Self-similar Solutions to a Kinetic Model for Grain Growth

We prove the existence of self-similar solutions to the Fradkov model for two-dimensional grain growth, which consists of an infinite number of nonlocally coupled transport equations for the number densities of grains with given area and number of neighbours (topological class). For the proof we introduce a finite maximal topological class and study an appropriate upwind-discretization of the time dependent problem in self-similar variables. We first show that the resulting finite dimensional differential system has nontrivial steady states. Afterwards we let the discretization parameter tend to zero and prove that the steady states converge to a compactly supported self-similar solution for a Fradkov model with finitely many equations. In a third step we let the maximal topology class tend to infinity and obtain self-similar solutions to the original system that decay exponentially. Finally, we use the upwind discretization to compute self-similar solutions numerically.Comment: 25 pages, several figure

A Kinetic Model for Grain Growth

We provide a well-posedness analysis of a kinetic model for grain growth introduced by Fradkov which is based on the von Neumann-Mullins law. The model consists of an infinite number of transport equations with a tri-diagonal coupling modelling topological changes in the grain configuration. Self-consistency of this kinetic model is achieved by introducing a coupling weight which leads to a nonlinear and nonlocal system of equations. We prove existence of solutions by approximation with finite dimensional systems. Key ingredients in passing to the limit are suitable super-solutions, a bound from below on the total mass, and a tightness estimate which ensures that no mass is transported to infinity in finite time.Comment: 24 page

Granular Matter: a wonderful world of clusters in far-from-equilibrium systems

In this paper, we recall various features of non equilibrium granular systems. Clusters with specific properties are found depending on the packing density, going from loose (a granular gas) to sintered (though brittle) polycrystalline materials. The phase space available can be quite different. Unexpected features, with respect to standard or expected ones in classical fluids or solids, are observed, - like slow relaxation processes or anomalous electrical and thermoelectrical transport property dependences. The cases of various pile structures and the interplay between classical phase transitions and self-organized criticality for avalanches are also outlined.Comment: 7 figures, 37 refs., to be published in Physica

A High-Mass Protobinary System in the Hot Core W3(H2O)

We have observed a high-mass protobinary system in the hot core W3(H2O) with the BIMA Array. Our continuum maps at wavelengths of 1.4mm and 2.8mm both achieve sub-arcsecond angular resolutions and show a double-peaked morphology. The angular separation of the two sources is 1.19" corresponding to 2.43X10^3 AU at the source distance of 2.04 kpc. The flux densities of the two sources at 1.4mm and 2.8mm have a spectral index of 3, translating to an opacity law of kappa ~ nu. The small spectral indices suggest that grain growth has begun in the hot core. We have also observed 5 K components of the CH3CN (12-11) transitions. A radial velocity difference of 2.81 km/s is found towards the two continuum peaks. Interpreting these two sources as binary components in orbit about one another, we find a minimum mass of 22 Msun for the system. Radiative transfer models are constructed to explain both the continuum and methyl cyanide line observations of each source. Power-law distributions of both density and temperature are derived. Density distributions close to the free-fall value, r^-1.5, are found for both components, suggesting continuing accretion. The derived luminosities suggest the two sources have equivalent zero-age main sequence (ZAMS) spectral type B0.5 - B0. The nebular masses derived from the continuum observations are about 5 Msun for source A and 4 Msun for source C. A velocity gradient previously detected may be explained by unresolved binary rotation with a small velocity difference.Comment: 38 pages, 9 figures, accepted by The Astrophysical Journa

Grain charging in protoplanetary discs

Recent work identified a growth barrier for dust coagulation that originates in the electric repulsion between colliding particles. Depending on its charge state, dust material may have the potential to control key processes towards planet formation such as MHD (magnetohydrodynamic) turbulence and grain growth which are coupled in a two-way process. We quantify the grain charging at different stages of disc evolution and differentiate between two very extreme cases: compact spherical grains and aggregates with fractal dimension D_f = 2. Applying a simple chemical network that accounts for collisional charging of grains, we provide a semi-analytical solution. This allowed us to calculate the equilibrium population of grain charges and the ionisation fraction efficiently. The grain charging was evaluated for different dynamical environments ranging from static to non-stationary disc configurations. The results show that the adsorption/desorption of neutral gas-phase heavy metals, such as magnesium, effects the charging state of grains. The greater the difference between the thermal velocities of the metal and the dominant molecular ion, the greater the change in the mean grain charge. Agglomerates have more negative excess charge on average than compact spherical particles of the same mass. The rise in the mean grain charge is proportional to N**(1/6) in the ion-dust limit. We find that grain charging in a non-stationary disc environment is expected to lead to similar results. The results indicate that the dust growth and settling in regions where the dust growth is limited by the so-called "electro-static barrier" do not prevent the dust material from remaining the dominant charge carrier.Comment: 18 pages, 10 figures, accepted for publication in Astronomy and Astrophysic

Review on the prediction of residual stress in welded steel components

Residual stress after welding has negative effects on the service life of welded steel components or structures. This work reviews three most commonly used methods for predicting residual stress, namely, empirical, semi-empirical and process simulation methods. Basic principles adopted by these methods are introduced. The features and limitations of each method are discussed as well. The empirical method is the most practical but its accuracy relies heavily on experiments. Mechanical theories are employed in the semi-empirical method, while other aspects, such as temperature variation and phase transformation, are simply ignored. The process simulation method has been widely used due to its capability of handling with large and complex components. To improve its accuracy and efficiency, several improvements need to be done for each simulation aspect of this method