If velocity scales as (Δv)rms∝ r(γ/3)−1, then simple power counting gives (ΔK)rms ∝ r1−(γ/6) and (Δε)rms ∝ 1/√(Δv)rms ∝ r(1/2)−(γ/6). In the Kolmogorov turbulence (γ=4) the intermittency exponent μ=(γ/3)-1=1/3 and (Δε)2=O(Re1/4). The scaling relation for the ε fluctuations is a consequence of cancellation of ultraviolet divergences in the equation of motion for the dissipation rate.
General solutions to the conformally self-dual, scalar flat equations for Riemannian Bianchi type IX diagonal metrics am given in terms of the Painleve VI transcendents. The Lax pair and Hamiltonian structure of these...
General solutions to the conformally self-dual, scalar flat equations for Riemannian Bianchi type IX diagonal metrics am given in terms of the Painleve VI transcendents. The Lax pair and Hamiltonian structure of these equations are also discussed briefly.
The Kolmogorov relation for the third order structure function is used to derive the energy spectrum in the far dissipation range (k→∞). This contains no unspecified constants. Using methods from matched asymptotic ...
The Kolmogorov relation for the third order structure function is used to derive the energy spectrum in the far dissipation range (k→∞). This contains no unspecified constants. Using methods from matched asymptotic expansions and mild analyticity assumptions, a uniformly valid form for the inertial through the dissipative ranges is obtained. An analogous energy spectrum is presented. This is compared with the results of physical and numerical experiments on the energy spectra E(k). The theoretical predictions are found to deviate by not more than a few percent from the measured data in the entire range of wave numbers where the energy spectrum E(k) varies by more than 30 orders of magnitude.
The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. It is shown that the interaction of the random and large-scale coherent components of t...
The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. It is shown that the interaction of the random and large-scale coherent components of the Clebsch fields is responsible for generation of two energy spectra E(k)∝k−7/3 and E(k)∝k−2 at scales somewhat larger than those corresponding to the -5/3 inertial range. This interaction is also responsible for the experimentally observed Gaussian statistics of the velocity differences at large scales, and the nontrivial scaling behavior of their high-order moments for inertial-range values of the displacement r. The ‘‘anomalous scaling exponents’’ are derived and compared with experimental data.
We report results showing that spatially periodic Bernstein-Greene-Kruskal (BGK) waves, which are exact nonlinear traveling wave solutions of the Vlasov-Maxwell equations for collisionless plasmas, satisfy a nonlinear...
We report results showing that spatially periodic Bernstein-Greene-Kruskal (BGK) waves, which are exact nonlinear traveling wave solutions of the Vlasov-Maxwell equations for collisionless plasmas, satisfy a nonlinear principle of superposition in the small-amplitude limit. For an electric potential consisting of N traveling waves, cphi(x,t)= Ji=1Ncphi(i)(x-νit), where νi is the velocity of the ith wave and each wave amplitude cphi(i) is of order ε which is small, we first derive a set of quantities scrĒ(i)(x,u,t) which are invariants through first order in ε for charged particle motion in this N-wave field. We then use these functions scrĒ(i)(x,u,t) to construct smooth distribution functions for a multispecies plasma which satisfy the Vlasov equation through first order in ε uniformly over the entire x-u phase plane for all time. By integrating these distribution functions to obtain the charge and current densities, we also demonstrate that the Poisson and Ampère equations are satisfied to within errors that are O(ε3/2). Thus the constructed distribution functions and corresponding field describe a self-consistent superimposed N-wave solution that is accurate through first order in ε. The entire analysis explicates the notion of small-amplitude multiple-wave BGK states which, as recent numerical calculations suggest, is crucial in the proper description of the time-asymptotic state of a plasma in which a large-amplitude electrostatic wave undergoes nonlinear Landau damping.
The existence of random fixed points for nonexpansive and pseudocontractive random multivalued operators defined on unbounded subsets of a Banach space is proved. A random coincidence point theorem for a pair of compa...
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作者：
DAVIS, CBMCNICHOLS, RJCharles B. Davis is principal statistician with Environmet- rics & Statistics Ltd. (EnviroStat
1853 Wellington Court Henderson NV 89014). After receiving his M.S. in mathematics and statistics and Ph.D. in statistics from the University of New Mexico he joined the Mathematics Department of the University of Toledo to establish its graduate program in statistics with emphasis on consulting and applications. He and McNichols became involved in consulting and research related to statistical issues arising in RCRA ground water monitoring regulation in 1985 and formed EnviroStat in 1990. Davis left academia in 1992 to concentrate on environmental statistics. Roger J. McNichols is professor and chairman of the Industrial Engineering Department at The University of Toledo
(Toledo OH 43606). After receiving his Ph.D. in industrial engineering from The Ohio State University he joined the faculty of Texas A and M University where he directed the Maintainability Engineering Graduate Program at Red River Army Depot. At University of Toledo he is also chairman of the Systems Doctoral Program and has served as associate dean of engineering. His research and consulting interests include reliability quality control manufacturing environmental monitoring mathematical modeling and applied statistics.
Current federal ground water monitoring statistical regulation dates from the revised RCRA Subtitle C Final Rule of 1988. That rule was a considerable advance over previous RCRA statistical rules. However, two major p...
Current federal ground water monitoring statistical regulation dates from the revised RCRA Subtitle C Final Rule of 1988. That rule was a considerable advance over previous RCRA statistical rules. However, two major problem areas remained: facility-wide false positive rate (FWFPR) control and spatial variability. Progress has been made in the 1991 Subtitle D Final Rule and in guidance;the 1992 Addendum to Interim Final Guidance in particular includes a substantial conceptual advance toward resolving the FWFPR problem. Other areas of improvement include normality testing and distribution assumptions, dropping the four independent samples per monitoring period requirement, allowing a preliminary evaluation short of a 40 CFR Part 258 Appendix II assessment upon finding a statistically significant increase, and suggesting superior alternatives to analyses of variance (ANOVAs) and tests of proportions. The problem of dealing with natural spatial variability remains. Although certain techniques listed in the regulations can control for inherent spatial variability and the performance standards require doing so ''when necessary,'' little attention has been paid to the ubiquity of such spatial variation. Moreover, regulatory traditions favoring upgradient-downgradient comparisons often make control of natural spatial variation difficult and ineffective. With new, lined facilities easily implemented statistical solutions are available;however, dealing with the several existing solid waste facilities which will now be regulated under Subtitle D will present major challenges. In short, the 1988 revision of the Subtitle C rules made it more possible to provide statistically sound monitoring programs, and there has been steady progress since then. Challenges remain, however. These vary from state to state, particularly with regard to controlling false positives and false negatives in the presence of natural spatial variability.
The military services are being moved in the direction of performance-based specifications and standards. They are being steered against dictating ''how to'' produce an item since such action foreclose...
The military services are being moved in the direction of performance-based specifications and standards. They are being steered against dictating ''how to'' produce an item since such action forecloses on the ability to gain access to components or technology that may have a commercial equivalent. Why should the engineering community embrace the new approach? Aside from the obvious weight of it being approved policy, therefore currently mandated, it warrants examination because it is the correct approach at this time when applied to appropriate products. Military specifications and standards are to be displaced then, by acceptable alternative contractor design solutions. Industry bidders will be allowed to propose the particular design details, permitting procurement flexibility by contractually citing only system level or interface requirements, both physical and functional. Hopefully, this can broaden the industrial base and increase competition with reduced costs to follow. Conceptually, the approach appears both performance-sensible and cost-attractive (there are, of course, consequent risks) but how does implementation proceed? Is it possible to pursue the goals envisioned along paths that are not in themselves experimental? Can the American postulate, minimal loss of life and limb to U.S. military people, continue to be honored? Experience and track record elsewhere imply encouraging possibilities in select situations-useful prospects are identified and discussed in practical terms.
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