Weak order for the discretization of the stochastic heat equation driven by impulsive noise

Considering a linear parabolic stochastic partial differential equation driven by impulsive space time noise, dX_t+AX_t dt= Q^{1/2}dZ_t, X_0=x_0\in H, t\in [0,T], we approximate the distribution of X_T. (Z_t)_{t\in[0,T]} is an impulsive cylindrical process and Q describes the spatial covariance structure of the noise; Tr(A^{-\alpha})0 and A^\beta Q is bounded for some \beta\in(\alpha-1,\alpha]. A discretization (X_h^n)_{n\in\{0,1,...,N\}} is defined via the finite element method in space (parameter h>0) and a \theta-method in time (parameter \Delta t=T/N). For \phi\in C^2_b(H;R) we show an integral representation for the error |E\phi(X^N_h)-E\phi(X_T)| and prove that |E\phi(X^N_h)-E\phi(X_T)|=O(h^{2\gamma}+(\Delta t)^{\gamma}) where \gamma<1-\alpha+\beta.Comment: 29 pages; Section 1 extended, new results in Appendix

Stability of three neutrino flavor conversion in supernovae

Neutrino-neutrino interactions can lead to collective flavor conversion in the dense parts of a core collapse supernova. Growing instabilities that lead to collective conversions have been studied intensely in the limit of two-neutrino species and occur for inverted mass ordering in the case of a perfectly spherical supernova. We examine two simple models of colliding and intersecting neutrino beams and show, that for three neutrino species instabilities exist also for normal mass ordering even in the case of a fully symmetric system. Whereas the instability for inverted mass ordering is associated with $\Delta m_{31}^2$, the new instability we find for normal mass ordering is associated with $\Delta m_{21}^2$. As a consequence, the growth rate of these new instabilities for normal ordering is smaller by about an order of magnitude compared to the rates of the well studied case of inverted ordering.Comment: 18 pages, 5 figures Minor update on the consistency of the formulae and prefactors, actualized plot

Coupling Reduces Noise

We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices. Noise from different lattice nodes can diffuse across the lattice and lower the noise level of individual nodes. We develop a theoretical model that explains this observed noise evolution and show how the coupled dynamics can naturally function as an averaging filter. Our numerical simulations are in excellent agreement with the model predictions

Universal transport signatures of Majorana fermions in superconductor-Luttinger liquid junctions

One of the most promising proposals for engineering topological superconductivity and Majorana fermions employs a spin-orbit coupled nanowire subjected to a magnetic field and proximate to an s-wave superconductor. When only part of the wire's length contacts to the superconductor, the remaining conducting portion serves as a natural lead that can be used to probe these Majorana modes via tunneling. The enhanced role of interactions in one dimension dictates that this configuration should be viewed as a superconductor-Luttinger liquid junction. We investigate such junctions between both helical and spinful Luttinger liquids, and topological as well as non-topological superconductors. We determine the phase diagram for each case and show that universal low-energy transport in these systems is governed by fixed points describing either perfect normal reflection or perfect Andreev reflection. In addition to capturing (in some instances) the familiar Majorana-mediated `zero-bias anomaly' in a new framework, we show that interactions yield dramatic consequences in certain regimes. Indeed, we establish that strong repulsion removes this conductance anomaly altogether while strong attraction produces dynamically generated effective Majorana modes even in a junction with a trivial superconductor. Interactions further lead to striking signatures in the local density of states and the line-shape of the conductance peak at finite voltage, and also are essential for establishing smoking-gun transport signatures of Majorana fermions in spinful Luttinger liquid junctions.Comment: 25 pages, 6 figures, v

Monopolelike probes for quantitative magnetic force microscopy: calibration and application

A local magnetization measurement was performed with a Magnetic Force Microscope (MFM) to determine magnetization in domains of an exchange coupled [Co/Pt]/Co/Ru multilayer with predominant perpendicular anisotropy. The quantitative MFM measurements were conducted with an iron filled carbon nanotube tip, which is shown to behave like a monopole. As a result we determined an additional in-plane magnetization component of the multilayer, which is explained by estimating the effective permeability of the sample within the \mu*-method.Comment: 3 pages, 3 figure

The effect of polar caps on obliquity

Rubincam has shown that the Martian obliquity is dependent on the seasonal polar caps. In particular, Rubincam analytically derived this dependence and showed that the change in obliquity is directly proportional to the seasonal polar cap mass. Rubincam concludes that seasonal friction does not appear to have changed Mars' climate significantly. Using a computer model for the evolution of the Martian atmosphere, Haberle et al. have made a convincing case for the possibility of huge polar caps, about 10 times the mass of the current polar caps, that exist for a significant fraction of the planet's history. Since Rubincam showed that the effect of seasonal friction on obliquity is directly proportional to polar cap mass, a scenario with a ten-fold increase in polar cap mass over a significant fraction of the planet's history would result in a secular increase in Mars' obliquity of perhaps 10 degrees. Hence, the Rubincam conclusion of an insignificant contribution to Mars' climate by seasonal friction may be incorrect. Furthermore, if seasonal friction is an important consideration in the obliquity of Mars, this would significantly alter the predictions of past obliquity