On empirical models of the upper atmosphere in the polar regions

Modified expression for exospheric temperature in Jacchia static diffusion models of upper atmosphere in polar region

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier

The sticking of micron sized dust particles due to surface forces in circumstellar disks is the first stage in the production of asteroids and planets. The key ingredients that drive this process are the relative velocity between the dust particles in this environment and the complex physics of dust aggregate collisions. Here we present the results of a collision model, which is based on laboratory experiments of these aggregates. We investigate the maximum aggregate size and mass that can be reached by coagulation in protoplanetary disks. We model the growth of dust aggregates at 1 AU at the midplane at three different gas densities. We find that the evolution of the dust does not follow the previously assumed growth-fragmentation cycles. Catastrophic fragmentation hardly occurs in the three disk models. Furthermore we see long lived, quasi-steady states in the distribution function of the aggregates due to bouncing. We explore how the mass and the porosity change upon varying the turbulence parameter and by varying the critical mass ratio of dust particles. Particles reach Stokes numbers of roughly 10^-4 during the simulations. The particle growth is stopped by bouncing rather than fragmentation in these models. The final Stokes number of the aggregates is rather insensitive to the variations of the gas density and the strength of turbulence. The maximum mass of the particles is limited to approximately 1 gram (chondrule-sized particles). Planetesimal formation can proceed via the turbulent concentration of these aerodynamically size-sorted chondrule-sized particles.Comment: accepted for publication in A&

Crossing barriers in planetesimal formation: The growth of mm-dust aggregates with large constituent grains

Collisions of mm-size dust aggregates play a crucial role in the early phases of planet formation. We developed a laboratory setup to observe collisions of dust aggregates levitating at mbar pressures and elevated temperatures of 800 K. We report on collisions between basalt dust aggregates of from 0.3 to 5 mm in size at velocities between 0.1 and 15 cm/s. Individual grains are smaller than 25 \mum in size. We find that for all impact energies in the studied range sticking occurs at a probability of 32.1 \pm 2.5% on average. In general, the sticking probability decreases with increasing impact parameter. The sticking probability increases with energy density (impact energy per contact area). We also observe collisions of aggregates that were formed by a previous sticking of two larger aggregates. Partners of these aggregates can be detached by a second collision with a probability of on average 19.8 \pm 4.0%. The measured accretion efficiencies are remarkably high compared to other experimental results. We attribute this to the rel. large dust grains used in our experiments, which make aggregates more susceptible to restructuring and energy dissipation. Collisional hardening by compaction might not occur as the aggregates are already very compact with only 54 \pm 1% porosity. The disassembly of previously grown aggregates in collisions might stall further aggregate growth. However, owing to the levitation technique and the limited data statistics, no conclusive statement about this aspect can yet be given. We find that the detachment efficiency decreases with increasing velocities and accretion dominates in the higher velocity range. For high accretion efficiencies, our experiments suggest that continued growth in the mm-range with larger constituent grains would be a viable way to produce larger aggregates, which might in turn form the seeds to proceed to growing planetesimals.Comment: 9 pages, 20 figure

Security of Quantum Bit-String Generation

We consider the cryptographic task of bit-string generation. This is a generalisation of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A {\bf 69}, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning both quantum and classical possibilities for large n cryptography. An experiment corresponding to the scheme analysed in this paper has been performed and is reported elsewhere.Comment: 16 pages. No figures. Accepted for publication in Phys. Rev. A. A corresponding experiment is reported in quant-ph/040812

Scaling in Complex Systems: Analytical Theory of Charged Pores

In this paper we find an analytical solution of the equilibrium ion distribution for a toroidal model of a ionic channel, using the Perfect Screening Theorem (PST). The ions are charged hard spheres, and are treated using a variational Mean Spherical Approximation (VMSA) . Understanding ion channels is still a very open problem, because of the many exquisite tuning details of real life channels. It is clear that the electric field plays a major role in the channel behaviour, and for that reason there has been a lot of work on simple models that are able to provide workable theories. Recently a number of interesting papers have appeared that discuss models in which the effect of the geometry, excluded volume and non-linear behaviour is considered. We present here a 3D model of ionic channels which consists of a charged, deformable torus with a circular or elliptical cross section, which can be flat or vertical (close to a cylinder). Extensive comparisons to MC simulations were performed. The new solution opens new possibilities, such as studying flexible pores, and water phase transformations inside the pores using an approach similar to that used on flat crystal surfaces