Tracing large-scale structures in circumstellar disks with ALMA

Planets are supposed to form in circumstellar disks. The gravitational potential of a planet perturbs the disk and leads to characteristic structures, i.e. spiral waves and gaps, in the disk's density profile. We perform a large-scale parameter study of the observability of these planet-induced structures in circumstellar disks with ALMA. On the basis of HD and MHD simulations, we calculated the disk temperature structure and (sub)mm images of these systems. These were used to derive simulated ALMA images. Because appropriate objects are frequent in Taurus, we focused on a distance of 140pc and a declination of 20{\deg}. The explored range of star-disk-planet configurations consists of 6 HD simulations (including magnetic fields and different planet masses), 9 disk sizes, 15 total disk masses, 6 different central stars, and two different grain size distributions. On almost all scales and in particular down to a scale of a few AU, ALMA is able to trace disk structures induced by planet-disk interaction or by the influence of magnetic fields on the wavelength range between 0.4 and 2.0mm. In most cases, the optimum angular resolution is limited by the sensitivity. However, within the range of typical masses of protoplanetary disks (0.1-0.001Msun) the disk mass has a minor impact on the observability. It is possible to resolve disks down to 2.67e-6Msun and trace gaps induced by a planet with M_p/M_s = 0.001 in disks with 2.67e-4Msun with a signal-to-noise ratio greater than three. The central star has a major impact on the observability of gaps, as well as the considered maximum grainsize of the dust in the disk. In general, it is more likely to trace planet-induced gaps in our MHD models, because gaps are wider in the presence of magnetic fields. We also find that zonal flows resulting from MRI create gap-like structures in the disk's re-emission radiation, which are observable with ALMA.Comment: 17 pages, 21 figure

Existence of vertical spin stiffness in Landau-Lifshitz-Gilbert equation in ferromagnetic semiconductors

We calculate the magnetization torque due to the spin polarization of the itinerant electrons by deriving the kinetic spin Bloch equations based on the $s$-$d$ model. We find that the first-order gradient of the magnetization inhomogeneity gives rise to the current-induced torques, which are consistent to the previous works. At the second-order gradient, we find an effective magnetic field perpendicular to the spin stiffness filed. This field is proportional to the nonadiabatic parameter $\beta$. We show that this vertical spin stiffness term can significantly modify the domain-wall structure in ferromagnetic semiconductors and hence should be included in the Landau-Lifshitz-Gilbert equation in studying the magnetization dynamics.Comment: 7 pages, 4 figure

Magnetization reversal and anomalous coercive field temperature dependence in MnAs epilayers grown on GaAs(100) and GaAs(111)B

The magnetic properties of MnAs epilayers have been investigated for two different substrate orientations: GaAs(100) and GaAs(111). We have analyzed the magnetization reversal under magnetic field at low temperatures, determining the anisotropy of the films. The results, based on the shape of the magnetization loops, suggest a domain movement mechanism for both types of samples. The temperature dependence of the coercivity of the films has been also examined, displaying a generic anomalous reentrant behavior at T$>$200 K. This feature is independent of the substrate orientation and films thickness and may be associated to the appearance of new pinning centers due to the nucleation of the $\beta$-phase at high temperatures.Comment: 9 pages, 7 figure

Domain walls in (Ga,Mn)As diluted magnetic semiconductor

We report experimental and theoretical studies of magnetic domain walls in an in-plane magnetized (Ga,Mn)As dilute moment ferromagnetic semiconductor. Our high-resolution electron holography technique provides direct images of domain wall magnetization profiles. The experiments are interpreted based on microscopic calculations of the micromagnetic parameters and Landau-Lifshitz-Gilbert simulations. We find that the competition of uniaxial and biaxial magnetocrystalline anisotropies in the film is directly reflected in orientation dependent wall widths, ranging from approximately 40 nm to 120 nm. The domain walls are of the N\'eel type and evolve from near-$90^{\circ}$ walls at low-temperatures to large angle [1$\bar{1}$0]-oriented walls and small angle [110]-oriented walls at higher temperatures.Comment: 5 pages, 4 figure

Giant Planar Hall Effect in Epitaxial (Ga,Mn)As Devices

Large Hall resistance jumps are observed in microdevices patterned from epitaxial (Ga,Mn)As layers when subjected to a swept, in-plane magnetic field. This giant planar Hall effect is four orders of magnitude greater than previously observed in metallic ferromagnets. This enables extremely sensitive measurements of the angle-dependent magnetic properties of (Ga,Mn)As. The magnetic anisotropy fields deduced from these measurements are compared with theoretical predictions.Comment: 3 figure

A smooth cascade of wrinkles at the edge of a floating elastic film

The mechanism by which a patterned state accommodates the breaking of translational symmetry by a phase boundary or a sample wall has been addressed in the context of Landau branching in type-I superconductors, refinement of magnetic domains, and compressed elastic sheets. We explore this issue by studying an ultrathin polymer sheet floating on the surface of a fluid, decorated with a pattern of parallel wrinkles. At the edge of the sheet, this corrugated profile meets the fluid meniscus. Rather than branching of wrinkles into generations of ever-smaller sharp folds, we discover a smooth cascade in which the coarse pattern in the bulk is matched to fine structure at the edge by the continuous introduction of discrete, higher wavenumber Fourier modes. The observed multiscale morphology is controlled by a dimensionless parameter that quantifies the relative strength of the edge forces and the rigidity of the bulk pattern.Comment: 4 pages, 4 figure

Determination of the micromagnetic parameters in (Ga,Mn)As using domain theory

The magnetic domain structure and magnetic properties of a ferromagnetic (Ga,Mn)As epilayer with perpendicular magnetic easy-axis are investigated. We show that, despite strong hysteresis, domain theory at thermodynamical equilibrium can be used to determine the micromagnetic parameters. Combining magneto-optical Kerr microscopy, magnetometry and ferromagnetic resonance measurements, we obtain the characteristic parameter for magnetic domains $\lambda_c$, the domain wall width and specific energy, and the spin stiffness constant as a function of temperature. The nucleation barrier for magnetization reversal and the Walker breakdown velocity for field-driven domain wall propagation are also estimated

Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal--vertical plane of the disk is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the mid-plane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the mid-plane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the mid-plane where the dust-to-gas ratio is significant. Nevertheless the dust density has a strong non-axisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the non-axisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4Comment: Accepted for publication in ApJ. Some minor changes due to referee report, most notably that the clumping mechanism has been identified as the streaming instability of Youdin & Goodman (2005). Movies of the simulations are still available at http://www.mpia.de/homes/johansen/research_en.ph

Nearly Optimal Private Convolution

We study computing the convolution of a private input $x$ with a public input $h$, while satisfying the guarantees of $(\epsilon, \delta)$-differential privacy. Convolution is a fundamental operation, intimately related to Fourier Transforms. In our setting, the private input may represent a time series of sensitive events or a histogram of a database of confidential personal information. Convolution then captures important primitives including linear filtering, which is an essential tool in time series analysis, and aggregation queries on projections of the data. We give a nearly optimal algorithm for computing convolutions while satisfying $(\epsilon, \delta)$-differential privacy. Surprisingly, we follow the simple strategy of adding independent Laplacian noise to each Fourier coefficient and bounding the privacy loss using the composition theorem of Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal noise to add to each Fourier coefficient using convex programming duality. Our algorithm is very efficient -- it is essentially no more computationally expensive than a Fast Fourier Transform. To prove near optimality, we use the recent discrepancy lowerbounds of Muthukrishnan and Nikolov and derive a spectral lower bound using a characterization of discrepancy in terms of determinants