Analytic study of the urn model for separation of sand

We present an analytic study of the urn model for separation of sand recently introduced by Lipowski and Droz (Phys. Rev. E 65, 031307 (2002)). We solve analytically the master equation and the first-passage problem. The analytic results confirm the numerical results obtained by Lipowski and Droz. We find that the stationary probability distribution and the shortest one among the characteristic times are governed by the same free energy. We also analytically derive the form of the critical probability distribution on the critical line, which supports their results obtained by numerically calculating Binder cumulants (cond-mat/0201472).Comment: 6 pages including 3 figures, RevTe

Analytic study of the three-urn model for separation of sand

We present an analytic study of the three-urn model for separation of sand. We solve analytically the master equation and the first-passage problem. We find that the stationary probability distribution obeys the detailed balance and is governed by the {\it free energy}. We find that the characteristic lifetime of a cluster diverges algebraically with exponent 1/3 at the limit of stability.Comment: 5pages, 4 figures include

Jet pumps for thermoacoustic applications: design guidelines based on a numerical parameter study

The oscillatory flow through tapered cylindrical tube sections (jet pumps) is characterized by a numerical parameter study. The shape of a jet pump results in asymmetric hydrodynamic end effects which cause a time-averaged pressure drop to occur under oscillatory flow conditions. Hence, jet pumps are used as streaming suppressors in closed-loop thermoacoustic devices. A two-dimensional axisymmetric computational fluid dynamics model is used to calculate the performance of a large number of conical jet pump geometries in terms of time-averaged pressure drop and acoustic power dissipation. The investigated geometrical parameters include the jet pump length, taper angle, waist diameter and waist curvature. In correspondence with previous work, four flow regimes are observed which characterize the jet pump performance and dimensionless parameters are introduced to scale the performance of the various jet pump geometries. The simulation results are compared to an existing quasi-steady theory and it is shown that this theory is only applicable in a small operation region. Based on the scaling parameters, an optimum operation region is defined and design guidelines are proposed which can be directly used for future jet pump design.Comment: The following article has been accepted by the Journal of the Acoustical Society of America. After it is published, it will be found at http://scitation.aip.org/JAS

The friction factor of two-dimensional rough-boundary turbulent soap film flows

We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.Comment: 4 pages, 3 figure

Breakdown of Burton-Prim-Slichter approach and lateral solute segregation in radially converging flows

A theoretical study is presented of the effect of a radially converging melt flow, which is directed away from the solidification front, on the radial solute segregation in simple solidification models. We show that the classical Burton-Prim-Slichter (BPS) solution describing the effect of a diverging flow on the solute incorporation into the solidifying material breaks down for the flows converging along the solidification front. The breakdown is caused by a divergence of the integral defining the effective boundary layer thickness which is the basic concept of the BPS theory. Although such a divergence can formally be avoided by restricting the axial extension of the melt to a layer of finite height, radially uniform solute distributions are possible only for weak melt flows with an axial velocity away from the solidification front comparable to the growth rate. There is a critical melt velocity for each growth rate at which the solution passes through a singularity and becomes physically inconsistent for stronger melt flows. To resolve these inconsistencies we consider a solidification front presented by a disk of finite radius $R_0$ subject to a strong converging melt flow and obtain an analytic solution showing that the radial solute concentration depends on the radius $r$ as $\sim\ln^{1/3}(R_0/r)$ and $\sim\ln(R_0/r)$ close to the rim and at large distances from it. The logarithmic increase of concentration is limited in the vicinity of the symmetry axis by the diffusion becoming effective at a distance comparable to the characteristic thickness of the solute boundary layer. The converging flow causes a solute pile-up forming a logarithmic concentration peak at the symmetry axis which might be an undesirable feature for crystal growth processes.Comment: 15 pages, 5 figure

Steady state representation of the homogeneous cooling state of a granular gas

The properties of a dilute granular gas in the homogeneous cooling state are mapped to those of a stationary state by means of a change in the time scale that does not involve any internal property of the system. The new representation is closely related with a general property of the granular temperature in the long time limit. The physical and practical implications of the mapping are discussed. In particular, simulation results obtained by the direct simulation Monte Carlo method applied to the scaled dynamics are reported. This includes ensemble averages and also the velocity autocorrelation function, as well as the self-diffusion coefficient obtained from the latter by means of the Green-Kubo representation. In all cases, the obtained results are compared with theoretical predictions

Cavitation inception of a van der Waals fluid at a sack-wall obstacle

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle and, depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon. Results obtained in this study strongly suggest that the viscous stress, interfacial contributions to the local pressure, and the Laplace pressure are relevant to the opening of a vapor cavity. This can be described by a generalization of Joseph's criterion that includes these contributions. A macroscopic investigation measuring mass flow rate behavior and discharge coefficient was also performed. As theoretically predicted, mass flow rate increases linearly with the square root of the pressure drop. However, when cavitation occurs, the mass flow growth rate is reduced and eventually it collapses into a choked flow state. In the cavitating regime, as theoretically predicted and experimentally verified, the discharge coefficient grows with the Nurick cavitation number

Travelling waves in pipe flow

A family of three-dimensional travelling waves for flow through a pipe of circular cross section is identified. The travelling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.Comment: 4 pages, 5 figure

CHIMERA: a wide-field, multi-colour, high-speed photometer at the prime focus of the Hale telescope

The Caltech HIgh-speed Multi-colour camERA (CHIMERA) is a new instrument that has been developed for use at the prime focus of the Hale 200-inch telescope. Simultaneous optical imaging in two bands is enabled by a dichroic beam splitter centred at 567 nm, with Sloan u′ and g′ bands available on the blue arm and Sloan r′, i′ and z_s bands available on the red arm. Additional narrow-band filters will also become available as required. An electron multiplying CCD (EMCCD) detector is employed for both optical channels, each capable of simultaneously delivering sub-electron effective read noise under multiplication gain and frame rates of up to 26 fps full frame (several 1000 fps windowed), over a fully corrected 5 × 5 arcmin field of view. CHIMERA was primarily developed to enable the characterization of the size distribution of sub-km Kuiper Belt Objects via stellar occultation, a science case that motivates the frame-rate, the simultaneous multi-colour imaging and the wide field of view of the instrument. In addition, it also has unique capability in the detection of faint near-Earth asteroids and will be used for the monitoring of short-duration transient and periodic sources, particularly those discovered by the intermediate Palomar Transient Factory (iPTF), and the upcoming Zwicky Transient Facility (ZTF)

Roughness-induced critical phenomena in a turbulent flow

I present empirical evidence that turbulent flows are closely analogous to critical phenomena, from a reanalysis of friction factor measurements in rough pipes. The data collapse found here corresponds to Widom scaling near critical points, and implies that a full understanding of turbulence requires explicit accounting for boundary roughness