Trace Formulas for Stochastic Evolution Operators: Weak Noise Perturbation Theory

Periodic orbit theory is all effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the standard field-theoretic formalism and weak noise perturbation theory written in terms of Feynman diagrams. The result is a stochastic analog of the next-to-leading ? corrections to the Gutzwiller trace formula, with long-time averages calculated from periodic orbits of the deterministic system. The perturbative corrections are computed analytically and tested numerically on a simple 1-dimensional system.     

Adsorbate-induced alloy phase separation: a direct view by high-pressure scanning tunneling microscopy

The influence of high pressures of carbon monoxide (CO) on the stability of a Au/Ni(111) surface alloy has been studied by high-pressure scanning tunneling microscopy. We show that CO induces a phase separation of the surface alloy at high pressures, and by means of time-lapsed STM movies we find that Ni atoms are removed from the surface layer during the process. Density functional theory calculations reveal the thermodynamic driving force for the phase separation to be the Au-induced compression of the CO overlayer with a resulting CO-CO repulsion. Furthermore, the atomistic mechanism of the process is shown to be kink-site carbonyl formation and evaporation which is found to be enhanced by the presence of Au.     

Construction of a Microstructured Collagen Membrane Mimicking the Papillary Dermis Architecture and Guiding Keratinocyte Morphology and Gene Expression

A papillary‐structured collagen fibril membrane is created, mimicking the 3D‐architecture of the human papillary dermis. Primary human keratinocytes cultured to confluency on papillar‐structured films are compared to keratinocytes cultured on flat membranes. Microscopical evaluation reveals the presence of morphologically distinct cells at the base of the papillar structures that are not observed on flat membranes. Gene expression microarrays and RT‐qPCR indicate that these cells are in a more proliferative/migrational state, whereas cells on flat membranes have a more differentiated expression profile. Immunohistochemical stainings confirm these results. In conclusion, specific collagen architecture can direct keratinocyte behavior, and this may be used to further improve skin regeneration.

     

Dynamic Bertrand Oligopoly

We study continuous time Bertrand oligopolies in which a small number of firms producing similar goods compete with one another by setting prices. We first analyze a static version of this game in order to better understand the strategies played in the dynamic setting. Within the static game, we characterize the Nash equilibrium when there are N players with heterogeneous costs. In the dynamic game with uncertain market demand, firms of different sizes have different lifetime capacities which deplete over time according to the market demand for their good. We setup the nonzero-sum stochastic differential game and its associated system of HJB partial differential equations in the case of linear demand functions. We characterize certain qualitative features of the game using an asymptotic approximation in the limit of small competition. The equilibrium of the game is further studied using numerical solutions. We find that consumers benefit the most when a market is structured with many firms of the same relative size producing highly substitutable goods. However, a large degree of substitutability does not always lead to large drops in price, for example when two firms have a large difference in their size.