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The Dynamic State Index with Moisture and Phase Changes
Get PDFThe dynamic state index (DSI) is a scalar field that combines variational information on the total energy and enstrophy of a flow field with the second law of thermodynamics. Its magnitude is a combined local measure for non-stationarity, diabaticity, and dissipation in the flow, and it has been shown to provide good qualitative indications for the onset and presence of precipitation and the organization of storms.
The index has been derived thus far for ideal fluid models only, however, so that one may expect improved and quantitative insights from a revised definition of the quantity that includes more complex aerothermodynamics. The present paper suggests definitions of the DSI for flows of moist air with phase changes and precipitation
Balanced data assimilation for highly-oscillatory mechanical systems
Get PDFData assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, the ensemble Kalman filter also has limitations due to its inherent Gaussian and linearity assumptions. These limitations can manifest themselves in dynamically inconsistent state estimates. We investigate this issue in this paper for highly oscillatory Hamiltonian systems with a dynamical behavior which satisfies certain balance relations. We first demonstrate that the standard ensemble Kalman filter can lead to estimates which do not satisfy those balance relations, ultimately leading to filter divergence. We also propose two remedies for this phenomenon in terms of blended time-stepping schemes and ensemble-based penalty methods. The effect of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for two model scenarios. First, we consider balanced motion for highly oscillatory Hamiltonian systems and, second, we investigate thermally embedded highly oscillatory Hamiltonian systems. The first scenario is relevant for applications from meteorology while the second scenario is relevant for applications of data assimilation to molecular dynamics
Raptor: A fast and space-efficient pre-filter for querying very large collections of nucleotide sequences
No full textWe present Raptor, a tool for approximately searching many queries in large collections of nucleotide sequences. In comparison with similar tools like Mantis and COBS, Raptor is 12-144 times faster and uses up to 30 times less memory. Raptor uses winnowing minimizers to define a set of representative k-mers, an extension of the Interleaved Bloom Filters (IBF) as a set membership data structure, and probabilistic thresholding for minimizers. Our approach allows compression and a partitioning of the IBF to enable the effective use of secondary memory.
Competing Interest Statement: The authors have declared no competing interest
Balanced data assimilation with a blended numerical model
Get PDFA challenge arising from the local Bayesian assimilation of data
in an atmospheric
ow simulation is the imbalances it may introduce.
Fast-mode imbalances of the order of the slower dynamics can be
negated by employing a blended numerical model with seamless
access to the compressible and the soundproof pseudo-incompressible
dynamics. Here, the blended modelling strategy by Benacchio et
al. (2014) is upgraded in an advanced numerical framework and
extended with a Bayesian local ensemble data assimilation method.
Upon assimilation of data, the model configuration is switched to
the pseudo-incompressible regime for one time-step. After that, the
model configuration is switched back to the compressible model for
the duration of the assimilation window. The switching between
model regimes is repeated for each subsequent assimilation window.
An improved blending strategy ensures that a single time-step in
the pseudo-incompressible regime is sufficient to filter imbalances.
This improvement is based on three innovations: (i) the association
of pressure fields computed at different stages of the numerical integration
with actual time levels; (ii) a conversion of pressure-related
variables between the model regimes derived from low Mach number
asymptotics; and (iii) a judicious selection of the pressure variables
used in converting numerical model states when a switch of models
occurs. Travelling vortex and bubble convection experiments show
that the imbalance arising from assimilation of the momentum fields
can be eliminated by using this blended model, thereby achieving balanced
analysis fields. The leftover imbalance in the thermodynamics
can be quanti�ed by scale analysis
Sharp-interface problem of the Ohta-Kawasaki model 2 for symmetric diblock copolymers
Get PDFAbstract
The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific
community of diffuse-interface methods. To accurately capture the long-time
evolution of the moving interfaces, we present a derivation of the corresponding
sharp-interface limit using matched asymptotic expansions, and show that
the limiting process leads to a Hele-Shaw type moving interface problem. The
numerical treatment of the sharp-interface limit is more complicated due to the
stiffness of the equations. To address this problem, we present a boundary integral
formulation corresponding to a sharp interface limit of the Ohta-Kawasaki
model. Starting with the governing equations defined on separate phase domains,
we develop boundary integral equations valid for multi-connected domains
in a 2D plane. For numerical simplicity we assume our problem is driven
by a uniform Dirichlet condition on a circular far-field boundary. The integral
formulation of the problem involves both double- and single-layer potentials due
to the modified boundary condition. In particular, our formulation allows one
to compute the nonlinear dynamics of a non-equilibrium system and pattern
formation of an equilibrating system. Numerical tests on an evolving slightly
perturbed circular interface (separating the two phases) are in excellent agreement
with the linear analysis, demonstrating that the method is stable, efficient
and spectrally accurate in space
Stochastic pH Oscillations in a Model of the Urea−Urease Reaction Confined to Lipid Vesicles
Get PDFABSTRACT: The urea−urease clock reaction is a pH switch from acid to basic that can turn
into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the
confinement of the reaction to lipid vesicles, which permit the exchange with an external
reservoir by differential transport, enabling the recovery of the pH level and yielding a constant
supply of urea molecules. For microscopically small vesicles, the discreteness of the number of
molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that
intrinsic noise induces a significant statistical variation of the oscillation period, which
increases as the vesicles become smaller. The mean period, however, is found to be remarkably
robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is
gradually destroyed for smaller vesicles. The observed oscillations are explained as a canardlike
limit cycle that differs from the wide class of conventional feedback oscillators
Wege der familialen Tradierung von Gewalt(erfahrungen). In: Leonhard, Nina; Dimbath, Oliver (Hg.): Gewaltgedächtnisse. Analysen zur Präsenz vergangener Gewalt. In der Reihe: Soziales Gedächtnis, Erinnern und Vergessen - Memory Studies, Wiesbaden: Springer VS, 233-258.
No full textDer Beitrag befasst sich aus gedächtnistheoretischer Perspektive mit der familialen Tradierung von Gewalt im Nationalsozialismus. Im Fokus stehen die Arten und Weisen der Thematisierung vergangener Gewalterfahrungen sowie die Nachwirkungen dieser Thematisierung auf familial und gesellschaftlich unterschiedlich positionierte Nachkommende. Dazu gehören auch Nachkommende, die selbst von Rassismus betroffen sind. Die Tradierung der Gewalterfahrungen wird vor dem Hintergrund verschiedener Ebenen sozialer Gedächtnisse diskutiert: der körperlichen, der interaktiven, der familialen sowie der transsituationalen Ebene. Abschließend wird für eine zusammenwirkende Betrachtung der Ebenen plädiert, um den Wegen der familialen Tradierung von Gewalt(erfahrungen) nachzuspüren
Stochastic homogenization of Λ-convex gradient flows
Get PDFIn this paper we present a stochastic homogenization result for a class of Hilbert space evolutionary gradient systems driven by a quadratic dissipation potential and a Λ-convex energy functional featuring random and rapidly oscillating coefficients. Specific examples included in the result are Allen-Cahn type equations and evolutionary equations driven by the p-Laplace operator with p∈(1,∞). The homogenization procedure we apply is based on a stochastic two-scale convergence approach. In particular, we define a stochastic unfolding operator which can be considered as a random counterpart of the well-established notion of periodic unfolding. The stochastic unfolding procedure grants a very convenient method for homogenization problems defined in terms of (Λ-)convex functionals
Mechanical properties of quartz sand and gypsum powder (plaster) mixtures: 25implications for laboratory model analoguesfor the Earth’s upper crust
No full textGranular materials are a useful analogue for the Earth’s crust in laboratory models of deformation. Constraining their mechanical properties is critical for such model’s scaling and interpretation. Much information exists about monomineralic granular materials, such as quartz sand, but the mechanical characteristics of bimineralic mixtures, such as commonly-used quartz sand mixed with gypsum powder (i.e. plaster), are largely unconstrained. We used several mechanical tests (density, tensile, extension, shear) to constrain the failure envelope of various sand-plaster mixtures. We then fitted linear Coulomb and parabolic Griffith failure criteria to obtain cohesions and friction coefficients. Tests of the effects of emplacement technique, compaction and humidity demonstrated that the most reproducible rheology is given by oven-drying, pouring and mechanically compacting sand-plaster mixtures into their experimentation container. As plaster content increases, the tensile strength of dry sand-plaster mixtures increases from near zero (pure quartz sand) to 166±24 Pa (pure plaster). The cohesion increases from near zero to 250±21 Pa. The friction coefficient varies from 0.54±0.08 (sand) to 0.96±0.08 (20 weight% plaster). The mechanical behaviour of the resulting mixtures shifts at 20-35 weight% plaster from brittle Coulomb failure along a linear failure criterion, to more complex brittle-ductile Coulomb-Griffith failure along a non-linear failure criterion. With increasing plaster content, the brittle-ductile transition occurs at decreasing depth within a pile of sand-plaster mixture. We infer that the identified transitions in mechanical behaviour with increasing plaster content relate to (1) increasing porosities, (2) increasing grain size distributions, and (3) a decrease in sand-sand grain contacts and corresponding increase in gypsum-gypsum grain contacts. The presented characterisation enables a more quantitative scaling of the mechanical behaviour of sand-plaster mixtures, including of their tensile strength. Sand-plaster mixtures can thereby realistically simulate brittle-ductile properties of the Earth’s crust in scaled laboratory models
Stein Variational Gradient Descent: many-particle and long-time asymptotics
Get PDFStein variational gradient descent (SVGD) refers to a class of methods for Bayesian inference based on interacting
particle systems. In this paper, we consider the originally proposed deterministic dynamics as well as
a stochastic variant, each of which represent one of the two main paradigms in Bayesian computational statistics:
variational inference and Markov chain Monte Carlo. As it turns out, these are tightly linked through
a correspondence between gradient flow structures and large-deviation principles rooted in statistical physics.
To expose this relationship, we develop the cotangent space construction for the Stein geometry, prove its basic
properties, and determine the large-deviation functional governing the many-particle limit for the empirical
measure. Moreover, we identify the Stein-Fisher information (or kernelised Stein discrepancy) as its leading
order contribution in the long-time and many-particle regime in the sense of T-convergence, shedding some light
on the finite-particle properties of SVGD. Finally, we establish a comparison principle between the Stein-Fisher
information and RKHS-norms that might be of independent interest