An efficient and general numerical method to compute steady uniform vortices

Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced “IVI diagram” stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.     

Determination of Complex Small‐Molecule Structures Using Molecular Alignment Simulation

Correct structural assignment of small molecules and natural products is critical for drug discovery and organic chemistry. Anisotropy‐based NMR spectroscopy is a powerful tool for the structural assignment of organic molecules, but it relies on the utilization of a medium that disrupts the isotropic motion of molecules in organic solvents. Here, we establish a quantitative correlation between the atomic structure of the alignment medium, the molecular structure of the small molecule, and molecule‐specific anisotropic NMR parameters. The quantitative correlation uses an accurate three‐dimensional molecular alignment model that predicts residual dipolar couplings of small molecules aligned by poly(γ‐benzyl‐l ‐glutamate). The technique facilitates reliable determination of the correct stereoisomer and enables unequivocal, rapid determination of complex molecular structures from extremely sparse NMR data.     

Pure In‐Phase Heteronuclear Correlation NMR Experiments

A general NMR approach to provide pure in‐phase (PIP) multiplets in heteronuclear correlation experiments is described. The implementation of a zero‐quantum filter efficiently suppresses any unwanted anti‐phase contributions that usually distort the multiplet pattern of cross‐peaks and can hamper their analysis. The clean pattern obtained in PIP‐HSQMBC experiments is suitable for a direct extraction of coupling constants in resolved signals, for a peak‐fitting process from a reference signal, and for the application of the IPAP technique in non‐resolved multiplets.     

NMR chemical shifts of xenon in aqueous solutions of amphiphiles: A new probe of the hydrophobic environment

The chemical shift of elemental xenon in solution is sensitive to the environment. The shift arises from van der Waals interactions in most liquids, but an additional effect is present in aqueous media yielding a larger shift than expected. In water the shift is affected by the presence of low molecular weight amphiphiles, and its variation with composition can reveal the presence of hydrophobic hydration of the amphiphile. The results are similar to the conclusions drawn from other physical studies. Data are presented for aqueous solutions of methanol, ethanol, n-propanol, iso-propanol, tert-butanol, dimethylsulfoxide, p-dioxane, and acetonitrile.     

Cramér-von Mises type estimation of the regression parameter: The rank analogue

A point estimator based on minimization of the rank analogue of the Cramér-von Mises statistic is proposed for the slope parameter β in the simple linear regression model. The asymptotic distribution of the estimator is derived and its variance is compared to the asymptotic variances of several common estimators for β at various underlying distributions.     

On one-factorizations of compositions of graphs

Let G[H] denote the composition of the graphs G and H. If G can be decomposed into one-factors and two-factors, H can be decomposed into one-factors, and H is not the empty graph on an odd number of vertices, then G[H] can be decomposed into one-factors.     

Chemoenzymatic synthesis of prodigiosin analogues--exploring the substrate specificity of PigC

Analogues of prodigiosin, a tripyrrolic pigment produced by Serratia species with potent immunosuppressive and anticancer activities, have been produced by feeding synthetic analogues of the normal precursor MBC to mutants of Serratia sp. ATCC 39006 or to engineered strains of Escherichia coli; in this way it has been shown that the prodigiosin synthesising enzyme, PigC, has a relaxed substrate-specificity.     

Lipophilicity Modulations by Fluorination Correlate with Membrane Partitioning

Bioactive compounds generally need to cross membranes to arrive at their site of action. The octanol-water partition coefficient (lipophilicity, logP_OW) has proven to be an excellent proxy for membrane permeability. In modern drug discovery, logP_OW and bioactivity are optimized simultaneously, for which fluorination is one of the relevant strategies. The question arises as to which extent the often subtle logP modifications resulting from different aliphatic fluorine-motif introductions also lead to concomitant membrane permeability changes, given the difference in molecular environment between octanol and (anisotropic) membranes. It was found that for a given compound class, there is excellent correlation between logP_OW values with the corresponding membrane molar partitioning coefficients (logK_p); a study enabled by novel solid-state ¹⁹F NMR MAS methodology using lipid vesicles. Our results show that the factors that cause modulation of octanol-water partition coefficients similarly affect membrane permeability.