Empty Spherical Cavity Research Articles

Effects of translational and rotational degrees of freedom on the properties of model water

Molecular dynamics simulations with separate thermostats for rotational and translational motions were used to study the effects of these degrees of freedom on the structure of water at a fixed density. To describe water molecules, we used the SPC/E model. The results indicate that an increase of the rotational temperature, $T_\textrm{R}$, causes a significant breaking of the hydrogen bonds. This is not the case, at least not to such an extent, when the translational temperature, $T_\textrm{T}$, is raised. The probability of finding an empty spherical cavity (no water molecule present) of a given size, strongly decreases with an increase of $T_\textrm{R}$, but this only marginally affects the free energy of the hydrophobe insertion. The excess internal energy increases proportionally with an increase of $T_\textrm{R}$, while an increase of $T_\textrm{T}$ yields a much smaller effect at high temperatures. The diffusion coefficient of water exhibits a non-monotonous behaviour with an increase of the rotational temperature.

Cavitation model of self-recovery of a magnetic-fluid membrane

A cavitation model describing the process of the expansion and collapse of an empty spherical cavity in a nonviscous fluid has been proposed for interpreting the dynamics of breakage and self-recovery of a magnetic-fluid membrane. The theoretical conclusions agree with the results of experiment.

Ultrasonic atomization on the tissue-bubble interface as a possible mechanism of tissue erosion in histotripsy.

When an intense ultrasound beam is directed at a free surface of a liquid, an acoustic fountain is produced that is typically accompanied by ejection of tiny droplets, i.e., liquid atomization. This phenomenon is usually attributed to instability of cavitation-produced capillary waves on the surface. In addition to capillary effects, a process called spallation may also contribute. Although the acoustic fountain is typically observed at a flat liquid surface, nothing prohibits the atomization from occurring at a curved surface. This brings about the possibility to create an acoustic fountain and droplet emission at the surface of a gas cavity in liquid or, similarly, in the bulk of soft biological tissue. The appropriate condition occurs when high-intensity ultrasound is focused in tissue and creates large (0.1–1 mm in diameter) bubbles due to acoustic cavitation or rapid boiling. To test this hypothesis, acoustic pressure distribution and the corresponding radiation force on the empty spherical cavity were calculated using finite difference modeling and spherical harmonic expansion. It is shown that in histotripsy regimes appropriate conditions appear for the atomization, which may be considered as a possible mechanism of tissue erosion. [Work supported by NIH EB007643, RFBR, and NSBRI through NASA NCC 9-58.]

Scattering of compressional waves by a cavity in an elastic solid: Geometric interpretation and beam illumination.

Aspects of the scattering of short‐wavelength compressional waves by an empty spherical cavity in an elastic solid may be predicted geometrically from the elastic wave reflection coefficient for a plane surface and the curvature of the reflecting surface. When the outgoing wave is a shear wave, it is necessary to include the modified ray‐tube parameters associated with mode conversion. Related geometrical considerations are also helpful for interpreting the scattering of a compressional wave Bessel beam by an empty spherical cavity centered on the beam in an elastic solid. The exact solution in that case follows from a generalization of the scattering analysis for acoustic Bessel beams [P. L. Marston, J. Acoust. Soc. Am. 121, 753–758 (2007)]. A modified analysis gives the directional dependence of the shear waves resulting from mode conversion for a cavity on the axis of a compressional wave Bessel beam. For both plane wave and Bessel beam illumination, the scattering pattern can depend strongly on the va...

Designs of a microwave TE/sub 011/ mode cavity for a space borne H-maser

Method of Lines and Finite Element Analysis investigations have been performed to optimize parameters in a TE011 mode cavity resonator suitable for a spaceborne hydrogen maser. We report on designs that were explored to find a global maximum in the important design parameters for the microwave cavity used in a hydrogen maser. The criteria sought in this exercise were both the minimization of the total volume of the cavity and the maximization of the product of the z-component of the magnetic energy filling factor and the cavity TE011 mode Q-factor (Q.eta). Different configurations were studied. They were a sapphire tube in a copper cylinder, a sapphire tube in a copper cylinder with Bragg reflectors, and spherical copper cavities both empty and sapphire-lined on the inside cavity surface. At 320 K, the simulations resulted in an optimum product Q.eta = 4.9 x 10(4), with an inner cavity radius of 80 mm and unity aspect ratio. This represents a 54% improvement over an earlier design. The expected increase in the product Q . eta) with the inclusion of Bragg reflectors to the sapphire tube was not achieved. Moreover, the z-component of the magnetic energy filling factor was greatly reduced due to an increase in the radial magnetic field. The sapphire-lined spherical cavity showed no better performance than an equivalent-sized empty copper spherical cavity. For the empty cavity the simulations resulted in the product Q.eta = 4.4 x 10(4). The empty spherical cavity resonator is not suitable for the spaceborne hydrogen maser as the total volume in this case is 33% larger than that of the optimized sapphire tube resonator.

High-Q whispering modes in empty spherical cavity resonators

This work presents the study of high-order modes in spherical cavity resonators. In general there are resonant mode families, degenerate in frequency, that "whisper" around the spherical surface. We call these whispering spherical (WS) mode sets. Each set includes the well-known whispering gallery (WG) mode, which propagates like a ray around the azimuth. Also, we identify a new mode, which we label the whispering longitudinal (WL) mode. This mode propagates as a wave front along the longitudinal direction. The rest of the degenerate set propagates like a combination of the WG and WL modes. We show that transverse electric WS modes have high geometric factors, greater than 2000, which increase linearly with frequency. This is an order of magnitude greater than that of a TM010 cylindrical resonator. Also, Q-factors as high as 65,000 at 13.3 GHz were measured at room temperature.

Polarimetric Variations of Binary Stars. II. Numerical Simulations for Circular and Eccentric Binaries in Mie Scattering Envelopes

We present numerical simulations of the periodic polarimetric variations produced by a binary star placed at the center of an empty spherical cavity inside a circumbinary ellipsoidal and optically thin envelope made of dust grains. Mie single-scattering is considered along with pre- and post-scattering extinction factors which produce a time-varying optical depth and affect the morphology of the periodic variations. We are interested in the effects that various parameters will have on the average polarization, the amplitude of the polarimetric variations, and the morphology of the variability. We show that the absolute amplitudes of the variations are smaller for Mie scattering than for Thomson scattering. Among the four grain types that we have studied, the highest polarizations are produced by grains with sizes in the range 0.1-0.2 micron. In general, the variations are seen twice per orbit. In some cases, because spherical dust grains have an asymmetric scattering function, the polarimetric curves produced also show variations seen once per orbit. Circumstellar disks produce polarimetric variations of greater amplitude than circumbinary envelopes. Another goal of these simulations is to see if the 1978 BME (Brown, McLean, & Emslie, ApJ, 68, 415) formalism, which uses a Fourier analysis of the polarimetric variations to find the orbital inclination for Thomson-scattering envelopes, can still be used for Mie scattering. We find that this is the case, if the amplitude of the variations is sufficient and the true inclinations is i_true > 45 deg. For eccentric orbits, the first-order coefficients of the Fourier fit, instead of second-order ones, can be used to find almost all inclinations.

Polarimetric Variations of Binary Stars. I. Numerical Simulations for Circular and Eccentric Binaries in Thomson Scattering Envelopes

We present numerical simulations of the polarimetric variations produced by a binary star placed at the center of an empty spherical cavity inside a circumbinary ellipsoidal and optically thin envelope. Thomson single-scattering is considered along with pre- and postscattering extinction factors which produce a time-varying optical depth. The orbits are circular or eccentric. The mass ratio (and luminosity ratio) is in general equal to 1.0. As a function of the orbital (and envelope) inclination, the polarization follows a sin2 (i) law. High polarization levels will result from a high inclination, a high optical depth, a flat envelope, or a big central cavity. Polarimetric variations are more apparent for a low inclination, a high optical depth, a flat envelope, a small cavity, or an orbit that brings the stars close to the inner edge of the cavity.

The Rayleigh-like collapse of a conical bubble

Key to the dynamics of the type of bubble collapse which is associated with such phenomena as sonoluminescence and the emission of strong rebound pressures into the liquid is the role of the liquid inertia. Following the initial formulation of the collapse of an empty spherical cavity, such collapses have been termed "Rayleigh-like." Today this type of cavitation is termed "inertial," reflecting the dominant role of the liquid inertia in the early stages of the collapse. While the inertia in models of spherical bubble collapses depends primarily on the liquid, experimental control of the liquid inertia has not readily been achievable without changing the liquid density and, consequently, changing other liquid properties. In this paper, novel experimental apparatus is described whereby the inertia at the early stages of the collapse of a conical bubble can easily be controlled. The collapse is capable of producing luminescence. The similarity between the collapses of spherical and conical bubbles is investigated analytically, and compared with experimental measurements of the gas pressures generated by the collapse, the bubble wall speeds, and the collapse times.

Local-Field Effects on Spontaneous Emission in a Dense Supercritical Gas

r 3 divergence at the origin. To incorporate these microscopic interactions local-field corrections are introduced. The approach is still macroscopic in nature, but the electric field at the radiating dipole, the local field, is different from the macroscopic field to incorporate local interactions. Macroscopic derivations of the local-field correction often imply the use of a cavity around the radiating dipole. The specific choice of the cavity is subtle matter [10], greatly complicating the interpretation of these models. Two limiting cases for a local-field model have been proposed. The empty-cavity model [11], in which the atom is inside a real empty spherical cavity in the dielectric, leads to

Initial phases of the collapse of an empty cavity in a liquid

This paper relates to the collapse of an empty spherical cavity in a liquid. The analysis is mainly theoretical, the object being to study the effects of liquid compressibility on the initial phases of the motion of the cavity. A method, similar to the Rayleigh-Janzen theory of subsonic aerodynamics, is described whereby the motion of the cavity can be systematically computed as it collapses from an initial radius R 0 down to a stage when the collapse Mach number approaches unity. Instead of the usual differential equation, a parameter R R ̈ .R 2 describes the cavity motion. Results obtained are in excellent agreement with those obtained from numerical computations. Distributions of fluid properties behind the cavity are obtained at different stages of the collapse. These results, apart from demonstrating the effects of liquid compressibility, also indicate the existence of high-intensity pressure fields in the surrounding flow field even at these subsonic speeds. A general feature of the present theory is that it offers a method by means of which the subsonic phase of the collapse can be linked with the supersonic phase.

Plasmon Cohesive Energy of Voids and Void Lattices in Irradiated Metals

The contribution of the long-range electron-Coulomb correlation to the surface energy of an empty spherical cavity in a metal is calculated from the zero-point energy of surface plasmons characteristic of the spherical void boundary. At large void radii one recovers the result previously derived for a planar metal-vacuum interface. Next it is shown that, owing to the overlapping of surface-plasmon zero-point oscillations around two neighboring voids, an effective attraction exists between them which is analogous to the van der Waals (dispersion) forces between small metal spheres in vacuum. However, because of the monopole nature of the fundamental surface-plasmon mode of a void, the effective void-void interaction is much stronger and of much longer range than the attraction of spherical particles for which the lowest-order plasmon mode is of dipole type only. It is therefore proposed that plasmons may be one of the important physical processes responsible for void nucleation and growth and also for the observed occurrence of three-dimensional void arrays in some heavily irradiated transition metals. In a void lattice, the plasmon modes of an isolated void split and broaden into bands. The resulting plasmon cohesive energy per void is estimated to be of the order of -1 eV for the observed bcc void array in molybdenum and -2.5 eV for the fcc nickel array.

Nonsimilar Effects in the Collapsing of an Empty Spherical Cavity in Water

The flow field behind, and the motion of an empty spherical cavity collapsing in water are calculated by means of a perturbation technique similar to Sakurai's theory for blast waves in gases. In order that the higher approximations may be uniformly valid, the radius coordinate is modified in accordance with Lighthill's principle. The present scheme applies only to the latter half of the collapse process when the cavity speed is highly supersonic and extends Hunter's self-similar solution to account for nonsimilar effects due to the finite sound speed at the interface as well as the finite cavity radius of curvature. The first-order theory is worked out for a sample cavity of initial radius 1 cm collapsing under a constant ambient pressure of 6 atm. The necessary coupling with the initial conditions is obtained from the results of some earlier numerical calculations. The present results indicate that while the nonsimilar effects modify the distributions of flow parameters, the cavity trajectory is practically unchanged from the self-similar law. Very high pressures are shown to accompany cavity collapse even at moderately high collapse speeds.

Similarity solutions for the flow into a cavity

An investigation is made into the possible types of similarity solutions that can describe the symmetric flow of a fluid into an empty spherical cavity. The flow is homentropic, and the fluid obeys a perfect gas law Similarity solutions in which the cavity collapses with constant velocity are given by the value n = 1, and such solutions are possible for all values of γ in the range considered.