Measurements of single spherical particle trajectories with lateral migration in a slit with one porous wall under laminar flow conditions

Lateral migration of spherical, neutrally buoyant particles moving in Poiseuille flow was measured in a slit with a porous membrane at one wall. Neutrally buoyant particles with diameters of 226 μm were injected into 22% glycerol-water solution flowing vertically in a slit channel (1.6 × 50 × 152 mm). The particles were illuminated with a strobe at 25 flashes/sec and photographed with a 4 × 5 camera under dark field conditions. Measured particle trajectories are compared with theoretically predicted trajectories based on Altena and Belfort's (1984) model. The theoretical trajectories are within the limits of error in the measured trajectories. By confirming the Altena and Belfort (1984) model within the range of experimental conditions tested here, inertial interactions should be included when modeling membrane fouling of dilute suspensions (Belfort et al. 1982).     

Maximal amplitudes of hyperelliptic solutions of the derivative nonlinear Schrödinger equation

A simple formula is proven for an upper bound for amplitudes of hyperelliptic (finite-gap or N-phase) solutions of the derivative nonlinear Schrödinger equation. The upper bound is sharp, viz, it is attained for some initial conditions. The method used to prove the upper bound is the same method, with necessary modifications, used to prove the corresponding bound for solutions of the focusing NLS equation (Wright OC, III. Sharp upper bound for amplitudes of hyperelliptic solutions of the focusing nonlinear Schrödinger equation. Nonlinearity. 2019;32:1929-1966).     

Detection of neutral products formed during excimer laser ablation of polyimide by UV and VUV laser photoionization/mass spectrometry

Some of the neutral species which are produced in the laser ablation of polyimide have been characterized using multiphoton ionization/time of flight mass spectrometry. Three different wavelengths (193 nm, 157 nm, and 118 nm) have been used in an attempt to effect soft ionization of the products formed during or after the initial laser ablation of the polymer. Neutral photo-ablation products detected using this scheme range from atomic to high molecular weight species which, depending on the probe wavelength, include pure carbon clusters as well as a broad distribution of heteroatom containing clusters. However, there is virtually no overlap in the mass spectra recorded at each probe wavelength. When probing with 193 nm, marked changes are observed in the mass spectra as a function of the probe flux used. At moderate fluxes, pure carbon clusters (fullerenes) are observed. The identification of a large distribution of species other than pure carbon clusters is in dramatic contrast to the recent observation [W.R. Creasy, J.T. Brenna: Chem. Phys. 126, 453 (1988)] of the positively charged ionic species produced, which are solely carbon clusters. These results suggest that the neutral and ionic products observed after ablation of the polymer are due to both condensation of the atomic and molecular fragments which form during the ablation laser pulse and nascent polymer fragments. Various implications of this result for the unambiguous determination of the true ablation product distribution are discussed.     

A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval

We examine the entropic measure, recently constructed by von Renesse and Sturm, a measure over the metric space of probability measures on the unit interval equipped with the 2-Wasserstein distance. We show that equipped with this measure, Wasserstein space over the interval does not admit generalized Ricci lower bounds in the entropic displacement convexity sense of Lott–Villani–Sturm. We discuss why this is contrary to what one might expect from heuristic considerations.     

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Doppler angle and flow velocity mapping by combined Doppler shift and Doppler bandwidth measurements in optical Doppler tomography

Accurate estimation of flow velocity requires measurement of Doppler angle, which is not available in general clinical applications. We describe a novel method of direct Doppler angle and flow velocity mapping that uses a conventional single-beam optical Doppler tomography system. The Doppler angle is estimated by combination of Doppler shift and Doppler bandwidth measurements, and flow velocity is calculated from the Doppler shift and the estimated Doppler angle. In vivo study of lip microvascularization demonstrates that this method is capable of providing both flow speed and flow direction information.     

A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds

We define a notion of renormalized volume of an asymptotically hyperbolic manifold. Moreover, we prove a sharp volume comparison theorem for metrics with scalar curvature at least ?6. Finally, we show that the inequality is strict unless the metric is isometric to one of the Anti-deSitter–Schwarzschild metrics.     

How far can a sodium ion travel within a lipid bilayer?

Analogues of a synthetic ion channel made from a helical peptide were used to study the mechanism of cation translocation within bilayer membranes. Derivatives bearing two, three, four, and six crown ethers used as ion relays were synthesized, and their transport abilities across lipid bilayers were measured. The results showed that the maximum distance a sodium ion is permitted to travel between two binding sites within a lipid bilayer environment is 11 ?.