TY - JOUR A1 - Högele, Michael A1 - Pavlyukevich, Ilya T1 - Metastability in a class of hyperbolic dynamical systems perturbed by heavy-tailed Levy type noise JF - Stochastics and dynamic N2 - We consider a finite dimensional deterministic dynamical system with finitely many local attractors K-iota, each of which supports a unique ergodic probability measure P-iota, perturbed by a multiplicative non-Gaussian heavy-tailed Levy noise of small intensity epsilon > 0. We show that the random system exhibits a metastable behavior: there exists a unique epsilon-dependent time scale on which the system reminds of a continuous time Markov chain on the set of the invariant measures P-iota. In particular our approach covers the case of dynamical systems of Morse-Smale type, whose attractors consist of points and limit cycles, perturbed by multiplicative alpha-stable Levy noise in the Ito, Stratonovich and Marcus sense. As examples we consider alpha-stable Levy perturbations of the Duffing equation and Pareto perturbations of a biochemical birhythmic system with two nested limit cycles. KW - Hyperbolic dynamical system KW - Morse-Smale property KW - physical SRB measures KW - stable limit cycle KW - small noise asymptotic KW - alpha-stable Levy process KW - multiplicative noise KW - Ito integral KW - Stratonovich integral KW - stochastic Marcus (canonical) differential equation KW - multiscale dynamics KW - metastability KW - embedded Markov chain KW - randomly forced Duffing equation KW - birhythmic behavior Y1 - 2015 U6 - https://doi.org/10.1142/S0219493715500197 SN - 0219-4937 SN - 1793-6799 VL - 15 IS - 3 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Pirhayati, Mohammad T1 - Boundary symbols in the cone algebra JF - Journal of pseudo-differential operators and applications N2 - Boundary value problems on a smooth manifold X with boundary have the structure of edge problems. Operators A are described in terms of a principal symbolic hierarchy, namely, according to the stratification of X, with the interior and the boundary We focus here on operators with and without the transmission property and establish a new relationship between boundary symbols and operators in the cone calculus transversal to the boundary. KW - Cone KW - Edge and corner pseudo-differential operators KW - Ellipticity of corner-degenerate operators KW - Iterated corner asymptotics of solutions Y1 - 2015 U6 - https://doi.org/10.1007/s11868-015-0123-y SN - 1662-9981 SN - 1662-999X VL - 6 IS - 3 SP - 307 EP - 339 PB - Springer CY - Basel ER - TY - JOUR A1 - Lyu, Xiaojing A1 - Qian, Tao A1 - Schulze, Bert-Wolfgang T1 - Order filtrations of the edge algebra JF - Journal of pseudo-differential operators and applications N2 - By edge algebra we understand a pseudo-differential calculus on a manifold with edge. The operators have a two-component principal symbolic hierarchy which determines operators up to lower order terms. Those belong to a filtration of the corresponding operator spaces. We give a new characterisation of this structure, based on an alternative representation of edge amplitude functions only containing holomorphic edge-degenerate Mellin symbols. Y1 - 2015 U6 - https://doi.org/10.1007/s11868-015-0126-8 SN - 1662-9981 SN - 1662-999X VL - 6 IS - 3 SP - 279 EP - 305 PB - Springer CY - Basel ER - TY - JOUR A1 - Ludewig, Matthias T1 - A semiclassical heat kernel proof of the Poincare-Hopf theorem JF - Manuscripta mathematica N2 - We consider the semiclassical asymptotic expansion of the heat kernel coming from Witten's perturbation of the de Rham complex by a given function. For the index, one obtains a time-dependent integral formula which is evaluated by the method of stationary phase to derive the Poincare-Hopf theorem. We show how this method is related to approaches using the Thom form of Mathai and Quillen. Afterwards, we use a more general version of the stationary phase approximation in the case that the perturbing function has critical submanifolds to derive a degenerate version of the Poincare-Hopf theorem. Y1 - 2015 U6 - https://doi.org/10.1007/s00229-015-0741-y SN - 0025-2611 SN - 1432-1785 VL - 148 IS - 1-2 SP - 29 EP - 58 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Asari, Seiki A1 - Wardinski, Ingo T1 - On magnetic estimation of Earth's core angular momentum variation JF - Journal of geophysical research : Solid earth N2 - We study systematically the estimation of Earth's core angular momentum (CAM) variation between 1962.0 and 2008.0 by using core surface flow models derived from the recent geomagnetic field model C(3)FM2. Various flow models are derived by changing four parameters that control the least squares flow inversion. The parameters include the spherical harmonic (SH) truncation degree of the flow models and two Lagrange multipliers that control the weights of two additional constraints. The first constraint forces the energy spectrum of the flow solution to follow a power law l-p, where l is the SH degree and p is the fourth parameter. The second allows to modulate the solution continuously between the dynamical states of tangential geostrophy (TG) and tangential magnetostrophy (TM). The calculated CAM variations are examined in reference to two features of the observed length-of-day (LOD) variation, namely, its secular trend and 6year oscillation. We find flow models in either TG or TM state for which the estimated CAM trends agree with the LOD trend. It is necessary for TM models to have their flows dominate at planetary scales, whereas TG models should not be of this scale; otherwise, their CAM trends are too steep. These two distinct types of flow model appear to correspond to the separate regimes of previous numerical dynamos that are thought to be applicable to the Earth's core. The phase of the subdecadal CAM variation is coherently determined from flow models obtained with extensively varying inversion settings. Multiple sources of model ambiguity need to be allowed for in discussing whether these phase estimates properly represent that of Earth's CAM as an origin of the observed 6year LOD oscillation. KW - Core KW - Earth rotation KW - Inversion KW - Geomagnetic field KW - rapid variations KW - Geodynamo Y1 - 2015 U6 - https://doi.org/10.1002/2014JB011458 SN - 2169-9313 SN - 2169-9356 VL - 120 IS - 10 SP - 6740 EP - 6757 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Samaras, Stefanos A1 - Nicolae, Doina A1 - Böckmann, Christine A1 - Vasilescu, Jeni A1 - Binietoglou, Ioannis A1 - Labzovskii, Lev A1 - Toanca, Florica A1 - Papayannis, Alexandros T1 - Using Raman-lidar-based regularized microphysical retrievals and Aerosol Mass Spectrometer measurements for the characterization of biomass burning aerosols JF - Journal of computational physics N2 - In this work we extract the microphysical properties of aerosols for a collection of measurement cases with low volume depolarization ratio originating from fire sources captured by the Raman lidar located at the National Institute of Optoelectronics (INOE) in Bucharest. Our algorithm was tested not only for pure smoke but also for mixed smoke and urban aerosols of variable age and growth. Applying a sensitivity analysis on initial parameter settings of our retrieval code was proved vital for producing semi-automatized retrievals with a hybrid regularization method developed at the Institute of Mathematics of Potsdam University. A direct quantitative comparison of the retrieved microphysical properties with measurements from a Compact Time of Flight Aerosol Mass Spectrometer (CToF-AMS) is used to validate our algorithm. Microphysical retrievals performed with sun photometer data are also used to explore our results. Focusing on the fine mode we observed remarkable similarities between the retrieved size distribution and the one measured by the AMS. More complicated atmospheric structures and the factor of absorption appear to depend more on particle radius being subject to variation. A good correlation was found between the aerosol effective radius and particle age, using the ratio of lidar ratios (LR: aerosol extinction to backscatter ratios) as an indicator for the latter. Finally, the dependence on relative humidity of aerosol effective radii measured on the ground and within the layers aloft show similar patterns. (C) 2015 Elsevier Inc. All rights reserved. KW - Aerosols KW - Microphysical properties KW - Lidar KW - AMS KW - AERONET Y1 - 2015 U6 - https://doi.org/10.1016/j.jcp.2015.06.045 SN - 0021-9991 SN - 1090-2716 VL - 299 SP - 156 EP - 174 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Class of Toeplitz Operators in Several Variables JF - Advances in applied Clifford algebras N2 - We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory. KW - Cauchy data spaces KW - Laplace-Beltrami operator KW - Toeplitz operators KW - Fredholm property Y1 - 2015 U6 - https://doi.org/10.1007/s00006-015-0546-9 SN - 0188-7009 SN - 1661-4909 VL - 25 IS - 4 SP - 811 EP - 828 PB - Springer CY - Basel ER - TY - JOUR A1 - Fedchenko, Dmitri A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators JF - Complex variables and elliptic equations N2 - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first-order partial differential equations in a bounded domain in R-n with smooth boundary. KW - Toeplitz operators KW - Fredholm property KW - index KW - Primary: 47B35 KW - Secondary: 47L80 Y1 - 2015 U6 - https://doi.org/10.1080/17476933.2015.1050007 SN - 1747-6933 SN - 1747-6941 VL - 60 IS - 12 SP - 1764 EP - 1787 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Moesta, Philip A1 - Andersson, Lars A1 - Metzger, Jan A1 - Szilagyi, Bela A1 - Winicour, Jeffrey T1 - The merger of small and large black holes JF - Classical and quantum gravit N2 - We present simulations of binary black-hole mergers in which, after the common outer horizon has formed, the marginally outer trapped surfaces (MOTSs) corresponding to the individual black holes continue to approach and eventually penetrate each other. This has very interesting consequences according to recent results in the theory of MOTSs. Uniqueness and stability theorems imply that two MOTSs which touch with a common outer normal must be identical. This suggests a possible dramatic consequence of the collision between a small and large black hole. If the penetration were to continue to completion, then the two MOTSs would have to coalesce, by some combination of the small one growing and the big one shrinking. Here we explore the relationship between theory and numerical simulations, in which a small black hole has halfway penetrated a large one. KW - black holes KW - numerical relativity KW - trapped surfaces Y1 - 2015 U6 - https://doi.org/10.1088/0264-9381/32/23/235003 SN - 0264-9381 SN - 1361-6382 VL - 32 IS - 23 PB - IOP Publ. Ltd. CY - Bristol ER -