Surface diffusion flow near spheres

We consider closed immersed hypersurfaces evolving by surface diffusion flow, and perform an analysis based on local and global integral estimates. First we show that a properly immersed stationary (ΔH ≡ 0) hypersurface in ${\mathbb{R}^3}$ or ${\mathbb{R}^4}$ with restricted growth of the curvature at infinity and small total tracefree curvature must be an embedded union of umbilic hypersurfaces. Then we prove for surfaces that if the L ² norm of the tracefree curvature is globally initially small it is monotonic nonincreasing along the flow. We also derive pointwise estimates for all derivatives of the curvature assuming that its L ² norm is locally small. Using these results we show that if a singularity develops the curvature must concentrate in a definite manner, and prove that a blowup under suitable conditions converges to a nonumbilic embedded stationary surface. We obtain our main result as a consequence: the surface diffusion flow of a surface initially close to a sphere in L ² is a family of embeddings, exists for all time, and exponentially converges to a round sphere.     

Amine-directed intramolecular hydroacylation of alkenes and alkynes

Medium-ring heterocycles are prepared via an amine-directed, rhodium(I)-catalyzed intramolecular hydroacylation. The presence of an allyl substituent on the amine accelerates the reaction and increases product yields.     

Chemical potential perturbation: extension of the method to lattice sum treatment of intermolecular potentials

The recently developed chemical potential perturbation (CPP) method [S. G. Moore and D. R. Wheeler, J. Chem. Phys. 134, 114514 (2011)] is extended to the lattice (Ewald) sum treatment of intermolecular potentials. The CPP method predicts chemical potentials for a range of composition points using the local (position-dependent) pressure tensor of an inhomogeneous system. When computing the local pressure tensor, one can use the Irving-Kirkwood (IK) or Harasima (H) contours of distributing the pressure. We compare these two contours and show that for a planar interface, the homogeneous pressure and resulting chemical potential can be approximated with the CPP method using either the IK or the H contour, though with the lattice sum method the H contour has much greater computational efficiency. The proposed methods are validated by calculating the chemical potentials of the Lennard-Jones fluid and extended simple point-charge (SPC/E) water, and results show a high level of agreement with respective equations of state.     

Chiral separations of transition metal complexes using capillary zone electrophoresis.

Several buffer additives that may facilitate chiral separation for optically active transition metal (TM) systems are investigated using capillary zone electrophoresis. The TM complexes evaluated exhibit considerable heterogeneity with respect to total complex charge (0 to 4+), ligand type, and identity of the central metal including Ru2+, Ni2+, Cr3+, and Co3+, threo-D[+]-Isocitrate, potassium antimonyl-d-tartrate and dibenzoyl-L-tartrate are identified as the most efficient chiral selectors. Interestingly, TM complexes exhibiting a (3+) total complex charge exhibit a reversal of enantiomer elution order versus all other complexes when separated using the tartrate additives. Operating parameters including pH, temperature, and capillary length are discussed, and chiral separations of complex mixtures are demonstrated.     

Unexpected nitrosyl-group bending in six-coordinate [M(NO)](6) sigma-bonded aryl(iron) and -(ruthenium) porphyrins.

The six-coordinate nitrosyl sigma-bonded aryl(iron) and -(ruthenium) porphyrin complexes (OEP)Fe(NO)(p-C(6)H(4)F) and (OEP)Ru(NO)(p-C(6)H(4)F) (OEP = octaethylporphyrinato dianion) have been synthesized and characterized. Single-crystal X-ray structure determinations reveal an unprecedented bending and tilting of the MNO group for both [MNO](6) species as well as significant lengthening of trans axial bond distances. In (OEP)Fe(NO)(p-C(6)H(4)F) the Fe-N-O angle is 157.4(2) degrees, the nitrosyl nitrogen atom is tilted off of the normal to the heme plane by 9.2 degrees, Fe-N(NO) = 1.728(2) A, and Fe-C(aryl) = 2.040(3) A. In (OEP)Ru(NO)(p-C(6)H(4)F) the Ru-N-O angle is 154.9(3) degrees, the nitrosyl nitrogen atom is tilted off of the heme normal by 10.8 degrees, Ru-N(NO) = 1.807(3) A, and Ru-C(aryl) = 2.111(3) A. We show that these structural features are intrinsic to the molecules and are imposed by the strongly sigma-donating aryl ligand trans to the nitrosyl. Density functional-based calculations reproduce the structural distortions observed in the parent (OEP)Fe(NO)(p-C(6)H(4)F) and, combined with the results of extended Hückel calculations, show that the observed bending and tilting of the FeNO group indeed represent a low-energy conformation. We have identified specific orbital interactions that favor the unexpected bending and tilting of the FeNO group. The aryl ligand also affects the Fe-NO pi-bonding as measured by infrared and (57)Fe M?ssbauer spectroscopies. The solid-state nitrosyl stretching frequencies for the iron complex (1791 cm(-)(1)) and the ruthenium complex (1773 cm(-)(1)) are significantly reduced compared to their respective [MNO](6) counterparts. The M?ssbauer data for (OEP)Fe(NO)(p-C(6)H(4)F) yield the quadrupole splitting parameter +0.57 mm/s and the isomer shift 0.14 mm/s at 4.2 K. The results of our study show, for the first time, that bent Fe-N-O linkages are possible in formally ferric nitrosyl porphyrins.     

Maze exploration and learning in C. elegans

The soil dwelling nematode, Caenorhabditis (C.) elegans, is a popular model system for studying behavioral plasticity. Noticeably absent from the C. elegans literature, however, are studies evaluating worm behavior in mazes. Here, we report the use of microfluidic mazes to investigate exploration and learning behaviors in wild-type C. elegans, as well as in the dopamine-poor mutant, cat-2. The key research findings include: (1)C. elegans worms are motivated to explore complex spatial environments with or without the presence of food/reward, (2) wild-type worms exhibit a greater tendency to explore relative to mutant worms, (3) both wild-type and mutant worms can learn to make unconditioned responses to food/reward, and (4) wild-type worms are significantly more likely to learn to make conditioned responses linking reward to location than mutant worms. These results introduce microfluidic mazes as a valuable new tool for biological behavioral analysis.     

Global Bifurcation of Rotating Vortex Patches

We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as the parameter tends to infinity, the minimum along the interface of the angular fluid velocity in the rotating frame becomes arbitrarily small. This is consistent with the conjectured existence [30, 38] of singular limiting patches with 90 corners at which the relative fluid velocity vanishes. For solutions close to the disk, we prove that there are “cat's-eyes”-type structures in the flow, and provide numerical evidence that these structures persist along the entire solution curves and are related to the formation of corners. We also show, for any rotating vortex patch, that the boundary is analytic as soon as it is sufficiently regular. © 2019 Wiley Periodicals, Inc.     

Resolution of a Classical Gravitational Second-Law Paradox

Sheehan and coworkers have claimed [D. P. Sheehan et al., Found. Phys. 30, 1227 (2000); 32, 441 (2002); D. P. Sheehan, in Quantum Limits to the Second Law, AIP Conference Proceedings 643 (American Institute of Physics, Melville, NY, 2002), p. 391] that a dilute gas trapped between an external shell and a gravitator can support a steady state in which energy flux by particles in one direction is balanced by energy flux by radiation in the opposite direction, and in which work can be extracted from an isothermal heat reservoir, thereby violating the second law of thermodynamics. In this paper, we identify a fundamental error in their simulation and analysis of their model system that vitiates their conclusions. We analyze a simpler, exactly soluble, three-dimensional model of a very dilute gas in a gravitational field between two thermal reservoirs, and show that their conclusions are not supported for the simple model. We show that their method of simulation, when applied to either the simple model or their more complex model under simpler conditions where the answers are known, leads to unphysical results. We also show that, when appropriate sampling is done, their model gives results in accord with the second law and detailed balance.