Real time plasma equilibrium reconstruction in a Tokamak

The problem of equilibrium of a plasma in a Tokamak is a free boundary problemdescribed by the Grad-Shafranov equation in axisymmetric configurations. The right hand side of this equation is a non linear source, which represents the toroidal component of the plasma current density. This paper deals with the real time identification of this non linear source from experimental measurements. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation

Growth of Dust as the Initial Step Toward Planet Formation

We discuss the results of laboratory measurements and theoretical models concerning the aggregation of dust in protoplanetary disks, as the initial step toward planet formation. Small particles easily stick when they collide and form aggregates with an open, often fractal structure, depending on the growth process. Larger particles are still expected to grow at collision velocities of about 1m/s. Experiments also show that, after an intermezzo of destructive velocities, high collision velocities above 10m/s on porous materials again lead to net growth of the target. Considerations of dust-gas interactions show that collision velocities for particles not too different in surface-to-mass ratio remain limited up to sizes about 1m, and growth seems to be guaranteed to reach these sizes quickly and easily. For meter sizes, coupling to nebula turbulence makes destructive processes more likely. Global aggregation models show that in a turbulent nebula, small particles are swept up too fast to be consistent with observations of disks. An extended phase may therefore exist in the nebula during which the small particle component is kept alive through collisions driven by turbulence which frustrates growth to planetesimals until conditions are more favorable for one or more reasons.Comment: Protostars and Planets V (PPV) review. 18 pages, 5 figure

Construct, Merge, Solve and Adapt: Application to the repetition-free longest common subsequence problem

In this paper we present the application of a recently proposed, general, algorithm for combinatorial optimization to the repetition-free longest common subsequence problem. The applied algorithm, which is labelled Construct, Merge, Solve & Adapt, generates sub-instances based on merging the solution components found in randomly constructed solutions. These sub-instances are subsequently solved by means of an exact solver. Moreover, the considered sub-instances are dynamically changing due to adding new solution components at each iteration, and removing existing solution components on the basis of indicators about their usefulness. The results of applying this algorithm to the repetition-free longest common subsequence problem show that the algorithm generally outperforms competing approaches from the literature. Moreover, they show that the algorithm is competitive with CPLEX for small and medium size problem instances, whereas it outperforms CPLEX for larger problem instances.Peer ReviewedPostprint (author's final draft

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments

The growth processes from protoplanetary dust to planetesimals are not fully understood. Laboratory experiments and theoretical models have shown that collisions among the dust aggregates can lead to sticking, bouncing, and fragmentation. However, no systematic study on the collisional outcome of protoplanetary dust has been performed so far so that a physical model of the dust evolution in protoplanetary disks is still missing. We intend to map the parameter space for the collisional interaction of arbitrarily porous dust aggregates. This parameter space encompasses the dust-aggregate masses, their porosities and the collision velocity. With such a complete mapping of the collisional outcomes of protoplanetary dust aggregates, it will be possible to follow the collisional evolution of dust in a protoplanetary disk environment. We use literature data, perform own laboratory experiments, and apply simple physical models to get a complete picture of the collisional interaction of protoplanetary dust aggregates. In our study, we found four different types of sticking, two types of bouncing, and three types of fragmentation as possible outcomes in collisions among protoplanetary dust aggregates. We distinguish between eight combinations of porosity and mass ratio. For each of these cases, we present a complete collision model for dust-aggregate masses between 10^-12 and 10^2 g and collision velocities in the range 10^-4 to 10^4 cm/s for arbitrary porosities. This model comprises the collisional outcome, the mass(es) of the resulting aggregate(s) and their porosities. We present the first complete collision model for protoplanetary dust. This collision model can be used for the determination of the dust-growth rate in protoplanetary disks.Comment: accepted by Astronomy and Astrophysic

Collisions of small ice particles under microgravity conditions (II): Does the chemical composition of the ice change the collisional properties?

Context: Understanding the collisional properties of ice is important for understanding both the early stages of planet formation and the evolution of planetary ring systems. Simple chemicals such as methanol and formic acid are known to be present in cold protostellar regions alongside the dominant water ice; they are also likely to be incorporated into planets which form in protoplanetary disks, and planetary ring systems. However, the effect of the chemical composition of the ice on its collisional properties has not yet been studied. Aims: Collisions of 1.5 cm ice spheres composed of pure crystalline water ice, water with 5% methanol, and water with 5% formic acid were investigated to determine the effect of the ice composition on the collisional outcomes. Methods: The collisions were conducted in a dedicated experimental instrument, operated under microgravity conditions, at relative particle impact velocities between 0.01 and 0.19 m s^-1, temperatures between 131 and 160 K and a pressure of around 10^-5 mbar. Results: A range of coefficients of restitution were found, with no correlation between this and the chemical composition, relative impact velocity, or temperature. Conclusions: We conclude that the chemical composition of the ice (at the level of 95% water ice and 5% methanol or formic acid) does not affect the collisional properties at these temperatures and pressures due to the inability of surface wetting to take place. At a level of 5% methanol or formic acid, the structure is likely to be dominated by crystalline water ice, leading to no change in collisional properties. The surface roughness of the particles is the dominant factor in explaining the range of coefficients of restitution

Heat transfer across surfaces in contact - Practical effects of transient temperature and pressure environments Semiannual report, 1 Oct. 1965 - 1 Apr. 1966

Heat transfer across metal surfaces under transient temperature and pressure environmen

The Refractory-to-Ice Mass Ratio in Comets

We review the complex relationship between the dust-to-gas mass ratio usually estimated in the material lost by comets, and the Refractory-to-Ice mass ratio inside the nucleus, which constrains the origin of comets. Such a relationship is dominated by the mass transfer from the perihelion erosion to fallout over most of the nucleus surface. This makes the Refractory-to-Ice mass ratio inside the nucleus up to ten times larger than the dust-to-gas mass ratio in the lost material, because the lost material is missing most of the refractories which were inside the pristine nucleus before the erosion. We review the Refractory-to-Ice mass ratios available for the comet nuclei visited by space missions, and for the Kuiper Belt Objects with well defined bulk density, finding the 1-σ lower limit of 3. Therefore, comets and KBOs may have less water than CI-chondrites, as predicted by models of comet formation by the gravitational collapse of cm-sized pebbles driven by streaming instabilities in the protoplanetary disc

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&

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Numerical Simulations of Highly Porous Dust Aggregates in the Low-Velocity Collision Regime

A highly favoured mechanism of planetesimal formation is collisional growth. Single dust grains, which follow gas flows in the protoplanetary disc, hit each other, stick due to van der Waals forces and form fluffy aggregates up to centimetre size. The mechanism of further growth is unclear since the outcome of aggregate collisions in the relevant velocity and size regime cannot be investigated in the laboratory under protoplanetary disc conditions. Realistic statistics of the result of dust aggregate collisions beyond decimetre size is missing for a deeper understanding of planetary growth. Joining experimental and numerical efforts we want to calibrate and validate a computer program that is capable of a correct simulation of the macroscopic behaviour of highly porous dust aggregates. After testing its numerical limitations thoroughly we will check the program especially for a realistic reproduction of various benchmark experiments. We adopt the smooth particle hydrodynamics (SPH) numerical scheme with extensions for the simulation of solid bodies and a modified version of the Sirono porosity model. Experimentally measured macroscopic material properties of silica dust are implemented. We calibrate and test for the compressive strength relation and the bulk modulus. SPH has already proven to be a suitable tool to simulate collisions at rather high velocities. In this work we demonstrate that its area of application can not only be extended to low-velocity experiments and collisions. It can also be used to simulate the behaviour of highly porous objects in this velocity regime to a very high accuracy.The result of the calibration process in this work is an SPH code that can be utilised to investigate the collisional outcome of porous dust in the low-velocity regime.Comment: accepted by Astronomy & Astrophysic