Rotation-limited growth of three dimensional body-centered cubic crystals

According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the microscopic rearrangement of mass between grains. Here we consider coarsening of body-centered cubic polycrystalline materials in three dimensions using the phase field crystal model. We observe as function of the quenching depth, a cross over between a state where grain rotation halts and the growth stagnates and a state where grains coarsen rapidly by coalescence through rotation and alignment of the lattices of neighboring grains. We show that the grain rotation per volume change of a grain follows a power law with an exponent of $-1.25$. The scaling exponent is consistent with theoretical considerations based on the conservation of dislocations

The correction for the gamma-ray component in neutron therapy

Neutron beams for therapy always contain some gamma ray contamination that varies with depth and with distance from the beam axis. The problem therefore arises how the varying gamma ray contribution should be accounted for in dose specification. Not infrequently a ``total effective dose'' DE is quoted that is equal to the neutron dose plus the gamma ray dose divided by a constant weight factor tau. On general biophysical considerations this appears to be not a valid approach since it must be assumed that tau decreases with increasing dose. The nature and the magnitude of this dose dependence is derived in the present article. Application of the results to actual doses per fraction and to factual gamma ray to neutron ratios demonstrates that the dose dependence of tau has, in fact, very minor influence on the numerical values of DE. Utilization of a constant value tau is therefore satisfactory in practice

Selecting the rank of truncated SVD by Maximum Approximation Capacity

Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization problem into a noisy channel coding problem. The optimal approximation capacity of this channel controls the appropriate strength of regularization to suppress noise. In simulation experiments, this information theoretic method to determine the optimal rank competes with state-of-the art model selection techniques.Comment: 7 pages, 5 figures; Will be presented at the IEEE International Symposium on Information Theory (ISIT) 2011. The conference version has only 5 pages. This version has an extended appendi

Monads in Double Categories

We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and define what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.Comment: 30 pages; v2: accepted for publication in the Journal of Pure and Applied Algebra; added hypothesis in Theorem 3.7 that source and target functors preserve equalizers; on page 18, bottom, in the statement concerning the existence of a left adjoint, "if and only if" was replaced by "a sufficient condition"; acknowledgements expande

Exact dynamics in the inhomogeneous central-spin model

We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. This formula is evaluated explicitly for initial conditions such that the bath spins are completely polarized at the beginning. For this case we find, after an initial decay, a persistent oscillatory behaviour of the central spin. For a large number of bath spins $N_b$, the oscillation frequency is proportional to $N_b$, whereas the amplitude behaves like $1/N_b$, to leading order. No asymptotic decay due to the non-uniform couplings is observed, in contrast to some recent studies.Comment: 7 pages, 3 figure

Velocity-Dependent Forces in Atomic Force Microscopy Imaging of Lipid Films

We have imaged adsorbed fluid lipid bilayers by atomic force microscopy. The patches were formed by rupture of phospholipid vesicles onto magnesium fluoride. We show that the membrane patches are fluid but can be stably imaged at scan rates higher than 6 p d s . At lower scan rates the tip penetrates through the layer. The penetrating tip does not destroy the fluid patches, and the previous image can be restored after increasing the scanning velocity. The dynamic forces that possibly explain the effect are discussed