Attenuation of ultrasound in milks and creams

Measurements of the attenuation of 1.5 to 7 MHz ultrasound in milks and creams, aqueous solutions of milk proteins and milk fat demonstrated that the attenuation due to the fat component was proportional to the fat concentration (at low volume fractions, less than 4%) and was caused by two effects: losses arising from its particulate nature and intrinsic attenuation (mass attenuation coefficient 1.1 cm² g⁻¹ at 7 MHz in pure milk fat). Comparison with theoretical equations showed that absorption by thermal conduction dominated the particulate losses and increased with decreasing fat globule size, over the range 1.5 to 7 MHz. This was confirmed by examining milks homogenized to different degrees. The losses in the non-fat components were mainly due to the protein components which also probably dominated the shape of the attenuation titration curves for skimmed milk, producing peaks in attenuation in the range pH 4–4.5 and about pH 11.3.     

Coherent anti-Stokes Raman scattering of slow light in a hollow planar periodically corrugated waveguide

Enhancement of coherent anti-Stokes Raman scattering (CARS) by molecular nitrogen in a hollow planar periodically corrugated waveguide is experimentally detected. The measured dependence of CARS efficiency on the thickness of the waveguide layer indicates that CARS enhancement under these conditions is at least partially due to the decrease in the group velocity of pump pulses around the photonic band gap.     

Resonant motion of a spherical pendulum

The weakly nonlinear, resonant response of a damped, spherical pendulum (length l, damping ratio δ, natural frequency ω₀) to the planar displacement εl cos ωt (ε ? 1) of its point of suspension is examined in a four-dimensional phase space in which the coordinates are slowly varying amplitudes of a sinusoidal motion. The loci of equilibrium points and the corresponding bifurcation points in this space are determined. The control parameters are $\text{α= 2δ/ε}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ and . If α < 0.441 there is a finite interval of v within which no stable equilibrium points exist. As v decreases through the upper bound (a Hopf-bifurcation point) of this interval the motion in the phase space becomes periodic and then, following a period-doubling cascade, chaotic. There may be alternating sub-intervals of chaotic and periodic motion. The chaotic trajectories in the phase space appear to lie on fractal attractors.     

Syn- and anti-selective Prins cyclizations of delta,epsilon-unsaturated ketones to 1,3-halohydrins with Lewis acids

Ten acyclic and monocyclic delta,epsilon-unsaturated ketones, with and without methyl substituents on the double bond, underwent halide-terminated Prins (halo-Prins) cyclizations under anhydrous conditions in the presence of Lewis acids. TiCl4, TiBr4, BCl3, and BBr3 promoted syn-selective cyclizations to sterically congested chloro- and bromohydrins, while SnCl4, SnBr4, InCl3, ZrCl4, and several other Lewis acids effected highly anti-selective reactions to furnish the corresponding trans halohydrins. The stronger Lewis acids (TiX4 and BX3) favor the syn process that involves axial delivery of a halide ligand. Competition experiments showed that substitution at the delta carbon (methallyl enones) led to increased rates (40-50-fold), while substitution at the epsilon position (cis and trans crotyl enones) retarded the rate and eroded the selectivity of the cyclizations. The trends in syn vs anti selectivity, reactivity, and effects of different Lewis acidic metal halides are rationalized by competitive reaction pathways proceeding through syn carbocation-halide ion pairs and a higher order transition state that leads to inversion of configuration and formation of trans halohydrins, along with cyclic olefins arising from proton elimination.     

Expansive Algebraic Actions of Countable Abelian Groups

This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic -actions given by Schmidt using complex varieties. Also included is an application to a natural class of examples arising from unit subgroups of integral domains. The author is very grateful for the helpful advice and comments of Tom Ward.     

Analytical model for viscous damping and the spring force for perforated planar microstructures acting at both audible and ultrasonic frequencies

The paper presents a model for the squeezed film damping, the resistance of the holes, and the corresponding spring forces for a periodic perforated microstructure including the effects of compressibility, inertia, and rarefied gas. The viscous damping and spring forces are obtained by using the continuity equation. The analytical formula for the squeezed film damping is applied to analyze the response of an ultrasonic transducer. The inclusion of these effects in a model significantly improves the agreement with measured results. Finally, it is shown that the frequency dependence of the total damping and total spring force for a cell are very similar to those corresponding to a rectangular open microstructure without holes. A separate analysis reveals the importance of each particular correction. The most important is the compressibility correction; the inertia has to be considered only for determining the spring force and the damping force for sufficiently high frequencies.     

Many-body localization in disorder-free systems: The importance of finite-size constraints

Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.     

Ricci Flow of Regions with Curvature Bounded Below in Dimension Three

We consider smooth complete solutions to Ricci flow with bounded curvature on manifolds without boundary in dimension three. Assuming an open ball at time zero of radius one has sectional curvature bounded from below by ?1, then we prove estimates which show that compactly contained subregions of this ball will be smoothed out by the Ricci flow for a short but well-defined time interval. The estimates we obtain depend only on the initial volume of the ball and the distance from the compact region to the boundary of the initial ball. Versions of these estimates for balls of radius r follow using scaling arguments.