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- Yamabe-Problem (1)
- Zahlbereichserweiterung (1)
- Zahlerwerb (1)
- Zellmotilität (1)
- Zeta-function (1)
- Zig-zag order (1)
- Zufallsvariable (1)
- Zustandsraum Wechselpunktdetektierung (1)
- Zustandsschätzung (1)
- Zählprozesse (1)
- a posteriori stopping rule (1)
- absorbing boundary (1)
- absorbing set (1)
- absorption (1)
- accelerated life time model (1)
- accelerated small (1)
- accuracy (1)
- acute severe (1)
- adaptive (1)
- adaptivity (1)
- adipose tissue (1)
- adrenal insufficiency (1)
- aerosol (1)
- aerosol distribution (1)
- aerosol-boundary layer interactions (1)
- aerosols (1)
- affine (1)
- affine invariance (1)
- algebra (1)
- algebra of rank n (1)
- algebraic systems (1)
- algebras (1)
- alignment (1)
- alternating direction implicit (1)
- amoeboid motion (1)
- amöboide Bewegung (1)
- analytic functional (1)
- analytic index (1)
- analytic perturbation theory (1)
- angewandte Mathematik (1)
- animal behavior (1)
- anisotropic spaces (1)
- anti-infective (1)
- antibiotics (1)
- antigen processing (1)
- antimicrobial stewardship (1)
- applied mathematics (1)
- approximation (1)
- approximative Differenzierbarkeit (1)
- aptitude tests (1)
- archaeomagnetism (1)
- articulation (1)
- assimilation (1)
- association (1)
- asteroseismology (1)
- asymptotic (1)
- asymptotic approximation (1)
- asymptotic expansions (1)
- asymptotic methods (1)
- asymptotic properties of eigenfunctions (1)
- asymptotic stable (1)
- asymptotical normal distribution (1)
- asymptotics (1)
- asymptotics of solutions (1)
- asymptotische Entwicklung (1)
- asymptotische Normalverteilung (1)
- attenuated Radon transform (1)
- aurora (1)
- autonomic nervous system (1)
- b-value (1)
- backtrajectories; (1)
- backward heat problem (1)
- balanced dynamics (1)
- bar with variable cross-section (1)
- basic ideas ('Grundvorstellungen') (1)
- bayessche Inferenz (1)
- bedingter Erwartungswert (1)
- behavior (1)
- bending of an orthotropic cusped plate (1)
- beta-functions (1)
- binding (1)
- bioinformatics (1)
- biological population equations (1)
- birhythmic behavior (1)
- black hole (1)
- black holes (1)
- body mass index procedure (1)
- body surface area (1)
- boun- dedness (1)
- boundary conditions (1)
- boundary element method (1)
- boundary values problems (1)
- bounds (1)
- branching processes (1)
- bridges of random walks (1)
- bundles (1)
- calculation (1)
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- canonical Marcus integration (1)
- canonical discretization schemes (1)
- category equivalence of clones (1)
- cell motility (1)
- certolizumab pegol (1)
- chain of semigroups (1)
- characteristic boundary point (1)
- characteristic points (1)
- characterization of point processes (1)
- chemical master equation (1)
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- classical and quantum reduction (1)
- classification with partial labels (1)
- clathrin (1)
- clifford semigroup (1)
- clone of operations (1)
- cluster (1)
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- clustering (1)
- coated and absorbing aerosols (1)
- coercivity (1)
- coherent set (1)
- collegial supervision (1)
- coloration of terms (1)
- colored solid varieties (1)
- compact resolvent (1)
- companies (1)
- comparison principle (1)
- completeness (1)
- completeness levels (1)
- complex systems (1)
- composition of terms (1)
- composition operator (1)
- compound Poisson processes (1)
- compound polyhedra (1)
- compressible Euler equations (1)
- computational biology (1)
- concentration (1)
- concentration inequalities (1)
- condition number (1)
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- conditional Wiener measure (1)
- conditional expectation value (1)
- conditioned (1)
- conditioned Feller diffusion (1)
- conditions (1)
- conditions of success (1)
- confidence interval (1)
- confidence intervals (1)
- congenital adrenal hyperplasia (1)
- congruence (1)
- connections (1)
- conormal asymptotic expansions (1)
- conormal asymptotics (1)
- conormal symbols (1)
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- conservative discretization (1)
- constitutive relations (1)
- constrained Hamiltonian systems (1)
- contact transformations (1)
- continuity in Sobolev spaces with double weights (1)
- continuous testing (1)
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- continuous time Markov chain (1)
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- control theory (1)
- convergence assessment (1)
- convergence rate (1)
- convolution (1)
- corner parametrices (1)
- corona virus (1)
- correlated noise (1)
- cortisol (1)
- coupled solution (1)
- covering (1)
- critical and subcritical Dawson-Watanabe process (1)
- criticality theorem (1)
- criticality theory (1)
- critically ill (1)
- crohn's disease (1)
- crossed product (1)
- curvature varifold (1)
- cusp (1)
- cusped bar (1)
- das Cauchyproblem (1)
- das Goursatproblem (1)
- das charakteristische Cauchyproblem (1)
- data-driven (1)
- dbar-Neumann problem (1)
- de Sitter model ; Fundamental solutions ; Decay estimates (1)
- decay of eigenfunctions (1)
- decomposition (1)
- deformation quantization (1)
- degenerate elliptic equations (1)
- degenerate elliptic systems (1)
- delaney-dress tiling theory (1)
- density estimation (1)
- density of a measure (1)
- derivative-free optimization (1)
- design elements (1)
- design research (1)
- determinant (1)
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- determinantische Punktprozesse (1)
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- die linearisierte Einsteingleichung (1)
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- diffusion maps (1)
- diffusion process (1)
- dimension functional (1)
- dimension reduction (1)
- direct and indirect climate observations (1)
- direkte und indirekte Klimaobservablen (1)
- disagreement percolation (1)
- discontinuous Robin condition (1)
- discontinuous drift (1)
- discrete Schrodinger (1)
- discrete Witten complex (1)
- discrete saymptotic types (1)
- discrete spectrum (1)
- disease activity (1)
- disjunction of identities (1)
- diskontinuierliche Drift (1)
- diskreter Witten-Laplace-Operator (1)
- distorted Brownian motion (1)
- distribution (1)
- distribution kernel (1)
- distribution with asymptotics (1)
- distributional boundary (1)
- distributions with one-sided support (1)
- division algebras (1)
- division ring of fractions (1)
- division rings (1)
- division trees (1)
- divisors (1)
- domains with singularities (1)
- doppelsemigroup (1)
- dried blood spots (1)
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- duale IT-Ausbildung (1)
- duality formulae (1)
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- dynamical system (1)
- dynamical system representation (1)
- e-Assessment (1)
- e-Learning (1)
- early mathematical education (1)
- earthquake hazards (1)
- earthquake interaction (1)
- earthquake precursor (1)
- edge Sobolev spaces (1)
- edge algebra (1)
- edge boundary value problems (1)
- edge quantizations (1)
- edge spaces (1)
- edge symbol (1)
- edge- and corner-degenerate symbols (1)
- eigenfunction (1)
- eigenvalue asymptotics (1)
- eigenvalue decay (1)
- eigenvalue estimate (1)
- eigenvalues (1)
- elastic bar (1)
- elasticity (1)
- electrodynamics (1)
- elliptic boundary (1)
- elliptic boundary conditions (1)
- elliptic complex (1)
- elliptic differential operators of firstorder (1)
- elliptic equation (1)
- elliptic functions (1)
- elliptic morphism (1)
- elliptic operators in subspaces (1)
- elliptic operators on non-compact manifolds (1)
- elliptic problem (1)
- elliptic problems (1)
- elliptic quasicomplexes (1)
- elliptic systems (1)
- ellipticity in the edge calculus (1)
- ellipticity of cone operators (1)
- ellipticity of corners operators (1)
- ellipticity with interface conditions (1)
- ellipticity with parameter (1)
- ellipticity with respect to interior and edge symbols (1)
- elliptische Gleichungen (1)
- elliptische Quasi-Komplexe (1)
- embedded Markov chain (1)
- embeddings (1)
- empirical Wasserstein distance (1)
- endomorphism semigroup (1)
- energetic space (1)
- enlargement of filtration (1)
- ensembles (1)
- entropy (1)
- equation (1)
- equation of motion (1)
- equatorial ionization anomaly (1)
- equatorial ionosphere (1)
- equatorial plasma bubbles (1)
- equivalence (1)
- ergodic diffusion processes (1)
- ergodic rates (1)
- error diagram (1)
- erste Variation (1)
- essential position in terms (1)
- estimation of regression (1)
- eta forms (1)
- exact simulation method (1)
- exact simulation methods (1)
- exact solution (1)
- exakte Simulation (1)
- exchange algorithms (1)
- exercise collection (1)
- exit calculus (1)
- expansion (1)
- exponential decay (1)
- exponential function (1)
- exponential stability (1)
- exterior tensor product (1)
- extinction probability (1)
- eye movements (1)
- false discovery rate (1)
- fat-free mass (1)
- feedback (1)
- feedback particle filter (1)
- fence-preserving transformations (1)
- fibration (1)
- fibre coordinates (1)
- fibroblasts (1)
- field-aligned currents (1)
- filtering (1)
- finite transformation semigroup (1)
- finiteness theorem (1)
- finsler distance (1)
- first exit location (1)
- first exit times (1)
- first passage times (1)
- first variation (1)
- fixational eye movements (1)
- fixed point formula (1)
- flocking (1)
- flood loss estimation (1)
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- foliated diffusion (1)
- force unification (1)
- forcing from below (1)
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- forecasting and prediction (1)
- formal (1)
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- formulas (1)
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- fracture (1)
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- fundamental solution (1)
- game (1)
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- gauge group (1)
- generalized Abelian gauge theory (1)
- generalized Bruck-Reilly *-extension (1)
- generalized Laplace operator (1)
- generalized eigenfunction (1)
- generalized eigenfunctions (1)
- generating sets (1)
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- geomagnetism (1)
- geometric optics approximation (1)
- geometric reproduction distribution (1)
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- geopotential theory (1)
- geordnete Gruppen von Conrad-Typ (1)
- global exact boundary controllability (1)
- global solution (1)
- global solutions (1)
- global-hyperbolisch (1)
- globally hyperbolic (1)
- globally hyperbolic spacetime (1)
- good-inner function (1)
- goodness of fit (1)
- goodness-of-fit (1)
- goodness-of-fit testing (1)
- gradient-free (1)
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- graph Laplacian (1)
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- group (1)
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- groups (1)
- guiding idea “Daten und Zufall” (1)
- heat (1)
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- higher singularities (1)
- highly (1)
- history of branching processes (1)
- hitting times (1)
- holomorphic function (1)
- holonomic constraints (1)
- host-parasite stochastic particle system (1)
- hybrid model (1)
- hybrids (1)
- hydraulic tomography (1)
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- höhere Operationen (1)
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- idealised turbulence (1)
- idleness (1)
- ill-posed (1)
- illposed problem (1)
- indecomposable varifold (1)
- independent splittings (1)
- index formula (1)
- index of elliptic operator (1)
- index of stability (1)
- induced field (1)
- inegral formulas (1)
- infinite-dimensional diffusions (1)
- infinitesimal generator (1)
- infliximab dosing (1)
- initial boundary value problem (1)
- instability of the process (1)
- integral Fourier operators (1)
- integral equation (1)
- integral representation method (1)
- integration by parts on path space (1)
- interacting particle system (1)
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- interassociativity (1)
- interfaces with conical singularities (1)
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- interstitial space fluid (1)
- intrinsic diameter (1)
- intrinsischer Diameter (1)
- invariance (1)
- invariant (1)
- invariant measure (1)
- inverse Probleme (1)
- inverse Sturm-Liouville problems (1)
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- isoperimetric estimates (1)
- isoperimetric inequality (1)
- isoperimetrische Ungleichung (1)
- iterated asymptotics (1)
- jump processes (1)
- k-means clustering (1)
- kanten- und ecken-entartete Symbole (1)
- kernel estimator of the hazard rate (1)
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- kernel-basierte Bayes'sche Inferenz (1)
- kleine Parameter (1)
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- least favorable configuration (1)
- least squares estimator (1)
- left ordered groups (1)
- left-right asymmetry (1)
- lifespan (1)
- likelihood function (1)
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- limit theorem for integrated squared difference (1)
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- locally indicable (1)
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- log-concavity (1)
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- logarithmic residue (1)
- logic (1)
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- logistische Regression (1)
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- low rank matrix recovery (1)
- low rank recovery (1)
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- magnetic field variations through (1)
- magnetisch (1)
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- magnitude errors (1)
- makromolekularer Zerfall (1)
- manifold (1)
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- manifolds with corners (1)
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- manifolds with cylindrical ends (1)
- manifolds with edge (1)
- manifolds with edge and boundary (1)
- many-electron systems (1)
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- mapping class groups (1)
- matching of asymptotic expansions (1)
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- method (1)
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- minor planets, asteroids: individual: (162173) Ryugu (1)
- mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung (1)
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- monoclonal antibodies (1)
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- new recursive algorithm (1)
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- nichtlineare Modelle (1)
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- nodal flow (1)
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- optimal order (1)
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- order reduction (1)
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- ordered group (1)
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- permanental and determinantal point processes (MSC 2010) 35K55 (1)
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Institute
- Institut für Mathematik (2166) (remove)
Natural gas can be temporarily stored in a variety of underground facilities, such as depleted gas and oil fields, natural aquifers and caverns in salt rocks. Being extensively monitored during operations, these systems provide a favourable opportunity to investigate how pressure varies in time and space and possibly induces/triggers earthquakes on nearby faults. Elaborate and detailed numerical modelling techniques are often applied to study gas reservoirs. Here we show the possibilities and discuss the limitations of a flexible and easily formulated tool that can be straightforwardly applied to simulate temporal pore-pressure variations and study the relation with recorded microseismic events. We use the software POEL (POroELastic diffusion and deformation) which computes the poroelastic response to fluid injection/extraction in a horizontally layered poroelastic structure. We further develop its application to address the presence of vertical impermeable faults bounding the reservoir and of multiple injection/extraction sources. Exploiting available information on the reservoir geometry and physical parameters, and records of injection/extraction rates for a gas reservoir in southern Europe, we perform an extensive parametric study considering different model configurations. Comparing modelled spatiotemporal pore-pressure variations with in situ measurements, we show that the inclusion of vertical impermeable faults provides an improvement in reproducing the observations and results in pore-pressure accumulation near the faults and in a variation of the temporal pore-pressure diffusion pattern. To study the relation between gas storage activity and recorded local microseismicity, we applied different seismicity models based on the estimated porepressure distribution. This analysis helps to understand the spatial distribution of seismicity and its temporal modulation. The results show that the observed microseismicity could be partly linked to the storage activity, but the contribution of tectonic background seismicity cannot be excluded.
We introduce the concept of TRAP (Traces and Permutations), which can roughly be viewed as a wheeled PROP (Products and Permutations) without unit. TRAPs are equipped with a horizontal concatenation and partial trace maps.
Continuous morphisms on an infinite-dimensional topological space and smooth kernels (respectively, smoothing operators) on a closed manifold form a TRAP but not a wheeled PROP.
We build the free objects in the category of TRAPs as TRAPs of graphs and show that a TRAP can be completed to a unitary TRAP (or wheeled PROP).
We further show that it can be equipped with a vertical concatenation, which on the TRAP of linear homomorphisms of a vector space, amounts to the usual composition. The vertical concatenation in the TRAP of smooth kernels gives rise to generalised convolutions.
Graphs whose vertices are decorated by smooth kernels (respectively, smoothing operators) on a closed manifold form a TRAP. From their universal properties we build smooth amplitudes associated with the graph.
We prove that optimal lower eigenvalue estimates of Zhong-Yang type as well as a Cheng-type upper bound for the first eigenvalue hold on closed manifolds assuming only a Kato condition on the negative part of the Ricci curvature.
This generalizes all earlier results on Lp-curvature assumptions.
Moreover, we introduce the Kato condition on compact manifolds with boundary with respect to the Neumann Laplacian, leading to Harnack estimates for the Neumann heat kernel and lower bounds for all Neumann eigenvalues, which provides a first insight in handling variable Ricci curvature assumptions in this case.
Each completely regular semigroup is a semilattice of completely simple semigroups. The more specific concept of a strong semilattice provides the concrete product between two arbitrary elements.
We characterize strong semilattices of rectangular groups by so-called disjunctions of identities. Disjunctions of identities generalize the classical concept of an identity and of a variety, respectively.
The rectangular groups will be on the one hand left zero semigroups and right zero semigroups and on the other hand groups of exponent p is an element of P, where P is any set of pairwise coprime natural numbers.
Reentrant tensegrity
(2021)
We present a three-periodic, chiral, tensegrity structure and demonstrate that it is auxetic. Our tensegrity structure is constructed using the chiral symmetry Pi(+) cylinder packing, transforming cylinders to elastic elements and cylinder contacts to incompressible rods. The resulting structure displays local reentrant geometry at its vertices and is shown to be auxetic when modeled as an equilibrium configuration of spatial constraints subject to a quasi-static deformation. When the structure is subsequently modeled as a lattice material with elastic elements, the auxetic behavior is again confirmed through finite element modeling. The cubic symmetry of the original structure means that the auxetic behavior is observed in both perpendicular directions and is close to isotropic in magnitude. This structure could be the simplest three-dimensional analog to the two-dimensional reentrant honeycomb. This, alongside the chirality of the structure, makes it an interesting design target for multifunctional materials.
Devising optimal interventions for constraining stochastic systems is a challenging endeavor that has to confront the interplay between randomness and dynamical nonlinearity.
Existing intervention methods that employ stochastic path sampling scale poorly with increasing system dimension and are slow to converge.
Here we propose a generally applicable and practically feasible methodology that computes the optimal interventions in a noniterative scheme.
We formulate the optimal dynamical adjustments in terms of deterministically sampled probability flows approximated by an interacting particle system.
Applied to several biologically inspired models, we demonstrate that our method provides the necessary optimal controls in settings with terminal, transient, or generalized collective state constraints and arbitrary system dynamics.
We consider the case of scattering by several obstacles in Rd for d ≥ 2.
In this setting, the absolutely continuous part of the Laplace operator Δ with Dirichlet boundary conditions and the free Laplace operator Δ0 are unitarily equivalent.
For suitable functions that decay sufficiently fast, we have that the difference g(Δ) - g(Δ0) is a trace-class operator and its trace is described by the Krein spectral shift function.
In this article, we study the contribution to the trace (and hence the Krein spectral shift function) that arises from assembling several obstacles relative to a setting where the obstacles are completely separated. In the case of two obstacles, we consider the Laplace operators Δ1 and Δ2 obtained by imposing Dirichlet boundary conditions only on one of the objects.
Our main result in this case states that then g(Δ) - g(Δ1) - g(Δ2) C g(Δ0) is a trace-class operator for a much larger class of functions (including functions of polynomial growth) and that this trace may still be computed by a modification of the Birman–Krein formula. In case g(x) D x 2 , 1 the relative trace has a physical meaning as the vacuum energy of the massless scalar field and is expressible as an integral involving boundary layer operators.
Such integrals have been derived in the physics literature using nonrigorous path integral derivations and our formula provides both a rigorous justification as well as a generalization.
We present the extension of the Kalmag model, proposed as a candidate for IGRF-13, to the twentieth century.
The dataset serving its derivation has been complemented by new measurements coming from satellites, ground-based observatories and land, marine and airborne surveys.
As its predecessor, this version is derived from a combination of a Kalman filter and a smoothing algorithm, providing mean models and associated uncertainties. These quantities permit a precise estimation of locations where mean solutions can be considered as reliable or not.
The temporal resolution of the core field and the secular variation was set to 0.1 year over the 122 years the model is spanning.
Nevertheless, it can be shown through ensembles a posteriori sampled, that this resolution can be effectively achieved only by a limited amount of spatial scales and during certain time periods.
Unsurprisingly, highest accuracy in both space and time of the core field and the secular variation is achieved during the CHAMP and Swarm era. In this version of Kalmag, a particular effort was made for resolving the small-scale lithospheric field.
Under specific statistical assumptions, the latter was modeled up to spherical harmonic degree and order 1000, and signal from both satellite and survey measurements contributed to its development.
External and induced fields were jointly estimated with the rest of the model. We show that their large scales could be accurately extracted from direct measurements whenever the latter exhibit a sufficiently high temporal coverage.
Temporally resolving these fields down to 3 hours during the CHAMP and Swarm missions, gave us access to the link between induced and magnetospheric fields. In particular, the period dependence of the driving signal on the induced one could be directly observed.
The model is available through various physical and statistical quantities on a dedicated website at https://ionocovar.agnld.uni-potsdam.de/Kalmag/.
We consider the initial value problem for the Navier-Stokes equations over R-3 x [0, T] with time T > 0 in the spatially periodic setting.
We prove that it induces open injective mappings A(s): B-1(s) -> B-2(s-1) where B-1(s), B-2(s-1) are elements from scales of specially constructed function spaces of Bochner-Sobolev typeparametrized with the smoothness index s is an element of N.
Finally, we prove that a map Asis surjective if and only if the inverse image A(s)(- 1) (K) of any pre compact set K from the range of the map Asis bounded in the Bochner space L-s([0, T], L-r(T-3))with the Ladyzhenskaya-Prodi-Serrin numbers s, r.
We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model.
This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O(10(4)) model runs, or more.
Moreover, the forward model is often given as a black box or is impractical to differentiate.
Therefore derivative-free algorithms are highly desirable. We propose a framework, which is built on Kalman methodology, to efficiently perform Bayesian inference in such inverse problems.
The basic method is based on an approximation of the filtering distribution of a novel mean-field dynamical system, into which the inverse problem is embedded as an observation operator.
Theoretical properties are established for linear inverse problems, demonstrating that the desired Bayesian posterior is given by the steady state of the law of the filtering distribution of the mean-field dynamical system, and proving exponential convergence to it.
This suggests that, for nonlinear problems which are close to Gaussian, sequentially computing this law provides the basis for efficient iterative methods to approximate the Bayesian posterior.
Ensemble methods are applied to obtain interacting particle system approximations of the filtering distribution of the mean-field model; and practical strategies to further reduce the computational and memory cost of the methodology are presented, including low-rank approximation and a bi-fidelity approach.
The effectiveness of the framework is demonstrated in several numerical experiments, including proof-of-concept linear/nonlinear examples and two large-scale applications: learning of permeability parameters in subsurface flow; and learning subgrid-scale parameters in a global climate model.
Moreover, the stochastic ensemble Kalman filter and various ensemble square-root Kalman filters are all employed and are compared numerically.
The results demonstrate that the proposed method, based on exponential convergence to the filtering distribution of a mean-field dynamical system, is competitive with pre-existing Kalman-based methods for inverse problems.