Boundary effects on granular shear flows of smooth disks

Summary We obtain boundary conditions for two-dimensional flows of identical, nearly elastic, circular disks that interact with a flat wall to which identical, evenly spaced half-disks have been attached. Expressions for the transfer of momentum and energy from the boundary to the flow are obtained by statistical averaging over all possible wall-flow disk collisions. We improve upon the expressions derived by Jenkins and Richman [1986] by employing in the averaging process a more elaborate velocity distribution function obtained through the method of moments. In addition we expand the distribution function about a point near the flat wall that guarantees positive slip velocities. With these boundary conditions, we analyze a two-dimensional shear flow driven by parallel bumpy boundaries. The constitutive theory employed includes both the effects of particle collisions and particle transport on the transfer of momentum and energy throughout the flow. We demonstrate how the resulting profiles of velocity, granular temperature, and solid fraction are affected by changes in the geometry of the boundary. We also predict how the induced stresses vary with the geometry of the boundary and the average solid fraction within the flow.

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Zusammenfassung Wir erhalten die Randbedingungen für die zweidimensionale Strömung identischer, beinahe elastischer, runder Scheiben, die sich in Wechselwirkung mit einer geraden Wand befinden, an der in gleichmäßigen Abständen Halbscheiben angebracht sind. Es werden Ausdrücke für die Übertragung von Impuls und Energie vom Rand auf den Strom aufgestellt, die durch den statisch errechneten Durchschnitt aller möglichen Scheibenkollisionen Wand-Strom erhalten werden. Wir verbessern die von Jenkins und Richman (1986) entwickelten Ausdrücke dadurch, daß bei der Berechnung der Mittelwerte eine erweiterte Geschwindigkeitsverteilung, die auf der Momentmethode beruht, einbezogen wurde. Außerdem entwickeln wir die Verteilungsfunktion an einem Punkt so nahe an der Wand, daß positive Gleitgeschwindigkeiten garantiert sind. Wir untersuchen eine zweidimensionale Scherströmung mit diesen Randbedingungen, die durch die parallelen unebenen Ränder getrieben wird. Die konstitutive Theorie, die wir anwenden, beinhaltet sowohl den Einfluß der Teilchenkollisionen als auch den des Teilchentransports auf die Übertragung von Impuls und Energie innerhalb der Strömung. Wir zeigen, wie die Profile der Geschwindigkeit, der Granu-lartemperatur und des Festkörperanteils, die sich ergeben, durch Veränderungen der Randgeometrie beeinflußt werden. Weiterhin können wir voraussagen, wie die erzeugten Spannungen sich mit der Randgeometrie und dem im Strom enthaltenen Festkörperanteil verändern.

     

A theory for grain-size reduction in granular flows of spheres

Summary We derive a kinetic theory for homogeneous granular shear flows of identical spheres in which collisions between particles result in small fractures on their peripheries and, over time, effectively reduce their average diameter. In obtaining statistically averaged constitutive relations for the rates of energy dissipation and mass loss, we employ the integral expression derived by Jenkins and Savage [1983] for the collisional source of a particle property. However, in calculating the stress, we modify their expression for the collisional flux in order to ensure that the stress is symmetric when the particles interact through central forces. The constitutive relations are employed in the balance equations for mass, momentum, and energy in order to predict, for a fixed shear rate and particle number density, the manner in which the solid fraction, granular temperature, and induced stresses vary with time.

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Zusammenfassung Wir entwickeln eine kinetische Theorie für die homogene Scherströmung von identischen Kugeln, in welcher die Zusammenstösse der Teilchen kleine Risse in ihrer Oberfläche verursachen und sich dadurch ihr mittlerer Durchmesser mit der Zeit verringert. Um die statistisch gemittelten konstitutiven Beziehungen für die Energiedissipations- und Massenverlustraten zu erhalten, verwenden wir den von Jenkins und Savage [1983] hergeleiteten Integralausdruck für die von den Kollisionen verursachte Quellenstärke einer Teilchenzustandsgrösse. Bei der Berechnung der Spannung verwenden wir jedoch einen abgeänderten Ausdruck für den Fluss durch Kollision; dadurch wird sichergestellt, dass der Spannungstensor symmetrisch ist, wenn die Kontaktkraft zwischen den Teilchen normal zur Kontaktebene wirkt. Die konstitutiven Beziehungen werden in die Gleichungen für die Erhaltung von Masse, Impuls und Energie eingesetzt, um zu berechnen, wie sich der Festkörperanteil, die Granulartemperatur und die induzierten Spannungen als Funktion der Zeit verändern; der Geschwindigkeitsgradient und die Anzahl Teilchen pro Volumen sind dabei konstant.

     

Turbulence measurements in a resonance tube

Experimental investigations of acoustically induced turbulence in a resonance tube have been performed. Frequency (f) and sound pressure level (I_p) effects have been studied. Measurements were made at various spatial locations on loops and nodes. Sampled data were processed to estimate the characteristics of turbulence. It is found that the acoustically induced turbulence appears when I_p exceeds 160 dB under the experimental conditions of f = 680–2740 Hz and I_p = 160–166 dB. The turbulent spectrum (F) and the wave number (κ) are found to satisfy a power law F ∝ K^s with $\text{s ? ?1·6}\text{to}\text{? 2·1}$. The r.m.s. turbulent velocity ($\text{u}\text{?}$) is experimentally found to have an $\text{I}{}_{\mathrm{p}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ dependence, yet is relatively insensitive to the variation of f. Throughout the whole measuring range of f and I_p, the rate of energy dissipation per unit mass (ε) is estimated to be in the order of 10⁶–10⁷cm²/s³.     

A study of high spin states in the transitional nucleus90Mo

The reaction⁵⁸Ni(³⁶Ar, 4p)⁹⁰Mo has been studied at a beam energy of 149 MeV. A detector array consisting of the OSIRIS spectrometer (12 Compton-suppressed Ge detectors), four charged-particleδE detectors and seven NE-213 neutron detectors at the VICKSI accelerator in Berlin has been used to measure the gamma radiation inγγ- and particle-γγ-coincidence mode. An additional Ge detector was placed at 162? to the beam direction to provide information on DCO ratios. The level scheme of⁹⁰Mo has been extended up to an excitation energy of about 12 MeV and probable spin 23?. Some 70 transitions and 40 levels have been newly identified. Spin assignments have been proposed on the basis of measured DCO ratios. Shell model calculations in a model space consisting of the proton 1f _5/2, 2p _3/2, 2p _1/2, and 1g _9/2 orbits and the neutron 2p _1/2, 1g _9/2, 1g _7/2, 2d _5/2, 2d _3/2, and 3s _1/2 orbits with some truncation were made for states above 9? and the predicted structure of these states is discussed.     

An unprecedented transformation mode in aluminium oxazoline-amido-phenolate complexes

This paper describes the effect of solvent-induced synthetic routes of aluminium pendant oxazoline-amido-phenolate complexes. Treatment of ligand precursor L with AlMe₃ in a 1:1 ratio in diethyl ether yielded the four-coordinated complex (LAlMe)₂. Reaction of ligand precursor L with AlMe₃ in a 1:2 ratio in hexane generated the four-coordinated complex L(AlMe₂)₂. A novel transformation mode occurred from L(AlMe₂)₂ to (LAlMe)₂ when using diethyl ether or tetrahydrofuran as solvent. A density functional theory computational study also supports a plausible mechanism. All results were supported by spectroscopic data and in agreement with single-crystal X-ray diffraction structural analysis.     

R~(2,1)中线性Weingarten曲面的Bcklund变换(英文)

本文对三维Minkowski空间R~(2,1)中具有性质K-2mH+m~2-l~2=0或H=constant的类时曲面定义了一个Darboux线汇,同时得到了相应的Bcklund变换。     

Femtosecond transform-limited Kerr-lens mode-locked dye lasers

Using SF6 glass plates as intracavity Kerr lenses and double-prism pairs for dispersion compensation, we achieve tunable femtosecond passive mode locking in rhodamine 590 (R6G) and 4-dicyanomethylene-2-methyl-16-p-dimethylaminostyryl-4H-pyran (DCM) dye lasers. The R6G laser produces transform limited 240–500 fs pulses between 577 and 606 nm, and the DCM laser produces 150 fs transform-limited pulses between 650 and 671 nm. We use dilute intracavity saturable-absorber jets to make the mode locking self-starting. Characteristics of the pulses and the stability regions of the lasers agree with general theories of passive mode locking.     

Multigrid algorithms for a vertex–centered covolume method for elliptic problems

Summary. We analyze V–cycle multigrid algorithms for a class of perturbed problems whose perturbation in the bilinear form preserves the convergence properties of the multigrid algorithm of the original problem. As an application, we study the convergence of multigrid algorithms for a covolume method or a vertex–centered finite volume element method for variable coefficient elliptic problems on polygonal domains. As in standard finite element methods, the V–cycle algorithm with one pre-smoothing converges with a rate independent of the number of levels. Various types of smoothers including point or line Jacobi, and Gauss-Seidel relaxation are considered. Received August 19, 1999 / Revised version received July 10, 2000 / Published online June 7, 2001     

WALL CONDUCTION EFFECT ON THE ONSET OF THERMAL INSTABILITY IN HORIZONTAL RECTANGULAR CHANNELS

The effect of peripheral thermal conduction in the bottom wall on the onset of thermal instability in the thermal entrance region of horizontal, rectangular, bottom-uniform-heated channels was studied by experiment and theoretical simulation. The predicted results of the onset of thermal instability for the cases of uniform peripheral wall heat flux are in agreement with the published experimental data, but the predicted results for the cases of uniform peripheral wall temperature exceed the previous data by about an order of magnitude. The present experimental data reconfirm the present predictions. The effect of increasing the peripheral wall conduction is shown to stabilize the flow.