Supramolecular Self-Sorting Networks using Hydrogen-Bonding Motifs

A current objective in supramolecular chemistry is to mimic the transitions between complex self-sorted systems that represent a hallmark of regulatory function in nature. In this work, a self-sorting network, comprising linear hydrogen motifs, was created. Selecting six hydrogen-bonding motifs capable of both high-fidelity and promiscuous molecular recognition gave rise to a complex self-sorting system, which included motifs capable of both narcissistic and social self-sorting. Examination of the interactions between individual components, experimentally and computationally, provided a rationale for the product distribution during each phase of a cascade. This reasoning holds through up to five sequential additions of six building blocks, resulting in the construction of a biomimetic network in which the presence or absence of different components provides multiple unique pathways to distinct self-sorted configurations.     

Oracles and Query Lower Bounds in Generalised Probabilistic Theories

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality (roughly, no signalling from the future), purification (each mixed state arises as the marginal of a pure state of a larger system), strong symmetry (existence of a rich set of nontrivial reversible transformations), and informationally consistent composition (roughly: the information capacity of a composite system is the sum of the capacities of its constituent subsystems). Sorkin has defined a hierarchy of conceivable interference behaviours, where the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. Given our oracle model, we show that if a classical computer requires at least n queries to solve a learning problem, because fewer queries provide no information about the solution, then the corresponding “no-information” lower bound in theories lying at the kth level of Sorkin’s hierarchy is \(\lceil {n/k}\rceil \). This lower bound leaves open the possibility that quantum oracles are less powerful than general probabilistic oracles, although it is not known whether the lower bound is achievable in general. Hence searches for higher-order interference are not only foundationally motivated, but constitute a search for a computational resource that might have power beyond that offered by quantum computation.     

Hydrodynamic attraction of swimming microorganisms by surfaces

Cells swimming in confined environments are attracted by surfaces. We measure the steady-state distribution of smooth-swimming bacteria (Escherichia coli) between two glass plates. In agreement with earlier studies, we find a strong increase of the cell concentration at the boundaries. We demonstrate theoretically that hydrodynamic interactions of the swimming cells with solid surfaces lead to their reorientation in the direction parallel to the surfaces, as well as their attraction by the closest wall. A model is derived for the steady-state distribution of swimming cells, which compares favorably with our measurements. We exploit our data to estimate the flagellar propulsive force in swimming E. coli.     

A computational study of x-ray emission from high-Z x-ray sources on the National Ignition Facility laser

We have begun to use 350–500 kJ of 1/3-micron laser light from the National Ignition Facility (NIF) laser to create millimeter-scale, bright multi-keV x-ray sources. In the first set of shots we achieved 15%–18% x-ray conversion efficiency into Xe M-shell (∼1.5–2.5 keV), Ar K-shell (∼3 keV) and Xe L-shell (∼4–5.5 keV) emission (Fournier et al., Phys. Plasmas 17, 082701, 2010), in good agreement with the emission modeled using a 2D radiation-hydrodynamics code incorporating a modern Detailed Configuration Accounting atomic model in non-LTE (Colvin et al., Phys. Plasmas, 17, 073111, 2010). In this paper we first briefly review details of the computational model and comparisons of the simulations with the Ar/Xe NIF data. We then discuss a computational study showing sensitivity of the x-ray emission to various beam illumination details (beam configuration, pointing, peak power, pulse shape, etc.) and target parameters (size, initial density, etc.), and finally make some predictions of how the x-ray conversion efficiency expected from NIF shots scales with atomic number of the emitting plasma.     

Synthesis and crystal structure of cyclopentadienyl(1,4-dimethyl-1,4-dibora-2,5-cyclohexadiene)cobalt

The synthesis of the organometallic derivative cyclopentadienyl(1,4-dimethyl-1,4-diboracyclohexa-2,5-diene)cobalt is described. This complex, [(CH₃BC₄H₄BCH₃)Co(η-C₅H₅)], forms red-oranged monoclinic crystals, space group P2₁/a with Z = 4 in a unit cell of dimensions a 11.362(7), b, 7.467(7), c 13.290(12) Å, β 103.76(6)°. The structure has been elucidated by heavy-atom methods from 1732 reflections (I > 2σ(I)) measured on a Syntex P2₁ four-circle diffractometer and refined to R = 0.055. In the coordination complex all six atoms of the cyclohexadiene ring are within bonding distance of the metal atom, but the two boron atoms bend away from the metal atom, and the ring elongates slightly in the B---B direction. As a standard of comparison the known geometry of the free ligand [1,4-difluoro-1,4-dibora-2,3,5,6-tetramethylcyclohexa-2,5-diene] is used. The terminal methyl groups on the boron atoms, by contrast, bend slightly back towards the metal atom. The cyclopentadienyl ring remains planar but is positionally disordered.     

Solution to torsion relations in finsler-spacetime tangent bundle

In the Finsler-spacetime tangent bundle, a simple solution is determined to the torsion relations that were obtained previously to maintain (1) compatibility with Cartan's theory of Finsler space, (2) the almost complex structure, and (3) the vanishing of the covariant derivative of the almost complex structure.