Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function Fincoh(q,t ) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function Cl(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

Finite Element Modeling of Shell Shape in the Freshwater Turtle Pseudemys concinna Reveals a Trade-Off between Mechanical Strength and Hydrodynamic Efficiency

Aquatic species can experience different selective pressures on morphology in different flow regimes. Species inhabiting lotic regimes often adapt to these conditions by evolving low-drag (i.e., streamlined) morphologies that reduce the likelihood of dislodgment or displacement. However, hydrodynamic factors are not the only selective pressures influencing organismal morphology and shapes well suited to flow conditions may compromise performance in other roles. We investigated the possibility of morphological trade-offs in the turtle Pseudemys concinna. Individuals living in lotic environments have flatter, more streamlined shells than those living in lentic environments; however, this flatter shape may also make the shells less capable of resisting predator-induced loads. We tested the idea that ‘‘lotic’’ shell shapes are weaker than ‘‘lentic’’ shell shapes, concomitantly examining effects of sex. Geometric morphometric data were used to transform an existing finite element shell model into a series of models corresponding to the shapes of individual turtles. Models were assigned identical material properties and loaded under identical conditions, and the stresses produced by a series of eight loads were extracted to describe the strength of the shells. ‘‘Lotic’’ shell shapes produced significantly higher stresses than ‘‘lentic’’ shell shapes, indicating that the former is weaker than the latter. Females had significantly stronger shell shapes than males, although these differences were less consistent than differences between flow regimes. We conclude that, despite the potential for many-to-one mapping of shell shape onto strength, P. concinna experiences a trade-off in shell shape between hydrodynamic and mechanical performance. This trade-off may be evident in many other turtle species or any other aquatic species that also depend on a shell for defense. However, evolution of body size may provide an avenue of escape from this trade-off in some cases, as changes in size can drastically affect mechanical performance while having little effect on hydrodynamic performance.

Hydrodynamic Characterization of Bile Salt Host-Guest Complexes by Pulsed Field Gradient NMR Spectroscopy

The work described herein is aimed at understanding primary and secondary aggregation of bile salt micelles and how micelles can perform chiral recognition of binapthyl analytes. Previous work with cholate and deoxycholate using micellar electrokinetic chromatography (MEKC) and nuclear magnetic resonance (NMR) has provided insightinto cholate and deoxycholate micelle formation, especially with respect to the critical micelle concentration (CMC). Chiral separations of the model analyte, 1,1â??-binaphthyl-2,2â??-diyl hydrogen phosphate (BNDHP), via cholate (C) and deoxycholate (DC) mediated MEKC separataions previously have shown the DC CMC to be 7-10 mM andthe cholate CMC at 14 mM at ph 12. A second model analyte,1,1â??-binaphthol (BN), was also previously investigated to probe micellar structure, but the MEKC data for this analyte implied a higher CMC, which may be interpreted as secondary aggregation. Thiswork extends the investigation of bile salts to include pulsed field gradient spin echo (PFGSE) NMR experiments being used to gain information about the size and degree of polydispersity of cholate and deoxycholate micelles. Concentrations of cholate below 10mM show a large variation in effective radius likely due to the existence of transient preliminary aggregates. The onset of the primary micelle shows a dramatic increase in effective radius of the micelle in cholate and deoxycholate. In the region of expectedsecondary aggregation a gradual increase of effective radius was observed with cholate; deoxycholate showed a persistent aggregate size in the secondary micelle region that is modulated by the presence of an analyte molecule. Effective radii of cholate anddeoxycholate (individually) were compared with and without R- and S-BNDHP in order to observe the effective radius difference of micelles with and without analyte present. The presence of S-BNDHP consistently resulted in a larger effective aggregate radius incholate and deoxycholate, confirming previous data of the S-BNDHP interacting more with the micelle than R-BNDHP. In total, various NMR techniques, like diffusion NMR can be used to gain a greater understanding of the bile salt micellization process and chiral resolution.

Added mass and wave radiation damping for flow-induced rotational vibrations of skinplates of hydraulic gates

One observed vibration mode for Tainter gate skinplates involves the bending of the skinplate about a horizontal nodal line. This vibration mode can be approximated as a streamwise rotational vibration about the horizontal nodal line. Such a streamwise rotational vibration of a Tainter gate skinplate must push away water from the portion of the skinplate rotating into the reservoir and draw water toward the gate over that portion of the skinplate receding from the reservoir. The induced pressure is termed the push-and-draw pressure. In the present paper, this push-and-draw pressure is analyzed using the potential theory developed for dissipative wave radiation problems. In the initial analysis, the usual circular-arc skinplate is replaced by a vertical, flat, rigid weir plate so that theoretical calculations can be undertaken. The theoretical push-and-draw pressure is used in the derivation of the non-dimensional equation of motion of the flow-induced rotational vibrations. Non-dimensionalization of the equation of motion permits the identification of the dimensionless equivalent added mass and the wave radiation damping coefficients. Free vibration tests of a vertical, flat, rigid weir plate model, both in air and in water, were performed to measure the equivalent added mass and the wave radiation damping coefficients. Experimental results compared favorably with the theoretical predictions, thus validating the theoretical analysis of the equivalent added mass and wave radiation damping coefficients as a prediction tool for flow-induced vibrations. Subsequently, the equation of motion of an inclined circular-arc skinplate was developed by incorporating a pressure correction coefficient, which permits empirical adaptation of the results from the hydrodynamic pressure analysis of the vertical, flat, rigid weir plate. Results from in-water free vibration tests on a 1/31-scale skinplate model of the Folsom Dam Tainter gate are used to demonstrate the utility of the equivalent added mass coefficient.

Biomechanics on the Half Shell: Functional Performance Influences Patterns of Morphological Variation in the Emydid Turtle carapace

This study uses the carapace of emydid turtles to address hypothesized differences between terrestrial and aquatic species. Geometric morphometrics are used to quantify shell shape, and performance is estimated for two shell functions: shell strength and hydrodynamics. Aquatic turtle shells differ in shape from terrestrial turtle shells and are characterized by lower frontal areas and presumably lower drag. Terrestrial turtle shells are stronger than those of aquatic turtles; many-to-one mapping of morphology to function does not entirely mitigate a functional trade-off between mechanical strength and hydrodynamic performance. Furthermore, areas of morphospace characterized by exceptionally poor performance in either of the functions are not occupied by any emydid species. Though aquatic and terrestrial species show no significant differences in the rate of morphological evolution, aquatic species show a higher lineage density, indicative of a greater amount of convergence in their evolutionary history. The techniques employed in this study, including the modeling of theoretical shapes to assess performance in unoccupied areas of morphospace, suggest a framework for future studies of morphological variation.

Polymerization of Styrene and Cyclization to Macrocyclic Polystyrene in a One-Pot, Two-Step Sequence

Dibrominated polystyrene (BrPStBr) was produced by atom transfer radical polymerization (ATRP) at 80 degrees C, using the bifunctional initiator benzal bromide to afford the telechelic precursor. The ATRP reaction was stopped around 40% monomer conversion and directly converted into an radical trap-assisted atom transfer radical coupling (RTA-ATRC) reaction by lowering the temperature to 50 degrees C, and adding the radical trap 2-methyl-2-nitrosopropane (MNP) along with additional catalyst, reducing agent, and ligand to match ATRC-type reaction conditions. In an attempt to induce intramolecular coupling, rather than solely intermolecular coupling and elongation, the total reaction volume was increased by the addition of varying amounts of THF. Cyclization, along with intermolecular coupling and elongation, occurred in all cases, with the extent of ring closure a function of the total reaction volume. The cyclic portion of the coupled product was found to have a (G) value around 0.8 by GPC analysis, consistent with the reduction in hydrodynamic volume of a cyclic polymer compared to its linear analog. Analysis of the sequence by H-1 NMR confirmed that propagation was suppressed nearly completely during the RTA-ATRC phase, with percent monomer conversion remaining constant after the ATRP phase. (C) 2013 Elsevier Ltd. All rights reserved.