Disk Aspect Ratio Research Articles

Analysis of plastic flow during high-pressure torsion

Finite-element modeling (FEM) was used to simulate processing by high-pressure torsion under quasi-constrained conditions using three different material conditions: strain-hardening, perfect-plastic, and flow-softening. The results show there is a tendency for flow localization during processing and this becomes more obvious during the processing of perfect-plastic, and flow-softening materials or when processing samples having high thickness to diameter ratios. The analysis demonstrates the effect of the material condition, the disk aspect ratio and the effect of friction between the disks and the anvil walls. It is demonstrated that the predictions from FEM correlate well with published experimental results.

Thermomagnetic and magnetorotational instabilities of thin Keplerian discs in poloidal magnetic fields

AbstractStability of thin hot Keplerian discs is investigated asymptotically in small disc's aspect ratio, ε. The study is carried out in the local approximation for short vertical waves in the disc‐thickness scale. Besides the radial rotation shear and the vertical magnetic field, the background configuration is characterized by a vertically near‐constant temperature profile with a small vertical gradient. The temperature‐gradient term in Ohm's law, which characterizes the thermomagnetic transport is found to be of the order of ε. The effect of the thermomagnetic transport slightly modifies the conventional magnetorotational instability (MRI), while a new thermomagnetic instability (TMI) emerges in regions of the wavenumber space where MRI is absent. Explicit solutions are obtained for a wide range of values of plasma beta, β, and thermomagnetic transport coefficient, λ. In particular, it is shown for λ ≪ 1 that the MRI dominates in weak magnetic fields, β ≫ 1, while the TMI is exhibited in strong magnetic fields, β ∼ 1, also with the growth rate of the order of inverse rotation period (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DISCOVERY OF SMALL-SCALE SPIRAL STRUCTURES IN THE DISK OF SAO 206462 (HD 135344B): IMPLICATIONS FOR THE PHYSICAL STATE OF THE DISK FROM SPIRAL DENSITY WAVE THEORY

We present high-resolution, H-band, imaging observations, collected with Subaru/HiCIAO, of the scattered light from the transitional disk around SAO 206462 (HD 135344B). Although previous sub-mm imagery suggested the existence of the dust-depleted cavity at r~46AU, our observations reveal the presence of scattered light components as close as 0.2" (~28AU) from the star. Moreover, we have discovered two small-scale spiral structures lying within 0.5" (~70AU). We present models for the spiral structures using the spiral density wave theory, and derive a disk aspect ratio of h~0.1, which is consistent with previous sub-mm observations. This model can potentially give estimates of the temperature and rotation profiles of the disk based on dynamical processes, independently from sub-mm observations. It also predicts the evolution of the spiral structures, which can be observable on timescales of 10-20 years, providing conclusive tests of the model. While we cannot uniquely identify the origin of these spirals, planets embedded in the disk may be capable of exciting the observed morphology. Assuming that this is the case, we can make predictions on the locations and, possibly, the masses of the unseen planets. Such planets may be detected by future multi-wavelengths observations.

RAPID MID-INFRARED VARIABILITY IN PROTOSTELLAR DISKS

Spectral energy distribution (SED) in protostellar disks is determined by the disks'internal dissipation and reprocessing of irradiation from their host stars. Around T Tauri stars, most mid-infrared (MIR) radiation (in a few to a few ten {\mu}m wavelength range) emerge from regions around a fraction to a few AU's. This region is interesting because it contains both the habitable zone and the snow line. Recent observations reveal that SED variations, in the MIR wavelength range. These variations are puzzling because they occur on time scale (a few days) which is much shorter than the dynamical (months to years) time scale at 1AU to a few AU's. They are probably caused by shadows casted by inner onto outer disk regions. Interaction between disks and their misaligned magnetized host stars can lead to warped structure and periodic SED modulations. Rapid aperiodic SED variations may also be induced by observed X-ray flares from T Tauri stars. These flares can significantly modulate the ionization fraction of the gas and the net charge carried by the grains near the surface of the inner disk. The newly charged grains may be accelerated by the stellar or disk magnetic field and adjust their distances from the midplane. Shadows casted by these grains attenuates the flux of stellar photons irradiated onto regions at several AU's from the central stars. We use this model to account for the observed rapid aperiodic SED variabilities. We suggest regular monitoring of SED variations will not only provide valuable information on the distribution of the disk aspect ratio near the habitable zone but also provide a probe on the interaction between the inner regions of the disk with the magnetosphere of their host stars.

Design of subwavelength-size, indium tin oxide (ITO)-clad optical disk cavities with quality-factors exceeding 10^4

Indium tin oxide is used as a top cladding electrode of optical disk resonators with subwavelength size in all dimensions. Calculated quality (Q)-factors exceed 10⁴ in visible wavelengths (650-670nm). The disk aspect ratio is an important parameter to optimize the resonator properties. The Q-factor and threshold material gain based on finite-difference time-domain method are optimized for eight different disk resonator optical modes. Proposed cavity designs are promising for building electrically-pumped, low-threshold nano-lasers at room temperature.

ON THE INTERACTION BETWEEN A PROTOPLANETARY DISK AND A PLANET IN AN ECCENTRIC ORBIT: APPLICATION OF DYNAMICAL FRICTION

We present a new analytic approach to the disk-planet interaction that is especially useful for planets with eccentricity larger than the disk aspect ratio. We make use of the dynamical friction formula to calculate the force exerted on the planet by the disk, and the force is averaged over the period of the planet. The resulting migration and eccentricity damping timescale agrees very well with the previous works in which the planet eccentricity is moderately larger than the disk aspect ratio. The advantage of this approach is that it is possible to apply this formulation to arbitrary large eccentricity. We have found that the timescale of the orbital evolution depends largely on the adopted disk model in the case of highly eccentric planets. We discuss the possible implication of our results to the theory of planet formation.

Multifactor-Controlled Non-Monotonic Plasmon Shift of Ordered Gold Nanodisk Arrays: Shape-Dependent Interparticle Coupling

Surface plasmon resonance (SPR) absorption spectra of gold nanodisks hexagonally arranged in planar arrays have been studied by using coupled dipole method and quasi-static approximation. The calculation results reveal that the increasing aspect ratio (AR) of gold disks in the close-packed nanoarray leads to SPR blue shift firstly and then red shift. The critical AR corresponding to the maximum blue shift can be controlled by tuning the interparticle distance and particle size. The physical mechanism of this non-monotonic SPR shift is investigated based on the competition between the influences from shape factor and arranging structure of the array. Although increasing the semi-minor axis of gold disk reduces the AR and leads to a blue shift of SPR, this increasing semi-minor axis also reduces the average gap between two neighboring disks and enhances their coupling. Furthermore, the coulombic attraction between two neighboring disks introduces an additional plasmon damping and results in a red shift of SPR. This competition between AR and interparticle coupling improves the tuning ability of SPR in anisotropic metallic nanoparticle arrays and presents a potential for design and fabrication of optical biochip based on SPR.

The nature of angular momentum transport in radiative self-gravitating protostellar discs

Semi-analytic models of self-gravitating discs often approximate the angular momentum transport generated by the gravitational instability using the phenomenology of viscosity. This allows the employment of the standard viscous evolution equations, and gives promising results. It is, however, still not clear when such an approximation is appropriate. This paper tests this approximation using high resolution 3D smoothed particle hydrodynamics (SPH) simulations of self-gravitating protostellar discs with radiative transfer. The nature of angular momentum transport associated with the gravitational instability is characterised as a function of both the stellar mass and the disc-to-star mass ratio. The effective viscosity is calculated from the Reynolds and gravitational stresses in the disc. This is then compared to what would be expected if the effective viscosity were determined by assuming local thermodynamic equilibrium or, equivalently, that the local dissipation rate matches the local cooling rate. In general, all the discs considered here settle into a self-regulated state where the heating generated by the gravitational instability is modulated by the local radiative cooling. It is found that low-mass discs can indeed be represented by a local "alpha-parametrisation", provided that the disc aspect ratio is small (H/R < 0.1) which is generally the case when the disc-to-star mass ratio q <0.5. However, this result does not extend to discs with masses approaching that of the central object. These are subject to transient burst events and global wave transport, and the effective viscosity is not well modelled by assuming local thermodynamic equilibrium. In spite of these effects, it is shown that massive (compact) discs can remain stable and not fragment, evolving rapidly to reduce their disc-to-star mass ratios through stellar accretion and radial spreading.

Hindrance function for sedimentation and creaming of colloidal disks

We report the first measurement of the hindrance function for sedimentation or creaming of disk-shaped colloids via the analytical centrifugation. Disks align with the external flow right above a volume fraction of a few percent, and this effect is extremely sensitive to the aspect ratio of disks. Due to this alignment effect, disk sedimentation or creaming demonstrates distinct trends in dilute and semidilute regions.

DEPENDENCE OF INNER ACCRETION DISK STRESS ON PARAMETERS: THE SCHWARZSCHILD CASE

We explore the parameter dependence of inner disk stress in black hole accretion by contrasting the results of a number of simulations, all employing 3-d general relativistic MHD in a Schwarzschild spacetime. Five of these simulations were performed with the intrinsically conservative code HARM3D, which allows careful regulation of the disk aspect ratio, H/R; our simulations span a range in H/R from 0.06 to 0.17. We contrast these simulations with two previously reported simulations in a Schwarzschild spacetime in order to investigate possible dependence of the inner disk stress on magnetic topology. In all cases, much care was devoted to technical issues: ensuring adequate resolution and azimuthal extent, and averaging only over those time-periods when the accretion flow is in approximate inflow equilibrium. We find that the time-averaged radial-dependence of fluid-frame electromagnetic stress is almost completely independent of both disk thickness and poloidal magnetic topology. It rises smoothly inward at all radii (exhibiting no feature associated with the ISCO) until just outside the event horizon, where the stress plummets to zero. Reynolds stress can also be significant near the ISCO and in the plunging region; the magnitude of this stress, however, depends on both disk thickness and magnetic topology. The two stresses combine to make the net angular momentum accreted per unit rest-mass 7-15% less than the angular momentum of the ISCO.

Evolution of warped and twisted accretion discs in close binary systems

We aim to examine the detailed disc structure that arises in a misaligned binary system as a function of the disc aspect ratio h, viscosity parameter alpha, disc outer radius R, and binary inclination angle gamma_F. We also aim to examine the conditions that lead to an inclined disc being disrupted by strong differential precession. We use a grid-based hydrodynamic code to perform 3D simulations. This code has a relatively low numerical viscosity compared with the SPH schemes that have been used previously to study inclined discs. This allows the influence of viscosity on the disc evolution to be tightly controlled. We find that for thick discs (h=0.05) with low alpha, efficient warp communication in the discs allows them to precess as rigid bodies with very little warping or twisting. Such discs are observed to align with the binary orbit plane on the viscous evolution time. Thinner discs with higher viscosity, in which warp communication is less efficient, develop significant twists before achieving a state of rigid-body precession. Under the most extreme conditions we consider (h=0.01, alpha=0.005 and alpha=0.1), we find that discs can become broken or disrupted by strong differential precession. Discs that become highly twisted are observed to align with the binary orbit plane on timescales much shorter than the viscous timescale, possibly on the precession time. We find agreement with previous studies that show that thick discs with low viscosity experience mild warping and precess rigidly. We also find that as h is decreased substantially, discs may be disrupted by strong differential precession, but for disc thicknesses that are significantly less (h=0.01) than those found in previous studies (h=0.03).

Endocytosis and Intracellular Distribution of PLGA Particles in Endothelial Cells: Effect of Particle Geometry

Targeting, internalization, and intracellular trafficking of carriers are key processes in drug delivery to endothelial cells. We synthesized PLGA particles with spherical and elliptical disk geometries and investigated the effect of particle shape on rate of particle endocytosis and their intracellular distribution in endothelial cells. Elliptical disks (aspect ratio of 5) were endocytosed at a slower rate compared to spheres (1.8 µm diameter) of the same volume. However, both particles were eventually internalized and accumulated around the nucleus. We quantified the orientation of elliptical disks and found that disks, on average, oriented tangentially with the nuclear membrane. The non-spherical geometry of elliptical disks brings unique aspects to the kinetics and equilibrium distribution of these particles in cells.

ON THE HORSESHOE DRAG OF A LOW-MASS PLANET. I. MIGRATION IN ISOTHERMAL DISKS

We investigate the unsaturated horseshoe drag exerted on a low-mass planet by an isothermal gaseous disk. In the globally isothermal case, we use a formal- ism, based on the use of a Bernoulli invariant, that takes into account pressure effects, and that extends the torque estimate to a region wider than the horse- shoe region. We find a result that is strictly identical to the standard horseshoe drag. This shows that the horseshoe drag accounts for the torque of the whole corotation region, and not only of the horseshoe region, thereby deserving to be called corotation torque. We find that evanescent waves launched downstream of the horseshoe U-turns by the perturbations of vortensity exert a feed-back on the upstream region, that render the horseshoe region asymmetric. This asymmetry scales with the vortensity gradient and with the disk's aspect ratio. It does not depend on the planetary mass, and it does not have any impact on the horseshoe drag. Since the horseshoe drag has a steep dependence on the width of the horseshoe region, we provide an adequate definition of the width that needs to be used in horseshoe drag estimates. We then consider the case of locally isothermal disks, in which the tempera- ture is constant in time but depends on the distance to the star. The horseshoe drag appears to be different from the case of a globally isothermal disk. The difference, which is due to the driving of vortensity in the vicinity of the planet, is intimately linked to the topology of the flow. We provide a descriptive inter- pretation of these effects, as well as a crude estimate of the dependency of the excess on the temperature gradient.

On the width and shape of the corotation region for low-mass planets

We study the coorbital flow for embedded, low mass planets. We provide a simple semi-analytic model for the corotation region, which is subsequently compared to high resolution numerical simulations. The model is used to derive an expression for the half-width of the horseshoe region, x_s, which in the limit of zero softening is given by x_s/r_p = 1.68(q/h)^(1/2), where q is the planet to central star mass ratio, h is the disc aspect ratio and r_p the orbital radius. This is in very good agreement with the same quantity measured from simulations. This result is used to show that horseshoe drag is about an order of magnitude larger than the linear corotation torque in the zero softening limit. Thus the horseshoe drag, the sign of which depends on the gradient of specific vorticity, is important for estimates of the total torque acting on the planet. We further show that phenomena, such as the Lindblad wakes, with a radial separation from corotation of ~ a pressure scale height H can affect x_s, even though for low-mass planets x_s << H. The effect is to distort streamlines and to reduce x_s through the action of a back pressure. This effect is reduced for smaller gravitational softening parameters and planets of higher mass, for which x_s becomes comparable to H.

Hall equilibrium of thin Keplerian discs embedded in mixed poloidal and toroidal magnetic fields

Axisymmetric steady-state weakly ionized Hall-MHD Keplerian thin disks are investigated by using asymptotic expansions in the small disk aspect ratio \epsilon. The model incorporates the azimuthal and poloidal components of the magnetic fields in the leading order in \epsilon. The disk structure is described by an appropriate Grad-Shafranov equation for the poloidal flux function \psi that involves two arbitrary functions of \psi for the toroidal and poloidal currents. The flux function is symmetric about the midplane and satisfies certain boundary conditions at the near-horizontal disk edges. The boundary conditions model the combined effect of the primordial as well as the dipole-like magnetic fields. An analytical solution for the Hall equilibrium is achieved by further expanding the relevant equations in an additional small parameter \delta that is inversely proportional to the Hall parameter. It is thus found that the Hall equilibrium disks fall into two types: Keplerian disks with (i) small (Rd ~\delta^0) and (ii) large (Rd > \delta^k, k > 0) radius of the disk. The numerical examples that are presented demonstrate the richness and great variety of magnetic and density configurations that may be achieved under the Hall-MHD equilibrium.

On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration

We study the torque on low-mass protoplanets on fixed circular orbits, embedded in a protoplanetary disc in the isothermal limit. We consider a wide range of surface density distributions including cases where the surface density increases smoothly outwards. We perform both linear disc response calculations and non-linear numerical simulations. We consider a large range of viscosities, including the inviscid limit, as well as a range of protoplanet mass ratios, with special emphasis on the co-orbital region and the corotation torque acting between disc and protoplanet. For low-mass protoplanets and large viscosity, the corotation torque behaves as expected from linear theory. However, when the viscosity becomes small enough to enable horseshoe turns to occur, the linear corotation torque exists only temporarily after insertion of a planet into the disc, being replaced by the horseshoe drag first discussed by Ward. This happens after a time that is equal to the horseshoe libration period reduced by a factor amounting to about twice the disc aspect ratio. This torque scales with the radial gradient of specific vorticity, as does the linear torque, but we find it to be many times larger. If the viscosity is large enough for viscous diffusion across the co-orbital region to occur within a libration period, we find that the horseshoe drag may be sustained. If not, the corotation torque saturates leaving only the linear Lindblad torques. As the magnitude of the non-linear co-orbital torque (horseshoe drag) is always found to be larger than the linear torque, we find that the sign of the total torque may change even for mildly positive surface density gradients. In combination with a kinematic viscosity large enough to keep the torque from saturating, strong sustained deviations from linear theory and outward or stalled migration may occur in such cases.

Simulations of eccentric disks in close binary systems

We study the development of finite eccentricity in accretion disks in close binary systems using a two-dimensional grid-based numerical scheme. We perform detailed parameter studies to explore the dependence on viscosity, disk aspect ratio, the inclusion of a mass-transfer stream and the role of the boundary conditions. We consider mass ratios 0.05<q<0.3 appropriate to superoutbursting cataclysmic binary systems. Instability to the formation of a precessing eccentric disk that attains a quasi-steady state with mean eccentricity in the range 0.3-0.5 occurs readily. The shortest growth times are ~15 binary orbits for the largest viscosities and the instability mechanism is for the most part consistent with the mode-coupling mechanism associated with the 3:1 resonance proposed by Lubow. However, the results are sensitive to the treatment of the inner boundary and to the incorporation of the mass-transfer stream. In the presence of a stream we found a critical viscosity below which the disk remains circular. Incorporation of a mass-transfer stream tends to impart stability for small enough viscosity (or, equivalently, mass-transfer rate through the disk) and does assist in obtaining a prograde precession rate that is in agreement with observations. For the larger q the location of the 3:1 resonance is pushed outwards towards the Roche lobe where higher-order mode couplings and nonlinearity occur. It is likely that three-dimensional simulations that properly resolve the disk's vertical structure are required to make significant progress in this case.

The radial structure of protostellar accretion disks: influence of jets

The radial structure of accretion disks is a fundamental issue regarding star and planet formation. Many theoretical studies, focussing on different aspects such as e.g. disk emissivity or ionization, have been conducted in the context of the Standard Accretion Disk (SAD) model, where no jet is present. We wish to calculate the structure of YSO accretion disks in an approach that takes into account the presence of the protostellar jets. The radial structure of these Jet Emitting Disks (JED) should then be compared to that of standard accretion disks. The analytical treatment used in this work is very similar to that of standard accretion disks but is using the parameter space of Magnetised Accretion-Ejection Structures that include the jet torque on the underlying disk. In this framework, the analytical expressions of key quantities, such as mid-plane temperatures, surface densities or disk aspect ratio are derived. It is found that JEDs present a structure very different from the SADs and that can be observationally tested. The implications on planet formation in the inner regions of accretion disks are briefly discussed. We also supply sets of analytical formulae, valid in different opacity regimes, for the disk quantities. These expressions can be readily used for any work where the disk structure is needed as an input for the model.

On the dynamics of a twisted disc immersed in a radiation field

We study the dynamics of a twisted tilted disc under the influence of an external radiation field. Assuming the effect of absorption and re-emission/scattering is that a pressure is applied to the disc surface where the local optical depth is of the order of unity, we determine the response of the vertical structure and the influence it has on the possibility of instability to warping. We derive a pair of equations describing the evolution of a small tilt as a function of radius in the small-amplitude regime that applies to both the diffusive and the bending wave regimes. We also study the non-linear vertical response of the disc numerically using an analogous one-dimensional slab model. For global warps, we find that in order for the disc vertical structure to respond as a quasi-uniform shift or tilt, as has been assumed in previous work, the product of the ratio of the external radiation momentum flux to the local disc mid-plane pressure, where it is absorbed, with the disc aspect ratio should be significantly less than unity. Namely, this quantity should be of the order of or smaller than the ratio of the disc gas density corresponding to the layer intercepting radiation to the mid-plane density, λ≪ 1. When this condition is not satisfied, the disc surface tends to adjust so that the local normal becomes perpendicular to the radiation propagation direction. In this case, dynamical quantities determined by the disc twist and warp tend to oscillate with a large characteristic period T*∼λ−1TK, where TK is some ‘typical’ orbital period of a gas element in the disc. The possibility of warping instability then becomes significantly reduced. In addition, when the vertical response is non-uniform, the possible production of shocks may lead to an important dissipation mechanism.

Plasmonic Properties of Supported Pt and Pd Nanostructures

The plasmonic properties of nanodisk arrays of Pt, Pd, and, for comparison, Ag are studied over a large size and spectral range and analyzed theoretically by an electrostatic model. Pt and Pd nanodisks exhibit broad localized surface plasmons with a higher sensitivity of the plasmon to the disk aspect ratio compared to Ag. Extinction cross-sections are generally about 50% smaller for Pt and Pd. The spectral plasmon positions, line-widths, and extinction cross-sections are well reproduced by the model.