TY - JOUR A1 - Acevedo, Walter A1 - De Wiljes, Jana A1 - Reich, Sebastian T1 - Second-order accurate ensemble transform particle filters JF - SIAM journal on scientific computing N2 - Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF) [S. Reich, SIAM T. Sci. Comput., 35, (2013), pp. A2013-A2014[ replaces the resampling step of a standard particle filter by a linear transformation which allows for a hybridization of particle filters with ensemble Kalman filters and renders the resulting hybrid filters applicable to spatially extended systems. However, the linear transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes. Here we address both of these shortcomings by developing second order accurate extensions of the ETPF. These extensions allow one in particular to replace the exact solution of a linear transport problem by its Sinkhorn approximation. It is also demonstrated that the nonlinear ensemble transform filter arises as a special case of our general framework. We illustrate the performance of the second-order accurate filters for the chaotic Lorenz-63 and Lorenz-96 models and a dynamic scene-viewing model. The numerical results for the Lorenz-63 and Lorenz-96 models demonstrate that significant accuracy improvements can be achieved in comparison to a standard ensemble Kalman filter and the ETPF for small to moderate ensemble sizes. The numerical results for the scene-viewing model reveal, on the other hand, that second-order corrections can lead to statistically inconsistent samples from the posterior parameter distribution. KW - Bayesian inference KW - data assimilation KW - particle filter KW - ensemble Kalman filter KW - Sinkhorn approximation Y1 - 2017 U6 - https://doi.org/10.1137/16M1095184 SN - 1064-8275 SN - 1095-7197 SN - 2168-3417 VL - 39 IS - 5 SP - A1834 EP - A1850 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Acevedo, Walter A1 - Fallah, Bijan A1 - Reich, Sebastian A1 - Cubasch, Ulrich T1 - Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model JF - Climate of the past : an interactive open access journal of the European Geosciences Union N2 - Paleoclimate data assimilation (DA) is a promising technique to systematically combine the information from climate model simulations and proxy records. Here, we investigate the assimilation of tree-ring-width (TRW) chronologies into an atmospheric global climate model using ensemble Kalman filter (EnKF) techniques and a process-based tree-growth forward model as an observation operator. Our results, within a perfect-model experiment setting, indicate that the "online DA" approach did not outperform the "off-line" one, despite its considerable additional implementation complexity. On the other hand, it was observed that the nonlinear response of tree growth to surface temperature and soil moisture does deteriorate the operation of the time-averaged EnKF methodology. Moreover, for the first time we show that this skill loss appears significantly sensitive to the structure of the growth rate function, used to represent the principle of limiting factors (PLF) within the forward model. In general, our experiments showed that the error reduction achieved by assimilating pseudo-TRW chronologies is modulated by the magnitude of the yearly internal variability in themodel. This result might help the dendrochronology community to optimize their sampling efforts. Y1 - 2017 U6 - https://doi.org/10.5194/cp-13-545-2017 SN - 1814-9324 SN - 1814-9332 VL - 13 SP - 545 EP - 557 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Acevedo, Walter A1 - Reich, Sebastian A1 - Cubasch, Ulrich T1 - Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques JF - Climate dynamics : observational, theoretical and computational research on the climate system N2 - This paper investigates the applicability of the Vaganov–Shashkin–Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) “switching recording” of 2 variables and (3) bounded response windows leading to “thresholded response”. We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL’s nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL’s formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL’s performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes. KW - Proxy forward modeling KW - Data assimilation KW - Fuzzy logic KW - Ensemble Kalman filter KW - Paleoclimate reconstruction Y1 - 2016 U6 - https://doi.org/10.1007/s00382-015-2683-1 SN - 0930-7575 SN - 1432-0894 VL - 46 SP - 1909 EP - 1920 PB - Springer CY - New York ER - TY - JOUR A1 - Afshari Moein, Mohammad J. A1 - Somogyvári, Márk A1 - Valley, Benoît A1 - Jalali, Mohammadreza A1 - Löw, Simon A1 - Bayer, Peter T1 - Fracture network characterization using stress-based tomography JF - Journal of geophysical research : JGR N2 - Information on structural features of a fracture network at early stages of Enhanced Geothermal System development is mostly restricted to borehole images and, if available, outcrop data. However, using this information to image discontinuities in deep reservoirs is difficult. Wellbore failure data provides only some information on components of the in situ stress state and its heterogeneity. Our working hypothesis is that slip on natural fractures primarily controls these stress heterogeneities. Based on this, we introduce stress-based tomography in a Bayesian framework to characterize the fracture network and its heterogeneity in potential Enhanced Geothermal System reservoirs. In this procedure, first a random initial discrete fracture network (DFN) realization is generated based on prior information about the network. The observations needed to calibrate the DFN are based on local variations of the orientation and magnitude of at least one principal stress component along boreholes. A Markov Chain Monte Carlo sequence is employed to update the DFN iteratively by a fracture translation within the domain. The Markov sequence compares the simulated stress profile with the observed stress profiles in the borehole, evaluates each iteration with Metropolis-Hastings acceptance criteria, and stores acceptable DFN realizations in an ensemble. Finally, this obtained ensemble is used to visualize the potential occurrence of fractures in a probability map, indicating possible fracture locations and lengths. We test this methodology to reconstruct simple synthetic and more complex outcrop-based fracture networks and successfully image the significant fractures in the domain. KW - fracture network KW - Bayesian inversion KW - stress variability KW - rock mechanics Y1 - 2018 U6 - https://doi.org/10.1029/2018JB016438 SN - 2169-9313 SN - 2169-9356 VL - 123 IS - 11 SP - 9324 EP - 9340 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Aizinger, Vadym A1 - Korn, Peter A1 - Giorgetta, Marco A1 - Reich, Sebastian T1 - Large-scale turbulence modelling via alpha-regularisation for atmospheric simulations JF - Journal of turbulence N2 - We study the possibility of obtaining a computational turbulence model by means of non-dissipative regularisation of the compressible atmospheric equations for climate-type applications. We use an -regularisation (Lagrangian averaging) of the atmospheric equations. For the hydrostatic and compressible atmospheric equations discretised using a finite volume method on unstructured grids, deterministic and non-deterministic numerical experiments are conducted to compare the individual solutions and the statistics of the regularised equations to those of the original model. The impact of the regularisation parameter is investigated. Our results confirm the principal compatibility of -regularisation with atmospheric dynamics and encourage further investigations within atmospheric model including complex physical parametrisations. KW - hydrostatic atmosphere KW - non-dissipative regularisations KW - Lagrangian-averaged equations Y1 - 2015 U6 - https://doi.org/10.1080/14685248.2014.991443 SN - 1468-5248 VL - 16 IS - 4 SP - 367 EP - 391 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Akhmatskaya, Elena A1 - Bou-Rabee, Nawaf A1 - Reich, Sebastian T1 - A comparison of generalized hybrid Monte Carlo methods with and without momentum flip N2 - The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/00219991 U6 - https://doi.org/10.1016/j.jcp.2008.12.014 SN - 0021-9991 ER - TY - JOUR A1 - Akhmatskaya, Elena A1 - Bou-Rabee, Nawaf A1 - Reich, Sebastian T1 - Erratum to "A comparison of generalized hybrid Monte Carlo methods with and without momentum flip" [J. Comput. Phys. 228 (2009), S. 2256 - 2265] N2 - The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC. Y1 - 2009 UR - http://www.sciencedirect.com/science/journal/00219991 U6 - https://doi.org/10.1016/j.jcp.2009.06.039 SN - 0021-9991 ER - TY - JOUR A1 - Al-Saedy, Ammar Jaffar Muhesin A1 - Tarchanov, Nikolaj Nikolaevič T1 - A degree theory for Lagrangian boundary value problems JF - Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics & physics N2 - We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems. N2 - Мы изучаем те нелинейные уравнения с частными производными, которые возникают как уравнения Эйлера-Лагранжа вариационных задач. Определяя слабые граничные значения решений таких уравнений, мы инициируем теорию лагранжевых краевых задач в функциональных пространствах подходящей гладкости. Мы также анализируем, применяется ли современная концепция степени отображения к лагранжевым проблемам. KW - nonlinear equations KW - Lagrangian system KW - weak boundary values KW - quasilinear Fredholm operators KW - mapping degree Y1 - 2020 U6 - https://doi.org/10.17516/1997-1397-2020-13-1-5-25 SN - 1997-1397 SN - 2313-6022 VL - 13 IS - 1 SP - 5 EP - 25 PB - Sibirskij Federalʹnyj Universitet CY - Krasnojarsk ER - TY - JOUR A1 - Albeverio, Sergio A1 - Brasche, Johannes F. A1 - Neidhardt, Hagen T1 - On inverse spectral theory: mixed types of spectra. Y1 - 1998 ER - TY - JOUR A1 - Alsaedy, Ammar A1 - Tarkhanov, Nikolai Nikolaevich T1 - Normally solvable nonlinear boundary value problems JF - Nonlinear analysis : theory, methods & applications ; an international multidisciplinary journal N2 - We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions. KW - Nonlinear Laplace operator KW - Boundary value problem KW - Dirichlet to Neumann operator Y1 - 2014 U6 - https://doi.org/10.1016/j.na.2013.09.024 SN - 0362-546X SN - 1873-5215 VL - 95 SP - 468 EP - 482 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Altundag, Hüseyin A1 - Böckmann, Christine A1 - Taseli, Hasan T1 - Inverse Sturm-Liouville problems with pseudospectral methods JF - International journal of computer mathematics N2 - In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigenvalues in iterative solution procedure is made by means of pseudospectral methods. A fairly detailed description of the numerical algorithm and its applications to specific examples are presented to illustrate the accuracy and convergence behaviour of the proposed approach. KW - 31A25 KW - 65F18 KW - regularization method KW - condition number KW - pseudospectral method KW - regular and singular inverse Sturm-Liouville problems Y1 - 2015 U6 - https://doi.org/10.1080/00207160.2014.939646 SN - 0020-7160 SN - 1029-0265 VL - 92 IS - 7 SP - 1373 EP - 1384 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Amendola, Luca A1 - Battaglia Mayer, Alexandra A1 - Capozziello, Salvatore A1 - Gottlöber, Stefan A1 - Müller, Volker A1 - Occhionero, Franco A1 - Schmidt, Hans-Jürgen T1 - Generalized sixth-order gravity and inflation JF - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 04 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Amezcua, Javier A1 - Ide, Kayo A1 - Kalnay, Eugenia A1 - Reich, Sebastian T1 - Ensemble transform Kalman-Bucy filters JF - Quarterly journal of the Royal Meteorological Society N2 - Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques. KW - Kalman-Bucy Filter KW - Ensemble Kalman Filter KW - stiff ODE KW - weight-based formulations Y1 - 2014 U6 - https://doi.org/10.1002/qj.2186 SN - 0035-9009 SN - 1477-870X VL - 140 IS - 680 SP - 995 EP - 1004 PB - Wiley-Blackwell CY - Hoboken 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 - Antonini, Paolo A1 - Azzali, Sara A1 - Skandalis, Georges T1 - Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations JF - Journal of functional analysis N2 - We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved. KW - Operator algebras KW - Bivariant K-theory KW - Rho invariants Y1 - 2016 U6 - https://doi.org/10.1016/j.jfa.2015.06.017 SN - 0022-1236 SN - 1096-0783 VL - 270 SP - 447 EP - 481 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Antoniouk, Alexandra Viktorivna A1 - Kiselev, Oleg M. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point JF - Ukrainian mathematical journal N2 - The Dirichlet problem for the heat equation in a bounded domain aS, a"e (n+1) is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t = c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii's paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior. Y1 - 2015 U6 - https://doi.org/10.1007/s11253-015-1038-8 SN - 0041-5995 SN - 1573-9376 VL - 66 IS - 10 SP - 1455 EP - 1474 PB - Springer CY - New York ER - TY - JOUR A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - Left-edges solid varieties of differential groupoids Y1 - 1999 ER - TY - JOUR A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - Groupoids of hypersubstitutions and G-solid varieties Y1 - 1997 ER - TY - JOUR A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - A new methods to study subvariety lattices of semigroup varieties Y1 - 1997 ER - TY - JOUR A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - Tree Transformations defined by Hypersubstitutions Y1 - 2001 SN - 1509 - 9415 ER -