TY - JOUR A1 - Glebov, Sergei A1 - Kiselev, Oleg A1 - Tarkhanov, Nikolai Nikolaevich T1 - Weakly nonlinear dispersive waves under parametric resonance perturbation N2 - We consider a solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver. The frequency of parametric perturbation varies slowly and passes through a resonant value, which leads to a solution change. We obtain a new connection formula for the asymptotic solution before and after the resonance. Y1 - 2010 UR - http://www3.interscience.wiley.com/cgi-bin/issn?DESCRIPTOR=PRINTISSN&VALUE=0022-2526 U6 - https://doi.org/10.1111/j.1467-9590.2009.00460.x SN - 0022-2526 ER - TY - JOUR A1 - Stepanenko, Victor A1 - Tarkhanov, Nikolai Nikolaevich T1 - The Cauchy problem for Chaplygin's system N2 - We discuss the Cauchy problem for the so-called Chaplygin system which often appears in gas, aero- and hydrodynamics. This system can be thought of as a nonlinear analogue of the Cauchy-Riemann system in the plane. We pose Cauchy data on a part of the boundary and apply variational approach to construct a solution to this ill-posed problem. The problem actually gives insight to fundamental questions related to instable problems for nonlinear equations. Y1 - 2010 UR - http://www.informaworld.com/openurl?genre=journal&issn=1747-6933 U6 - https://doi.org/10.1080/17476930903394978 SN - 1747-6933 ER - TY - JOUR A1 - Bär, Christian A1 - Bessa, C. Pacelli T1 - Stochastic completeness and volume growth N2 - It was suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested implication is not true in general. We also give counterexamples to a converse implication. Y1 - 2010 UR - http://www.ams.org/proc/ U6 - https://doi.org/10.1090/S0002-9939-10-10281-0 SN - 0002-9939 ER - TY - JOUR A1 - Geese, Anne A1 - Mandea, Mioara A1 - Lesur, Vincent A1 - Hayn, Michael T1 - Regional modelling of the Southern African geomagnetic field using harmonic splines N2 - Over the southern African region the geomagnetic field is weak and changes rapidly. For this area series of geomagnetic field measurements exist since the 1950s. We take advantage of the existing repeat station surveys and observatory annual means, and clean these data sets by eliminating jumps and minimizing external field contributions in the original time-series. This unique data set allows us to obtain a detailed view of the geomagnetic field behaviour in space and time by computing a regional model. For this, we use a system of representation similar to harmonic splines. Initially, the technique is systematically tested on synthetic data. After systematically testing the method on synthetic data, we derive a model for 1961-2001 that gives a detailed view of the fast changes of the geomagnetic field in this region. Y1 - 2010 UR - http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1365-246X U6 - https://doi.org/10.1111/j.1365-246X.2010.04575.x SN - 0956-540X ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Brietzke, Gilbert B. A1 - Zöller, Gert T1 - Quantitative earthquake forecasts resulting from static stress triggering N2 - In recent years, the triggering of earthquakes has been discussed controversially with respect to the underlying mechanisms and the capability to evaluate the resulting seismic hazard. Apart from static stress interactions, other mechanisms including dynamic stress transfer have been proposed to be part of a complex triggering process. Exploiting the theoretical relation between long-term earthquake rates and stressing rate, we demonstrate that static stress changes resulting from an earthquake rupture allow us to predict quantitatively the aftershock activity without tuning specific model parameters. These forecasts are found to be in excellent agreement with all first-order characteristics of aftershocks, in particular, (1) the total number, (2) the power law distance decay, (3) the scaling of the productivity with the main shock magnitude, (4) the foreshock probability, and (5) the empirical Bath law providing the maximum aftershock magnitude, which supports the conclusion that static stress transfer is the major mechanism of earthquake triggering. Y1 - 2010 UR - http://www.agu.org/journals/jb/ U6 - https://doi.org/10.1029/2010jb007473 SN - 0148-0227 ER - TY - JOUR A1 - Weiße, Andrea Y. A1 - Middleton, Richard H. A1 - Huisinga, Wilhelm T1 - Quantifying uncertainty, variability and likelihood for ordinary differential equation models N2 - Background: In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results: The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well- known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions: While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations. Y1 - 2010 UR - http://www.biomedcentral.com/1752-0509/ U6 - https://doi.org/10.1186/1752-0509-4-144 SN - 1752-0509 ER - TY - JOUR A1 - Bailey, Iain W. A1 - Ben-Zion, Yehuda A1 - Becker, Thorsten W. A1 - Holschneider, Matthias T1 - Quantifying focal mechanism heterogeneity for fault zones in central and southern California N2 - P>We present a statistical analysis of focal mechanism orientations for nine California fault zones with the goal of quantifying variations of fault zone heterogeneity at seismogenic depths. The focal mechanism data are generated from first motion polarities for earthquakes in the time period 1983-2004, magnitude range 0-5, and depth range 0-15 km. Only mechanisms with good quality solutions are used. We define fault zones using 20 km wide rectangles and use summations of normalized potency tensors to describe the distribution of double-couple orientations for each fault zone. Focal mechanism heterogeneity is quantified using two measures computed from the tensors that relate to the scatter in orientations and rotational asymmetry or skewness of the distribution. We illustrate the use of these quantities by showing relative differences in the focal mechanism heterogeneity characteristics for different fault zones. These differences are shown to relate to properties of the fault zone surface traces such that increased scatter correlates with fault trace complexity and rotational asymmetry correlates with the dominant fault trace azimuth. These correlations indicate a link between the long-term evolution of a fault zone over many earthquake cycles and its seismic behaviour over a 20 yr time period. Analysis of the partitioning of San Jacinto fault zone focal mechanisms into different faulting styles further indicates that heterogeneity is dominantly controlled by structural properties of the fault zone, rather than time or magnitude related properties of the seismicity. Y1 - 2010 UR - http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1365-246X U6 - https://doi.org/10.1111/j.1365-246X.2010.04745.x SN - 0956-540X ER - TY - JOUR A1 - Garifullinevich, Rustem Nail A1 - Suleimanov, Bulat Irekovich A1 - Tarkhanov, Nikolai Nikolaevich T1 - Phase shift in the Whitham zone for the Gurevich-Pitaevskii special solution of the Korteweg-de Vries equation N2 - We get the leading term of the Gurevich-Pitaevskii special solution of the KdV equation in the oscillation zone without using averaging methods. Y1 - 2010 UR - http://www.sciencedirect.com/science/journal/03759601 U6 - https://doi.org/10.1016/j.physleta.2010.01.057 SN - 0375-9601 ER - TY - JOUR A1 - Dimitrova, Ilinka A1 - Koppitz, Jörg T1 - On some anti-inverse transformation semigroups N2 - A semigroup S is called anti-inverse if for all a E S there is a b is an element of S such that aba = b and bab = a. Each anti-inverse semigroup is regular. In the present paper, we study anti-inverse subsemigroups within the semigroup T-n of all transformations on an n-element set (1 <= n is an element of N). In particular, we characterize all anti-inverse semigroups within the J-classes of T-n and illustrate our result by four examples. Y1 - 2010 UR - http://www.proceedings.bas.bg/ SN - 1310-1331 ER - TY - JOUR A1 - Devchand, Chandrashekar A1 - Nuyts, Jean A1 - Weingart, Gregor T1 - Matryoshka of Special Democratic Forms N2 - Special p-forms are forms which have components phi_{mu_1...mu_p} equal to +1,-1 or 0 in some orthonormal basis. A p-form phiin Lambda^p R^d is called democratic if the set of nonzero components {phi_{mu_1...mu_p}} is symmetric under the transitive action of a subgroup of O(d,Z) on the indices {1,...,d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P geq p and D geq d. In particular, we display a remarkable nested stucture of special forms including a U(3)-invariant 2-form in six dimensions, a G_2-invariant 3-form in seven dimensions, a Spin(7)- invariant 4-form in eight dimensions and a special democratic 6-form Omega in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form. Y1 - 2010 UR - http://www.springerlink.com/content/dn2h0l040x382q07/ SN - 143-0916 ER - TY - JOUR A1 - Gaci, Said A1 - Zaourar, Naima A1 - Hamoudi, Mehdi A1 - Holschneider, Matthias T1 - Local regularity analysis of strata heterogeneities from sonic logs N2 - Borehole logs provide geological information about the rocks crossed by the wells. Several properties of rocks can be interpreted in terms of lithology, type and quantity of the fluid filling the pores and fractures. Here, the logs are assumed to be nonhomogeneous Brownian motions (nhBms) which are generalized fractional Brownian motions (fBms) indexed by depth-dependent Hurst parameters H(z). Three techniques, the local wavelet approach (LWA), the average-local wavelet approach (ALWA), and Peltier Algorithm (PA), are suggested to estimate the Hurst functions (or the regularity profiles) from the logs. First, two synthetic sonic logs with different parameters, shaped by the successive random additions (SRA) algorithm, are used to demonstrate the potential of the proposed methods. The obtained Hurst functions are close to the theoretical Hurst functions. Besides, the transitions between the modeled layers are marked by Hurst values discontinuities. It is also shown that PA leads to the best Hurst value estimations. Second, we investigate the multifractional property of sonic logs data recorded at two scientific deep boreholes: the pilot hole VB and the ultra deep main hole HB, drilled for the German Continental Deep Drilling Program (KTB). All the regularity profiles independently obtained for the logs provide a clear correlation with lithology, and from each regularity profile, we derive a similar segmentation in terms of lithological units. The lithological discontinuities (strata' bounds and faults contacts) are located at the local extrema of the Hurst functions. Moreover, the regularity profiles are compared with the KTB estimated porosity logs, showing a significant relation between the local extrema of the Hurst functions and the fluid-filled fractures. The Hurst function may then constitute a tool to characterize underground heterogeneities. Y1 - 2010 UR - http://www.copernicus.org/EGU/npg/npg.htm U6 - https://doi.org/10.5194/npg-17-455-2010 SN - 1023-5809 ER - TY - JOUR A1 - Fradon, Myriam A1 - Roelly, Sylvie T1 - Infinitely many Brownian globules with Brownian radii N2 - We consider an infinite system of non-overlapping globules undergoing Brownian motions in R-3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinite-dimensional stochastic differential equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures. Y1 - 2010 UR - http://www.worldscinet.com/sd/sd.shtml U6 - https://doi.org/10.1142/S021949371000311x SN - 0219-4937 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Wang, Rongjiang T1 - Impact of the receiver fault distribution on aftershock activity N2 - Aftershock models are usually based either on purely empirical relations ignoring the physical mechanism or on deterministic calculations of stress changes on a predefined receiver fault orientation. Here we investigate the effect of considering more realistic fault systems in models based on static Coulomb stress changes. For that purpose, we perform earthquake simulations with elastic half-space stress interactions, rate-and-state dependent frictional earthquake nucleation, and extended ruptures with heterogeneous (fractal) slip distributions. We find that the consideration of earthquake nucleation on multiple receiver fault orientations does not influence the shape of the temporal Omori-type aftershock decay, but changes significantly the predicted spatial patterns and the total number of triggered events. So-called stress shadows with decreased activity almost vanish, and activation decays continuously with increasing distance from the main shock rupture. The total aftershock productivity, which is shown to be almost independent of the assumed background rate, increases significantly if multiple receiver fault planes exist. The application to the 1992 M7.3 Landers, California, aftershock sequence indicates a good agreement with the locations and the total productivity of the observed directly triggered aftershocks. Y1 - 2010 UR - http://www.agu.org/journals/jb/ U6 - https://doi.org/10.1029/2008jb006224 SN - 0148-0227 ER - TY - JOUR A1 - Shin, Seoleun A1 - Sommer, Matthias A1 - Reich, Sebastian A1 - Névir, Peter T1 - Evaluation of three spatial discretization schemes with the Galewsky et al. test N2 - We evaluate the Hamiltonian particle methods (HPM) and the Nambu discretization applied to shallow-water equations on the sphere using the test suggested by Galewsky et al. (2004). Both simulations show excellent conservation of energy and are stable in long-term simulation. We repeat the test also using the ICOSWP scheme to compare with the two conservative spatial discretization schemes. The HPM simulation captures the main features of the reference solution, but wave 5 pattern is dominant in the simulations applied on the ICON grid with relatively low spatial resolutions. Nevertheless, agreement in statistics between the three schemes indicates their qualitatively similar behaviors in the long-term integration. Y1 - 2010 UR - http://www3.interscience.wiley.com/cgi-bin/jhome/106562719 U6 - https://doi.org/10.1002/Asl.279 SN - 1530-261X ER - TY - JOUR A1 - Andersson, Lars A1 - Metzger, Jan T1 - Curvature estimates for stable marginally trapped surfaces N2 - We derive local integral and sup-estimates for the curvature of stable marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situations of physical interest, such as dynamical horizons. Y1 - 2010 UR - http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jdg SN - 0022-040X ER - TY - JOUR A1 - Glebov, Sergei A1 - Kiselev, Oleg A1 - Tarkhanov, Nikolai Nikolaevich T1 - Autoresonance in a dissipative system N2 - We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations. Y1 - 2010 UR - http://iopscience.iop.org/1751-8121/ U6 - https://doi.org/10.1088/1751-8113/43/21/215203 SN - 1751-8113 ER - TY - JOUR A1 - Bär, Christian A1 - Pfaeffle, Frank T1 - Asymptotic heat kernel expansion in the semi-classical limit N2 - Let H-h = h(2)L + V, where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of H-h as h SE arrow 0. As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive h by the classical partition function. Y1 - 2010 UR - http://www.springerlink.com/content/100467 U6 - https://doi.org/10.1007/s00220-009-0973-3 SN - 0010-3616 ER - TY - JOUR A1 - Bergemann, Kay A1 - Reich, Sebastian T1 - A mollified ensemble Kalman filter N2 - It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high-frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter. Y1 - 2010 UR - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1477-870X U6 - https://doi.org/10.1002/Qj.672 SN - 0035-9009 ER - TY - JOUR A1 - Bergemann, Kay A1 - Reich, Sebastian T1 - A localization technique for ensemble Kalman filters N2 - Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase- space dimension is typically much larger than the number of ensemble members, which leads to inaccurate results in the computed covariance matrices. These inaccuracies can lead, among other things, to spurious long-range correlations, which can be eliminated by Schur-product-based localization techniques. In this article, we propose a new technique for implementing such localization techniques within the class of ensemble transform/square-root Kalman filters. Our approach relies on a continuous embedding of the Kalman filter update for the ensemble members, i.e. we state an ordinary differential equation (ODE) with solutions that, over a unit time interval, are equivalent to the Kalman filter update. The ODE formulation forms a gradient system with the observations as a cost functional. Besides localization, the new ODE ensemble formulation should also find useful application in the context of nonlinear observation operators and observations that arrive continuously in time. Y1 - 2010 UR - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1477-870X U6 - https://doi.org/10.1002/Qj.591 SN - 0035-9009 ER -