Geometrical Cross Section Research Articles

Active volume sound absorber

The absorbtion cross section (ACS) of a passive volume sound absorber asymptotically equals its geometric cross section. On the other hand, the ACS of an active absorber principally could be arbitrarily large. However, the increase of the ACS results in a rapid growth of the near acoustic fields. This puts restrictions on the practically achievable values of the ACS. The talk presents the results of a simulation of sound field levels generated by active absorbers of spherical shape and different wave sizes in response to incident plane waves. It is shown that near the absorber the level of the sound field increases as compared to the passive absorber of the same size. In the far zone the field of the active absorber corresponds to the field of the passive absorber with larger geometric scale. It is demonstrated that sound energy is absorbed rather on the back side of the absorber then on its front face (with respect to the direction of incident wave).

Properties and applications of externally impregnated shaped fibers

Abstract Polymeric fibers have been produced in an array of geometric cross-sections, all of which possess deep channels along the length of the fiber. These shaped fibers have been made in many different formats including wovens, nonwovens, and parallel arrays. A number of polymeric materials are suitable to retain these nonround cross-sections during spinning; they include polyolefins, polyesters, and polyamides. Specific cross-sections have been observed to capture and tenaciously retain high levels of both liquids and finely divided solids within the channels of the fibers. The liquids are held through capillary forces, while the solids are mechanically entrapped within the channels and do not require adhesives to bond. Their retention is sufficient to allow these impregnated fibers to be used in high-flow applications without experiencing loss of the reagents. Exploiting this property, one can use this type of fiber to support a host of reagents in a practical format for various applications.

Wolf-Rayet Wind Models: Photometric and Polarimetric Variability

AbstractWe have modelled the observed random variation in broad band intensity and polarization of some isolated Wolf-Rayet stars assuming that their winds have localized, enhanced density regions (blobs). Our model is based on a Monte Carlo code that treats all Stokes parameters of the radiation bundle. This study indicates that the blobs must have sizes comparable to the stellar dimension and be near the base of the envelope. These blobs can be interpreted as a variable structure of large geometric cross section causing the observed polarimetric and photometric variability.

Penning ionization of C60 and C70

Using crossed beams and mass spectrometric ion detection we have measured the cross-sections for Penning ionization of the fullerene molecules C60 and C70 in thermal energy collisions with metastable He*, Ne*, Ar*, and Kr* atoms and with laser-excited Ar*(4p3D3) atoms. For both C60 and C70, the Penning ionization cross-sections are found to increase exponentially by about a factor of 100 with rising excitation energy (from 10 to 20 eV), in contrast to the geometrical collision cross-sections which are nearly the same (∼200×10−20 m2) for all studied collision pairs. For He*+C60, we determine the absolute value of the Penning ionization cross-section as 77×10−20 m2 with reference to the He I (21.22 eV) photoionization cross-section of C60 which we estimate to be 8.3×10−20 m2. The findings are discussed in terms of statistical processes in the electron system on the sub-ps time scale.

Ten years (1986–1995) of lidar observations of temporal and vertical structure of stratospheric aerosols over Siberia

The data of laser sensing of the vertical aerosol distribution obtained at Siberian Lidar Station of the Institute of Atmospheric Optics, Tomsk (56.5°N, 85.1°E), Russia in 1986–1995 are analyzed. The data are presented in the form of the scattering ratio R( H), the aerosol backscattering coefficient β a π ( H), and the integrated aerosol backscattering coefficient between 15 and 30 km Σ β a π at the wavelength λ=532 nm. During the period from summer 1986 to summer 1991, Σ β a π varied in the range 0.8×10 -4–3×10 -4 sr -1. Average profiles of R( H) and β a π ( H) for the main seasons, the annual behaviour of the altitude of the peak scattering ratio and of the tropopause height, and the eigenvectors of the correlation matrix of R( H) are also presented for this period. In succeeding years, the behavior of the stratospheric aerosol layer (SAL) was primarily determined by the Pinatubo volcanic aerosol. Based on an analysis of the scattering ratio profiles, the formation of the vertical volcanic aerosol stratification above Tomsk is demonstrated. The maximum values of Σ β a π ≈4×10 -3 sr -1, caused by the volcanic aerosol, were observed in January–February 1992. Between 15 and 30 km, the 1/e-decay time of the stratospheric volcanic aerosol was 357±37 days. Lidar measurements carried out on certain days simultaneously at λ=532, 353, and 628 nm allowed us to investigate the transformation of the exponent A( H) that characterizes the spectral dependence of the volcanic aerosol backscattering coefficient in the wavelength range 353–532 nm and to estimate the geometric cross section of particles S( r).

Quenching of metastable states of antiprotonic helium atoms by collisions with H2 molecules

Laser resonance transitions between normally metastable states of antiprotonic helium atoms were induced making use of state dependent quenching effects caused by trace admixtures of H2 to the target helium gas. With this method of “H2-assisted inverse resonances” the decay rates of the states (n,l)=(39,l),l=36,37,38, and (38,l),l=35,36,37 of p̄He+ were determined as a function of the H2 admixture. The quenching cross sections at 30 K deduced therefrom for the states with n=39 were found to be of the order of the geometrical cross section for p̄He+–H2 collisons (2⋅10−15 cm2), with a moderate decrease with increasing l. Within a given cascade with constant v=n−l−1, the quenching cross sections for states with n=38 are smaller by a factor of 4–6 than those for states with n=39.

Optical properties of dust aggregates in the disk of Beta Pictoris

Dust particles in the disk of Beta Pictoris (β Pic) is modeled by fluffy aggregates consisting of slightly modified interstellar grains. We calculate the optical properties by Discrete Dipole Approximation with a1-term method. It is found that the characteristic size of an aggregate is defined by the radius of volume-equivalent sphere. The wavelength dependence of the scattering efficiency in visible becomes flat when the volume-equivalent sphere exceeds 1 μm irrespective of the monomer size, while the infrared silicate feature is present even for aggregates larger than 10 μm. Therefore, our model can account for the coexistence of the neutral scattering and silicate feature in the β Pic disk without detailed tuning of the dust size distribution. Due to the enhancement of geometrical cross section, aggregates generally show higher scattering and absorption efficiencies in visible compared with the volume-equivalent sphere. In contrast, the absorption efficiency for an aggregate is comparable to that for the volume-equivalent sphere when the size is smaller than wavelength. These properties are also consistent with the observed superheat and high albedo of the dust particles in the β Pic disk.

Constraints on Saturn's G Ring from the Voyager 2 Radio Astronomy Instrument

We have reanalyzed the data acquired by the planetary radio astronomy (PRA) experiment during the passage of Voyager 2 through the outer part of Saturn's G ring, originally published by Aubieret al.(1983.Geophys. Res. Lett.10, 5–8). This study closely parallels the reanalysis of the Voyager 1 PRA data during the E-ring passage (Meyer-Vernetet al.1996.Icarus123, 113–128). The instrument detected dust grain impacts on the spacecraft in a region of ≈1000 km vertical extent around the ring plane with a maximum at ring plane crossing. The signal is mainly produced by grains of radius of a few micrometers. We find a size distribution less steep than ther−6law inferred for submicrometer grains by Showalter and Cuzzi (1993.Icarus103, 124–143) from photometric data. These results can be reconciled if the slope of the size distribution flattens above 0.5 μ. Assuming a rough continuity between the distributions deduced from the two data sets and anr−qlaw for the grains detected by PRA, we infer that the differential power law indexq< 3.5 for grain radii between about a half micrometer and a few micrometers. From the observed vertical profile, we deduce an effective ring vertical thicknessH≈ 1200/(q− 1) km. Whenqvaries in the range 3.5–2,Hvaries in the range 500–1200 km and the geometric cross section per unit area is a few times 10−6.

Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments

We have developed a methodology that can be used in reconstruction algorithms to quantify the optical coefficients and the geometrical cross section of a weakly abnormal optical target embedded in an otherwise homogeneous medium. This novel procedure uses differenttime-dependent point-spread functions to analyze the diffusive and absorptive contrasts obtained from time-of-flight measurements. Data obtained from time-resolved transillumination of a tissuelike phantom are used to test the accuracy of this new deconvolution methodology.

Resonant and non-resonant charge transfer in and collisions

Charge transfer cross sections were measured for the single-electron charge transfer reactions as a function of the collision energy E in the range 200 - 2100 eV. For both processes the absolute values of the cross sections are similar to the geometrical cross sections and decrease with increasing collision energy below E = 400 eV. In the case of projectiles, the charge transfer cross section remains almost constant for larger collision energies while increases in the case of capture by beyond 400 eV and saturates around 1350 eV. From an interpretation of the measured cross sections using very simple models it can be concluded that the electron transfer is resonant in collisions between and , as would be expected, and has both resonant and non-resonant contributions for projectiles. The qualitative agreement of the experimental results with very simple one-electron models developed to describe the general trends of the charge transfer cross sections determined in ion - atom collisions in the intermediate energy range (where the semiclassical impact parameter method can be applied) is quite surprising.

Focused ion beam milling: Depth control for three-dimensional microfabrication

Ion milling with a focused ion beam (FIB) is a potential method for making micromolds, which will then be the primary elements in the mass production of micro- or mini-objects by embossing or injection molding. The challenge lies in controlling the ion milling to produce cavities with predefined, arbitrary geometric cross-sections. This work involves programming variations as a function of position into the algorithm that generates the dwell times in the pixel address scheme of a FIB. These variations are done according to whether an axis of symmetry or a plane of symmetry determines the final geometry, and the result is 26 new cross-sectional shapes, such as hemispherical pits, parabolic pits, hemispherical domes, etc. The ion milling control programs were used to generate parabolic cross-section trenches, sinusoidal trenches, sinusoidal cross-section rings on an annulus, and hemispherical domes. We observed reasonable agreement between the shapes ion milled in Si(100) and the expected geometry. The dwell times are generated assuming each pixel has a unique dose and the ion yield is constant with angle of incidence. Deviations from ideality are ascribed to the variation in sputter yield with changing angle of incidence, and to the dwell time control algorithm. Redeposition also compounds the deviation from ideality, but it is difficult to estimate the magnitude of this effect.

Influence of the shape of a wavelength-tunable light filter on its spectral properties

A study has been made of the influence of the geometric shape of a wavelength-tunable light filter on its following properties: 1) the tuning range of the wavelength selected by the light filter; 2) the ratio of the geometric cross sections of the input and output light beams; 3) the angle between the incident radiation and the filtered radiation. A calculation is made of the optimal ratios of the prism faces and angles suitable for making light filters. The reasons for the formation of so-called “parasitic” rays are considered with methods for eliminating them.

Short pulse acoustic excitation of microbubbles

When a bubble is excited at or near its natural frequency it is a very effective scatterer and absorber of sound. In fact at resonance, scattering and absorption cross sections are of the order of 1000 times greater than the geometric cross section for typical marine microbubbles. As with any resonant system, a bubble takes a finite, albeit short time to ring up to steady-state oscillation and continues to oscillate for a finite time after the driving force ceases. A number of studies have been carried out to attempt to describe how acoustic absorption and backscatter depend on the duration of the driving force. Most notable of these are the backscatter measurements for short pulses in near surface sea water [Akulichev et al., Sov. Phys. Acoust. 23(3), 177–180 (1986)] and the forward transmission laboratory measurements for short pulse lengths at 120 kHz [H. R. Suiter, J. Acoust. Soc. Am. 91, 1383–1387 (1992)]. Akulichev observed a decrease in acoustic backscatter for short pulses at three discrete frequencies, whereas Suiter found no corresponding enhancement in forward transmission. This paper details a comprehensive study which measured acoustic attenuation through a well defined bubble cloud over the frequency range 20–200 kHz and for pulse lengths from 20 cycles down to a single cycle using a parametric transmitter. The experiment simulated the conditions for which a decrease in attenuation with decreasing pulse length might have been expected. No effect was observed for two different but well-defined bubble distributions.

Proton Decay and Deficit Angle of Cosmic String**The project supported in part by National Natural Science Foundation of China and the Education DevelopingFoundation of Shanghai

A cosmic string may catalyze baryon number violating processes with strong interaction cross sections rather than the much smaller geometric cross sections. The catalysis cross sections are calculated using the second-quantized prescription. Our results show that catalysis cross sections depend sensitively on the deficit angle of cosmic string.

Comparison between positive and negative charging of helium droplets

Helium droplets of approximately 104–108 atoms have been produced in free jet expansions of liquid helium through a 5 μm nozzle into vacuum. The size distributions of the positively and negatively charged droplets were measured as a function of the electron emission current. A simple model has been developed to describe the charging process and formulas for production of singly and doubly charged droplets were derived. The ratio of the ionization cross section to the geometrical cross section and its dependence on N was obtained. In the experiment single negatively and positively charged droplets were observed. Only for sizes N larger than a certain threshold size Nth ≈ 2 × 105 the positively charged droplets were found to be doubly ionized. These observations are in good agreement with the assumption, that the positively charge carriers are stable “snowballs” while the negative droplets contain an excess electron located in the inside within a metastably bound “bubble”. The threshold size Nth corresponds to a simple model in which for smaller droplets a positively charged cluster of about 50 atoms is ejected.

Latitudinal Variation of Aerosol Sizes Inferred from Titan's Shadow

We measured the location, size, and shape of Titan's shadow in five images taken with the Hubble Space Telescope in 1995. We inferred the altitude of Titan's optical limb at wavelengths of 337–954 nm to an accuracy of 15 km. At each wavelength, altitudes are constant north of −5° and also constant but lower south of −50° latitude, with a linear transition region inbetween. The amplitude of the variation of altitude with latitude increases from close to zero at wavelength 337 nm to 130 km at 954 nm. We conclude that Titan's aerosols are larger (0.3 μm mean radius) at northern latitudes where we probe the detached haze layer than at southern latitudes (0.1 μm south of −50°) where we probe the main haze layer below. The geometric cross section of aerosols at probed altitudes (∼300 km) does not show a significant latitudinal variation. The wavelength dependence of the size of Titan's shadow is not consistent with a spherical shape of aerosols, but gives evidence of their fractal nature.

Mobility and formation kinetics of NH4+(NH3)n cluster ions (n=0–3) in helium and helium/ammonia mixtures

NH4+(NH3)n (n=0–3) cluster ions are produced in a field-free flow tube section of a selected ion flow–drift tube (SIFDT) apparatus. Cluster ion mobilities are measured in mixtures of He and NH3 and used to obtain the individual mobilities in helium and in ammonia by applying Blanc’s law to the mixtures. Mobilities of the cluster ions are also measured in pure helium by producing the ions in the ion source of a flowing afterglow, selected ion flow–drift tube apparatus (FA-SIFDT). The measurements in pure helium compare well with the mobilities in helium obtained by applying Blanc’s law to the mixtures. The zero field mobilities of the cluster ions in helium are 22.1±0.4 cm2 V−1 s−1 for NH4+, 16.6±0.4 cm2 V−1 s−1 for NH4+(NH3), 12.2±0.4 cm2 V−1 s−1 for NH4+(NH3)2, and 12.1±0.4 cm2 V−1 s−1 for NH4+(NH3)3. The decrease with increasing size of the cluster can be explained in terms of the sizes of the geometric cross sections. The zero-field mobilities in NH3 are 0.94±0.35 cm2 V−1 s−1 for NH4+, 0.83±0.22 cm2 V−1 s−1 for NH4+(NH3), 0.50±0.27 cm2 V−1 s−1 for NH4+(NH3)2, and 0.25±0.20 cm2 V−1 s−1 for NH4+(NH3)3. The small values of the mobilities in these polar gas systems are understood in terms of the strong ion–dipole interactions. Calculated mobilities in NH3 are obtained by computing the collision cross section with the ion–dipole interactions taken into account; the results compare well with the measurements for NH4+ and NH4+(NH3). However, the measured mobilities of the larger cluster ions are smaller than the computed values. The discrepancies may be due to several factors including dipole–dipole interactions, ligand exchange reactions, formation of long-lived quasibound complexes, and efficient transfer of kinetic energy into internal energy of the cluster ion and the ammonia molecules.

The mobilities of NO+(CH3CN)n cluster ions (n=0–3) drifting in helium and in helium–acetonitrile mixtures

The mobilities of NO+(CH3CN)n cluster ions (n=0–3) drifting in helium and in mixtures of helium and acetonitrile (CH3CN) are measured in a flow-drift tube. The mobilities in helium decrease with cluster size [the mobility at zero field, K(0)0, is 22.4±0.5 cm2 V−1 s−1 for NO+, 12.3±0.3 cm2 V−1 s−1 for NO+(CH3CN), 8.2±0.2 cm2 V−1 s−1 for NO+(CH3CN)2 and 7.5±0.5 cm2 V−1 s−1 for NO+(CH3CN)3] and depend only weakly on the characteristic parameter E/N (electric field strength divided by the number density of the buffer gas). The size dependence is explained in terms of the geometric cross sections of the different cluster ions. The rate constants for the various cluster formation and dissociation reactions have also been determined in order to rule out the possibility that reactions occurring in the drift region influence the measurements in the mixtures. Since high pressures of acetonitrile are required to form NO+(CH3CN)2 and NO+(CH3CN)3, the mobilities of these ions are found to be dependent on the acetonitrile concentration, as a result of anomalously small mobilities of these ions in acetonitrile [K(0)0=0.041±0.004 cm2 V−1 s−1 for NO+(CH3CN)2 and 0.044±0.004 cm2 V−1 s−1 for NO+(CH3CN)3]. These values are at least an order of magnitude smaller than any previously reported ion mobility, which can be partly explained by the large ion-permanent dipole interaction between the cluster ions and acetonitrile. The remaining discrepancies may be the result of momentum transfer outside the capture cross section, dipole–dipole interactions, ligand exchange, the formation of long-lived collision complexes or the transfer of kinetic energy into internal energy of the cluster ion and the acetonitrile molecule.

The Brownian Motion of Dust Particles in the Solar Nebula: An Experimental Approach to the Problem of Pre-planetary Dust Aggregation

Laboratory experiments were performed to study the Brownian motion of μm-sized dust grains and small aggregates under pre-planetary nebula conditions, i.e., in a thin gas atmosphere (Epstein drag regime), in the ballistic limit, and under microgravity conditions. The results of these experiments, i.e., the grain diffusivities, are in quantitative agreement with theoretical predictions for single spherical grains. Deviations from particle sphericity, i.e., in our case aggregates consisting of monodisperse spherical grains, cause only minor deviations between the Epstein drag formula for spheres and our experimental results for equal particle cross section. Thus, we find a quantitative agreement of our measurements with the Epstein relationD∝ 1/σabetween grain diffusivity and geometrical (aerodynamic) cross section.The results of our investigations can be used for the calculation of the gas–grain stopping time τf= ϵ (m/σa) (1/ρgvm) which, in turn, is an important grain characteristic for the calculation of pre-planetary dust aggregation. Here,mand σaare the mass and the aerodynamic, i.e., geometric cross section of the grain, ρgandvmare the mass density of the gas and the mean thermal velocity of the gas molecules, and ϵ is a proportionality factor which we determined to be ϵ = 0.68 ± 0.10. The gas–grain stopping time describes the strength of grain coupling to a given gas motion and its value determines relative velocties and, hence, collision frequencies between dust grains due to sedimentation, drag-induced orbital decay, and gas turbulence in the solar nebula.

Spin relaxation of muonium-substituted ethyl radicals (MuCH2ĊH2) in the gas phase

The spin relaxation of the muonium-substituted ethyl radical (MuCH2ĊH2) and its deuterated analog (MuCD2ĊD2) has been studied in the gas phase in both transverse and longitudinal magnetic fields spanning the range ∼0.5–35 kG, over a pressure range from ∼1–16 atm at ambient temperature. The Mu13CH213ĊH2 radical has also been investigated, at 2.7 atm. For comparison, some data is also reported for the MuCH2Ċ(CH3)2 (Mu-t-butyl) radical at a pressure of 2.6 atm. This experiment establishes the importance of the μSR technique in studying spin relaxation phenomena of polyatomic radicals in the gas phase, where equivalent ESR data is sparse or nonexistent. Both T1 (longitudinal) and T2 (transverse) μSR relaxation rates are reported and interpreted with a phenomenological model. Relaxation results from fluctuating terms in the spin Hamiltonian, inducing transitions between the eigenstates assumed from an isotropic hyperfine interaction. Low-field relaxation is primarily due to the electron, via both the nuclear hyperfine (S⋅A⋅I) and the spin rotation interactions (S⋅J), communicated to the muon via the isotropic muon–electron hyperfine interaction. At the highest fields, direct spin flips of the muon become important, due to fluctuations in the anisotropic part of the muon–electron hyperfine interaction. In the intermediate field region a muon–electron ‘‘flip–flop’’ relaxation mechanism dominates, due partly to the anisotropic hyperfine interaction and partly to modulation of the isotropic muon–electron hyperfine coupling. In the case of the T2 rates, electron relaxation mechanisms dominate over a much wider field range than for the T1 rates, and inhomogeneous line broadening also contributes. The fluctuations that induce both the T1 and T2 relaxation rates are described by a single correlation time, τc, inversely proportional to the pressure. An effective spin-reorientation cross section is deduced from this pressure dependence, σJ∼100±20 Å2, for all isotopically substituted ethyl radicals. This is similar to the geometrical cross section, but about a factor of 4 larger than values of σJ found for similar-sized diamagnetic molecules by gas phase NMR, primarily reflecting the longer range of the electron-induced intermolecular potential.