Perfect Cylinder Research Articles

Electron magnetic resonance imaging of the Fermi surface of Sr 2RuO 4

We have carried out detailed angle dependent studies of the normal state microwave (40–112 GHz) magneto-conductivity of several single crystal samples of the perovskite superconductor Sr 2RuO 4. As previously reported [Phys. Rev. Lett. 84 (2000) 3374], we observe a series of resonant absorptions which we attribute to cyclotron resonance of quasiparticles belonging to the three well-known Fermi surfaces for this material. From the angle dependence, we confirm the two-dimensional character of these resonances, i.e. the cyclotron frequencies scale as the inverse cosine of the angle between the magnetic field and the normal to the conducting layers. Furthermore, by performing measurements on several samples, and in different electromagnetic field configurations, we are able to couple to different cyclotron modes (+ harmonics) which derive from deformations (warpings) of the Fermi surfaces from perfect cylinders. These mode couplings will be discussed in the light of recent angle dependent de Haas–van Alphen measurements.

Postbuckling strength of an axially compressed elastic circular cylinder with all symmetry broken

Axially compressed circular cylinders repeat symmetry-breaking bifurcation in the postbuckling region. There exist stable equilibria with all symmetry broken in the buckled configuration, and the minimum postbuckling strength is attained at the deep bottom of closely spaced equilibrium branches. The load level corresponding to such postbuckling stable solutions is usually much lower than the initial buckling load and may serve as a strength limit in shell stability design. The primary concern in the present paper is to compute these possible postbuckling stable solutions at the deep bottom of the postbuckling region. Two computational approaches are used for this purpose. One is the application of individual procedures in computational bifurcation theory. Path-tracing, pinpointing bifurcation points and (local) branch-switching are all applied to follow carefully the postbuckling branches with the decreasing load in order to attain the target at the bottom of the postbuckling region. The buckled shell configuration loses its symmetry stepwise after each (local) branch-switching procedure. The other is to introduce the idea of path jumping (namely, generalized global branch-switching) with static imperfection. The static response of the cylinder under two-parameter loading is computed to enable a direct access to postbuckling equilibria from the prebuckling state. In the numerical example of an elastic perfect circular cylinder, stable postbuckling solutions are computed in these two approaches. It is demonstrated that a direct path jump from the undeformed state to postbuckling stable equilibria is possible for an appropriate choice of static perturbations.

Optimal fixture design for drilling through deformable plate workpieces part I: model formulation

This is the first part of two manuscripts that address the development of scientifically based methodologies that use finite element methods and optimization algorithms to design optimal fixturing layouts for the drilling process. Part I focuses on the problem formulation and Part II discusses the results. The fixturing problem formulation is posed as a constrained optimization problem, in which the physical fixture constraints define the domain, and the desired fixturing characteristics are optimized in accordance with a selected objective function. The optimal fixturing model developed includes a material removal strategy that enables one to calculate the shape and dimensions of the machined hole surface. The boundary value problem associated with the optimal fixturing simulations is first formulated. Five different objective functions capable of describing various geometrical aspects of the machined hole have been developed and tested. These functions evaluate the square differences between the simulated and nominal radii and diameter values, minimize the maximum values of the latter quantities, and minimize the deviations of the drilled surface from a perfect cylinder.

Static perfect fluid cylinders - a new approach to Kramer's equations

Using Kramer's formulation of static cylindrically symmetric perfect fluid solutions, we propose a fairly general integration procedure which yields existing solutions as special cases. Foremost, we reduce the problem of finding the cylindrically symmetric analogue of the Schwarzchild interior solution to that of solving a nonlinear second-order ordinary differential equation for the generating function. Although we cannot solve this equation exactly, we provide an asymptotic analysis of its solution under the assumption that the pressure is very small within the source.

The electrohydrodynamic stability of a liquid bridge: microgravity experiments on a bridge suspended in a dielectric gas

The electrohydrodynamic stability of a liquid bridge was studied in steady and oscillatory axial electric fields with a novel apparatus aboard a space shuttle. To avoid interphase transport, which complicates matters in terrestrial, matched-density systems, the experiments focused on a liquid column surrounded by a dielectric gas. The micro-gravity acceleration level aboard the spacecraft kept the Bond number small; so interface deformation by buoyancy was negligible. To provide microgravity results for comparison with terrestrial data, the behaviour of a castor oil bridge in a silicone oil matrix liquid was studied first. The results from these experiments are in excellent agreement with earlier work with isopycnic systems as regards transitions from a perfect cylinder to the amphora shape and the separation of an amphora into drops. In addition, the location of the amphora bulge was found to be correlated with the field direction, contrary to the leaky dielectric model but consistent with earlier results from terrestrial experiments. Next, the behaviour of a bridge surrounded by a dielectric gas, sulphur hexa fluoride (SF6), was investigated. In liquid–gas experiments, electrohydrodynamic ejection of liquids from ‘Taylor cones’ was used to deploy fluid and form bridges by remote control. Experiments with castor oil bridges in SF6 identified the conditions for two transitions: cylinder–amphora, and pinch-off. In addition, new behaviour was uncovered with liquid–gas interfaces. Contrary to expectations based on perfect dielectric behaviour, castor oil bridges in SF6 could not be stabilized in AC fields. On the other hand, a low-conductivity silicone oil bridge, which could not be stabilized by a DC field, was stable in an AC field.

Effects of hydrogen molecule diffusion on LP 0m mode coupling of long-period gratings

We analyzed the effects of hydrogen molecule diffusion on LP 0 m mode coupling of long-period gratings with two assumptions. The fibers were treated in a H 2 chamber at a temperature 90°C and pressure around 107 atm for five days. And then we fabricated long-period gratings with these fibers after holding them at room temperature and one atmosphere pressure for 15 min to 55 h and measured coupling of LP 0 m mode. We used diffusion coefficient of hydrogen molecule, which considered the fiber as a perfect cylinder, and assumed that the core and the cladding have the same diffusion coefficient. Corning ‘Flexcor1060’ was used as a photosensitive fiber which has cutoff wavelength, 920 ± 50 nm, and the cladding/coating diameter, 125 ± 2.0 μm/250 ± 15 μm. Core diameter is 5.0 μm and numerical aperture is 0.14. The hydrogen molecule concentration is averaged in the region of the core and the cladding with time and LP 0 m mode coupling was simulated with coupled mode theory and two assumptions. We were able to predict the coupling peak wavelengths that change with time. These results were useful for designing the transmission spectrum of long-period gratings.

Solutions of Kramer's Equations for Perfect Fluid Cylinders

Kramer's formulation of Einstein's fieldequations for static perfect fluid cylinders isconsidered. Three approaches are followed in seekingsolutions of Kramer's equations. First, a particularintegral is found which reproduces a previously knownclass of four solutions. Second, a fairly general ansatzis suggested, whereby a class of six new solutions isderived. Finally, the problem for an incompressible perfect fluid, with constant energy density, isreduced to a single second order equation. All solutionsare regular everywhere. Constraints are imposed on thesolutions parameters such that energy conditions are satisfied and hence the solutions arephysically reasonable.

Stationary perfect fluid cylinders

Using the formalism of Kramer for the stationary, cylindrically symmetric and rigidly rotating perfect fluid, two models are derived explicitly. The solutions are regular on the axis and the energy conditions are satisfied for a certain range of the angular velocity. In the limit of no rotation they are reduced to the Kramer (p = (-1)µ) and Evans (µ = 5p+constant) static cylindrically symmetric metrics.

Static perfect fluid cylinders

The field equations for cylindrically symmetric perfect fluid models with a non-scale invariant equation of state where the energy density is linearly related to the pressure are rewritten as a set of first order coupled ordinary differential equations. Variables are chosen such that the resulting phase space is compact and everywhere regular. The dynamical systems approach, used in the past mainly for scale invariant matter sources, is subsequently used to gain qualitative information about the space of solutions. It leads to a simple way of demonstrating the existence and properties of interior sources for cylindrically symmetric vacuum solutions. The models are shown to exhibit asymptotic scale invariance.

Melt-bearing shear zones: analogue experiments and comparison with examples from southern Madagascar

Analogue model experiments were conducted to investigate the influence of irregularly distributed weak sites in localising strain, as an aid to understanding shear zone development in partially molten rocks. The very weak inclusions consisted of Vaseline in a homogeneous matrix of paraffin wax, which has a power-law viscous rheology. Boundary conditions were those of pure shear at constant natural strain rate and confining stress σ 3. The inclusions were initially perfect cylinders with axes parallel to the intermediate bulk strain axis Y. Conjugate shear zones nucleate on the inclusions and link up to form an anastomosing pattern of high strain zones of concentrated shear surrounding much more weakly deformed pods of near coaxial strain. The zones initiate at angles near 45° to the bulk shortening axis Z but stretch and rotate towards the X axis with increasing bulk strain. All inclusions nucleate shear zones, so that with increasing development of the anastomosing pattern, weak material occurs only within the high strain zones. The restriction of migmatite leucosomes to shear zones in natural examples could also reflect a corresponding control of melt on the sites of shear zone nucleation, rather than implying accumulation from the surrounding wall-rock. The model geometry is very similar to that observed in small-scale shear zones in migmatites of southern Madagascar. Elongate zones rich in weak inclusions, originally either perpendicular or at 45° to the Z axis, were also modelled for direct comparison with the regional-scale geometry of the Pan-African high-grade ‘shear zones’ on Madagascar.

Is the mammalian porin channel, VDAC, a perfect cylinder in the high conductance state?

The mammalian porin channel (VDAC, porin-31BM) was reconstituted in planar lipid bilayers under voltage clamp conditions. The radii of both entrances of the channel were examined using a method that consisted in filling the channel with different non-electrolytes through its cis or trans entrances while recording single channel conductances. As a result it was found that the geometry of channels formed by porin-31BM could not be approximated by a perfectly cylindrical pore. In fact there is an asymmetry in the geometry of the channel: the diameters of the cis and trans entrances were estimated to be ∼2 nm and ∼4 nm respectively.

Finite elements and absorbing boundary conditions for scattering problems on a parallel distributed memory computer

An efficient finite element method is presented to compute time harmonic microwave field in three dimensional configurations. Nodal-based finite elements have been coupled with an algorithm boundary condition to solve open boundary problems. Modeling real devices is made possible using parallel computation. This paper describes first the time harmonic formulation with the absorbing boundary condition and the sequential code. A new algorithm is then proposed to implement this formulation on a cluster of workstations (10 DEC ALPHA 300X). Analysis of efficiency is performed using simple problems. The electromagnetic scattering of a plane wave by a perfect electric conductor cylinder is finally given as example.

Investigation of the stability of imperfect cylinders using structural models

A combined analytical and experimental programme on the buckling of cylinders under axial compression, external pressure, and combined loading was conducted to develop a methodology for predicting the buckling of shell structures with manufacturing induced imperfections. A unique method of fabricating test cylinders from Lexan without longitudinal seams was developed. Cylindrical blanks formed by blow moulding were thermoformed and machined to the correct wall thickness to form perfect cylinders. The co-ordinates were measured and the cylinders tested. After testing, the cylinders were thermoformed on a second mandrel containing the desired imperfection shape and amplitude, remeasured, and tested. Excellent correlation to predictions from the BOSOR 4 and ABAQUS computer codes was achieved.

An iterative solution for TM scattering from perturbed circular dielectric cylinders

The electromagnetic scattering from an infinite length dielectric cylinder with a nearly homogeneous and circular cross section is considered, with the electric field of the incident plane wave aligned parallel to the infinite axis (TM/sub z/). An iterative approach is adopted, similar to Born's method, but making use of the Green's function for a perfect circular cylinder. As long as the deviations from a homogeneous circular cylinder are minor, the approach is computationally efficient and accurate, a claim demonstrated by comparisons with a moment-method solution. The issue of convergence is explored with respect to shapes and permittivities of perturbations. A method for a priori determination of the success of the iterative method for arbitrary geometries is also given.

Scattering of a modulated pulse by a circular cylinder with longitudinal slots: Reaction in the cylinder

Transient response from a cylinder with longitudinal slots is more complicated than that from a perfect cylinder because the electromagnetic waves are reflected from various parts of the slotted cylinder: exterior surfaces, interior surfaces, and edges. We gave the numerical analysis for E‐polarized and H‐polarized cases by combining the modified point matching method (MPMM) with the fast inversion of Laplace transform method (FILT). Numerical results for the inner field are presented and discussed. The physical meaning of the transient waveform is discussed in detail. Also, the precision of the analysis is checked carefully.

Statistical verification of conformance to geometric tolerance

Modern coordinate measurement machines have provided industry with new tools for inspecting complex parts. The paper develops statistical procedures that complement these inspection methods, and it ties the conformance problem into the hypothesis testing formalism of conventional statistics. Also, the paper suggests strategies for efficient sampling of the part surface, and an implementation of the usual decision-theoretic formulation of the tradeoff between false acceptance and false rejection of part geometries. These ideas are illustrated through the analysis of real and simulated data for perfect and imperfect cylinders.

Particle Bounce or Capture—Search for an Adequate Theory: I. Conservation-of-Energy Model for a Simple Collision Process

Particle-surface collisions have been the object of a number of studies. In two of these studies, Dahneke (1971) and Wall et al (1990) derived simple models for predicting collision dynamics and particle bounce or capture. Neither model has yet provided full rationalization of measured bounce-or-capture data. In fact, the two models sometimes predict different results. Some confusion is evident, as is the need for a simple, reliable theory founded on basic physical laws to provide improved understanding of simple collisions and guide modeling of more complex ones. We rederive the Dahneke and Wall et al models considering the collision process in greater detail. We consider the simplest particle-surface-collision processes, namely, the idealized collision of a homogeneous, solid, non-rotating particle (a perfect sphere or right circular cylinder striking a surface end-on with its symmetry axis oriented normal to the surface) moving at normal incidence towards a flat, smooth surface of a solid body in vacuu...

Low-frequency line shapes in guided acoustic-wave Brillouin scattering

Guided acoustic-wave Brillouin scattering (GAWBS) measurements were performed on 20-cm lengths of optical fibers with particular attention focused on the lowest lying resonance. In 125-μm-diam silica fibers, this resonance was observed to occur at ∼22 MHz and have a line shape which varied erratically from sample to sample. Significant line shape fluctuations were evident even between sequential samples from the same fiber spool. We speculate that the observed effects are attributable to 0.01–0.1 μm distributed geometric deviations from a perfect cylinder.

Friction fractor and holdup studies for lubricated pipelining—II Laminar and [formula omitted] models of eccentric core flow

A model of core-annular flow in which the oil core is a perfect cylinder with generators parallel to the pipe wall, but off-center, is studied in laminar and turbulent flow to assess the effects of eccentricity and the volume flow rate ratio on the friction factor and holdup ratio. The study is tilted toward water lubrication of heavy crude viscous oil. For the turbulence analysis, the water is assumed to be turbulent and the core laminar. A standard k-ε model with a low Reynolds number capability is adopted for the turbulence case. The agreement between model predictions, which have no adjustable parameters, and experimental and field data from all sources, is satisfactory.

Space-group degeneracy in the packing of a non-selfcomplementary Z-DNA hexamer.

The X-ray diffraction pattern of the crystals of the non-selfcomplementary hexadeoxyribonucleotide d(CGCACG).d(CGTGCG) can be indexed in four different space groups: (i) P6(5) and P2(1), with cell parameters a = 17.75 (1), b = 17.76 (1), c = 42.77 (3) A, alpha = 90, beta = 90, gamma = 120 degrees, and (ii) P2(1)2(1)2(1) and C2, with cell parameters a = 17.75 (1), b = 30.74 (2), c = 42.77 (3) A, alpha = 90, beta = 90, gamma = 90 degrees. While the R(merge) for the equivalent reflections in the different space groups indicates that P2(1) is the correct choice in the present case, it is demonstrated that the near degeneracy of the space groups arises out of the fact that the DNA molecule is nearly cylindrical. A perfect cylinder would show perfect degeneracy.