Hyperboloid Shape Research Articles

Single mode photonic quantum ring laser fabricated in hyperboloid drum shape

From three dimensional whispering gallery cavities of GaAs photonic quantum ring fabricated in hyperboloid drum shape by chemically assisted ion beam etching with the central active region diameter of 0.9μm, we have observed single mode lasing near 838nm with a record low injection threshold of 300nA (Jth=47.1A∕cm2) in continuous wave operation at room temperature. This indicates that the quantum ring lasing phenomena associated with the three dimensional whispering gallery modes continue to persist, even at the submicron range overcoming the conventional two dimensional whispering gallery mode limit.

Preference reversals with losses

People who prefer larger, later gains over smaller, sooner gains when considering outcomes far in the future often reverse their preference as the alternatives become closer in time. This finding, which is contrary to a normative economic account of intertemporal choice, has been interpreted as support for hyperboloid discounting, but the results can also be explained by steeper discounting of smaller amounts. The present study is the first to demonstrate that analogous preference reversals occur with losses: People who preferred a smaller, sooner loss over a larger, later loss when the outcomes were far in the future reversed their preference when these alternatives were closer in time. Because there was no magnitude effect (i.e., smaller losses were not discounted more steeply than larger losses), the present findings strongly support the proposition that reversals in preference between delayed outcomes occur because of the hyperboloid shape of the discounting function.

Design and manufacture of a polyvinyl alcohol (PVA) cryogel tri-leaflet heart valve prosthesis

Although current artificial heart valves are life sustaining medical devices, improvements are still necessary to address deficiencies. Bioprosthetic valves have a compromised fatigue life, while mechanical valves have better durability but are prone to thromboembolic complications. A novel, one-piece, tricuspid valve, consisting of leaflets, stent and sewing ring, made entirely from the hydrogel, polyvinyl alcohol cryogel (PVA-C), has been developed and demonstrated. This valve has three thin leaflets attached to a cylindrical stent. In order to approximate the complex shape of the surface of the natural heart valve leaflets, two different geometries have been proposed: revolution about an axis of a hyperboloid shape and revolution about an axis of an arc subtending (joining) two straight lines. The parameters of both geometries were examined based on a compromise between avoiding sharp curvature of leaflets and minimization of the central opening of the valve when closed. The revolution of an arc subtending two straight lines was selected as the preferred geometry since it has the benefit of a smaller central opening when the value of the maximum curvature for the leaflets is the same for each valve geometry. A cavity mold has been designed and constructed to form the PVA-C heart valve. The three leaflets were formed and integrated into the stent and sewing ring in a single process. Prototype heart valves were manufactured in the mold from a solution of PVA and water, by controlled freezing and thawing cycles.

Potential distribution and field intensity for a hyperboloidal probe in a uniform field

The scalar potential and electric field distributions in the gap region of a probe-substrate system are calculated. The probe, modeled as a dielectric medium with the geometry of a one sheeted hyperboloid of revolution, is located above a charged substrate surface which is modeled as a dielectric half space interfaced with a uniform surface charge density. The potential and field distributions are then calculated as functions of the dielectric constant of the medium filling the space between the tip and the surface, and as functions of the hyperboloidal shape parameter. Comparisons are made with the case of a dielectric spheroidal body. The analytical results attained can be used to study other related quantities such as energy density or Coulomb interaction in the neighborhood of the nanometer sized apex region without resorting to numerical methods. This investigation allows for tip shape related field variation in various dielectric media to be studied. Application of this approach to modeling probe tip-sample (probe tip-substrate) interaction in scanning probe microscopy, or to modeling dielectric breakdown processes, are examples of the potential use of the method.

Biomechanics of the hip joint capsule —a mathematical model and clinical implications

Objective. Our aim was to develop a mathematical model to calculate forces, tension and stretching in the hip joint capsule, under conditions caused by the joint effusion usually accompanying hip disease. Design. A mathematical model was developed, based on experimental data from cadaver studies. Background. Intracapsular pressure is important with respect to the degree of painless movement in the hip. Previously, we established the relations between the rotation around the axis of the neck of the femur, joint effusion, intracapsular pressure and joint stability. Methods. In six cadaver adult hips the joint distraction, the traction force along and the rotation around the axis of the neck of the femur and the intracapsular pressure, were simultaneously monitored as the volume of intracapsularly infused saline was increased. The elasticity-constants included in the extracted formula for the fluid pressure were calculated in a designed computer software based on these experimental data. Results. Presented in Figures 3–12. Conclusions. In the normal joint there is no increase in intracapsular pressure, nor any tension in the hyperboloid shape capsule within the normal range of rotation around the axis of the neck of the femur. This shape is distorted in a hip with effusion, rotation then resulting in an increased intracapsular pressure and tension in the capsule, with potential risk of ruptures.

Principles determining the structure of β-sheet barrels in proteins I. A theoretical analysis

The major feature of many proteins is a large β-sheet that twists and coils to form a closed structure in which the first strand is hydrogen bonded to the last: the β-sheet barrel. McLachlan classified barrels in terms of two integral parameters: the number of strands in the β-sheet, n, and the “shear number”, S, a measure of the stagger of the strands in the β-sheet. He showed that the mean radius of a barrel and the extent to which strands are tilted relative to its axis are determined by the values of n and S. Here we show that the ( n, S) values determine all the other general structural features of regular β-sheet barrels, in particular, optimal values of the twist and coiling angles that produce the closed β-sheet, the hyperboloidal shape and the arrangement of residues in the barrel interior. Consideration of the residue arrangements in the interiors of different potential barrel structures, and of side-chain volumes, suggest that barrels, in which the interiors are close packed by the residues in β-sheets with good geometries, have structures that correspond to one of only ten different combinations of n and S. In the accompanying paper, we demonstrate, by an analysis of all observed protein structures that contain β-sheet barrels and for which atomic co-ordinates are available, the validity of these theoretical results.

On the 〈110〉 cylindrical fermi surface and the anisotropic cyclotron resonance peak in lead

The angular dependence of the Azbel'-Kaner cyclotron resonance peaks in lead is analyzed. All of the anisotropies in the cyclotron resonance peaks originating from the 〈110〉 arms of the Fermi surface in the third band are shown to be characterized by a set of three effective masses with one negative, corresponding to a hyperboloidal shape of the Fermi surface. The splitting of the cyclotron resonance peaks found by Khaikin and Mina [ Sov. Phys.-JETP 15, 24 (1962)] is also explained by the set of masses in terms of the approximately 3.2 degree misalignment of the (001) sample surface.

Natural frequencies of cooling tower shells

Approximate explicit formulae are presented for (i) the fundamental natural frequency of vibration of a uniform hyperboloidal cooling tower shell mounted on a rigid base, and (ii) for the circumferential wavenumber associated with fundamental mode. These formulae agree well with results previously obtained by finite element computation and they may be adapted readily for use with cooling tower shells mounted on non-rigid supports. The simplicity of the formulae is a consequence of various approximations which are made in the analysis. “Shallow shell” equations are used, and it is assumed that the dominant structural effects in the shell are longitudinal stretching and circumferential bending. The equations are applied first to the more straightforward case of a cylindrical shell which is clamped at one end and free at the other. The various assumptions are examined systematically, and a wide domain is established in which the resulting formulae for fundamental natural frequency and circumferential wavenumber are valid. The most appropriate dimensionless form of the length of the shell in this domain is Λ=Lh 1/2 / a 3/2 , where L is length, h is thickness and a is radius. A simple scheme is presented, with justification, for the adaptation of the results to a shell which is mounted on a non-rigid base. The equations are then applied to a hyperboloidal shell, and the corresponding formulae are obtained. Again the dimensionless group Λ is appropriate, but it must now be supplemented by a second parameter which defines the hyperboloidal shape of the shell. Remarks are made concerning the design of ring stiffeners for the upper edge, the sensitivity of the fundamental frequency to small changes in any of the leading dimensions of the tower and cases in which the elastic modulus of the material may be different in different parts of the shell.

Centering the secondary mirror of the Tirgo telescope

A procedure for centering the secondary mirror of a Cassegrainian telescope on its mechanical mount has been devised, using the classical principle of observing the movement of a reflected image when the mirror is rotated. The centering is obtained by iteration, keeping the reflecting surface in contact with a circular centered edge. The achievable accuracy, accounting for the change in the hyperboloid shape of the mirror from a sphere, has been calculated; the theoretical values were checked using the procedure for centering the secondary mirror of the Tirgo infrared telescope.

The Husking Test by two Rollers having a Shape of Hyperboloid of one Sheet of Revolution

The Husking Test by two Rollers having a Shape of Hyperboloid of one Sheet of Revolution

De Haas-van Alphen Effect in Arsenic by the Torque Method

The de Haas-van Alphen (dHvA) effect in arsenic has been studied using a torque magnetometer. Techniques were used employing detection of torque, first or second derivative of torque, and torque with magnetic field modulation. An effect that showed hysteresis and a discontinuity in each dHvA oscillation was observed. The effect is explained in terms of the finite angular compliance of the magnetometer coupled with the periodicity of the curve of torque versus reciprocal magnetic field. The dHvA periods are reported for the magnetic field in the bisectrix-trigonal, binary-trigonal, and binary-bisectrix planes. Long periods are from necks of hyperboloidal shape tipped -10\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}1\ifmmode^\circ\else\textdegree\fi{} from the trigonal direction. Short periods are from carriers of two sets of pockets with tilt angles of minimum area from the trigonal direction of +86\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}1\ifmmode^\circ\else\textdegree\fi{} for $\ensuremath{\beta}$ carriers and +38\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}1\ifmmode^\circ\else\textdegree\fi{} for $\ensuremath{\alpha}$ carriers. These data support Lin and Falicov's model of the Fermi surface of arsenic.