Statistical properties of aggregation with injection

We study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For one-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are continuously injected. The steady-state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension. The response of the system to a perturbation (i.e., relaxation) is characterized by either a power law decay (t ^– ,1) or a compressed exponential decay [exp(–t ),>1].     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Correlated atomic force microscopy and fluorescence lifetime imaging of live bacterial cells

We report on imaging living bacterial cells by using a correlated tapping-mode atomic force microscopy (AFM) and confocal fluorescence lifetime imaging microscopy (FLIM). For optimal imaging of Gram-negative Shewanella oneidensis MR-1 cells, we explored different methods of bacterial sample preparation, such as spreading the cells on poly-L-lysine coated surfaces or agarose gel coated surfaces. We have found that the agarose gel containing 99% ammonium acetate buffer can provide sufficient local aqueous environment for single bacterial cells. Furthermore, the cell surface topography can be characterized by tapping-mode in-air AFM imaging for the single bacterial cells that are partially embedded. Using in-air rather than under-water AFM imaging of the living cells significantly enhanced the contrast and signal-to-noise ratio of the AFM images. Near-field AFM-tip-enhanced fluorescence lifetime imaging (AFM-FLIM) holds high promise on obtaining fluorescence images beyond optical diffraction limited spatial resolution. We have previously demonstrated near-field AFM-FLIM imaging of polymer beads beyond diffraction limited spatial resolution. Here, as the first step of applying AFM-FLIM on imaging bacterial living cells, we demonstrated a correlated and consecutive AFM topographic imaging, fluorescence intensity imaging, and FLIM imaging of living bacterial cells to characterize cell polarity.     

Electron-stimulated production of molecular hydrogen at the interfaces of amorphous solid water films on Pt(111)

The electron-stimulated production of molecular hydrogen (D(2), HD, and H(2)) from amorphous solid water (ASW) deposited on Pt(111) is investigated. Experiments with isotopically layered films of H(2)O and D(2)O are used to profile the spatial distribution of the electron-stimulated reactions leading to hydrogen within the water films. The molecular hydrogen yield has two components that have distinct reaction kinetics due to reactions that occur at the ASW/Pt interface and the ASW/vacuum interface, but not in the bulk. However, the molecular hydrogen yield as a function of the ASW film thickness in both pure and isotopically layered films indicates that the energy for the reactions is absorbed in the bulk of the films and electronic excitations migrate to the interfaces where they drive the reactions.     

Cup and cap products in intersection (co)homology

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincaré duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.     

Nevanlinna–Pick interpolation on distinguished varieties in the bidisk

This article treats Nevanlinna–Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.     

On the Osipov–Pickup–Dunmur chirality index: why pseudoscalar functions are generally unsuitable to quantify chirality

The applicability of pseudoscalar functions, in general, and of the Osipov–Pickup–Dunmur chirality index, in particular, as consistent chirality measures is discussed. It is shown that due to the presence of chiral zeros these functions are unsuited to measure the chirality of objects described by more than two independent parameters.     

A Two-Step Synthesis of the “Queen Substance” of the Honey Bee

A synthesis of the “queen substance” was accomplished in two steps from readily available starting materials. The key step was a novel one-pot reduction of 7-oxooctanoic acid to 7-oxooctanal followed by condensation with malonic acid.     

Thermal measurements using ultrasonic acoustical pyrometry

Reflections from geometric discontinuities can be used with ultrasonic energy to predict the temperature of an interface where classical temperature measurement techniques are impractical because of physical access limitations or harsh environmental conditions. Additionally, these same ultrasonic measurements can be used with inversion methods commonly applied to ill-posed heat transfer problems to increase the accuracy of the measurement of surface temperature or heat flux at the surface of interest. Both methods for determining surface temperature are presented, along with a comparison of results both from a verification example and using data gathered in a field test of the methods. The results obtained with these two methods are shown to be in good agreement with an empirical relationship used in the design of large caliber guns.