Solution-Based,Anion-Doping of Li4Ti5O12 Nanoflowers for Lithium-Ion Battery Applications

Solution-based, anionic doping represents a convenient strategy with which to improve upon the conductivity of candidate anode materials such as Li₄Ti₅O₁₂ (LTO). As such, novel synthetic hydrothermally-inspired protocols have primarily been devised herein, aimed at the large-scale production of unique halogen-doped, micron-scale, three-dimensional, hierarchical LTO flower-like motifs. Although fluorine (F) doping has been explored, the use of chlorine (Cl) dopants is the primary focus here. Several experimental variables, such as dopant amount, lithium hydroxide concentration, and titanium butoxide purity, were probed and perfected. Furthermore, the Cl doping process did not damage the intrinsic LTO morphology. The analysis, based on interpreting a compilation of SEM, XRD, XPS, and TEM-EDS results, was used to determine an optimized dopant concentration of Cl. Electrochemical tests demonstrated an increased capacity via cycling of 12 % for a Cl-doped sample as compared with pristine LTO. Moreover, the Cl-doped LTO sample described in this study exhibited the highest discharge capacity yet reported at an observed rate of 2C for this material at 143mAh g⁻¹. Overall, these data suggest that the Cl dopant likely enhances not only the ion transport capabilities, but also the overall electrical conductivity of our as-prepared structures. To help explain these favorable findings, theoretical DFT calculations were used to postulate that the electronic conductivity and Li diffusion were likely improved by the presence of increased Ti³⁺ ion concentration coupled with widening of the Li migration channel.     

Crystal structures of two isostructural compounds: a second polymorph of dipotassium hydrogen citrate,K2HC6H5O7, and potassium rubidium hydrogen citrate,KRbHC6H5O7

The crystal structures of a new polymorph of dipotassium hydrogen citrate, 2K⁺·HC₆H₅O₇^2?, and potassium rubidium hydrogen citrate, K⁺·Rb⁺·HC₆H₅O₇^2?, have been solved and refined using laboratory powder X‐ray diffraction and optimized using density functional techniques. In the new polymorph of the dipotassium salt, KO₇ and KO₈ coordination polyhedra share corners and edges to form a three‐dimensional framework with channels parallel to the a axis and [111]. The hydrophobic methylene groups face each other in the channels. The un‐ionized carboxylic acid group forms a strong charge‐assisted hydrogen bond to the central ionized carboxylate group. The hydroxy group forms an intermolecular hydrogen bond to a different central carboxylate group. In the potassium rubidium salt, the K⁺ and Rb⁺ cations are disordered over two sites, in approximately 0.72:0.28 and 0.28:0.72 ratios. KO₈ and RbO₉ coordination polyhedra share corners and edges to form a three‐dimensional framework with channels parallel to the a axis. The un‐ionized carboxylic acid group forms a strong charge‐assisted hydrogen bond to an ionized carboxylate group. The hydroxy group forms an intermolecular hydrogen bond to the central carboxylate group. Density functional theory (DFT) calculations on the ordered cation structures suggest that interchange of K⁺ and Rb⁺ at the two cation sites changes the energy insignificantly.     

Corrections to Lee's visibility polygon algorithm

We present a modification and extension of the (linear time) visibility polygon algorithm of Lee. The algorithm computes the visibility polygon of a simple polygon from a viewpoint that is either interior to the polygon, or in its blocked exterior (the cases of viewpoints on the boundary or in the free exterior being simple extensions of the interior case). We show by example that the original algorithm by Lee, and a more complex algorithm by El Gindy and Avis, can fail for polygons that wind sufficiently. We present a second version of the algorithm, which does not extend to the blocked exterior case.This work was partially supported by grants from the Central Research Fund of the University of Alberta and the Natural Sciences and Engineering Research Council of Canada.     

Symmetric inertial-confinement-fusion-capsule implosions in a double-z-pinch-driven hohlraum

An inertial-confinement-fusion (ICF) concept using two 60-MA Z pinches to drive a cylindrical hohlraum to 220 eV has been recently proposed. The first capsule implosions relevant to this concept have been performed at the same physical scale with a lower 20-MA current, yielding a 70+/-5 eV capsule drive. The capsule shell shape implies a polar radiation symmetry, the first high-accuracy measurement of this type in a pulsed-power-driven ICF configuration, within a factor of 1.6-4 of that required for scaling to ignition. The convergence ratio of 14-21 is to date the highest in any pulsed-power ICF system.     

Dynamics of Simple Balancing Models with Time-Delayed Switching Feedback Control

Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the state of the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits originate in various discontinuity-induced bifurcations. We also show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.     

A base-matrix lemma for sets of rationals modulo nowhere dense sets

We study some properties of the quotient forcing notions ${Q_{tr(I)} = \wp(2^{< \omega})/tr(I)}$ and P _I ?= B(2 ^ω )/I in two special cases: when I is the σ-ideal of meager sets or the σ-ideal of null sets on 2 ^ω . We show that the remainder forcing R _I =?Q _tr(I)/P _I is σ-closed in these cases. We also study the cardinal invariant of the continuum ${\mathfrak{h}_{\mathbb{Q}}}$ , the distributivity number of the quotient ${Dense(\mathbb{Q})/nwd}$ , in order to show that ${\wp(\mathbb{Q})/nwd}$ collapses ${\mathfrak{c}}$ to ${\mathfrak{h}_{\mathbb{Q}}}$ , thus answering a question addressed in Balcar et?al. (Fundamenta Mathematicae 183:59–80, 2004).     

A note on a boundary-layer collision on a rotating sphere

A recent study of the unsteady boundary layer near the equator of a spinning sphere provided strong numerical evidence that the solution develops a singularity a finite time after the motion is initiated. In this paper we reformulate and complete the asymptotic structure proposed to describe this singularity. It is then self-consistent and provides convincing evidence of the accuracy of the computations and of the existence of the singularity.

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Zusammenfassung Eine neuere Untersuchung über die nicht-stationäre Grenzschicht nahe am Äquator einer rotierenden Kugel ergab starke numerische Evidenz für das Auftreten einer Singularität in der Lösung nach einer endlichen Zeit, vom Beginn der Bewegung gerechnet. In dieser Arbeit wird die asymptotische Struktur zur Beschreibung der Singularität neu formuliert und ergänzt. Sie wird selbstkonsistent und gibt ein wichtiges Zeugnis für die Genauigkeit der Berechnungen und für die Existenz der Singularität.

     

Ein in der reinen Zahlentheorie unbeweisbarer Satz über endliche Folgen von natürlichen Zahlen

Ohne Zusammenfassung     

Not All Fluorescent Nanodiamonds Are Created Equal: A Comparative Study

Fluorescent nanodiamonds (FNDs) are vital to many emerging nanotechnological applications, from bioimaging and sensing to quantum nanophotonics. Yet, understanding and engineering the properties of fluorescent defects in nanodiamonds remain challenging. The most comprehensive study to date is presented, of the optical and physical properties of five different nanodiamond samples, in which fluorescent nitrogen‐vacancy (NV) centers are created using different fabrication techniques. The FNDs' fluorescence spectra, lifetime, and spin relaxation time (T₁) are investigated via single‐particle confocal fluorescence microscopy and in ensemble measurements in solution (T₁ excepted). Particle sizes and shapes are determined using scanning electron microscopy and correlated with the optical results. Statistical tests are used to explore correlations between the properties of individual particles and also analyze average results to directly compare different fabrication techniques. Spectral unmixing is used to quantify the relative NV charge‐state (NV^? and NV⁰) contributions to the overall fluorescence. A strong variation is found and quantified in the properties of individual particles within all analyzed samples and significant differences between the different particle types. This study is an important contribution toward understanding the properties of NV centers in nanodiamonds. It motivates new approaches to the improved engineering of NV‐containing nanodiamonds for future applications.     

Measure theory and weak König's lemma

We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive on open sets.The research of both authors was partially supported by NSF Grant DMS-8701481.