Mixing dependency lengths from sequences of different length is a common practice in language research. However, the empirical distribution of dependency lengths of sentences of the same length differs from that of sentences of varying length. The distribution of dependency lengths depends on sentence length for real sentences and also under the null hypothesis that dependencies connect vertice...

The method of matched asymptotic expansions, which has been used in previous studies of steady natural convection flow, is extended here to transient natural convection flow at high Prandtl number (Pr). Second-order expansion solutions, valid for large Prandtl numbers, are presented for the transient natural convection flow near a vertical surface which undergoes a step change in temperature. T...

In the present study, conjugate heat transfer predictions are performed for forced convection and natural convection in a twodimensional, vertical channel attached with surface mounted obstacles and having a solid wall of considerable thickness. The Streamline Upwind Petrov-Galerkin (SUPG) Finite Element (FE) method with Cartesian frame work is used for solving the equations governing Newtonian...

Three{dimensional simulations of turbulent and fully compressible thermal convection in deep atmospheres are presented and analyzed in terms of velocity power spectra, mixing{length theory, and production of vorticity. Density contrasts across these convective layers are typically around 11. The uid model is that of an ideal gas with a constant thermal conductivity. The Piecewise-Parabolic Meth...

We prove a new upper bound on the vertical heat transport in Rayleigh-Bénard convection of the form c Ra 1 3 (lnRa) 2 3 under the assumption that the ratio of Prandtl number over Rayleigh number satisfies Pr Ra ≥ c0 where the non-dimensional constant c0 depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) Ra 1 3 bound (modulo logarithmic correction) ...

Complex hydrodynamic behavior of circulating fluidized beds makes their scale-up very complicated. In particular, large-scale lateral solids segregation causes a complex two-phase flow pattern which influences significantly their pe$ormance. Lateral solids segregation has been attributed to direct collisional interactions between particles as well as to interaction between gas-phase eddies and ...

We report on measurements of a two-dimensional (2D) dye concentration field in turbulent Rayleigh–Bénard (RB) convection using the planar laser-induced fluorescence technique. The measurements were made in a vertical plane near the sidewall of a rectangular convection cell filled with water and with the Rayleigh number Ra varying from 109 to 1010, all at a fixed Prandtl number Pr = 5.3 and Schm...

Using simulations of helically driven turbulence, it is shown that the ratio of kinetic to magnetic energy dissipation scales with the magnetic Prandtl number in power law fashion with an exponent of approximately 0.6. Over six orders of magnitude in the magnetic Prandtl number the magnetic field is found to be sustained by large-scale dynamo action of alphasquared type. This work extends a sim...