Geometrical Cross Section Research Articles

Problem of Critical Convective Flows in Horizontal-Cylindrical Cavities

The results of an analysis of the linear perturbations of equilibrium of a viscous heat-conducting fluid or gas in cavities with simple geometric cross-sections are given. Both plane motions and motions periodic in the direction of the horizontal generator of the boundary surface are considered. Variants in which the acceleration of the mass force field can be both constant and periodically modulated are calculated. The solutions of the problem for the stream function (or the vertical velocity component) and the temperature are represented in the form of double or triple Fourier series. For the coefficients in the expansions an infinite system of equations which admits reduction is obtained. The results are found to be in good agreement with the known data.

Plasmonically enhanced diffusive and subdiffusive metal nanoparticle-dye random laser

We report on surface plasmon (SP)-enhanced random laser emission from a suspension of silver nanoparticles in a laser dye operating at diffusive and subdiffusive scattering strengths. SP resonance enhances the scattering cross section, while the geometrical cross section remains small, thus providing a large gain volume. The localized electromagnetic field near the particle surface leads to enhanced absorption of excitation light and larger amplification of fluorescence. The metal-nanoparticle-based random laser yields larger linewidth narrowing at lower pump fluence threshold than a dielectric-scatterer-based random laser under equivalent conditions. These findings open the door to studies of applications related to light amplification assisted by SP in metallic nanoparticles.

Critical current of Nb and NbN thin‐film structures: The cross‐section dependence

We present results of a systematic study of the critical current in superconducting Nb and NbN thin film bridges. The bridges with a width from 50 nm to 10 µm were patterned from thin superconducting films by means of electron-beam lithography and ion milling. For both materials the nominal critical current density extrapolated to zero temperature varied with the bridge width and thickness. We attribute these variations to a fabrication-enhanced reduction of the effective, superconducting cross-section of the bridges with respect to their geometric cross-section and to an uneven distribution of the super-current over the superconducting core of the bridge. In very thin bridges, i.e. 5 nm and 8 nm for NbN and Nb, respectively, the nominal current density increased drastically when the bridge width became smaller than 500 nm. We associate the enhancement of the critical current density in narrow bridges with the crossover from depinning of magnetic vortices to either their nucleation or breaking of Cooper pairs. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Laser densification of extruded dental porcelain bodies in multi‐material laser densification process

PurposeCommercial dental porcelain powder was deposited via slurry extrusion and laser densified to fabricate dental restorations in a multi‐material laser densification (MMLD) process.Design/methodology/approachA dental porcelain slurry was made from ball milled dental porcelain powders and extruded using the MMLD system. Extruded lines and rings were laser densified under different conditions in order to study how to build fully dense porcelain layers without warping and cracking during the MMLD process.FindingsThe geometric cross section of laser densified porcelain lines were dependent on laser processing parameters. Laser densified single ring showed no warping, and multiple layer body after laser densification showed cracks in the rings. The interface microstructure suggested good bonding between multiple layers. The mechanism to achieve single porcelain ring without warping and cracking is discussed. Alternate ways to build physical tooth layer by layer are proposed.Originality/valueIn the MMLD process, dental porcelain slurry was extruded from a human tooth computer file and laser densified to manufacture dental restorations based on solid freeform fabrication (SFF) principles. The understanding developed will pave the way for fabricating a physical dental restoration unit in the near future.

Optically tunable nanoparticle contrast agents for early cancer detection: model-based analysis of gold nanoshells

Many optical diagnostic approaches rely on changes in scattering and absorption properties to generate optical contrast between normal and diseased tissue. Recently, there has been increasing interest in using exogenous agents to enhance this intrinsic contrast with particular emphasis on the development for targeting specific molecular features of disease. Gold nanoshells are a class of core-shell nanoparticles with an extremely tunable peak optical resonance ranging from the near-UV to the mid-IR wavelengths. Using current chemistries, nanoshells of a wide variety of core and shell sizes can easily be fabricated to scatter and/or absorb light with optical cross sections often several times larger than the geometric cross section. Using gold nanoshells of different size and optical parameters, we employ Monte Carlo models to predict the effect of varying concentrations of nanoshells on tissue reflectance. The models demonstrate the importance of absorption from the nanoshells on remitted signals even when the optical extinction is dominated by scattering. Furthermore, because of the strong optical response of nanoshells, a considerable change in reflectance is observed with only a very small concentration of nanoshells. Characterizing the optical behavior of gold nanoshells in tissue will aid in developing nanoshells as contrast agents for optical diagnostics.

Size-Controlled Synthesis of Nanoparticles. 2. Measurement of Extinction, Scattering, and Absorption Cross Sections.

Extinction, scattering, and absorption cross sections and efficiencies were experimentally measured for chemically clean silver nanoparticles in water for 16 different sizes ranging from 29 to 136 nm. The measured efficiencies indicate that particles interact with light 4-10 times stronger than the geometric cross section suggests. Absorption and scattering components of the plasmon resonance were separately measured across the visible spectral range. A method, termed standard subtraction, is suggested for the simple and reliable determination of particle concentrations independent of their size, shape, and aggregation state.

Black hole production in particle collisions and higher curvature gravity

The problem of black hole production in trans-Planckian particle collisions is revisited, in the context of large extra dimensions scenarios of TeV-scale gravity. The validity of the standard description of this process (two colliding Aichelburg--Sexl shock waves in classical Einstein gravity) is questioned. It is observed that the classical spacetime has large curvature along the transverse collision plane, as signaled by the curvature invariant ${(R}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\lambda}\ensuremath{\sigma}}{)}^{2}.$ Thus quantum gravity effects, and in particular higher curvature corrections to the Einstein gravity, cannot be ignored. To give a specific example of what may happen, the collision is reanalyzed in the Einstein--Lanczos--Lovelock gravity theory, which modifies the Einstein--Hilbert Lagrangian by adding a particular ``Gauss--Bonnet'' combination of curvature squared terms. The analysis uses a series of approximations, which reduce the field equations to a tractable second order nonlinear PDE of the Monge--Amp\`ere type. It is found that the resulting spacetime is significantly different from the pure Einstein case in the future of the transverse collision plane. These considerations cast serious doubts on the geometric cross section estimate, which is based on the classical Einstein gravity description of the black hole production process.

Growth and form of planetary seedlings: results from a sounding rocket microgravity aggregation experiment.

In a second microgravity experiment on the formation of dust agglomerates by Brownian motion-induced collisions we find that the agglomerates have fractal dimensions as low as 1.4. Because of much better data, we are now able to derive the diffusion constant of the agglomerates as a function of mass, to show that a power law with an exponent of 1.7 describes the temporal evolution of the mean agglomerate mass very well and to prove that the collision cross section is proportional to the geometrical cross section. In addition to that we derived the universal mass-distribution function of the agglomerates.

Mueller matrix imaging of targets in turbid media: effect of the volume scattering function.

Detecting objects in turbid media by use of just radiance signals has been a subject of study for many years. The use of Mueller matrix imaging methods has only recently been used as a tool for target detection. We will show not only that can targets still be detected by Mueller matrix methods even after their detection has escaped normal radiance schemes but also that their surface features can also still be distinguished. We will also show how the shape of the volume scattering function as well as the target and medium albedo strongly influences various elements of the Mueller matrix. One of the more interesting features of Mueller matrix imaging is that the diagonal elements are sensitive to perturbations in the environment surrounding the target. This implies that targets can be detected far beyond their geometric cross section. The methods presented here will have applications to submersible object detection, remote sensing in the atmosphere, and the detection of inhomogeneities in tissue.

Statistical energy distribution model for the decay of hollow atoms formed in collisions of slow(v<1a.u.)highly charged ions andC60

It is now well known that electron-capture processes in high impact parameter collisions between slow highly charged ions and clusters (as ${\mathrm{C}}_{60}$ for instance) or surfaces populate high Rydberg levels of the projectile forming a so-called ``hollow atom.'' We present in this paper a statistical energy distribution (SED) model for the analysis of the decay of such hollow atoms. The overbarrier model is employed to estimate the initial binding energy of captured electrons and total geometrical cross sections. We show that although the model firstly derived by Russek was incomplete, a simple modification to it that accounts for hollow atom specifications leads to a better agreement with experimental cross sections over a wide range of projectile ions of different atomic numbers (Ar, Kr, Xe) and different charge states $(q=16--30).$ We present also a quantum-mechanics-based formulation of a SED model that allows us to reproduce rather nicely experimental cross sections too. The presented model applied better for high projectile charge states allowing the capture of a great number of electrons that populate a quasicontinuum of Rydberg states for which we do not have to take into account individual Auger transitions.

Mode conversion and birefringence adjustment by focused-ion-beam etching for slanted rib waveguide walls.

We describe how focused-ion-beam (FIB) etching of slanted rib waveguide walls can be used to modify the differential group delay in a waveguide and introduce TE to TM mode conversion in a silicon-on-insulator rib waveguide. We achieved mode conversion by modifying the geometric cross section of a single-mode rib by FIB trimming. Waveguides with different lengths of 45 degrees slant angle rib waveguide walls were fabricated and characterized. We measured the differential group delays and the mode conversion achieved for waveguides with different lengths of a FIB-trimmed slanted rib wall.

Effects of electrical stress on mid-gap interface trap density and capture cross sections in n-MOSFETs characterized by pulsed interface probing measurements

High field electrical stress effects on the mid-gap interface trap density ( D it0) and geometric mean capture cross sections ( σ 0) in n-MOSFETs have been studied using the pulsed interface probing method. The results show that the PIP technique is sensitive to changes in mid-gap trap cross section values caused by the Fowler–Nordheim (F–N) electrical stress. The decrease of mid-gap trap cross sections following the F–N tunneling injection is found. Our works also provide further insight into the influence of electrical stress on mid-gap interface trap generation in n-MOSFETs without the assumption of the constant capture cross section value during F–N stresses.

Analysis of dynamic characteristics of micro-drills

Micro-drills were modeled as long twisted beams. Models for the critical speeds and the critical buckling loads were developed based on the finite element method of analysis. The effects of transverse shear, rotary inertia and gyroscopic moments were included in this analysis. The models have the capability of analyzing a wide variety of geometrical cross-sections. A computer program was developed for the calculation of the variations of the critical speeds and of the buckling loads. The effects of drill geometry, boundary condition, rotational speed, and cross-sectional area on the buckling loads and the critical speeds were analyzed.

Identified charged particle azimuthal anisotropy in PHENIX at RHIC

Event anisotropy is expected to have sensitivity to the early stage of ultra-relativistic heavy-ion collisions at RHIC. The possible formation of a quark gluon plasma (QGP) could affect how the initial anisotropy in the space coordinate is transfered into the momentum space for the initial state. The anisotropy parameter (v 2) is an amplitude of the 2nd harmonic parameter of the azimuthal distribution with respect to the reaction plane. We present here v 2 of identified and inclusive charged particles measured in the PHENIX central arm detector (∣η∣ < 0.35) with respect to the reaction plane defined at ∣η∣ = 3 ∼ 4 in 200 GeV Au + Au collisions. We find that v 2 increases from central to mid-central collisions reaching a maximum at about 50% of the geometric cross section and then decreases again for more peripheral collisions. As a function of transverse momentum in minimum-bias collisions, the v 2 parameter increases linearly with p T up to p T ≅ 2 GeV/c and then saturates for inclusive charged particles. the v 2 parameter of identified particles (π +, π −, K +, K −, p and p ¯ follow a hydro-dynamic behavior up to 2 GeV/c in p T, where the lighter mass particles haver larger v 2 at a given p T. However there is an indication that this trend is reversed at around p T ≅ 2GeV/c, where p and p ¯ have larger v 2 than π and K.

Quantum production of black holes

We give a path integral expression for the quantum amplitude to produce a black hole from particle collisions. When expanded about an appropriate classical solution it yields the leading order contribution to the production amplitude in a curvature expansion. Classical solutions describing black hole production resulting from two particle scattering at non-zero impact parameter, combined with our formalism, indicate a geometric cross section for the quantum process. In TeV gravity scenarios these solutions may exhibit large curvatures, but (modulo a mild assumption about quantum gravity) corrections to the semi-classical cross section are small.

A semi-empirical method for the calculation of cross sections for the electron-impact ionization of negatively charged fullerenes

We extended our previously developed semi-empirical method for the calculation of cross section functions (absolute value and energy dependence) for the electron-impact ionization of the neutral fullerenes C60 and C70 and of the ionized fullerenes C60q+ (q=1–3) to the calculation of multiple ionization processes of the negatively charged fullerenes Cm− (m=60, 70, and 84). Systematic trends and tendencies are highlighted and a detailed comparison with available experimental data is made. Predictions are also made for cross sections for the ionization of the neutral fullerene C84 up to charge state z=6. An attempt is made to elucidate the origin of an experimentally observed scaling law that relates the ratio of the measured ionization cross sections of different fullerenes m and m′, σ−1,z(m)/σ−1,z(m′), where the subscript “−1” refers to the fact that the initial target is negatively charged and “z” denotes the charge state of the final ion, to the corresponding ratio of the geometric cross sections σgeom(m)/σgeom(m′) to the power “z”.

Carbon Particle Cloud Generation for a Solar Particle Receiver

The development and performance of a full-scale carbon particle cloud generator together with the evaluation of nine commercial carbon blacks is reported. Large variations were found in the dispersability and settling properties of the investigated powders. Scanning electron microscope analysis of cloud samples from different powders showed unequal state of agglomeration and particle size. The particle population distribution of the most suitable powder was determined, showing that the particle cloud consisted of 99.8% spheroid primary particles (25–570 nm dia) and 0.2% large irregularly shaped agglomerates. Although the numerical fraction of the agglomerates was only 0.2%, they contributed 40% to the cloud’s geometrical cross section. Significant variations in the population distribution were found from different batches of the same particle powder. The developed full-scale particle generator was capable of sustained operation, creating a particle cloud with an extinction coefficient exceeding 40m−1 at a nominal flow rate of 25 SLPM. The dispersal efficiency of the system with the optimal ejection nozzle was 25%, compared to less than 1% for free ejection. The particle dispersal rate was 30 g/hr at 25 SLPM at an evacuation efficiency of 87%. Specific extinction cross-sections of 5.8m2/g were measured for particle mass loading higher than 2g/m3.

Assessment of a microscopic photobleaching technique for measuring the spectral absorption efficiency of individual phytoplankton cells

Measurements of the absorptance of photosynthetic pigments in individual phytoplankton cells were made using an epifluorescence microscope equipped with a spectrograph and CCD array detector. Correction for light loss due to scattering was achieved by bleaching the cells with intense light from a mercury arc lamp, and using the bleached cells as a spectrophotometric blank. Absorption efficiency factors were calculated from knowledge of the geometrical cross-section of the cells obtained fromcalibrated video images acquired at the time of measurement. The single-cell efficiency factors were consistent with the average absorption efficiencies of cell suspensions measured using a spectrophotometer over most of the visible spectrum, but they were significantly lower below 420 nm. Cells of the diatom Cyclotella cryptica and the chlorophyte Chlorella salina showed clear spectral differences in spectral shape that could be related to taxonomic differences in pigment content, but absorption efficiency factors of approximately 0.4 at 675 nm were found for both species.

Magnetic Aggregation: Dynamics and Numerical Modeling

Focusing on preplanetary grains growth, we discuss the properties of dust aggregation driven by magnetic dipole forces. While there is no direct evidence for the existence of magnetic grains present in the solar nebula, there are reasons to assume they may have been present. We derive analytical expressions for the cross section of two interacting dipoles. The effective cross section depends upon the strength of the magnetic dipoles and the initial velocities. For typical conditions the magnetic cross section is between two and three orders of magnitude larger than the geometric cross section. We study the growth dynamics of magnetic grains and find that the mass of the aggregates should increase with time as t 3.2 whereas Brownian motion growth behaves as t 2. A numerical tool is introduced which can be used to model dust aggregation in great detail, including the treatment of contact forces, aggregate restructuring processes, and long-range forces. This tool is used to simulate collisions between magnetic grains or clusters and to validate the analytical cross sections. The numerically derived cross section is in excellent agreement with the analytical expression. The numerical tool is also used to demonstrate that structural changes in the aggregates during collisions can be significant.

Classical and quantum cross-section for black hole production in particle collisions

We suggest a simple model to study the problem of the black hole production in particle collisions. The cross-section for the classical and quantum production is analysed within this model. In particular, the possibility to form a black hole in collision of low energy particles (or at large impact parameter) via the quantum tunneling mechanism is pointed out. It is found that, in this model, the geometric cross-section gives a good estimate for the production at low and high energies. We also reconsider the arguments in favor of exponential suppression for the production of trans-Planckian black hole and conclude that no such suppression in fact appears. Analyzing the probability for the black hole production we point out on the importance of the back-reaction and reevaluate the contribution of the black hole formed in gravitational collapse to the Euclidean path integral.