The Experts below are selected from a list of 4257 Experts worldwide ranked by ideXlab platform
Leonard A Smith - One of the best experts on this subject based on the ideXlab platform.
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Pseudo Orbit data assimilation part ii assimilation with imperfect models
Journal of the Atmospheric Sciences, 2014Co-Authors: Leonard A SmithAbstract:Data assimilation and state estimation for nonlinear models is a challenging task mathematically. Performing this task in real time, as in operational weather forecasting, is even more challenging as the models are imperfect: the mathematical system that generated the observations (if such a thing exists) is not a member of the available model class (i.e., the set of mathematical structures admitted as potential models). To the extent that traditional approaches address structural model error at all, most fail to produce consistent treatments. This results in questionable estimates both of the model state and of its uncertainty. A promising alternative approach is proposed to produce more consistent estimates of the model state and to estimate the (state dependent) model error simultaneously. This alternative consists of Pseudo-Orbit data assimilation with a stopping criterion. It is argued to be more efficient and more coherent than one alternative variational approach [a version of weak-constraint fourdimensional variational data assimilation (4DVAR)]. Results that demonstrate the Pseudo-Orbit data assimilation approach can also outperform an ensemble Kalman filter approach are presented. Both comparisons are made in the context of the 18-dimensional Lorenz96 flow and the two-dimensional Ikeda map. Many challenges remain outsidethe perfect model scenario,both in defining the goalsof data assimilation and in achievinghigh-quality state estimation. The Pseudo-Orbit data assimilation approach provides a new tool for approaching this open problem.
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Pseudo Orbit data assimilation part i the perfect model scenario
Journal of the Atmospheric Sciences, 2014Co-Authors: Leonard A SmithAbstract:State estimation lies at the heart of many meteorological tasks. Pseudo-Orbit-based data assimilation provides an attractive alternative approach to data assimilation in nonlinear systems such as weather forecasting models. In the perfect model scenario, noisy observations prevent a precise estimate of the current state. In this setting, ensemble Kalman filter approaches are hampered by their foundational assumptions of dynamical linearity, while variational approaches may fail in practice owing to local minima in their cost function. The Pseudo-Orbit data assimilation approach improves state estimation by enhancing the balance between the information derived from the dynamic equations and that derived from the observations. The potential use of this approach for numerical weather prediction is explored in the perfect model scenario within two deterministic chaotic systems: the two-dimensional Ikeda map and 18-dimensional Lorenz96 flow. Empirical results demonstrate improved performance over that of the two most common traditional approaches of data assimilation (ensemble Kalman filter and four-dimensional variational assimilation).
Jiri Lipovsky - One of the best experts on this subject based on the ideXlab platform.
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Pseudo Orbit approach to trajectories of resonances in quantum graphs with general vertex coupling fermi rule and high energy asymptotics
Journal of Mathematical Physics, 2017Co-Authors: Pavel Exner, Jiri LipovskyAbstract:The aim of the paper is to investigate resonances in quantum graphs with a general self-adjoint coupling in the vertices and their trajectories with respect to varying edge lengths. We derive formulae determining the Taylor expansion of the resonance pole position up to the second order, which represent, in particular, a counterpart to the Fermi rule derived recently by Lee and Zworski for graphs with the standard coupling. Furthermore, we discuss the asymptotic behavior of the resonances in the high-energy regime in the situation where the leads are attached through δ or δs′ conditions, and we prove that in the case of δs′ coupling the resonances approach to the real axis with the increasing real parts as O((Rek)−2).
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Pseudo Orbit approach to trajectories of resonances in quantum graphs with general vertex coupling fermi rule and high energy asymptotics
arXiv: Mathematical Physics, 2016Co-Authors: Pavel Exner, Jiri LipovskyAbstract:The aim of the paper is to investigate resonances in quantum graphs with a general self-adjoint coupling in the vertices and their trajectories with respect to varying edge lengths. We derive formulae determining the Taylor expansion of the resonance pole position up to the second order which represent, in particular, a counterpart to the Fermi rule derived recently by Lee and Zworski for graphs with the standard coupling. Furthermore, we discuss the asymptotic behavior of the resonances in the high-energy regime in the situation where the leads are attached through $\delta$ or $\delta_\mathrm{s}'$ conditions, and we prove that in the case of $\delta_\mathrm{s}'$ coupling the resonances approach to the real axis with the increasing real parts as $\mathcal{O}\big((\mathrm{Re\,}k)^{-2}\big)$.
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Pseudo Orbit expansion for the resonance condition on quantum graphs and the resonance asymptotics
arXiv: Mathematical Physics, 2015Co-Authors: Jiri LipovskyAbstract:In this note we explain the method how to find the resonance condition on quantum graphs, which is called Pseudo Orbit expansion. In three examples with standard coupling we show in detail how to obtain the resonance condition. We focus on non-Weyl graphs, i.e. the graphs which have fewer resonances than expected. For these graphs we explain benefits of the method of "deleting edges" for simplifying the graph.
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Pseudo Orbit expansion for the resonance condition on quantum graphs and the resonance asymptotics
Acta Physica Polonica A, 2015Co-Authors: Jiri LipovskyAbstract:In this note we explain the method how to find the resonance condition on quantum graphs, which is called Pseudo Orbit expansion. In three examples with standard coupling we show in detail how to obtain the resonance condition. We focus on non-Weyl graphs, i.e. the graphs which have fewer resonances than expected. For these graphs we explain benefits of the method of “deleting edges” for simplifying the graph. PACS: 03.65.Ge, 03.65.Nk, 02.10.Ox
Klaus Richter - One of the best experts on this subject based on the ideXlab platform.
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subdeterminant approach for Pseudo Orbit expansions of spectral determinants in quantum maps and quantum graphs
Physical Review E, 2013Co-Authors: Daniel Waltner, Sven Gnutzmann, Gregor Tanner, Klaus RichterAbstract:We study the implications of unitarity for Pseudo-Orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group Pseudo-Orbits into subdeterminants. We show explicitly that the cancellation of long Orbits is elegantly described on this level and that unitarity can be built in using a simple subdeterminant identity which has a nontrivial interpretation in terms of Pseudo-Orbits. This identity yields much more detailed relations between Pseudo-Orbits of different lengths than was known previously. We reformulate Newton identities and the spectral density in terms of subdeterminant expansions and point out the implications of the subdeterminant identity for these expressions. We analyze furthermore the effect of the identity on spectral correlation functions such as the autocorrelation and parametric cross-correlation functions of the spectral determinant and the spectral form factor.
Pavel Exner - One of the best experts on this subject based on the ideXlab platform.
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Pseudo Orbit approach to trajectories of resonances in quantum graphs with general vertex coupling fermi rule and high energy asymptotics
Journal of Mathematical Physics, 2017Co-Authors: Pavel Exner, Jiri LipovskyAbstract:The aim of the paper is to investigate resonances in quantum graphs with a general self-adjoint coupling in the vertices and their trajectories with respect to varying edge lengths. We derive formulae determining the Taylor expansion of the resonance pole position up to the second order, which represent, in particular, a counterpart to the Fermi rule derived recently by Lee and Zworski for graphs with the standard coupling. Furthermore, we discuss the asymptotic behavior of the resonances in the high-energy regime in the situation where the leads are attached through δ or δs′ conditions, and we prove that in the case of δs′ coupling the resonances approach to the real axis with the increasing real parts as O((Rek)−2).
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Pseudo Orbit approach to trajectories of resonances in quantum graphs with general vertex coupling fermi rule and high energy asymptotics
arXiv: Mathematical Physics, 2016Co-Authors: Pavel Exner, Jiri LipovskyAbstract:The aim of the paper is to investigate resonances in quantum graphs with a general self-adjoint coupling in the vertices and their trajectories with respect to varying edge lengths. We derive formulae determining the Taylor expansion of the resonance pole position up to the second order which represent, in particular, a counterpart to the Fermi rule derived recently by Lee and Zworski for graphs with the standard coupling. Furthermore, we discuss the asymptotic behavior of the resonances in the high-energy regime in the situation where the leads are attached through $\delta$ or $\delta_\mathrm{s}'$ conditions, and we prove that in the case of $\delta_\mathrm{s}'$ coupling the resonances approach to the real axis with the increasing real parts as $\mathcal{O}\big((\mathrm{Re\,}k)^{-2}\big)$.
F Steiner - One of the best experts on this subject based on the ideXlab platform.
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asymptotic distribution of the Pseudo Orbits and the generalized euler constant gamma delta for a family of strongly chaotic systems
Physical Review A, 1992Co-Authors: R Aurich, F SteinerAbstract:Dynamical zeta functions, defined as Euler products over classical periodic Orbits, have recently received enhanced attention as an important tool for the quantization of chaos. Their representation as a Dirichlet series over Pseudo-Orbits has proven to be particularly useful, since these series seem to possess in the general case much better convergence properties than the original Euler product. The convergence of the Dirichlet series depends crucially on the asymptotic distribution of the Pseudo-Orbits and thus on the ergodicity of the underlying dynamical system. It is shown that the lengths ${\mathit{l}}_{\mathit{n}}$ (or rather exp${\mathit{l}}_{\mathit{n}}$) of the classical periodic Orbits play mathematically the role of generalized prime numbers. Based on the theory of Beurling's generalized prime numbers, we derive an exact law for the proliferation of psuedo-Orbits for the Hadamard-Gutzwiller model, which is one of the main testing grounds of our ideas about quantum chaos. The strength of growth of the Pseudo-Orbits is determined by the ratio ZETA(2)/ZETA'(1), where ZETA(s) denotes the Selberg zeta function. Two explicit, complementary representations are given that allow the computation of this ratio solely from the length spectrum {${\mathit{l}}_{\mathit{n}}$} of the classical periodic Orbits, or from the quantal energy spectrum {${\mathit{E}}_{\mathit{n}}$}. One of these relations depends exponentially on the generalized Euler constant ${\ensuremath{\gamma}}_{\mathrm{\ensuremath{\Delta}}}$, which is therefore also studied. The formulas are applied to two strongly chaotic systems. It turns out that our asymptotic law describes the mean proliferation of Pseudo-Orbits very well not only in the asymptotic region, but also surprisingly well down to the shortest Pseudo-Orbit.
