Diophantine approximation on Veech surfaces

We show that Y. Cheung's general $Z$-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates. The saddle connection continued fractions then allow one to recognize certain transcendental directions by their developments

Mapping the Conditions for Hydrodynamic Instability on Steady State Accretion Models of Protoplanetary Disks

Hydrodynamical instabilities in disks around young stars depend on the thermodynamic stratification of the disk and on the local rate of thermal relaxation. Here, we map the spatial extent of unstable regions for the Vertical Shear Instability (VSI), the Convective OverStability (COS), and the amplification of vortices via the Subcritical Baroclinic Instability (SBI). We use steady state accretion disk models, including stellar irradiation, accretion heating and radiative transfer. We determine the local radial and vertical stratification and thermal relaxation rate in the disk, in dependence of the stellar mass, disk mass and mass accretion rate. We find that passive regions of disks - i.e. the midplane temperature dominated by irradiation - are COS unstable about one pressure scale height above the midplane and VSI unstable at radii $> 10 \, \text{au}$. Vortex amplification via SBI should operate in most parts of active and passive disks. For active parts of disks (midplane temperature determined by accretion power) COS can become active down to the midplane. Same is true for the VSI because of the vertically adiabatic stratification of an internally heated disk. If hydro instabilities or other non-ideal MHD processes are able to create $\alpha$-stresses ($> 10^{-5}$) and released accretion energy leads to internal heating of the disk, hydrodynamical instabilities are likely to operate in significant parts of the planet forming zones in disks around young stars, driving gas accretion and flow structure formation. Thus hydro-instabilities are viable candidates to explain the rings and vortices observed with ALMA and VLT.Comment: 24 pages, 13 figures, Accepted for publication in Ap

The FireBird Mission – A Scientific Mission for Earth Observation and Hot SpotDetection

More than 10 years ago the first specialized small satellite for hot spot recognition and fire observation was designed, built and operated by several DLR departments. This BIRD (Bi-spectral Infra Red Detection) satellite demonstrated the capability of fire monitoring from space by using a dedicated small satellite and sensor system. On the other hand it has shown that DLR is capable to manage nearly a complete space mission “in house”. The comparison of typical BIRD data with the well-known MODIS fire products led to the label “fire zoom” for BIRD data. It is due to the high geometric and radiometric resolution of BIRD fire products. Typically small fires with a diameter of 4m could be detected. The precise estimation of fire parameters was successfully shown without problems like false alarms. The success of BIRD opened the doors for next steps. The scientific DLR Earth observation mission “FireBird” will continue the fire monitoring topic by using two small satellites (TET-1, launched June 2012, BIROS launch planed 2014). The paper shall present this mission. It will finally be focused on possible interfaces for a desired worldwide international scientific cooperation within this running space mission

High-resolution simulations of planetesimal formation in turbulent protoplanetary discs

We present high-resolution computer simulations of dust dynamics and planetesimal formation in turbulence generated by the magnetorotational instability. We show that the turbulent viscosity associated with magnetorotational turbulence in a non-stratified shearing box increases when going from 256^3 to 512^3 grid points in the presence of a weak imposed magnetic field, yielding a turbulent viscosity of $\alpha\approx0.003$ at high resolution. Particles representing approximately meter-sized boulders concentrate in large-scale high-pressure regions in the simulation box. The appearance of zonal flows and particle concentration in pressure bumps is relatively similar at moderate (256^3) and high (512^3) resolution. In the moderate-resolution simulation we activate particle self-gravity at a time when there is little particle concentration, in contrast with previous simulations where particle self-gravity was activated during a concentration event. We observe that bound clumps form over the next ten orbits, with initial birth masses of a few times the dwarf planet Ceres. At high resolution we activate self-gravity during a particle concentration event, leading to a burst of planetesimal formation, with clump masses ranging from a significant fraction of to several times the mass of Ceres. We present a new domain decomposition algorithm for particle-mesh schemes. Particles are spread evenly among the processors and the local gas velocity field and assigned drag forces are exchanged between a domain-decomposed mesh and discrete blocks of particles. We obtain good load balancing on up to 4096 cores even in simulations where particles sediment to the mid-plane and concentrate in pressure bumps.Comment: Accepted for publication in Astronomy & Astrophysics, with some changes in response to referee repor

Enforcing Secure Object Initialization in Java

Sun and the CERT recommend for secure Java development to not allow partially initialized objects to be accessed. The CERT considers the severity of the risks taken by not following this recommendation as high. The solution currently used to enforce object initialization is to implement a coding pattern proposed by Sun, which is not formally checked. We propose a modular type system to formally specify the initialization policy of libraries or programs and a type checker to statically check at load time that all loaded classes respect the policy. This allows to prove the absence of bugs which have allowed some famous privilege escalations in Java. Our experimental results show that our safe default policy allows to prove 91% of classes of java.lang, java.security and javax.security safe without any annotation and by adding 57 simple annotations we proved all classes but four safe. The type system and its soundness theorem have been formalized and machine checked using Coq