PopCORN: Hunting down the differences between binary population synthesis codes

Binary population synthesis (BPS) modelling is a very effective tool to study the evolution and properties of close binary systems. The uncertainty in the parameters of the model and their effect on a population can be tested in a statistical way, which then leads to a deeper understanding of the underlying physical processes involved. To understand the predictive power of BPS codes, we study the similarities and differences in the predicted populations of four different BPS codes for low- and intermediate-mass binaries. We investigate whether the differences are caused by different assumptions made in the BPS codes or by numerical effects. To simplify the complex problem of comparing BPS codes, we equalise the inherent assumptions as much as possible. We find that the simulated populations are similar between the codes. Regarding the population of binaries with one WD, there is very good agreement between the physical characteristics, the evolutionary channels that lead to the birth of these systems, and their birthrates. Regarding the double WD population, there is a good agreement on which evolutionary channels exist to create double WDs and a rough agreement on the characteristics of the double WD population. Regarding which progenitor systems lead to a single and double WD system and which systems do not, the four codes agree well. Most importantly, we find that for these two populations, the differences in the predictions from the four codes are not due to numerical differences, but because of different inherent assumptions. We identify critical assumptions for BPS studies that need to be studied in more detail.Comment: 13 pages, +21 pages appendix, 35 figures, accepted for publishing in A&A, Minor change to match published version, most important the added link to the website http://www.astro.ru.nl/~silviato/popcorn for more detailed figures and informatio

The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation

We establish the existence of a real solution y(x,T) with no poles on the real line of the following fourth order analogue of the Painleve I equation, x=Ty-({1/6}y^3+{1/24}(y_x^2+2yy_{xx})+{1/240}y_{xxxx}). This proves the existence part of a conjecture posed by Dubrovin. We obtain our result by proving the solvability of an associated Riemann-Hilbert problem through the approach of a vanishing lemma. In addition, by applying the Deift/Zhou steepest-descent method to this Riemann-Hilbert problem, we obtain the asymptotics for y(x,T) as x\to\pm\infty.Comment: 27 pages, 5 figure

Progenitors of Supernovae Type Ia

Despite the significance of Type Ia supernovae (SNeIa) in many fields in astrophysics, SNeIa lack a theoretical explanation. The standard scenarios involve thermonuclear explosions of carbon/oxygen white dwarfs approaching the Chandrasekhar mass; either by accretion from a companion or by a merger of two white dwarfs. We investigate the contribution from both channels to the SNIa rate with the binary population synthesis (BPS) code SeBa in order to constrain binary processes such as the mass retention efficiency of WD accretion and common envelope evolution. We determine the theoretical rates and delay time distribution of SNIa progenitors and in particular study how assumptions affect the predicted rates.Comment: 6 pages, 6 figures, appeared in proceedings for "The 18th European White Dwarf Workshop

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

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

Stable isotope paleoecology (d¹³C and d¹⁸O) of early Eocene <i>Zeauvigerina aegyptiaca</i> from the North Atlantic (DSDP Site 401)

Within the expanded and clay-enriched interval following the Paleocene-Eocene Thermal Maximum (PETM; ~55.8 Ma) at Deep Sea Drilling Project (DSDP) Site 401 (eastern North Atlantic), high abundances of well-preserved biserial planktic foraminifera such as Zeauvigerina aegyptiaca and Chiloguembelina spp. occur. The paleoecological preferences of these taxa are only poorly constrained, largely because existing records are patchy in time and space. The thin-walled Z. aegyptiaca is usually rather small (13C and d18O) study of well-preserved specimens of Z. aegyptiaca and several planktic foraminiferal species (Morozovella subbotinae, Subbotina patagonica, Chiloguembelina wilcoxensis) enabled us to determine the preferred depth habitat and mode of life for Z. aegyptiaca. Oxygen isotope values of Z. aegyptiaca range from -1.57‰ to -2.07‰ and overlap with those of M. subbotinae indicating that their habitat is (1) definitely planktic, which has been questioned by some earlier isotopic studies, and (2) probably within the lower surface mixed layer. Carbon isotope ratios range from 0.99‰ to 1.34‰ and are distinctly lower than values for non-biserial planktic species. This may indicate isotopic disequilibrium between ambient seawater and the calcareous tests of Z. aegyptiaca, which we relate to vital effects and to its opportunistic behavior. The observed isotopic signal of Z. aegyptiaca relative to the other planktic foraminiferal species is highly similar to many other microperforate bi- and triserial planktic genera that have appeared through geological time such as Heterohelix, Guembelitria, Chiloguembelina, Streptochilus and Gallitellia and we suggest that Z. aegyptiaca shares a similar ecology and habitat. Thus, in order for the opportunistic Z. aegyptiaca to bloom during the aftermath of the PETM, we assume that at that time, the surface waters at Site 401 were influenced by increased terrestrial run-off and nutrient availability

Scholar-activists in an expanding European food sovereignty movement

This article analyzes the roles, relations, and positions of scholar-activists in the European food sovereignty movement. In doing so, we document, make visible and question the political dimensions of researchers' participation in the movement. We argue that scholar-activists are part of the movement, but are distinct from the affected constituencies, put in place to ensure adequate representation of key movement actors. This is because scholar-activists lack a collective identity, have no processes to formulate collective demands, and no mechanisms for inter-researcher and researchers-movement communication. We reflect on whether and how scholar-activists could organize, and discuss possible pathways for a more cohesive and stronger researcher engagement in the movement.</p

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

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights

We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the limit $n \to \infty$, after appropriate rescaling, the paths fill out a region in the $tx$-plane that we describe explicitly. In particular, the paths initially stay away from the hard edge at $x = 0$, but at a certain critical time $t^*$ the smallest paths hit the hard edge and from then on are stuck to it. For $t \neq t^*$ we obtain the usual scaling limits from random matrix theory, namely the sine, Airy, and Bessel kernels. A key fact is that the positions of the paths at any time $t$ constitute a multiple orthogonal polynomial ensemble, corresponding to a system of two modified Bessel-type weights. As a consequence, there is a $3 \times 3$ matrix valued Riemann-Hilbert problem characterizing this model, that we analyze in the large $n$ limit using the Deift-Zhou steepest descent method. There are some novel ingredients in the Riemann-Hilbert analysis that are of independent interest.Comment: 59 pages, 11 figure

Integral equation methods for acoustic scattering by fractals

We study sound-soft time-harmonic acoustic scattering by general scatterers, including fractal scatterers, in 2D and 3D space. For an arbitrary compact scatterer $\Gamma$ we reformulate the Dirichlet boundary value problem for the Helmholtz equation as a first kind integral equation (IE) on $\Gamma$ involving the Newton potential. The IE is well-posed, except possibly at a countable set of frequencies, and reduces to existing single-layer boundary IEs when $\Gamma$ is the boundary of a bounded Lipschitz open set, a screen, or a multi-screen. When $\Gamma$ is uniformly of $d$-dimensional Hausdorff dimension in a sense we make precise (a $d$-set), the operator in our equation is an integral operator on $\Gamma$ with respect to $d$-dimensional Hausdorff measure, with kernel the Helmholtz fundamental solution, and we propose a piecewise-constant Galerkin discretization of the IE, which converges in the limit of vanishing mesh width. When $\Gamma$ is the fractal attractor of an iterated function system of contracting similarities we prove convergence rates under assumptions on $\Gamma$ and the IE solution, and describe a fully discrete implementation using recently proposed quadrature rules for singular integrals on fractals. We present numerical results for a range of examples and make our software available as a Julia code