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Spectral stability of nonlinear gravity waves in the atmosphere
No full textWe apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which represent exact solutions to the inviscid Boussinesq equations, are spectrally stable with respect to their nonlinear modulation equations under the same conditions as what is known as modulational stability from weakly nonlinear theory. In contrast to Boussinesq, the pseudo-incompressible regime does fully account for the altitudinal varying background density. Second,we show for the first time that upward-traveling non-plane wave fronts solving the inviscid nonlinear modulation equations, that compare to pseudo-incompressible theory, are unconditionally unstable. Both inviscid regimes turn out to be ill-posed as the spectra allow for arbitrarily large instability growth rates. Third, a regularization is found by including dissipative effects. The corresponding nonlinear traveling wave solutions have localized amplitude. As a consequence of the nonlinearity, envelope and linear group velocity, as given by the derivative of the frequency with respect to wavenumber, do not coincide anymore. These waves blow up unconditionally by embedded eigenvalue instabilities but the instability growth rate is bounded from above and can be computed analytically. Additionally, all three types of nonlinear modulation equations are solved numerically to further investigate and illustrate the nature of the analytic stability results
The physics of open systems for the simulation of complex molecular environments in soft matter
No full textMolecular dynamics (MD) has become one of the most powerful tools of investigation in soft matter. Despite such success, simulations of large molecular environments are mostly run using the approximation of closed systems without the possibility of exchange of matter. Due to the molecular complexity of soft matter systems, an optimal simulation strategy would require the application of concurrent multiscale resolution approaches such that each part of a large system can be considered as an open subsystem at a high resolution embedded in a large coarser reservoir of energy and particles. This paper discusses the current capability and the future perspectives of multiscale adaptive resolution MD methods to satisfy the conceptual principles of open systems and to perform simulations of complex molecular environments in soft matter
Modulational stability of nonlinear saturated gravity waves
No full textStationary gravity waves, such as mountain lee waves, are effectively described by Grimshaw’s dissipative modulation equations even in high altitudes where they become nonlinear due to their large amplitudes. In this theoretical study, a wave-Reynolds number is introduced to characterize general solutions to these modulation equations. This nondimensional number relates the vertical linear group velocity with wavenumber, pressure scale height and kinematic molecular/eddy viscosity. It is demonstrated by analytic and numerical methods that Lindzen-type waves in the saturation region, i.e. where the wave-Reynolds number is of order unity, destabilize by transient perturbations. It is proposed that this mechanism may be a generator for secondary waves due to direct wave-mean-flow interaction. By assumption the primary waves are exactly such that altitudinal amplitude growth and viscous damping are balanced and by that the amplitude is maximized. Implications of these results on the relation between mean-flow acceleration and wave breaking heights are discussed
On the geometry of Stein variational gradient descent
Get PDFBayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely on iterated steepest descent steps with respect to a reproducing kernel Hilbert space norm. This construction leads to interacting particle systems, the mean-field limit of which is a gradient flow on the space of probability distributions equipped with a certain geometrical structure. We leverage this viewpoint to shed some light on the convergence properties of the algorithm, in particular addressing the problem of choosing a suitable positive definite kernel function. Our analysis leads us to considering certain nondifferentiable kernels with adjusted tails. We demonstrate significant performs gains of these in various numerical experiments
Affine invariant interacting Langevin dynamics for Bayesian inference
Get PDFWe propose a computational method (with acronym ALDI) for sampling from a given target distribution based on first-order (overdamped) Langevin dynamics which satisfies the property of affine invariance. The central idea of ALDI is to run an ensemble of particles with their empirical covariance serving as a preconditioner for their underlying Langevin dynamics. ALDI does not require taking the inverse or square root of the empirical covariance matrix, which enables application to high-dimensional sampling problems. The theoretical properties of ALDI are studied in terms of non-degeneracy and ergodicity. Furthermore, we study its connections to diffusions on Riemannian manifolds and Wasserstein gradient flows.
Bayesian inference serves as a main application area for ALDI. In case of a forward problem with additive Gaussian measurement errors, ALDI allows for a gradient-free implementation in the spirit of the ensemble Kalman filter. A computational comparison between gradient-free and gradient-based ALDI is provided for a PDE constrained Bayesian inverse problem
Non-Markovian barrier crossing with two-time-scale memory is dominated by the faster memory component
Get PDFWe investigate non-Markovian barrier-crossing kinetics of a massive particle in one dimension in the presence of a memory function that is the sum of two exponentials with different memory times τ 1 and τ 2 . Our Langevin simulations for the special case where both exponentials contribute equally to the total friction show that the barrier crossing time becomes independent of the longer memory time if at least one of the two memory times is larger than the intrinsic diffusion time. When we associate memory effects with coupled degrees of freedom that are orthogonal to a one-dimensional reaction coordinate, this counterintuitive result shows that the faster orthogonal degrees of freedom dominate barrier-crossing kinetics in the non-Markovian limit and that the slower orthogonal degrees become negligible, quite contrary to the standard time-scale separation assumption and with important consequences for the proper setup of coarse-graining procedures in the non-Markovian case. By asymptotic matching and symmetry arguments, we construct a crossover formula for the barrier crossing time that is valid for general multi-exponential memory kernels. This formula can be used to estimate barrier-crossing times for general memory functions for high friction, i.e. in the overdamped regime, as well as for low friction, i.e. in the inertial regime. Typical examples where our results are important include protein folding in the high-friction limit and chemical reactions such as proton-transfer reactions in the low-friction limit
Molybdenum systematics of subducted crust record reactive fluid flow from underlying slab serpentine dehydration
Get PDFFluids liberated from subducting slabs are critical in global geochemical cycles. We investigate
the behaviour of Mo during slab dehydration using two suites of exhumed fragments of
subducted, oceanic lithosphere. Our samples display a positive correlation of δ98/95MoNIST
3134 with Mo/Ce, from compositions close to typical mantle (−0.2‰and 0.03, respectively)
to very low values of both δ98/95MoNIST 3134 (−1‰) and Mo/Ce (0.002). Together with new,
experimental data, we show that molybdenum isotopic fractionation is driven by preference
of heavier Mo isotopes for a fluid phase over rutile, the dominant mineral host of Mo in
eclogites. Moreover, the strongly perturbed δ98/95MoNIST 3134 and Mo/Ce of our samples
requires that they experienced a large flux of oxidised fluid. This is consistent with channelised,
reactive fluid flow through the subducted crust, following dehydration of the
underlying, serpentinised slab mantle. The high δ98/95MoNIST 3134 of some arc lavas is the
complement to this process
Anforderungen an wirkungsvolle Methoden für transdisziplinäre Wissensintegration
No full textUmweltsoziolog*innen beschäftigen sich aus sozialwissenschaftlicher Sicht mit Umweltproblemen, Fragen der Nachhaltigkeit oder Beziehungen zwischen Gesellschaft
und Natur. Diese Themen stehen oft auch im Zentrum transdisziplinärer Nachhaltigkeitsforschung, da es zur Bearbeitung komplexer Nachhaltigkeitsprobleme mehr als
nur das Wissen einer Einzeldisziplin bedarf. Ziel dieses Beitrags ist es einerseits, den transdisziplinären Forschungsmodus vorzustellen, und andererseits aufzuzeigen, wie durch bewusste Methodenwahl gesellschaftliche Wirkungen von transdisziplinären Forschungsprojekten bereits während des Forschungsprozesses befördert werden können. Nach einer Einführung in den transdisziplinären Forschungsmodus wird das grundlegende Methodenverständnis transdisziplinärer Forschung geklärt und dasdiesem Beitrag zugrunde liegende Forschungsprojekt TransImpact vorgestellt. Anhand eines Fallbeispiels werden im Ergebnisteil Anforderungen an die Methodenwahl für wirkungsvolle transdisziplinäre Forschung illustriert. Die Ergebnisse und ihre Verortung werden abschließend diskutier
A gradient system with a wiggly energy and relaxed EDP-convergence
Get PDFIf gradient systems depend on a microstructure, we want to derive a macroscopic
gradient structure describing the effective behavior of the microscopic system. We introduce
a notion of evolutionary Gamma-convergence that relates the microscopic energy
and the microscopic dissipation potential with their macroscopic limits via Gammaconvergence.
We call this notion relaxed EDP-convergence since the special structure of
the dissipation functional may not be preserved under Gamma-convergence. However,
by investigating the kinetic relation we derive the macroscopic dissipation potential
Sampling sup‐normalized spectral functions for Brown–Resnick processes
No full textSup-normalized spectral functions form building blocks of max-stable and Pareto processes and therefore play an important role in modelling spatial extremes. For one of the most popular examples, the Brown–Resnick process, simulation is not straightforward. In this paper, we generalize two approaches for simulation via Markov chain Monte Carlo methods and rejection sampling by introducing new classes of proposal densities. In both cases, we provide an optimal choice of the proposal density with respect to sampling efficiency. The performance of the procedures is demonstrated in an example