On possible Chern Classes of stable Bundles on Calabi-Yau threefolds

Supersymmetric heterotic string models, built from a Calabi-Yau threefold $X$ endowed with a stable vector bundle $V$, usually lead to an anomaly mismatch between $c_2(V)$ and $c_2(X)$; this leads to the question whether the difference can be realized by a further bundle in the hidden sector. In math.AG/0604597 a conjecture is stated which gives sufficient conditions on cohomology classes on $X$ to be realized as the Chern classes of a stable reflexive sheaf $V$; a weak version of this conjecture predicts the existence of such a $V$ if $c_2(V)$ is of a certain form. In this note we prove that on elliptically fibered $X$ infinitely many cohomology classes $c\in H^4(X, {\bf Z})$ exist which are of this form and for each of them a stable SU(n) vector bundle with $c=c_2(V)$ exists.Comment: 12 pages latex, minor change

Invariant solutions organizing pipe flow turbulence

Peer ReviewedPostprint (published version

Analysis of the discontinuous Galerkin method for elliptic problems on surfaces

We extend the discontinuous Galerkin (DG) framework to a linear second-order elliptic problem on a compact smooth connected and oriented surface. An interior penalty (IP) method is introduced on a discrete surface and we derive a-priori error estimates by relating the latter to the original surface via the lift introduced in Dziuk (1988). The estimates suggest that the geometric error terms arising from the surface discretisation do not affect the overall convergence rate of the IP method when using linear ansatz functions. This is then verified numerically for a number of test problems. An intricate issue is the approximation of the surface conormal required in the IP formulation, choices of which are investigated numerically. Furthermore, we present a generic implementation of test problems on surfaces.Comment: 21 pages, 4 figures. IMA Journal of Numerical Analysis 2013, Link to publication: http://imajna.oxfordjournals.org/cgi/content/abstract/drs033? ijkey=45b23qZl5oJslZQ&keytype=re

A finite element method for a fourth order surface equation with application to the onset of cell blebbing

A variational problem for a fourth order parabolic surface partial differential equation is discussed. It contains nonlinear lower order terms, on which we only make abstract assumptions, and which need to be defined for specified problems.We derive a semi-discrete scheme based on the surface finite element method, show a-priori error estimates, and use the analytical results to prove well-posedness. Furthermore, we present a computational framework where specific problems can be conveniently implemented and, later on, altered with relative ease. It uses a domain specific language implemented in Python. The high level program control can also be done within the Python scripting environment. The computationally expensive step of evolving the solution over time is carried out by binding to an efficient C++ software back-end. The study is motivated by cell blebbing, which can be instrumental for cell migration. Starting with a force balance for the cell membrane, we derive a continuum model for some mechanical and geometrical aspects of the onset of blebbing in a form that fits into the abstract framework. It is flexible in that it allows for amending force contributions related to membrane tension or the presence of linker molecules between membrane and cell cortex. Cell membrane geometries given in terms of a parametrisation or obtained from image data can be accounted for by the software. The use of a domain specific language to describe the model makes is straightforward to add additional effects such as reaction-diffusion equations modelling some biochemistry on the cell membrane.Some numerical simulations illustrate the approach

Two-dimensional N=2\mathcal{N}=2 Super-Yang-Mills Theory

Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the $\mathcal{N}=1$ Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional $\mathcal{N}=2$ SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.Comment: 8 pages, 3 figures, 2 tables, talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Insider trading in Germany: Do corporate insiders exploit inside information?

Our study analyzes a large sample of transactions carried out by corporate insiders reported to the German regulatory authority BaFin in the period July 1, 2002 to April 30, 2005 employing event study methodology. In particular, we focus on the question whether corporate insiders exploit inside information while trading in their company's stock. Therefore we use a distinct property of German law, i.e. company's obligation to reveal inside information through ad-hoc news disclosures, to link trading of insiders to their foreknowledge of important corporate news. We find strong evidence that insiders exploit inside information as they earn above average profits by front-running on subsequent news disclosures. Furthermore, looking at the type of insider, we find that members of the supervisory board (directors) and the group of other insiders (basically family members of senior managers and directors) profit substantially from exploiting inside information. In contrast, members of the executive board (senior managers) can be largely exculpated from exploiting inside information as they realize below average returns with their rare front-running transactions. --insider trading,inside information,§15a WpHG,German stock market,regulation of financial markets

Saving, Microinsurance: Why You Should Do Both or Nothing. A Behavioral Experiment on the Philippines

This paper analyzes data from a novel field experiment designed to test the impact of two different insurance products and a secret saving device on solidarity in risk-sharing groups among rural villagers in the Philippines. Risk is simulated by a lottery, risk-sharing is possible in solidarity groups of three and insurance is introduced via less risky lotteries. Our main hypothesis is that formal market-based products lead to lower transfers among network members. We also test for the persistence of this crowding-out of solidarity. We find evidence for a reduction of solidarity by insurance if shocks are observable. Depending on insurance design, there is also evidence for persistence of this effect even if insurance is removed. Simulations using our regression results show that the benefits of insurance are completely offset by the reduction in transfers. However, if secret saving is possible solidarity is very low in general and there is no crowding out effect of insurance. This suggests that introducing formal insurance is not as effective as it is hoped for when the monetary situation can be closely monitored, but that it might be a very important complement when savings inhibit observing financial resources. --