An introduction to Multitrace Formulations and Associated Domain Decomposition Solvers

Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We introduce in this paper MTFs on a simple model problem using concepts familiar to researchers in domain decomposition. This allows us to get a new understanding of MTFs and a natural block Jacobi iteration, for which we determine optimal relaxation parameters. We then show how iterative multitrace formulation solvers are related to a well known domain decomposition method called optimal Schwarz method: a method which used Dirichlet to Neumann maps in the transmission condition. We finally show that the insight gained from the simple model problem leads to remarkable identities for Calderon projectors and related operators, and the convergence results and optimal choice of the relaxation parameter we obtained is independent of the geometry, the space dimension of the problem{\color{black}, and the precise form of the spatial elliptic operator, like for optimal Schwarz methods. We illustrate our analysis with numerical experiments

Asymptotics for a special solution to the second member of the Painleve I hierarchy

We study the asymptotic behavior of a special smooth solution y(x,t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of Hamiltonian perturbations of hyperbolic equations. The asymptotic behavior of y(x,t) if x\to \pm\infty (for fixed t) is known and relatively simple, but it turns out to be more subtle when x and t tend to infinity simultaneously. We distinguish a region of algebraic asymptotic behavior and a region of elliptic asymptotic behavior, and we obtain rigorous asymptotics in both regions. We also discuss two critical transitional asymptotic regimes.Comment: 19 page

Where are Hf and REE hosted in CV – CK chondrites? Clues to understanding the εHf heterogeneities in CHUR.

第3回極域科学シンポジウム/第35回南極隕石シンポジウム 11月30日（金） 国立国語研究所 2階講

Noninvasive Embedding of Single Co Atoms in Ge(111)2x1 Surfaces

We report on a combined scanning tunneling microscopy (STM) and density functional theory (DFT) based investigation of Co atoms on Ge(111)2x1 surfaces. When deposited on cold surfaces, individual Co atoms have a limited diffusivity on the atomically flat areas and apparently reside on top of the upper pi-bonded chain rows exclusively. Voltage-dependent STM imaging reveals a highly anisotropic electronic perturbation of the Ge surface surrounding these Co atoms and pronounced one-dimensional confinement along the pi-bonded chains. DFT calculations reveal that the individual Co atoms are in fact embedded in the Ge surface, where they occupy a quasi-stationary position within the big 7-member Ge ring in between the 3rd and 4th atomic Ge layer. The energy needed for the Co atoms to overcome the potential barrier for penetration in the Ge surface is provided by the kinetic energy resulting from the deposition process. DFT calculations further demonstrate that the embedded Co atoms form four covalent Co-Ge bonds, resulting in a Co4+ valence state and a 3d5 electronic configuration. Calculated STM images are in perfect agreement with the experimental atomic resolution STM images for the broad range of applied tunneling voltages.Comment: 19 pages, 15 figures, 3 table

Belgian-Japanese search for Antarctic meteorites during the 2010.2011 field season.

第2回極域科学シンポジウム/第34回南極隕石シンポジウム 11月17日（木） 国立国語研究所 2階講

Something interacting and solvable in 1D

We present a two-parameter family of exactly solvable quantum many-body systems in one spatial dimension containing the Lieb-Liniger model of interacting bosons as a particular case. The principal building block of this construction is the previously-introduced (arXiv:1712.09375) family of two-particle scattering matrices. We discuss an $SL(2)$ transformation connecting the models within this family and make a correspondence with generalized point interactions. The Bethe equations for the ground state are discussed with a special emphasis on "non-interacting modes" connected by the modular subgroup of $SL(2)$. The bound state solutions are discussed and are conjectured to follow some correlated version of the string hypothesis. The excitation spectrum of the new models in this family is derived in analogy to the Lieb-Liniger model and we show that for certain choices of parameters a spectrum inversion occurs such that the Umklapp solutions become the new ground state.Comment: 11 pages, 6 figure

Effects of a flat rate introduction: shifts in farm activity and impact on farmers' income

Current thoughts on CAP changes, e.g. the "Health Check", emphasize the necessity to move away from payments based on historical receipts towards a "flatter rate" system. The aim of current research is to simulate the impact of a flat rate system (equal payments per hectare of cultivated land) compared to the current historical system (payments based on individual historic entitlements). Impact on production and income of arable, dairy and cattle farms of two different flat rate scenario's, is assessed with a farm-based sector model for Flanders. The model maximizes income at farm level, calibrated to observed farming behavior in 2001-2003. Farm data can be selected by farm type, size and region, simulations could be run for specific sub sectors, size classes or regions. In the two simulated flat rate scenario's subsectors will gain subsidies at the expense of other subsectors. However, farms can compensate a substantial part of their income loss by changing activity choice.Positive Mathematical Programming, farm model, Common Agricultural Policy, Payment Entitlements., Agricultural and Food Policy, Agricultural Finance, Farm Management, Research Methods/ Statistical Methods,

System occupancy of a two-class batch-service queue with class-dependent variable server capacity

Due to their wide area of applications, queueing models with batch service, where the server can process several customers simultaneously, have been studied frequently. An important characteristic of such batch-service systems is the size of a batch, that is the number of customers that are processed simultaneously. In this paper, we analyse a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common first-come-first served single-server queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the number of consecutive same-class customers. After establishing the system equations that govern the system behaviour, we deduce an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. Also, some numerical examples are given that provide further insight in the impact of the different parameters on the system performance

Critical behavior in Angelesco ensembles

We consider Angelesco ensembles with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], for a < 0. As a \to -1 the particles around 0 experience a phase transition. This transition is studied in a double scaling limit, where we let the number of particles of the ensemble tend to infinity while the parameter a tends to -1 at a rate of order n^{-1/2}. The correlation kernel converges, in this regime, to a new kind of universal kernel, the Angelesco kernel K^{Ang}. The result follows from the Deift/Zhou steepest descent analysis, applied to the Riemann-Hilbert problem for multiple orthogonal polynomials.Comment: 32 pages, 9 figure