Micromagnetic Simulation of Nanoscale Films with Perpendicular Anisotropy

A model is studied for the theoretical description of nanoscale magnetic films with high perpendicular anisotropy. In the model the magnetic film is described in terms of single domain magnetic grains with Ising-like behavior, interacting via exchange as well as via dipolar forces. Additionally, the model contains an energy barrier and a coupling to an external magnetic field. Disorder is taken into account in order to describe realistic domain and domain wall structures. The influence of a finite temperature as well as the dynamics can be modeled by a Monte Carlo simulation. Many of the experimental findings can be investigated and at least partly understood by the model introduced above. For thin films the magnetisation reversal is driven by domain wall motion. The results for the field and temperature dependence of the domain wall velocity suggest that for thin films hysteresis can be described as a depinning transition of the domain walls rounded by thermal activation for finite temperatures.Comment: Revtex, Postscript Figures, to be published in J. Appl.Phy

Calder\'on-Zygmund operators in the Bessel setting

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.Comment: 21 page

Dynamics of Domains in Diluted Antiferromagnets

We investigate the dynamics of two-dimensional site-diluted Ising antiferromagnets. In an external magnetic field these highly disordered magnetic systems have a domain structure which consists of fractal domains with sizes on a broad range of length scales. We focus on the dynamics of these systems during the relaxation from a long-range ordered initial state to the disordered fractal-domain state after applying an external magnetic field. The equilibrium state with applied field consists of fractal domains with a size distribution which follows a power law with an exponential cut-off. The dynamics of the system can be understood as a growth process of this fractal-domain state in such a way that the equilibrium distribution of domains develops during time. Following these ideas quantitatively we derive a simple description of the time dependence of the order parameter. The agreement with simulations is excellent.Comment: Revtex, 6 pages, 5 Postscript figure

Riesz-Jacobi transforms as principal value integrals

We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz-Jacobi transforms of odd orders express as principal value integrals against kernels having non-integrable singularities on the diagonal. On the other hand, we show that the Riesz-Jacobi transforms of even orders are not singular operators. In fact they are given as usual integrals against integrable kernels plus or minus, depending on the order, the identity operator. Our analysis indicates that similar results, existing in the literature and corresponding to several other settings related to classical discrete and continuous orthogonal expansions, should be reinvestigated so as to be refined and in some cases also corrected.Comment: 30 page

Neighboring suboptimal control for vehicle guidance

The neighboring optimal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied (neighboring suboptimal control). This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. Neighboring suboptimal control is applied to the lunar launch problem. Two approaches, single optimization and multiple optimization for calculating the gains are used, and the gains are tested in a guidance simulation with a mismatch in the acceleration of gravity. Both approaches give acceptable results, but multiple optimization keeps the perturbed path closer to the nominal path

Heat and work distributions for mixed Gauss-Cauchy process

We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional external noise, with both sources of perturbations considered as additive and statistically independent forcings. We define thermodynamic quantities for trajectories of the process and analyze contributions to mechanical work and heat. As a working example we consider a particle subjected to a drag force and two independent Levy white noises with stability indices $\alpha=2$ and $\alpha=1$. The fluctuations of dissipated energy (heat) and distribution of work performed by the force acting on the system are addressed by examining contributions of Cauchy fluctuations to either bath or external force acting on the system

Peering into the formation history of β Pictoris b with VLTI/GRAVITY long-baseline interferometry

Context. β Pictoris is arguably one of the most studied stellar systems outside of our own. Some 30 yr of observations have revealed a highly-structured circumstellar disk, with rings, belts, and a giant planet: β Pictoris b. However very little is known about how this system came into being. Aims. Our objective is to estimate the C/O ratio in the atmosphere of β Pictoris b and obtain an estimate of the dynamical mass of the planet, as well as to refine its orbital parameters using high-precision astrometry. Methods. We used the GRAVITY instrument with the four 8.2 m telescopes of the Very Large Telescope Interferometer to obtain K-band spectro-interferometric data on β Pic b. We extracted a medium resolution (R = 500) K-band spectrum of the planet and a high-precision astrometric position. We estimated the planetary C/O ratio using two different approaches (forward modeling and free retrieval) from two different codes (ExoREM and petitRADTRANS, respectively). Finally, we used a simplified model of two formation scenarios (gravitational collapse and core-accretion) to determine which can best explain the measured C/O ratio. Results. Our new astrometry disfavors a circular orbit for β Pic b (e = 0.15_(−0.04)^(+0.05)). Combined with previous results and with HIPPARCOS/Gaia measurements, this astrometry points to a planet mass of M = 12.7 ± 2.2 M_(Jup). This value is compatible with the mass derived with the free-retrieval code petitRADTRANS using spectral data only. The forward modeling and free-retrieval approches yield very similar results regarding the atmosphere of β Pic b. In particular, the C/O ratios derived with the two codes are identical (0.43 ± 0.05 vs. 0.43_(−0.03)^(+0.04)). We argue that if the stellar C/O in β Pic is Solar, then this combination of a very high mass and a low C/O ratio for the planet suggests a formation through core-accretion, with strong planetesimal enrichment