TY - GEN A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1221 KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-540417 SN - 1866-8372 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - GEN A1 - Wallenta, Daniel T1 - A Lefschetz fixed point formula for elliptic quasicomplexes T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 885 KW - elliptic complexes KW - Fredholm complexes KW - Lefschetz number Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-435471 SN - 1866-8372 IS - 885 SP - 577 EP - 587 ER - TY - GEN A1 - Straube, Arthur V. A1 - Pikovskij, Arkadij T1 - Pattern formation induced by time-dependent advection T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this can be explained as crossing a threshold of Turing instability due to effective increase of one of the diffusion constants. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 575 KW - pattern formation KW - reaction-advection-diffusion equation Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413140 SN - 1866-8372 IS - 575 SP - 138-147 ER - TY - GEN A1 - Seiß, Martin A1 - Spahn, Frank T1 - Hydrodynamics of Saturn’s dense rings T2 - Postprints der Universität Potsdam : Postprint Mathematisch Naturwissenschaftliche Reihe N2 - The space missions Voyager and Cassini together with earthbound observations re-vealed a wealth of structures in Saturn’s rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn’s moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Further-more, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn’s dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 574 KW - granular gas KW - instabilities KW - hydrodynamics KW - planetary rings Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413139 SP - 191 EP - 218 ER - TY - GEN A1 - Roelly, Sylvie A1 - Thieullen, Michèle T1 - Duality formula for the bridges of a Brownian diffusion : application to gradient drifts N2 - In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths C[0; 1]; R-d) Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov. KW - reciprocal processes KW - stochastic bridge KW - mixture of bridges KW - integration by parts formula KW - Malliavin calculus KW - entropy KW - time reversal Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6710 ER - TY - GEN A1 - Roelly, Sylvie A1 - Sortais, Michel T1 - Space-time asymptotics of an infinite-dimensional diffusion having a long- range memory N2 - We develop a cluster expansion in space-time for an infinite-dimensional system of interacting diffusions where the drift term of each diffusion depends on the whole past of the trajectory; these interacting diffusions arise when considering the Langevin dynamics of a ferromagnetic system submitted to a disordered external magnetic field. KW - Random Field Ising Model KW - Langevin Dynamics KW - Interacting Diffusion Processes KW - Space-Time Cluster Expansions Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6700 ER - TY - GEN A1 - Roelly, Sylvie A1 - Dereudre, David T1 - Propagation of Gibbsiannes for infinite-dimensional gradient Brownian diffusions N2 - We study the (strong-)Gibbsian character on R Z d of the law at time t of an infinitedimensional gradient Brownian diffusion , when the initial distribution is Gibbsian. KW - infinite-dimensional Brownian diffusion KW - Gibbs measure KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6918 ER - TY - GEN A1 - Roelly, Sylvie A1 - Dereudre, David T1 - On Gibbsianness of infinite-dimensional diffusions N2 - The authors analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the d-dimensional lattice. In the first part of the paper, these processes are characterized as Gibbs states on path spaces. In the second part of the paper, they study the Gibbsian character on R^{Z^d} of the law at time t of the infinite-dimensional diffusion X(t), when the initial law is Gibbsian. AMS Classifications: 60G15 , 60G60 , 60H10 , 60J60 KW - infinite-dimensional Brownian diffusion KW - Gibbs field KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6692 ER - TY - GEN A1 - Roelly, Sylvie A1 - Dai Pra, Paolo T1 - An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift N2 - We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter. KW - infinite-dimensional Brownian diffusion KW - space-time Gibbs field KW - cluster expansion Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6684 ER - TY - GEN A1 - Reich, Sebastian T1 - Smoothed dynamics of highly oscillatory Hamiltonian systems N2 - We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 031 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15639 ER -