ALBERT

Notes: Based on a closed surface of triangles fitted to atomic coordinates determined crystallographically, Brune and Kim [Proc. Natl. Acad. Sci. USA 90, 3835–3839 (1993)] proposed a boundary-element Stokes-flow technique for ab initio computation of a translational diffusion coefficient and the rotational diffusion tensor Dr of globular proteins. They applied their approach to atomic coordinates for a tetragonal structure of hen egg-white lysozyme, and reported that computed values of a translational diffusion coefficient and Dr=tr(Dr)/3 agreed well with experiment. After establishing the identity between the infinite-dilution tracer diffusion coefficient of the protein macroion (D+ for lysozyme cation) and the "translational diffusion coefficient" computed by Brune and Kim, we adopt a somewhat different computational approach and show how convergence of D+ and Dr for tetragonal lysozyme depends on two computational parameters characterizing the fidelity of the geometric approximation to the protein surface and two others characterizing the accuracy of the Stokes-flow computations. We then compute D+ and Dr for lysozyme using atomic coordinates for the triclinic crystal structure, three structures determined by nuclear magnetic resonance spectroscopy in the liquid phase (presumably corresponding more closely to in vivo structures), the solvated tetragonal structure (with 108 water molecules) considered by Brune and Kim, and a "dry" version of the same structure. These computations show that D+ and Dr computed for all of the dry crystal structures are in excellent agreement with those for the liquid-phase conformations. Values of D+ and Dr computed for the solvated structure are lower, consistent with the larger volume and area of the corresponding polyhedral surface. We also show that several choices of the origin of the force system [discussed by Brenner, J. Colloid Interface Sci. 23, 407–436 (1967)] give rise to nearly identical translational diffusion coefficients. Finally, we show how to estimate the thickness of the "solvation shell" contributing to the hydrodynamic resistance of the protein cation, and use the binary Nernst–Hartley equation to then estimate the effective cation charge at the two pH values at which the binary diffusion coefficient has been accurately measured in recent interferometric experiments. © 2002 American Institute of Physics.

Notes: The effect of the viscosity–temperature relation, μ(T), on the onset of convection in a horizontal fluid layer is discussed. Linear analysis shows that, for aqueous glycerol solutions, the critical Rayleigh numbers (Racrit) obtained using the Arrhenius approximation, μA(T), are in excellent agreement with those employing the actual μ(T) data. The results for the exponential approximation μe(T) differ to an extent that depends on the glycerol mass fraction and the temperature difference (ΔT) between the plates. The error associated with use of μe(T), while small, is of the same order as, or larger than, the uncertainty in careful experiments. For the broad class of liquids for which μA(T) is an excellent approximation to μ, we have assessed the errors in Racrit associated with the widely used μe(T). As ΔT and the viscosity contrast increase, the values of Racrit deviate increasingly from those predicted using μA(T). Also, the relative error in Racrit is much smaller than the maximum relative error in the coefficients [involving μ(T) and its derivatives with respect to T] of the linear disturbance equations.

Notes: It is rigorously proved that the most critical small disturbances to a stratified viscous plane parallel shear flow between rigid horizontal boundaries must be either two-dimensional (2-D) transverse or longitudinal modes, and that there are no marginally stable flows for which truly 3-D disturbances are marginally stable. This allows the linear stability analysis to be restricted to (two classes of ) 2-D disturbances.

Notes: Two extensions of the classical proper orthogonal decomposition (POD) methodology exposited by Lumley for turbulent flows are presented. First, the extended POD (EPOD) can deal with flows lacking statistical stationarity by summing the velocity correlations of an ensemble of time series. Thus it reduces to the classical POD for a statistically stationary flow, and to the "snapshot'' of Sirovich for data from a single instant in each realization of an ensemble. Second, the EPOD can deal with flows having one or more length scales exceeding the spatial range over which simultaneous measurements can be made, by generating composite modes using nonsimultaneous, spatially overlapping data. Both new capabilities have been exercised by applying the EPOD to the streamwise velocity component measured by a cross-stream hot-wire rake in an anharmonically forced turbulent plane mixing layer that is not statistically stationary, and is statistically homogeneous in only one direction. It is discovered that as few as three one-dimensional modes are capable of capturing as much as 78% of the "action'' in data from ten wires in a cross-stream rake.

Notes: The onset of convective instability is investigated in a multicomponent fluid layer in which the density depends on N stratifying agencies with different diffusivities. The general equations required to determine the topology of the neutral curves and stability boundaries are given. We show that 1+2[(N−1)/2] (where [α] is the integer part of α) critical Rayleigh numbers are sometimes required to specify the linear stability criteria. This multivaluedness can be traced to the existence of disconnected neutral curves. The general theory is illustrated by a numerical example for the quintuply diffusive case (N=5).

Notes: The steady distributions of temperature and concentration in a reactive fluid adjacent to a catalytic wall are investigated. It is shown that for the mass action kinetics considered, the number of steady solutions is either one or three. Several simple sufficient criteria, as well as a slightly more complicated necessary and sufficient criterion, are given for the uniqueness of the steady solution. If the Lewis number Le (ratio of molecular and thermal diffusivities) is at least one, then a steady state that is unique is always stable with respect to small disturbances. For Le≥1, the high and low temperature steady states are stable when the number of steady states is three. When Le〈1, even a unique steady state can be unstable, and when there are three steady states, one, two, or three of them can be unstable. The Le≥1 and Le〈1 cases are further distinguished by the fact that oscillatory instability can occur for Le〈1 but not for Le≥1.