Effects of the inclination of a rigid wall on the free vibration characteristics of acoustic modes in a trapezoidal cavity

The coupling between rigid-walled modes of a rectangular cavity (RC modes) is used to obtain the shapes and resonance frequencies of rigid-walled modes of a trapezoidal cavity (TC modes) with an inclined rigid wall. A method is established to identify the TC modes, where the modes can be defined to evolve from individual RC modes. The wall inclination generates two coupling mechanisms, namely, the local coupling where the RC modes couple at the inclined wall, and the global coupling where the RC modes couple throughout the trapezoidal volume. The latter arises from the nonorthogonality of the RC modes in the trapezoidal volume. Both couplings are selective that only RC modes with the same number of nodes in the direction perpendicular to the inclination are coupled to each other. For small inclinations, each TC mode possesses the distorted shape of the RC mode that evolves it. When the inclination is increased, the TC-mode shape becomes complicated and unrecognizable, and extrema can also exist in the resonance frequency of the TC mode. These behaviors are determined by the behaviors of the local and global couplings of the RC mode. This paper provides an understanding of how the free vibration characteristics of TC modes change with the inclination and what determines these changes.     

Geometrical perturbation of an inclined wall on decay times of acoustic modes in a trapezoidal cavity with an impedance surface

Decay times of acoustic modes of a trapezoidal cavity (TC modes) with an inclined wall are studied. Each cavity wall is successively assigned an impedance surface and the other five walls are rigid. The decay times are obtained from the coupling between rigid-walled modes of the rectangular cavity (RC modes) that bounds the trapezoidal cavity. Two coupling mechanisms are identified, namely, the damping coupling and the geometrical coupling. The former is related to the coupling of RC modes at the impedance surface, while the latter is related to the coupling of RC modes at the inclined wall. Both mechanisms include the same volume coupling where RC modes couple throughout the trapezoidal cavity. When the impedance surface is at either of the two trapezoidal walls, the grouping of TC modes with same decay times and the decay time variation with the wall inclination are determined only by the damping coupling. When the surface is at any of the other rectangular walls, both the damping and geometrical couplings are at work. This paper provides an understanding of how the inclined wall and the impedance surface location affect the TC-mode grouping, and what determines the decay time variation with the inclination.     

A dedicated small‐angle X‐ray scattering beamline with a superconducting wiggler source at the NSRRC

At the National Synchrotron Radiation Research Center (NSRRC), which operates a 1.5 GeV storage ring, a dedicated small‐angle X‐ray scattering (SAXS) beamline has been installed with an in‐achromat superconducting wiggler insertion device of peak magnetic field 3.1 T. The vertical beam divergence from the X‐ray source is reduced significantly by a collimating mirror. Subsequently the beam is selectively monochromated by a double Si(111) crystal monochromator with high energy resolution (ΔE/E? 2 × 10^?4) in the energy range 5–23 keV, or by a double Mo/B₄C multilayer monochromator for 10–30 times higher flux (～10¹¹ photons s^?1) in the 6–15 keV range. These two monochromators are incorporated into one rotating cradle for fast exchange. The monochromated beam is focused by a toroidal mirror with 1:1 focusing for a small beam divergence and a beam size of ～0.9 mm × 0.3 mm (horizontal × vertical) at the focus point located 26.5 m from the radiation source. A plane mirror installed after the toroidal mirror is selectively used to deflect the beam downwards for grazing‐incidence SAXS (GISAXS) from liquid surfaces. Two online beam‐position monitors separated by 8 m provide an efficient feedback control for an overall beam‐position stability in the 10 µm range. The beam features measured, including the flux density, energy resolution, size and divergence, are consistent with those calculated using the ray‐tracing program SHADOW. With the deflectable beam of relatively high energy resolution and high flux, the new beamline meets the requirements for a wide range of SAXS applications, including anomalous SAXS for multiphase nanoparticles (e.g. semiconductor core‐shell quantum dots) and GISAXS from liquid surfaces.     

On the steady-state and the transient decay methods for the estimation of reverberation time

The discrepancy between reverberation times of an enclosed sound field measured by the steady-state method and by the transient decay method is well-known. So far, no clear explanation has been obtained. In this paper, the steady-state bandlimited energy in an enclosure and bandlimited power flow into modally reactive boundaries are derived to describe the energy balance relationship and thus the reverberation time in a frequency band. This reverberation time is then compared to that obtained from the transient decay of the sound field based on the modal analysis. The comparison provides an understanding of the discrepancy mentioned above as well as the physical interpretations of the reverberation times estimated by both methods.     

Molecularly Imprinted Polymer Nanomaterials and Nanocomposites: Atom‐Transfer Radical Polymerization with Acidic Monomers

Molecularly imprinted polymers (MIPs) are artificial receptors which can be tailored to bind target molecules specifically. A new method, using photoinitiated atom‐transfer radical polymerization (ATRP) for their synthesis as monoliths, thin films and nanoparticles is described. The synthesis takes place at room temperature and is compatible with acidic monomers, two major limitations for the use of ATRP with MIPs. The method has been validated with MIPs specific for the drugs testosterone and S‐propranolol. This study considerably widens the range of functional monomers and thus molecular templates which can be used when MIPs are synthesized by ATRP, as well as the range of physical forms of these antibody mimics, in particular films and lithographic patterns, and their post‐functionalization from living chain‐ends.     

Characteristics of surface sound pressure and absorption of a finite impedance strip for a grazing incident plane wave

Distributions of sound pressure and intensity on the surface of a flat impedance strip flush-mounted on a rigid baffle are studied for a grazing incident plane wave. The distributions are obtained by superimposing the unperturbed wave (the specularly reflected wave as if the strip is rigid plus the incident wave) with the radiated wave from the surface vibration of the strip excited by the unperturbed pressure. The radiated pressure interferes with the unperturbed pressure and distorts the propagating plane wave. When the plane wave propagates in the baffle-strip-baffle direction, it encounters discontinuities in acoustical impedance at the baffle-strip and strip-baffle interfaces. The radiated pressure is highest around the baffle-strip interface, but decreases toward the strip-baffle interface where the plane wave distortion reduces accordingly. As the unperturbed and radiated waves have different magnitudes and superimpose out of phase, the surface pressure and intensity increase across the strip in the plane wave propagation direction. Therefore, the surface absorption of the strip is nonzero and nonuniform. This paper provides an understanding of the surface pressure and intensity behaviors of a finite impedance strip for a grazing incident plane wave, and of how the distributed intensity determines the sound absorption coefficient of the strip.     

Droplet size scaling of water-in-oil emulsions under turbulent flow

The size of droplets in emulsions is important in many industrial, biological, and environmental systems, as it determines the stability, rheology, and area available in the emulsion for physical or chemical processes that occur at the interface. While the balance of fluid inertia and surface tension in determining droplet size under turbulent mixing in the inertial subrange has been well established, the classical scaling prediction by Shinnar half a century ago of the dependence of droplet size on the viscosity of the continuous phase in the viscous subrange has not been clearly validated in experiment. By employing extremely stable suspensions of highly viscous oils as the continuous phase and using a particle video microscope (PVM) probe and a focused beam reflectance method (FBRM) probe, we report measurements spanning 2 orders of magnitude in the continuous phase viscosity for the size of droplets in water-in-oil emulsions. The wide range in measurements allowed identification of a scaling regime of droplet size proportional to the inverse square root of the viscosity, consistent with the viscous subrange theory of Shinnar. A single curve for droplet size based on the Reynolds and Weber numbers is shown to accurately predict droplet size for a range of shear rates, mixing geometries, interfacial tensions, and viscosities. Viscous subrange control of droplet size is shown to be important for high viscous shear stresses, i.e., very high shear rates, as is desirable or found in many industrial or natural processes, or very high viscosities, as is the case in the present study.     

Physical and Optical Properties of Calcium Zinc Borophosphate Glasses Doped with Manganese Ions

This article reports on the physical and optical properties, absorption, and luminescence spectra in the visible region, of calcium zinc borophosphate glasses doped with manganese ions. The manganese composition was varied up to 10 mol%. The aim of this work was to investigate the effect of the luminescence properties when the glasses were doped with different compositions of manganese ions. X-ray diffraction profiles confirmed their glassy nature. The optical absorption spectrum showed bands characteristic of manganese ions in octahedral symmetry. Both excitation and emission spectra were recorded for these glasses to understand their optical performances. The emission spectrum showed a single broad band (green region) in octahedral symmetry at 582 nm as a result of transition from the upper ⁴T_1g state to the ⁶A_1g ground state of manganese ions. As the concentration of manganese ions increased, the emission band increased from 582 nm (green-light emission) to 650 nm (red-light emission). Apart from the spectral analysis, different physical properties of these glasses were also analyzed. Based on the physical and optical properties, we found the samples to be more promising for their use as novel luminescent optical materials.     

A front-tracking method with Catmull–Clark subdivision surfaces for studying liquid capsules enclosed by thin shells in shear flow

This paper presents a front-tracking method for studying the large deformation of a liquid capsule enclosed by a thin shell in a shear flow. The interaction between the fluid and the shell body is accomplished through an implicit immersed boundary method. An improved thin-shell model for computing the forces acting on the shell middle surface during the deformation is described in surface curvilinear coordinates and within the framework of the principle of virtual displacements. This thin-shell model takes full account of in-plane tensions and bending moments developing due to the shell thickness and a preferred three-dimensional membrane structure. The approximation of the shell middle surface is performed through the use of the Catmull–Clark subdivision surfaces. The resulting limit surface is C²-continuous everywhere except at a small number of extraordinary nodes where it retains C¹ continuity. The smoothness of the limit surface significantly improves the ability of our method in simulating capsules enclosed by hyperelastic thin shells with different shapes and physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, ellipsoidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, swinging, tumbling and transition from tumbling to swinging have been studied over a range of shear rates, viscosity ratios and bending modulus.