Interplay of Rayleigh and Peierls Instabilities in Metallic Nanowires

A quantum-mechanical stability analysis of metallic nanowires within the free-electron model is presented. The stability is determined by an interplay of electron-shell effects, the Rayleigh instability due to surface tension, and the Peierls instability. Although the latter effect limits the maximum length also for wires with "magic radii", it is found that nanowires in the micrometer range can be stable at room temperature.Comment: 4 pages, 4 figure

Analysis of B cell selection mechanisms in the adaptive immune response

The essential task of a germinal centre reaction is the selection of those B cells that bind the antigen with high affinity. The exact mechanisms of B cell selection is still unknown and rather difficult to be accessed in experiment. With the help of an already established agent-based model for the space-time-dynamics of germinal centre reactions [1,2] we compare the most important hypotheses for what the limiting factor for B cell rescue may be. We discuss competition for antigen sites on follicular dendritic cells, a refractory time for centrocytes after every encounter with follicular dendritic cells, competition for the antigen itself, the role of antigen masking with soluble antibodies, and competition for T cell help. The unexpected result is that neither competition for interaction sites nor competition for antigen nor antigen masking are in agreement with present experimental data on germinal centre reactions. We show that these most popular selection mechanisms do not lead to sufficient affinity maturation and do not respect the observed robustness against changes of initial conditions. However, the best agreement with data was found for the newly hypothesized centrocyte refractory time and for competition for T cell help. Thus the in silico experiments point towards selection mechanisms that are not in the main focus of current germinal centre research. Possible experiments to test these hypotheses are proposed

An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type

We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time. We derive optimal $hp$-version error estimates and show that exponential rates of convergence can be achieved for solutions with singular (temporal) behavior near $t=0$ caused by the weakly singular kernel. Moreover, we prove that by using nonuniformly refined time steps, optimal algebraic convergence rates can be achieved for the $h$-version DG method. We then combine the DG time-stepping method with a standard finite element discretization in space, and present an optimal error analysis of the resulting fully discrete scheme. Our theoretical results are numerically validated in a series of test problems