Thin Circular Disk Research Articles

Orbits and origins of the young stars in the central parsec of the galaxy

We present new proper motions from the 10 m Keck telescopes for a puzzling population of massive, young stars located within a parsec of the supermassive black hole at the Galactic Center. Our proper motion measurements have uncertainties of only 0.07 mas yr-1 (3 km s-1), which is ≳ 7 times better than previous proper motion measurements for these stars, and enables us to measure accelerations as low as 0.2 mas yr-2 (7 km s-1 yr-1). These measurements, along with stellar line-of-sight velocities from the literature, constrain the true orbit of each individual star and allow us to directly test the hypothesis that the massive stars reside in two stellar disks as has been previously proposed. Analysis of the stellar orbits reveals only one disk of young stars using a method that is capable of detecting disks containing at least 7 stars. The detected disk contains 50% (38 of 73) of the young stars, is inclined by ∼ 115° from the plane of the sky, and is oriented at a position angle of ∼ 100° East of North. The on-disk and off-disk populations have similar K-band luminosity functions and radial distributions that decrease at larger radii as ∞ r-2. The disk has an out-of-the-disk velocity dispersion of 28 ± 6 km s-1, which corresponds to a half-opening angle of 7° ± 2°, and several candidate disk members have eccentricities greater than 0.2. Our findings suggest that the young stars may have formed in situ but in a more complex geometry than a simple thin circular disk.

Quasi-Static Thermal Stresses Due to Heat Generation in a Thin Hollow Circular Disk

The present paper deals with the determination of displacement and thermal stresses in a thin hollow circular disk defined by a ≤ r ≤ b due to internal heat generation within it. Time dependent heat flux Q(t) is applied at the outer circular boundary (r = b), whereas inner circular boundary (r = a) is at zero heat flux. Also, initially the circular disk is at arbitrary temperature F(r). The governing heat conduction equation has been solved by the method of integral transform technique. The radial stress function σrr is zero at inner and outer circular boundaries (r = a and r = b). The results are obtained in a series form in terms of Bessel's functions. The results for displacement and stresses have been computed numerically and illustrated graphically.

Flow over a thin circular disk at low to moderate Reynolds numbers

Computation of viscous flow over a circular disk of aspect ratio 10 (thickness/diameter) in the Reynolds number (Re) range of 10 to 300 was performed. The following flow regimes were observed: (I) steady axisymmetric flow whenRe< 135, with the presence of a toroidal vortex behind the disk; (II) regular bifurcation with loss of azimuthal symmetry but with planar symmetry and a double-threaded wake, for 135 ≤Re< 155; (III) three-dimensional flow with periodic shedding of double-sided hairpin-shaped vortex structures and periodic motion of the separation region for 155 ≤Re< 172; (IV) regular shedding of double-sided hairpin-shaped vortex structures with planar and spatio-temporal symmetry for 172 ≤Re< 280; (V) periodic three-dimensional flow with irregular rotation of the separation region whenRe= 280–300. This transition process for the disk differs from that for the sphere as we observe a loss of the symmetry plane in Regime III due to a twisting motion of the axial vorticity strands in the wake of the disk. The periodic flow was characterized by double-sided hairpin structures, unlike the one-sided vortex loops observed for the sphere. This resulted in the drag coefficient oscillating at twice the frequency of the axial velocity. In Regime IV, the vortex loops were shed from diametrically opposite locations and with equal strength, resulting in the lift coefficient oscillating symmetrically about a zero mean. These results imply the presence of spatio-temporal symmetry.

Numerical-analytical solution of plane problems in thermoelasticity

The scaled-boundary method is used as a numerical-analytical method to solve problems of thermoelasticity. As an example, the stress intensity factor for a heated thin circular orthotropic disk with an internal crack is evaluated

On the terminal motion of sliding spinning disks with uniform Coulomb friction

We review previous investigations concerning the terminal motion of disks sliding and spinning with uniform dry friction across a horizontal plane. Previous analyses show that a thin circular ring or uniform circular disk of radius R always stops sliding and spinning at the same instant. Moreover, under arbitrary nonzero initial values of translational speed v and angular rotation rate ω , the terminal value of the speed ratio ϵ 0 = v / R ω is always 1.0 for the ring and 0.653 for the uniform disk. In the current study we show that an annular disk of radius ratio η = R 1 / R 2 stops sliding and spinning at the same time, but with a terminal speed ratio dependent on η . For a two-tier disk with lower tier of thickness H 1 and radius R 1 and upper tier of thickness H 2 and radius R 2 , the motion depends on both η and the thickness ratio λ = H 1 / H 2 . While translation and rotation stop simultaneously, their terminal ratio ϵ 0 either vanishes when k > 2 / 3 , is a nonzero constant when 1 / 2 < k < 2 / 3 , or diverges when k < 1 / 2 , where k is the normalized radius of gyration. These three regimes are in agreement with those found by Goyal et al. [S. Goyal, A. Ruina, J. Papadopoulos, Wear 143 (1991) 331] for generic axisymmetric bodies with varying radii of gyration using geometric methods. New experiments with PVC disks sliding on a nylon fabric stretched over a plexiglass plate only partially corroborate the three different types of terminal motions, suggesting more complexity in the description of friction.

Dipole-exchange spin waves in perpendicularly magnetized discs: Role of the Oersted field

We develop the theory of the exchange dipole spin waves in thin circular discs for the case where the magnetization is nominally perpendicular to the plane. Our interest is in the circumstance where a transport current is injected into the disc, with current also perpendicular to the plane of the disc. Such a current creates an azimuthal magnetic field, referred to often as the Oersted field. We develop the theory of the influence of the Oersted field on the spin-wave spectrum of the disc. This field produces a vortex state. We suggest that this vortex state is stable down to zero applied field. If the external applied field ${H}_{0}$ is in the $+z$ direction, perpendicular to the plane of the disc, the vortex state has magnetization at the center of the disc also parallel to $+z$ always. This is the case even when ${H}_{0}l4\ensuremath{\pi}{M}_{S}$, where the magnetization at the center of the disc is antiparallel to the local field ${H}_{0}\ensuremath{-}4\ensuremath{\pi}{M}_{S}$ there. We present calculations of the current dependence of spin-wave frequencies of several modes as a function of applied magnetic field. We also address an issue overlooked in previous studies of spin waves in thin discs. This is that for quantitative purposes, it is not sufficient to describe internal dipole fields generated by the spin motions simply by adding an effective internal field $\ensuremath{-}4\ensuremath{\pi}{m}_{z}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ to the equations of motion, with ${m}_{z}$ the component of dynamic magnetization normal to the surface. For samples of present interest, we derive terms we call gradient corrections, and these play a role quantitatively comparable to exchange itself in the analysis of the spin-wave frequencies. Quantitative studies of spin dynamics in such samples thus must include the gradient corrections.

Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc

The distribution of stresses due to step input of temperature on the boundaries of a homogeneous transversely isotropic circular disc is investigated by applying Laplace transform technique in the context of generalized theories of thermo-elasticity. The inverse of the transformed solution is carried out by applying a method of Bellman et al. The stresses are computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (CTE, CCTE, TRDTE(GL), TEWED(GN)) and the effect of anisotropy on the stresses are also presented. When the material is isotropic and outer radius of the disc tends to infinity, the corresponding result agrees with that of existing literature.

Droplet Shape of an Anisotropic Liquid

We investigate how a droplet of a complex liquid is modified by its internal nanoscale structure. As the liquid passes from an isotropic disordered state to an anisotropic layered morphology, the droplet shape switches from a smooth spherical cap to a terraced hyperbolic profile, which can be modeled as a stack of thin concentric circular disks with a repulsion between adjacent disk edges. Our ability to resolve the detailed shape of these defect-free droplets offers a unique opportunity to explore the underlying physics.

Thermal buckling of a thin uniform circular disk: a comparison of predictions

AbstractThe conditions for thermally-induced buckling of an unloaded thin, circular disk are compared from two well-known but unconnected studies: an approximate solution by Freund for a constant thickness disk, which must neglect the free edge condition, and an exact solution by Mansfield but only for a disk whose thickness tapers to zero in a particular manner. It is shown that buckling occurs at slightly higher values compared to a finite element analysis of a constant thickness disk but that the case of variable thickness seems to offer a closer result, which suggests that it better models the boundary layer behaviour near the free edge.

Design, analysis, and measurement of a new dual-band compact hybrid resonator antenna

A new dual-band compact hybrid resonator antenna is proposed in this article. The analysis is based on electric-field and magnetic-field integral equations. In the proposed design, the structure uses a combination of a thin circular disk dielectric resonator (DR) and a microstrip-fed dog-bone slot. This dog-bone slot works as a half-wavelength radiator and as a feed circuit for the DR. By optimizing the structure's parameters, the hybrid structure allows not only the DR to resonate at one frequency band but also the dog-bone slot to resonate at the other one with the required frequency separation. Based on the above design concept, an antenna prototype for wireless communication applications centered at 1.9 and 2.45 GHz is successfully designed, fabricated, and tested. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.

Layer Growing/Removing Method for Determination of Residual Stresses in Thin Orthotropic Inhomogeneous Discs

An algorithm of the layer growing/removing method for computing of the residual stresses in thin orthotropic inhomogeneous circular disc is presented. The stresses are calculated from strain measurements on the free stationary contour or on the lateral surface, or from X-ray diffraction measurements on the disc’s moving contour. The suggested algorithm is programmed for PC. Two illustrative examples are presented.

Calibration of cylindrical detectors using a simplified theoretical approach

The calibration of cylindrical detectors using different types of radioactive sources is a matter of routine. The most accurate method, that of experiment, is limited by several factors when the energy interval is broad, requiring a relatively large number of primary standards, implying considerable investment of money and time. Several other techniques can be used instead, including Monte Carlo simulations and semi-empirical methods. Calculations based on the first technique require good definition of the geometry and materials, including the dead layer and window thickness together with an accurate set of cross-sections. The second technique requires two different types of experimental input, the first being from use of sources emitting cascade γ rays and the second from use of sources emitting isolated γ rays in order to cover the wide energy range and provide coincidence-summing corrections, respectively. Here, we introduce a new theoretical approach based on the Direct Statistical method proposed by Selim and Abbas to calculate the total and the full-energy peak (photopeak) efficiencies for both point and thin circular disk sources for scintillation and semiconductor detectors. The present method combines calculation of the average path length covered by the photon inside the detector active volume and the geometrical solid angle Ω, to obtain a simple formula for the different efficiencies. Results from the present model were tested against data sets obtained with previous treatments in order to underline how simple and fast our calculations are.

A 3-balls-on-3-balls strength test for ceramic disks

In the usual tests to determine strength or lifetime under tension, bending or compression loading, the uniaxial stress state is present. However, in components very often multiaxial stresses occur. But also under uniaxial external loading, multiaxial stresses are possible, for instance, in notched components. Common tests are bending tests on thin circular disks. Following the description of conventional tests, a recently developed test using three loading and three supporting balls shall be addressed. For this test, the maximum principal stresses and the biaxiality are determined for a wide range of geometries by using the finite element method. First experimental results carried out on glass and alumina are reported. It was found that in all cases the results of the 3-balls-on-3-balls (3B3B) tests are slightly lower than the strengths obtained from the ball-on-3-balls (1B3B) tests. The main reason for this tendency is assumed to be the influence of the different effective surfaces involved in the two types of tests. The Weibull exponents m for these tests overlap within the 90% confidence intervals.

Compact Independent Dual-Band Hybrid Resonator Antenna With Multifunctional Beams

This paper presents a new compact independent dual-band hybrid resonator antenna with multifunctional beams. The proposed antenna uses the combination of a thin circular disk dielectric resonator (DR) and a T-shaped microstrip line. In this configuration, the T-shaped microstrip line performs the functions of a radiator and a feed for the DR. By optimizing the structure parameters, the hybrid structure allows not only the DR to resonate at one band with the broadside patterns but also the microstrip line to resonate at another band with the conical like patterns, and the two bands can be independently designed. Based on the above design concept, an antenna prototype suitable for wireless communication applications centered at 1.9 and 2.45 GHz was successfully designed, fabricated and tested.

Sedimentation of a circular disk in power law fluids

The continuity and momentum equations have been solved numerically for the two-dimensional steady flow of power law fluids over a thin circular disk oriented normal to the direction of flow. Extensive results on the individual and total drag coefficients are obtained as functions of the power law flow behavior index ( 0.4 ⩽ n ⩽ 1.0 ), Reynolds number ( 1 ⩽ Re ⩽ 100 ) and the blockage ratio, disk-to-cylinder diameter ratio ( 0.02 ⩽ e ⩽ 0.5 ), which can be used to estimate the settling velocity of a circular disk. The numerical predictions of drag are consistent with the scant experimental results available in the literature.

Temperature and density relaxation close to the liquid-gas critical point: An analytical solution for cylindrical cells

We present a study of the temperature and density equilibration near the liquid-gas critical point of a composite system consisting of a thin circular disk of near-critical fluid surrounded by a copper wall. This system is a simplified model for a proposed space experiment cell that would have 60 thin fluid layers separated by perforated copper plates to aid in equilibration. Upper and lower relaxation time limits that are based on radial and transverse diffusion through the fluid thickness are shown to be too significantly different for a reasonable estimate of the time required for the space experiment. We therefore have developed the first rigorous analytical solution of the piston effect in two dimensions for a cylindrically symmetric three-dimensional cell, including the finite conductivity of the copper wall. This solution covers the entire time evolution of the system after a boundary temperature step, from the early piston effect through the final diffusive equilibration. The calculation uses a quasistatic approximation for the copper and a Laplace-transform solution to the piston effect equation in the fluid. Laplace inversion is performed numerically. The results not only show that the equilibration is divided into three temporal regimes but also give an estimate of the amplitudes of the remaining temperature and density inhomogeneity in each regime. These results yield characteristic length scales for each of the regimes that are used to estimate the expected relaxation times in the one- and two-phase regions near the critical point.

Magnetic anisotropy of FeGa alloys

Cubic magnetocrystalline anisotropy constants, K1 and K2, for Fe1−xGax alloys were measured using magnetization curves with x=0.05, 0.125, 0.14, 0.18, and 0.20. Thin circular (110) disks all with 〈100〉, 〈110〉, and 〈111〉 in the plane of the disk were used to measure K1 and K2. K1 was also measured with (100) circular disks. K1 for 5 at. % Ga content was found to be larger than that of pure Fe. (All compositions mentioned hereafter are atomic percents.) K1 and K2 both drop gradually up to 18 at. % Ga substitution. Then there is a sharp drop in the magnitude of both constants. K2 was found to be equal to −9K1/4 and the 〈110〉 and 〈111〉 directions were equally hard magnetically for all compositions considered in this study. Calculation of the anisotropy energy density verifies this result. K1 measured from both (110) and (100) disks was reasonably consistent.

Thin Circular Disk Shells of OH Masers Toward SNRs

We propose a new model of distinct thin circular disk shells to analyze Gaussian fits to spectral features of OH emission at 1720 MHz toward supernova remnants. We have inferred that the OH(1720 MHz) maser features toward G348.5+0.1 are radiated from three distinct thin circular disk shells, and have obtained the parameters of the shells.

Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures.

Seeding and autocatalytic reduction of platinum salts in aqueous surfactant solution using ascorbic acid as the reductant leads to remarkable dendritic metal nanostructures. In micellar surfactant solutions, spherical dendritic metal nanostructures are obtained, and the smallest of these nanodendrites resemble assemblies of joined nanoparticles and the nanodendrites are single crystals. With liposomes as the template, dendritic platinum sheets in the form of thin circular disks or solid foamlike nanomaterials can be made. Synthetic control over the morphology of these nanodendrites, nanosheets, and nanostructured foams is realized by using a tin-porphyrin photocatalyst to conveniently and effectively produce a large initial population of catalytic growth centers. The concentration of seed particles determines the ultimate average size and uniformity of these novel two- and three-dimensional platinum nanostructures.

Fabrication of translucent MgO ceramics using nanopowders

Translucent MgO ceramics have been fabricated by hot-pressing using nanopowder of MgO containing 2–4% LiF as a fugitive additive. Thin circular discs were pressed uniaxially with the LiF-containing nanopowders. The hot-pressing was carried out either in Ar or in vacuum, holding at 1100 °C for 30 to 60 min at either 24 or 45 MPa. The samples were then annealed in air by either conventional or microwave processing. The annealed samples were highly dense and optically translucent.