Elliptical Disk Research Articles

Vortex precession in thin elliptical ferromagnetic nanodisks

The magnetostatic energy is calculated for a magnetic vortex in a noncircular elliptical nanodisk. It is well-known that the energy of a vortex in the circular disk is minimized though an ansatz that eliminates the magnetostatic charge at the disk edge. Beginning with this ansatz for the circular disk, a conformal mapping of a circle interior onto the interior of an ellipse results in the magnetization of the elliptical disk. This magnetization in the interior of an ellipse also has no magnetostatic charge at the disk edge also minimizing the magnetostatic energy. As expected the energy has a quadratic dependence on the displacement of the vortex core from the ellipse center, but reflecting the lower symmetry of the ellipse. Through numerical integration of the magnetostatic integral a general expression for the energy is obtained for ellipticity values from 1.0 to about 0.3. Finally a general expression for the gyrotropic frequency as described by the Thiele equation is obtained.

A frequency-reconfigurable elliptical monopole antenna for cognitive radio networks

In this paper, an elliptical disk monopole antenna with seven switchable states, including an ultrawideband (UWB) state and six narrowband states, is presented. It consists of an elliptical disk radiator to operate in the UWB mode for cognitive radio (CR) sensing. To operate in the narrowband mode, the antenna is fed through a defected ground structure (DGS) integrated microstrip line. Frequency reconfigurability is achieved by changing the DGS slot length using six electronic switches. The simple proposed design can cover a wide range of frequency bands from 0.75 to 12 GHz, has an omnidirectional radiation pattern with high gain, and is especially suitable as a CR front-end. The fabricated prototype shows good impedance matching in the specified frequency range.

Numerical ranges of the product of operators

We study containment regions of the numerical range of the product of operators $A$ and $B$ such that $W(A)$ and $W(B)$ are line segments. It is shown that the containment region is equal to the convex hull of elliptical disks determined by the spectrum of $AB$, and conditions on $A$ and $B$ for the set equality holding are obtained. The results cover the case when $A$ and $B$ are self-adjoint operators extending the previous results on the numerical range of the product of two orthogonal projections.

Dynamics of Miura-patterned foldable sheets in shear flow.

We study the dynamics of piecewise rigid sheets containing predefined crease lines in shear flow. The crease lines act like hinge joints along which the sheet may fold rigidly, i.e. without bending any other crease line. We choose the crease lines such that they tessellate the sheet into a two-dimensional array of parallelograms. Specifically, we focus on a particular arrangement of crease lines known as a Miura-pattern in the origami community. When all the hinges are fully open the sheet is planar, whereas when all are closed the sheet folds over itself to form a compact flat structure. Due to rigidity constraints, the folded state of a Miura-sheet can be described using a single fold angle. The hinged sheet is modeled using the framework of constrained multibody systems in the absence of inertia. The hydrodynamic drag on each of the rigid panels is calculated based on an inscribed elliptic disk, but intra-panel hydrodynamic interactions are neglected. We find that when the motion of a sheet remains symmetric with respect to the flow-gradient plane, after a sufficiently long time, the sheet either exhibits asymptotically periodic tumbling and breathing, indicating approach to a limit cycle; or it reaches a steady state by completely unfolding, which we show to be a half-stable node in the phase space. In the case of asymmetric motion of the sheet with respect to the flow-gradient plane, we find that the terminal state of motion is one of - (i) steady state with a fully unfolded or fully folded configuration, (ii) asymptotically periodic tumbling, indicating approach to a limit cycle, (iii) cyclic tumbling without repetition, indicating a quasiperiodic orbit, or (iv) cyclic tumbling with repetition after several cycles, indicating a resonant quasiperiodic orbit. No chaotic behavior was found.

Thermoelastic-induced vibrations on an elliptical disk with internal heat sources

ABSTRACTIn this study, integral transform technique is used to investigate the thermally induced vibration of an elliptical disk. The axisymmetric temperature distribution in the disk is determined by conductivity equation and the corresponding initial and boundary conditions using an extended integral transform technique. The problem of thermally induced vibration of the disk with both ends clamped extremes is solved by developing an integral transform for double Laplace differential equation. The thermal moment is derived on the basis of temperature field, whereas maximum normal stresses are derived based on resultant bending moments per unit width. The results are obtained in series form in terms of Mathieu functions, and numerical results are shown in figures.

Relative Effect of Inclinations for Moonlets in the Triple Asteroidal Systems

We present the analysis and computational results for the inclination relative effect of moonlets of triple asteroidal systems. Perturbations on moonlets due to the primarys non-sphericity gravity, the solar gravity, and moonlets relative gravity are discussed. The inclination vector for each moonlet follows a periodic elliptical motion; the motion period depends on the moonlets semi-major axis and the primarys J2 perturbations. Perturbation on moonlets from the Solar gravity and moonlets relative gravity makes the motion of the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 to be periodic.The mean motion of x component and the y component of the inclination vector of each moonlet forms an ellipse. However, the instantaneous motion of x component and the y component of the inclination vector may be an elliptical disc due to the coupling effect of perturbation forces. Furthermore, the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 form a quasi-periodic motion. Numerical calculation of dynamical configurations of two triple asteroidal systems (216) Kleopatra and (153591) 2001 SN263 validates the conclusion.

Möbius transformations and Blaschke products: The geometric connection

Let B be a degree-n Blaschke product and, for λ∈T, let z1,λ,…,zn,λ, ordered according to increasing argument, denote the (distinct) solutions to B(z)−λ=0. Then there is a smooth curve C such that for each λ the line segments joining zj,λ and zj+1,λ are tangent to C. We study the situation in which C is an ellipse and describe the relation to the action of the points zj,λ under elliptic disk automorphisms. These results provide a condition for the numerical range of a compressed shift operator with finite Blaschke symbol to be an elliptical disk. We also consider infinite Blaschke products and the action of parabolic and hyperbolic disk automorphisms.

A SUBTLE INFRARED EXCESS ASSOCIATED WITH A YOUNG WHITE DWARF IN THE EDINBURGH-CAPE BLUE OBJECT SURVEY

ABSTRACT We report the discovery of a subtle infrared excess associated with the young white dwarf EC 05365–4749 at 3.35 and 4.6 μm. Follow-up spectroscopic observations are consistent with a hydrogen atmosphere white dwarf of effective temperature 22,800 K and log [g (cm s−2)] = 8.19. High-resolution spectroscopy reveals atmospheric metal pollution with logarithmic abundances of [Mg/H] = −5.36 and [Ca/H] = −5.75, confirming the white dwarf is actively accreting from a metal-rich source with an intriguing abundance pattern. We find that the infrared excess is well modeled by a flat, opaque debris disk, though disk parameters are not well constrained by the small number of infrared excess points. We further demonstrate that relaxing the assumption of a circular dusty debris disk to include elliptical disks expands the widths of acceptable disks, adding an alternative interpretation to the subtle infrared excesses commonly observed around young white dwarfs.

Morphology of Cyprid Attachment Organs Compared Across Disparate Barnacle Taxa: Does It Relate to Habitat?

This study used morphometric analyses to compare the structure of the third antennular segment, also called the attachment organ, in cyprid larvae from cirripede species representing a diverse set of taxonomic groups. The aim was to investigate the degree of morphological variation in view of the diversity of habitats, settlement substrata, and modes of life found in the Cirripedia. In all cyprids the third segment features a flat surface (the attachment disc) covered with small cuticular villi thought to function in adhesion. The parameters analyzed were the angle of this disc relative to the long axis of the antennule, its shape (outline), the density of cuticular villi, and the type of cuticular structure encircling the disc. The 10 species studied came from most major groups of cirripedes, and comprised shallow-water forms inhabiting hard bottoms (Capitulum mitella, Pollicipes pollicipes, Semibalanus balanoides, Austrominius modestus, Megabalanus rosa), sublittoral forms (Verruca stroemia, Scalpellum scalpellum), epibiotic forms settling on live, soft tissues (Balanus spongicola, Savignium crenatum), and a parasite (Peltogaster paguri). Significant structural variation was found among the species, but due to limited taxon sampling it was unclear whether the differences relate to ecological factors or phylogenetic affiliation. The disc perimeter is guarded by either a series of long and thin cuticular fringes overreaching the rim of the disc (= a velum) or a few low, but very broad cuticular flaps (= a skirt). The presence of a velum (in all rocky-shore species) or a skirt (all other species) around the attachment disc was the only parameter that was clearly correlated with habitat. The shape of the third antennular segment varied from a symmetrical bell shape with a distally facing attachment disc having a circular disc outline, to segments that were elongated in side view, with a very tilted ventral disc surface having an elliptical disc outline. The bell shape may be most common in forms from rocky shores, but in our test of morphometric parameters only Scalpellum scalpellum (sublittoral), Savignium crenatum (epibiotic in corals), and Peltogaster paguri (parasitic) had shapes that differed significantly from the other species. The density of villi on the attachment disc varied significantly, but also showed no clear-cut correlation with substratum or habitat. Attachment organ structure is clearly the most variable feature in cirripede cyprids. To evaluate the degree to which attachment organ structure is correlated with habitat, settlement substratum, and mode of life, future studies should employ a more refined statistical analysis on an enlarged dataset, with much increased taxon sampling and a more multifaceted definition of ecological variables.

SOAR observations of the high-viscosity accretion disc of the dwarf nova V4140 Sagitarii in quiescence and in outburst

We report the analysis of 22 B-band light curves of the dwarf nova V4140 Sgr obtained with SOI/SOAR during two nights along the decline of a superoutburst in 2006 Sep 12-24 and in quiescence over 50 days following the superoutburst. Three-dimensional eclipse mapping of the outburst light curves indicates that the accretion disc is elliptical (eccentricity e=0.13) and that superhump maximum occurs when the mass donor star is aligned with the bulge of the elliptical disc. The accretion disc is geometrically thin both in outburst and in quiescence; it fills the primary Roche lobe in outburst and shrinks to about half this size in quiescence. The stability of the eclipse shape, width and depth along quiescence and the derived disc surface brightness distribution indicate that the quiescent accretion disc is in a high-viscosity, steady-state. Flickering mapping of the quiescent data reveal that the low-frequency flickering arises from an azimuthally-extended stream-disc impact region at disc rim and from the innermost disc region, whereas the high-frequency flickering originates in the accretion disc. Assuming the disc-related flickering to be caused by fluctuations in the energy dissipation rate induced by magneto-hydrodynamic turbulence (Gertseema & Achterberg 1992), we find that the quiescent disc viscosity parameter is large (alpha ~ 0.2-0.4) at all radii. The high-viscosity quiescent disc and the inferred low disc temperatures in superoutburst are inconsistent with expectations of the disc-instability model, and lead to the conclusion that the outbursts of V4140 Sgr are powered by mass transfer bursts from its donor star.

Spatial potential of a weakly compressed elliptical disk

The problem of expanding spatial potential in terms of eccentricity e accurate to e2 has been formulated and solved for a homogeneous gravitating (or charged with static electric charge) elliptical disk. An original method that makes it possible to obtain the desired result using the superposition of a perturbation layer and a circular disk has been developed. The potential of such a layer has been derived. The first term of the expansion of the potential (zero power of parameter e) coincides with the potential of a homogeneous circular disk and the coefficient of the first power of the parameter e is zero. The main term of the expansion of the potential proportional to e2 is analytically derived. The resulting expression makes it possible to determine the potential in the entire space, including the inner region of the disk.

Free-standing gold elliptical nanoantenna with tunable wavelength in near-infrared region for enhanced Raman spectroscopy

The purpose of this work is to present a surface-enhanced Raman scattering (SERS) amplifying antenna for the possible usage in the near-infrared region. Instead of the visible-light range amplifying antenna such as a bowtie, the finite-difference time-domain (FDTD) simulation results indicate that elliptical antenna could provide large electromagnetic field enhancement at near-infrared wavelength by combining the free-standing enhancement property with large aspect ratios of the ellipse geometry. The simulation results consist with the enhancement factors characterized by SERS measurements at the excited wavelength of 785 nm for different aspect ratios and periodicities. In addition to the redshift of the resonance wavelength as the aspect ratio of ellipse increases, the free-standing structure modifies the resonance behavior and the dielectric environment of antenna by elevating the elliptical disk from the substrate. To interpret the simulation results, the analytical solution of resonance wavelength for ellipsoid dimmer is derived based on Lorentz–Mie theory, and comparisons are made between the analytical solution and simulation results. The quasi-static analytical solution provides a way to characterize the resonance behavior of two ellipsoid particles as a function of the gap distance, aspect ratio, and dielectric environment. The electrodynamic analysis for the periodic structure was performed in our FDTD simulations.

A Photoexcited Broadband Absorption Based on Au Nano Cross Elliptical Disks Structure with Polarization-Insensitive and Wide-Angle for Visible Light

We present the design and numerical simulations of a polarization-insensitive and wide-angle photoexcited broadband metamaterial absorption in the visible region base on Au nano cross elliptical disks structure. The Au nano cross elliptical disks structure comprises a periodic array of metal-dielectric multilayered structure and a no transmission metallic functional layer on the bottom. Utilizing 3D finite difference time domain (FDTD) algorithm, the hybrid surface plasmon and the polarization-insensitive absorption of above 90 % for a wide range of incident angles of 40° are observed in the whole visible light (3.8–7.8 × 1014 Hz).

Experimental Study on Depositing Arch Jamming of Elliptical Disks in a Two-Dimensional Static Hopper

AbstractDepositing arch jamming of elliptical disks at the opening of a two-dimensional static hopper is studied experimentally. The hopper slope and opening width, and the aspect ratio of elliptical disks, are varied to determine their influence on the jamming probability. The jamming probability increases as the aspect ratio increases for gentle hopper slopes, while fluctuations of jamming probability appear for more steeper hopper slopes. Increasing hopper slope decreases the jamming probability in most cases. Most jamming arches result from the strong force chains along the shorter axes of elliptical disks. The disk number consisting of jamming arches decreases as the hopper slope increases. For smaller hopper openings, it decreases as the aspect ratio increases, whilst a nearly reverse tendency appears for elliptical disks with smaller aspect ratios. The study delivers a physical mechanism of jamming phenomena in depositing elliptical disks in a two- dimensional static hopper.

Visible light broadband perfect absorbers

The visible light broadband perfect absorbers based on the silver (Ag) nano elliptical disks and holes array are studied using finite difference time domain simulations. The semiconducting indium silicon dioxide thin film is introduced as the space layer in this sandwiched structure. Utilizing the asymmetrical geometry of the structures, polarization sensitivity for transverse electric wave (TE)/transverse magnetic wave (TM) and left circular polarization wave (LCP)/right circular polarization wave (RCP) of the broadband absorption are gained. The absorbers with Ag nano disks and holes array show several peaks absorbance of 100% by numerical simulation. These simple and flexible perfect absorbers are particularly desirable for various potential applications including the solar energy absorber.

A New Differential Pressure Flow Meter for Measurement of Human Breath Flow: Simulation and Experimental Investigation.

The development and performance characterization of a new differential pressure-based flow meter for human breath measurements is presented in this article. The device, called a "Confined Pitot Tube," is comprised of a pipe with an elliptically shaped expansion cavity located in the pipe center, and an elliptical disk inside the expansion cavity. The elliptical disk, named Pitot Tube, is exchangeable, and has different diameters, which are smaller than the diameter of the elliptical cavity. The gap between the disk and the cavity allows the flow of human breath to pass through. The disk causes an obstruction in the flow inside the pipe, but the elliptical cavity provides an expansion for the flow to circulate around the disk, decreasing the overall flow resistance. We characterize the new sensor flow experimentally and theoretically, using Comsol Multiphysics® software with laminar and turbulent models. We also validate the sensor, using inhalation and exhalation tests and a reference method.

NMPC-based Trajectory Tracking and Collison Avoidance of Underactuated Vessels with Elliptical Ship Domain

Abstract: This paper presents a Nonlinear Model Predictive Control (NMPC) for position and velocity tracking of underactuated surface vessels of elliptical ship domains with a collision avoidance scheme. A constrained nonlinear optimization problem is formulated to minimize vessel states’ deviation from a time varying reference generated by a virtual vessel over a finite horizon. Linear constraints is imposed on input force and moment to be within the physical limits. Collision avoidance is represented as separation of each pair of the elliptic disks, representing the ship domain of our vessel and each encountered one, and is formulated as nonlinear time-varying constraint over the prediction horizon. A real-time C-code is generated using the ACADO toolkit and qpOASES solver with multiple shooting technique for discretization and Gauss-Newton iteration algorithm. This algorithm is computationally efficient, thus enabling real-time implementation of the proposed technique. MATLAB simulations are used to assess the validity of the proposed technique.

Vortex dynamics in thin elliptic ferromagnetic nanodisks

Vortex gyrotropic motion in thin ferromagnetic nanodisks of elliptical shape is described here for a pure vortex state and for a situation with thermal fluctuations. The system is analyzed using numerical simulations of the Landau–Lifshitz–Gilbert (LLG) equations, including the demagnetization field calculated with a Green's function approach for thin film problems. At finite temperature the thermalized dynamics is found using a second order Heun algorithm for a magnetic Langevin equation based on the LLG equations. The vortex state is stable only within a limited range of ellipticity, outside of which a quasi-single-domain becomes the preferred minimum energy state. A vortex is found to move in an elliptical potential, whose force constants along the principal axes are determined numerically. The eccentricity of vortex motion is directly related to the force constants. Elliptical vortex motion is produced spontaneously by thermal fluctuations. The vortex position and velocity distributions in thermal equilibrium are Boltzmann distributions. The results show that vortex motion in elliptical disks can be described by a Thiele equation.

Polarization-Induced Tunability of Plasmonic Light Absorption in Arrays of Sub-Wavelength Elliptical Disks

Polarization-independent plasmonic light absorbers have been widely investigated in the past decades. Nevertheless, the feasibility for artificial manipulation of the optical properties by controlling the polarization state is desirable for numerous applications including the coloring, displaying, filtering, etc. Here, we present a straightforward method to achieve tunable multiple narrowband light absorption by using the polarization-dependent plasmonic cavity resonances in a common metal-dielectric-metal structure consisting of an elliptical disk array. Multiple light absorption bands with the maximal absorption of 98 % are achieved. Moreover, by controlling the illumination polarization state, artificial spectral modulation depth of these light absorption bands can be up to 90 % based on this structure platform. In addition, since this multispectral polarization-manipulated absorber is realized in such a common sub-wavelength plasmonic structure, it will open up a simple and universal approach for multispectral nanophotonic devices including the high-compact polychromatic color filtering, imaging, and detecting.

Modeling the arrangement of particles in natural swelling-clay porous media using three-dimensional packing of elliptic disks.

Swelling clay minerals play a key role in the control of water and pollutant migration in natural media such as soils. Moreover, swelling clay particles' orientational properties in porous media have significant implications for the directional dependence of fluid transfer. Herein we investigate the ability to mimic the organization of particles in natural swelling-clay porous media using a three-dimensional sequential particle deposition procedure [D. Coelho, J.-F. Thovert, and P. M. Adler, Phys. Rev. E 55, 1959 (1997)]. The algorithm considered is first used to simulate disk packings. Porosities of disk packings fall onto a single master curve when plotted against the orientational scalar order parameter value. This relation is used to validate the algorithm used in comparison with existing ones. The ellipticity degree of the particles is shown to have a negligible effect on the packing porosity for ratios ℓ(a)/ℓ(b) less than 1.5, whereas a significant increase in porosity is obtained for higher values. The effect of the distribution of the geometrical parameters (size, aspect ratio, and ellipticity degree) of particles on the final packing properties is also investigated. Finally, the algorithm is used to simulate particle packings for three size fractions of natural swelling-clay mineral powders. Calculated data regarding the distribution of the geometrical parameters and orientation of particles in porous media are successfully compared with experimental data obtained for the same samples. The results indicate that the obtained virtual porous media can be considered representative of natural samples and can be used to extract properties difficult to obtain experimentally, such as the anisotropic features of pore and solid phases in a system.