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1.
Flow visualization of chemical flocs in a simple extensional flow field reveals two distinct mechanisms for their breakage: splitting into a relatively small number of daughter fragments whose sizes are comparable to the parent flocs, along with continual disintegration by erosion to produce extremely fine particles from the extremities of the parent floc along the axis of extension. In turbulent flow, these two mechanisms still occur, although the kinematics of flow are more complex. This work presents a formulation of the population balance equation that governs the floc size distribution in turbulent flow, incorporating both the splitting and erosion mechanisms discussed above. Experiments were conducted in which floc size distributions of dilute suspensions are measured by a combination of techniques, including computerized optical scanning of photographs and pulse height analysis of signals from a light blockage transducer. The experimentally determined size distributions are then fit to those computed from the population balance equation, using constrained nonlinear least squares. This yields best values of certain coefficients that appear in the governing equation, providing a strategy to obtain a data base to promote deeper theoretical analysis. The method is demonstrated by analyzing data for kaolin-Fe(OH)3 flocs in aqueous suspensions. 相似文献
2.
Sanford TW Allshouse GO Marder BM Nash TJ Mock RC Spielman RB Seamen JF McGurn JS Jobe D Gilliland TL Vargas M Struve KW Stygar WA Douglas MR Matzen MK Hammer JH De Groot JS Eddleman JL Peterson DL Mosher D Whitney KG Thornhill JW Pulsifer PE Apruzese JP Maron Y 《Physical review letters》1996,77(25):5063-5066
3.
Summary The general course of reactions between [MCl4 ]2– (M = Pd, Pt) and primary and secondary phosphines containing phenyl, cyclohexyl, or 2-cyanoethyl groups, in polar solvents, is to yield L3MCl2 complexes which are probably ionic [L3MCl]+Cl– These compounds can be isolated and characterized in the solid state, but in solution they are labile, and tend to react to give phosphines plus L2 MCI2. 相似文献
4.
Lundblad N Lee PJ Spielman IB Brown BL Phillips WD Porto JV 《Physical review letters》2008,100(15):150401
We load cold atoms into an optical lattice dramatically reshaped by radio-frequency coupling of state-dependent lattice potentials. This radio-frequency dressing changes the unit cell of the lattice at a subwavelength scale, such that its curvature and topology departs strongly from that of a simple sinusoidal lattice potential. Radio-frequency dressing has previously been performed at length scales from mm to tens of mum, but not at the single-optical-wavelength scale. At this length scale significant coupling between adiabatic potentials leads to nonadiabatic transitions, which we measure as a function of lattice depth and dressing amplitude. We also investigate the dressing by measuring changes in the momentum distribution of the dressed states. 相似文献
5.
We perform a smoothed analysis of a termination phase for linear programming algorithms. By combining this analysis with
the smoothed analysis of Renegar's condition number by Dunagan, Spielman and Teng (http://arxiv.org/abs/cs.DS/0302011) we
show that the smoothed complexity of interior-point algorithms for linear programming is O(m
3
log(m/Σ)). In contrast, the best known bound on the worst-case complexity of linear programming is O(m
3 L), where L could be as large as m. We include an introduction to smoothed analysis and a tutorial on proof techniques that have been useful in smoothed analyses.
Received: December 10, 2002 / Accepted: April 28, 2003
Published online: June 5, 2003
Key words. smoothed analysis – linear programming – interior-point algorithms – condition numbers
Mathematics Subject Classification (1991): 90C05, 90C51, 68Q25 相似文献
6.
Sanford T.W.L. Spielman R.B. Allshouse G.O. Chandler G.A. Fehl D.L. Stygar W.A. Struve K.W. Deeney C. Nash T.J. Seamen J.F. Mock R.C. Gilliland T.L. McGurn J.S. Jobe D.O. 《IEEE transactions on plasma science. IEEE Nuclear and Plasma Sciences Society》1998,26(4):1086-1093
Doubling the number of tungsten wires from 120 to 240, keeping the mass fixed, increased the radiated X-ray power relative to the electrical power at the insulator stack of the Z accelerator by (35±15)% for 8.75- and 20-mm radii Z-pinch wire arrays. One-dimensional radiation magneto hydrodynamic calculations suggest that the arrays were operating in a quasi “plasma-shed” regime, where the plasma generated by the individual wires partially merge prior to the inward implosion of the entire array 相似文献
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9.
Jeffrey L Spielman 《Journal of multivariate analysis》1976,6(3):426-446
Let be a real separable Hilbert space; let X(t), t?[0, 1], be a separable, stochastically continuous, -valued stochastic process with independent increments. Then a decomposition of X(t) into a uniformly convergent sum of independent processes is found. In this decomposition one of the processes is Gaussian with continuous sample functions, and the remainder of the processes have sample functions whose discontinuities correspond to those of certain real-valued Poisson processes. The decomposition of X(t) leads to a Levy-Khintchine representation of the characteristic functional of X(t). In addition, the case when X(t) has finite variance is explored, and, as a consequence of the above decomposition, a Kolmogorov-type representation of the characteristic functional of X(t) is derived. 相似文献
10.
We give an elementary proof of a generalization of Bourgain and Tzafriri’s Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for finding the desired subspace. 相似文献