Mechanical properties of a degradable phosphate glass fibre reinforced polymer composite for internal fracture fixation

NOTICE: this is the author’s version of a work that was accepted for publication in Materials Science and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Materials Science and Engineering, [VOL 30, ISSUE 7, (2010)] DOI: 10.1016/j.msec.2010.04.017

Gas- and dust evolution in protoplanetary disks

Context. Current models of the size- and radial evolution of dust in protoplanetary disks generally oversimplify either the radial evolution of the disk (by focussing at one single radius or by using steady state disk models) or they assume particle growth to proceed monodispersely or without fragmentation. Further studies of protoplanetary disks - such as observations, disk chemistry and structure calculations or planet population synthesis models - depend on the distribution of dust as a function of grain size and radial position in the disk. Aims. We attempt to improve upon current models to be able to investigate how the initial conditions, the build-up phase, and the evolution of the protoplanetary disk influence growth and transport of dust. Methods. We introduce a new version of the model of Brauer et al. (2008) in which we now include the time-dependent viscous evolution of the gas disk, and in which more advanced input physics and numerical integration methods are implemented. Results. We show that grain properties, the gas pressure gradient, and the amount of turbulence are much more influencing the evolution of dust than the initial conditions or the build-up phase of the protoplanetary disk. We quantify which conditions or environments are favorable for growth beyond the meter size barrier. High gas surface densities or zonal flows may help to overcome the problem of radial drift, however already a small amount of turbulence poses a much stronger obstacle for grain growth.Comment: accepted to A&

Dust retention in protoplanetary disks

Context: Protoplanetary disks are observed to remain dust-rich for up to several million years. Theoretical modeling, on the other hand, raises several questions. Firstly, dust coagulation occurs so rapidly, that if the small dust grains are not replenished by collisional fragmentation of dust aggregates, most disks should be observed to be dust poor, which is not the case. Secondly, if dust aggregates grow to sizes of the order of centimeters to meters, they drift so fast inwards, that they are quickly lost. Aims: We attempt to verify if collisional fragmentation of dust aggregates is effective enough to keep disks 'dusty' by replenishing the population of small grains and by preventing excessive radial drift. Methods: With a new and sophisticated implicitly integrated coagulation and fragmentation modeling code, we solve the combined problem of coagulation, fragmentation, turbulent mixing and radial drift and at the same time solve for the 1-D viscous gas disk evolution. Results: We find that for a critical collision velocity of 1 m/s, as suggested by laboratory experiments, the fragmentation is so effective, that at all times the dust is in the form of relatively small particles. This means that radial drift is small and that large amounts of small dust particles remain present for a few million years, as observed. For a critical velocity of 10 m/s, we find that particles grow about two orders of magnitude larger, which leads again to significant dust loss since larger particles are more strongly affected by radial drift.Comment: Letter accepted 3 July 2009, included comments of language edito

Trapped surfaces in spherical expanding open universes

Consider spherically symmetric initial data for a cosmology which, in the large, approximates an open $k = -1 ,\Lambda = 0$ Friedmann-Lema{\^\i}tre universe. Further assume that the data is chosen so that the trace of the extrinsic curvature is a constant and that the matter field is at rest at this instant of time. One expects that no trapped surfaces appear in the data if no significant clump of excess matter is to be found. This letter confirms this belief by displaying a necessary condition for the existence of trapped surfaces.This necessary condition, simply stated, says that a relatively large amount of excess matter must be concentrated in a small volume for trapped surfaces to appear.Comment: 8 pages, Late

Bounds for the greatest characteristic root of an irreducible nonnegative matrix

AbstractA new lower bound for the Perron root for irreducible, non-negative matrices is obtained which is, in particular, a better bound than the Frobenius bound [w = max(akk)] if all the main diagonal elements are zero

Dust size distributions in coagulation/fragmentation equilibrium: Numerical solutions and analytical fits

Context. Grains in circumstellar disks are believed to grow by mutual collisions and subsequent sticking due to surface forces. Results of many fields of research involving circumstellar disks, such as radiative transfer calculations, disk chemistry, magneto-hydrodynamic simulations largely depend on the unknown grain size distribution. Aims. As detailed calculations of grain growth and fragmentation are both numerically challenging and computationally expensive, we aim to find simple recipes and analytical solutions for the grain size distribution in circumstellar disks for a scenario in which grain growth is limited by fragmentation and radial drift can be neglected. Methods. We generalize previous analytical work on self-similar steady-state grain distributions. Numerical simulations are carried out to identify under which conditions the grain size distributions can be understood in terms of a combination of power-law distributions. A physically motivated fitting formula for grain size distributions is derived using our analytical predictions and numerical simulations. Results. We find good agreement between analytical results and numerical solutions of the Smoluchowski equation for simple shapes of the kernel function. The results for more complicated and realistic cases can be fitted with a physically motivated "black box" recipe presented in this paper. Our results show that the shape of the dust distribution is mostly dominated by the gas surface density (not the dust-to-gas ratio), the turbulence strength and the temperature and does not obey an MRN type distribution.Comment: 16 pages, 9 figures, accepted for publication in A&

Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

Functional organization of the language network in three- and six-year-old children

The organization of the language network undergoes continuous changes during development as children learn to understand sentences. In the present study, functional magnetic resonance imaging and behavioral measures were utilized to investigate functional activation and functional connectivity (FC) in three-year-old (3yo) and six-year-old (6yo) children during sentence comprehension. Transitive German sentences varying the word order (subject-initial and object-initial) with case marking were presented auditorily. We selected children who were capable of processing the subject-initial sentences above chance level accuracy from each age group to ensure that we were tapping real comprehension. Both age groups showed a main effect of word order in the left posterior superior temporal gyrus (pSTG), with greater activation for object-initial compared to subject-initial sentences. However, age differences were observed in the FC between left pSTG and the left inferior frontal gyrus (IFG). The 6yo group showed stronger FC between the left pSTG and Brodmann area (BA) 44 of the left IFG compared to the 3yo group. For the 3yo group, in turn, the FC between left pSTG and left BA 45 was stronger than with left BA 44. Our study demonstrates that while task-related activation was comparable, the small behavioral differences between age groups were reflected in the underlying functional organization revealing the ongoing development of the neural language network