The Prandtl number effect near the onset of Bénard convection in a porous medium

This note focuses on Kladias and Prasad's claim that the critical Rayleigh number for the onset of Bénard convection in an infinite horizontal porous layer increases as the Prandtl number decreases, and argues that the critical Rayleigh number (Ra_c) depends only on the Darcy number (Da), as linear stability analysis indicates. The two-dimensional steady-convection problem is then solved numerically to document the convection heat transfer effect of the Rayleigh number, Darcy number, Prandtl number, and porosity. The note concludes with an empirical correlation for the overall Nusselt number, which shows the effect of Prandtl number at above-critical Rayleigh numbers. The correlation is consistent with the corresponding correlation known for Bénard convection in a pure fluid.     

Anisotropic Mixed-Norm Hardy Spaces

We introduce and explore Hardy spaces defined by mixed Lebesgue norms and anisotropic dilations. We prove that the definitions of these spaces in terms of smooth, non-tangential, auxiliary, grand, and Poisson maximal operators coincide. We also study the relation between anisotropic mixed-norm Hardy spaces and mixed-norm Lebesgue spaces.     

Convective mass transfer across fluid interfaces in straight angular pores

Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated. This situation is relevant to a variety of mass transport process in porous media, including the fate of residual non-aqueous phase liquid ganglia and gas bubbles. The model incorporates the essential physics of capillarity and solute mass transfer by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid–fluid contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface shear (‘perfect-slip’) and infinite surface shear (‘no-slip’) at the fluid–fluid interface are considered. The governing equations for laminar flow within the corner filament and convective diffusion to or from the fluid–fluid interface are solved using finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance of corner filaments against recent numerical solutions by Patzek and Kristensen (J. Colloid Interface Sci 236, 305–317 2001). Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical equations appropriate for implementation in pore network models. Finally, a previously published “2D-slit” approximation to the problem at hand is checked and found to be in considerable error.     

Brownian dynamics simulations on the self-assembly behavior of AB hybrid dendritic-star copolymers

The micellization behavior of hybrid dendritic-star copolymers with solvophilic dendritic units is studied by means of Brownian dynamics simulations. The critical micelle concentration and the micelle size and shape are examined for different solvophobic/solvophilic ratios r as a function of the number of the dendritic and linear arms. Hybrid dendritic-star copolymers with one dendritic and up to three solvophobic linear branches form spherical micelles with preferential aggregation number. Those with two dendritic arms and three solvophobic branches form micelles with wide aggregation numbers only for small values of r. For hybrid dendritic-star copolymers with three dendritic arms and two or three solvophobic linear arms, micelles with wide aggregation numbers are also formed but for slightly higher values of r. Our results for the aggregation number are compared with existing results of other architectures obtained at the same temperature, and an inequality for the aggregation number is proposed.     

End‐to‐End Distances in Four‐Junction Polymers

The various end‐to‐end distances of four‐junction polymers are investigated. The sizes of the different kinds of equal length branches and the backbone of two different polymers, with either nine or eleven branches, are estimated by means of both renormalization‐group and MC calculations. The comparisons of first‐order ε = 4 − d predictions with the MC results are satisfactory. The same trends are present in both techniques. The excluded‐volume interactions from additional branches further expand the various parts of the chains so that internal branches are larger than external ones. The branch ratios in the eleven‐branch case are expanded even more than the corresponding ratios of the nine‐branch polymer.

     

A Longitudinal Study Revisiting the Notion of Early Number Sense: Algebraic Arithmetic AS a Catalyst for Number Sense Development

The aim of this study was to propose a new conceptualization of early number sense. Six-year-old students’ (n = 204) number sense was tracked from the beginning of Grade 1 through the beginning of Grade 2. Data analysis suggested that elementary arithmetic, conventional arithmetic, and algebraic arithmetic contributed to the latent construct early number sense, and the invariance of the model over time was validated empirically. Algebraic arithmetic represents the dimension of early number sense that moves beyond conventional arithmetic and encompasses an abstract understanding of the relations between numbers. A parallel process growth model showed that the three components of number sense adopt a linear growth rate. A structural model showed that the growth rate of the algebraic arithmetic component has a direct effect on the growth rate of conventional arithmetic, and subsequently the growth rate of conventional arithmetic predicts the growth rate of elementary arithmetic.     

Stochastic metallic-glass cellular structures exhibiting benchmark strength

By identifying the key characteristic "structural scales" that dictate the resistance of a porous metallic glass against buckling and fracture, stochastic highly porous metallic-glass structures are designed capable of yielding plastically and inheriting the high plastic yield strength of the amorphous metal. The strengths attainable by the present foams appear to equal or exceed those by highly engineered metal foams such as Ti-6Al-4V or ferrous-metal foams at comparable levels of porosity, placing the present metallic-glass foams among the strongest foams known to date.     

X-ray and NMR studies on the rotational isomerism about the C(5)-C(6) bond of 6-substituted methyl 2,3,4,-tri-O-acetyl-6-X-α-D-glucopyranoside derivatives

The rotamers about the C(5)–C(6) bond of a series of 2,3,4-tri-O-acetyl-6-X--D-glucopyranozide derivatives resulting by substitution at C(6) or O(6) have been studies with¹H-NMR spectroscopy (400 MHz) and X-ray structure analysis. The methyl 2,3,4-tri-O-acetyl-6-O-triphenylmethyl--D-glucopyranoside and the N-(I-O-methyl-2,3,4-tri-O-acetyl--D-glucopyranose-6-yl)-pyridinium nitrate crystallize in the P2₁ space group with =14.940(1),b=11.232(1),c=9.0773(7), and =94.480(7) anda=7.670(1),b=15.384(3),c=9.624(1) and =104.90(1), respectively; the methyl 2,3,4-tri-O-acetyl-6-O-nitro--D-glucopyranoside and methyl 2,3,4-tri-O-acetyl-6-O-deoxy-6-iodo--D-glucopyrano-side crystallize in the P2₁2₁2₁ space group witha=5.630(1),b=14.360(1) andc=22.388(3), anda=5.556(1),b=14.303(6) andc=21.963(6), respectively.     

Kinetic discrimination of sequence-specific DNA-drug binding measured by surface plasmon resonance imaging and comparison to solution-phase measurements

We demonstrate the use of surface plasmon resonance (SPR) imaging for direct detection of small-molecule binding to surface-bound DNA probes. Using a carefully designed array surface, we quantitatively discriminate between the interactions of a model drug with different immobilized DNA binding sites. Specifically, we measure the association and dissociation intercalation rates of actinomycin-D (ACTD) to and from double-stranded 5'-TGCT-3' and 5'-GGCA-3' binding sites. The rates measured provide mechanistic information about the DNA-ACTD interaction; ACTD initially binds nonspecifically to DNA but exerts its activity by dissociating slowly from strong affinity sites. We observe a slow dissociation time of kd-1 = 3300 +/- 100 s for ACTD bound to the strong affinity site 5'-TGCT-3' and a much faster dissociation time (210 +/- 15 s) for ACTD bound weakly to the site 5'-GGCA-3'. These dissociation rates, which differ by an order of magnitude, determine the binding affinity for each site (8.8 x 10(6) and 1.0 x 10(6) M(-1), respectively). We assess the effect the surface environment has on these biosensor measurements by determining kinetic and thermodynamic constants for the same DNA-ACTD interactions in solution. The surface suppresses binding affinities approximately 4-fold for both binding sites. This suppression suggests a barrier to DNA-drug association; ACTD binding to duplex DNA is approximately 100 times slower on the surface than in solution.