Aharonov-Bohm effect in a draining bathtub vortex

We study planar waves in a circulating, draining fluid flow, which: (i) exhibit an analogue of the Aharonov-Bohm (AB) effect in Quantum Mechanics; (ii) obey a Klein-Gordon equation on an ‘effective spacetime’ which resembles the Kerr spacetime of General Relativity; and (iii) may be observed in the laboratory using gravity waves in a shallow basin. We describe a modified AB effect which depends on two dimensionless parameters, associated with the circulation α and draining β rates; we call this the ‘αβ effect’. We show that the αβ effect is inherently asymmetric even in the low-frequency limit, and that it leads to novel interference patterns which carry the signature of both rotation and absorption.     

Nonparametric estimation of the anisotropic probability density of mixed variables

The problem of nonparametric estimation of the joint probability density of a vector of continuous and ordinal/nominal categorical random variables with bounded support is considered. There are numerous publications devoted to the cases of either continuous or categorical variables, and the curse of dimensionality and strong regularity assumptions are the two familiar issues in the literature. Mixed variables occur in practically all applications of the statistical science and, nonetheless, the literature devoted to the joint density estimation is practically next to none. This paper develops the theory of estimation of the density of mixed variables which is on par with results known for simpler settings. Specifically, a data-driven estimator is developed that adapts to unknown anisotropic smoothness of the joint density and, whenever the density depends on a smaller number of variables, performs a dimension reduction that implies the corresponding optimal rate of the mean integrated squared error (MISE) convergence. The results hold without traditional, in the density estimation literature, minimal regularity assumptions like differentiability or continuity of the density. The procedure of estimation is based on mimicking an oracle-estimator that knows the underlying density, and the main theoretical result is the oracle inequality which relates the MISEs of the estimator and the oracle-estimator. The proof is based on a new exponential inequality for Sobolev statistics which is of interest on its own merits.     

Stabilization and tracking control for a class of nonlinear systems

This paper discusses stabilization and tracking control using linear matrix inequalities for a class of systems with Lipschitz nonlinearities. A nonlinear state feedback stabilization control is proposed for systems containing a more general case of Lipschitz nonlinearity. The main objective of the present study is to provide, for multi-input multi-output nonlinear systems, a tracking control approach based on nonlinear state feedback, which guarantees global asymptotic output and state tracking with zero tracking error in the steady state. Further, the tracking control is formulated for optimal disturbance rejection, using $L_2$ gain reduction based performance criteria. The proposed methodologies are illustrated herein using two simulation examples of chaotic and unstable dynamical systems.     

Force coefficients and Strouhal numbers of three circular cylinders subjected to a cross-flow

In this paper, wind tunnel experiments were conducted to measure the mean force coefficients and Strouhal numbers for three circular cylinders of equal diameters in an equilateral-triangular arrangement when subjected to a cross-flow. These experiments were carried out at five subcritical Reynolds numbers ranging from 1.26 × 10⁴ to 6.08 × 10⁴. The pressure distributions on the surface of the cylinders were measured using pressure transducers. Furthermore, the hot-wire anemometer was employed to measure the vortex shedding frequencies behind each cylinder. Six spacing ratios (l/d) varying from 1.5 to 4 were investigated. It is observed that for l/d > 2, the upstream cylinder experiences a lower mean drag coefficient compared with the downstream cylinders. The minimum values of the drag coefficient for the downstream cylinders occur at l/d = 1.5 and l/d = 2, because there is no vortex shedding from the foregoing cylinders. Also, the value of the pressure coefficient behind the upstream cylinder reduces by increasing l/d. Moreover, by decreasing the value of l/d, the Strouhal number for the upstream cylinder increases. It can be concluded that the flow pattern and aerodynamic coefficients are basically dependent on l/d; in other words, decreasing l/d results in an increase in the effects of the flow interference between the cylinders.     

Encapsulation of conventional and unconventional water dimers by water-binding foldamers

Water-binding foldamers have been rarely studied. By orienting both H-bond donors and acceptors toward their interior, two pyridine-derived crescent-shaped folding oligoamides were found to be capable of trapping both conventional and unconventional water dimer clusters in their cavity (～2.5 ? radius). In the unconventional water dimer cluster, the two water molecules stay in contact via an unusual H-H interaction (2.25 ?) rather than the typical H-bond.     

Does Hydrogen‐Bonding Donation to Manganese(IV)–Oxo and Iron(IV)–Oxo Oxidants Affect the Oxygen‐Atom Transfer Ability? A Computational Study

Iron(IV)–oxo intermediates are involved in oxidations catalyzed by heme and nonheme iron enzymes, including the cytochromes P450. At the distal site of the heme in P450 Compound I (Fe^IV–oxo bound to porphyrin radical), the oxo group is involved in several hydrogen‐bonding interactions with the protein, but their role in catalysis is currently unknown. In this work, we investigate the effects of hydrogen bonding on the reactivity of high‐valent metal–oxo moiety in a nonheme iron biomimetic model complex with trigonal bipyramidal symmetry that has three hydrogen‐bond donors directed toward a metal(IV)–oxo group. We show these interactions lower the oxidative power of the oxidant in reactions with dehydroanthracene and cyclohexadiene dramatically as they decrease the strength of the O? H bond (BDE_OH) in the resulting metal(III)–hydroxo complex. Furthermore, the distal hydrogen‐bonding effects cause stereochemical repulsions with the approaching substrate and force a sideways attack rather than a more favorable attack from the top. The calculations, therefore, give important new insights into distal hydrogen bonding, and show that in biomimetic, and, by extension, enzymatic systems, the hydrogen bond may be important for proton‐relay mechanisms involved in the formation of the metal–oxo intermediates, but the enzyme pays the price for this by reduced hydrogen atom abstraction ability of the intermediate. Indeed, in nonheme iron enzymes, where no proton relay takes place, there generally is no donating hydrogen bond to the iron(IV)–oxo moiety.     

Characterizations and Electric Conductivities of Phosphorous Oxychloride-Treated Polymers Containing Methyl Vinyl Ketone

Abstract

Studies have been made on the characterizations and conductivities of poly(methyl vinyl ketone) (PMVK) and its copolymer with methyl methacrylate (poly(MVK-co-MMA)) after being reacted with phosphorus oxychloride (POCl₃). The POCl₃?treated polymers containing methyl vinyl ketone (MVK) were characterized by IR and UV spectroscopies to prove the structure of conjugated double bonds. The conductivities of all the MVK-containing polymers treated with POCl₃ were very low, ca. 10^?17 S/cm, in a vacuum regardless of the treatment time. The conductivities of the polymers when doped with iodine are in the range of the order of 10^?4 to 10^?6 S/cm. It was found that the conductivity of the POCl₃?treated copolymer is slightly lower than that of PMVK.     

Reverse Mathematics and parameter-free Transfer

Recently, conservative extensions of Peano and Heyting arithmetic in the spirit of Nelson's axiomatic approach to Nonstandard Analysis, have been proposed. In this paper, we study the Transfer axiom of Nonstandard Analysis restricted to formulas without parameters. Based on this axiom, we formulate a base theory for the Reverse Mathematics of Nonstandard Analysis and prove some natural reversals, and show that most of these equivalences do not hold in the absence of parameter-free Transfer.     

On transformations of constant depth propositional proofs

This paper studies the complexity of constant depth propositional proofs in the cedent and sequent calculus. We discuss the relationships between the size of tree-like proofs, the size of dag-like proofs, and the heights of proofs. The main result is to correct a proof construction in an earlier paper about transformations from proofs with polylogarithmic height and constantly many formulas per cedent.