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- ItemWeak-strong uniqueness for the general Ericksen-Leslie system in three dimensions(Springfield, Mo. : American Institute of Mathematical Sciences, 2018) Emmrich, Etienne; Lasarzik, RobertWe study the Ericksen-Leslie system equipped with a quadratic free energy functional. The norm restriction of the director is incorporated by a standard relaxation technique using a double-well potential. We use the relative energy concept, often applied in the context of compressible Euler- or related systems of fluid dynamics, to prove weak-strong uniqueness of solutions. A main novelty, not only in the context of the Ericksen-Leslie model, is that the relative energy inequality is proved for a system with a nonconvex energy.
- ItemAnisotropic solid-liquid interface kinetics in silicon: An atomistically informed phase-field model(Bristol : IOP Publ., 2017) Bergmann, S.; Albe, K.; Flege, E.; Barragan-Yani, D.A.; Wagner, B.We present an atomistically informed parametrization of a phase-field model for describing the anisotropic mobility of liquid–solid interfaces in silicon. The model is derived from a consistent set of atomistic data and thus allows to directly link molecular dynamics and phase field simulations. Expressions for the free energy density, the interfacial energy and the temperature and orientation dependent interface mobility are systematically fitted to data from molecular dynamics simulations based on the Stillinger–Weber interatomic potential. The temperature-dependent interface velocity follows a Vogel–Fulcher type behavior and allows to properly account for the dynamics in the undercooled melt.
- ItemVibrations of a laboratory-scale gas-stirred ladle with two eccentric nozzles and multiple sensors([Singapore] : Springer Singapore, 2019) Alia, Najib; Pylvänäinen, Mika; Visuri, Ville-Valtteri; John, Volker; Ollila, SeppoDuring ladle stirring, a gas is injected into the steel bath to generate a mixing of the liquid steel. The optimal process control requires a reliable measurement of the stirring intensity, for which the induced ladle wall vibrations have proved to be a potential indicator. An experimental cold water ladle with two eccentric nozzles and eight mono-axial accelerometers was thus investigated to measure the vibrations. The effect of the sensors’ positions with respect to the gas plugs on the vibration intensity was analyzed, and experimental data on several points of the ladle were collected for future numerical simulations. It is shown that the vibration root-mean-square values depend not only on process parameters, such as gas flow rate, water, and oil heights, but also on the radial and axial positions of the sensors. The vibration intensity is clearly higher, close to the gas plumes, than in the opposite side. If one of the nozzles is clogged, the vibration intensity close to the clogged nozzle drops drastically (−36 to −59%), while the vibrations close to the normal operating nozzle are hardly affected. Based on these results, guidelines are provided for an optimized vibration-based stirring.
- ItemA rough path perspective on renormalization(Amsterdam [u.a.] : Elsevier, 2019) Bruned, Y.; Chevyrev, I.; Friz, P.K.; Preiß, R.We develop the algebraic theory of rough path translation. Particular attention is given to the case of branched rough paths, whose underlying algebraic structure (Connes-Kreimer, Grossman-Larson) makes it a useful model case of a regularity structure in the sense of Hairer. Pre-Lie structures are seen to play a fundamental rule which allow a direct understanding of the translated (i.e. renormalized) equation under consideration. This construction is also novel with regard to the algebraic renormalization theory for regularity structures due to Bruned–Hairer–Zambotti (2016), the links with which are discussed in detail. © 2019 The Author(s)
- ItemA continuum model for yttria-stabilized zirconia incorporating triple phase boundary, lattice structure and immobile oxide ions(Berlin ; Heidelberg ; New York : Springer, 2019) Vágner, Petr; Guhlke, Clemens; Miloš, Vojtěch; Müller, Rüdiger; Fuhrmann, JürgenA continuum model for yttria-stabilized zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to (i) modeling of the YSZ-metal-gas triple phase boundary, (ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and (iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations. The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion. © 2019, The Author(s).
- ItemBoundary conditions for electrochemical interfaces(Bristol : IOP Publishing, 2017) Landstorfer, ManuelConsistent boundary conditions for electrochemical interfaces, which cover double layer charging, pseudo-capacitive effects and transfer reactions, are of high demand in electrochemistry and adjacent disciplines. Mathematical modeling and optimization of electrochemical systems is a strongly emerging approach to reduce cost and increase efficiency of super-capacitors, batteries, fuel cells, and electro-catalysis. However, many mathematical models which are used to describe such systems lack a real predictive value. Origin of this shortcoming is the usage of oversimplified boundary conditions. In this work we derive the boundary conditions for some general electrode-electrolyte interface based on non-equilibrium thermodynamics for volumes and surfaces. The resulting equations are widely applicable and cover also tangential transport. The general framework is then applied to a specific material model which allows the deduction of a current-voltage relation and thus a comparison to experimental data. Some simplified 1D examples show the range of applicability of the new approach.
- ItemExample dataset for the hMRI toolbox(Amsterdam [u.a.] : Elsevier, 2019) Callaghan, Martina F.; Lutti, Antoine; Ashburner, John; Balteau, Evelyne; Corbin, Nadège; Draganski, Bogdan; Helms, Gunther; Kherif, Ferath; Leutritz, Tobias; Mohammadi, Siawoosh; Phillips, Christophe; Reimer, Enrico; Ruthotto, Lars; Seif, Maryam; Tabelow, Karsten; Ziegler, Gabriel; Weiskopf, NikolausThe hMRI toolbox is an open-source toolbox for the calculation of quantitative MRI parameter maps from a series of weighted imaging data, and optionally additional calibration data. The multi-parameter mapping (MPM) protocol, incorporating calibration data to correct for spatial variation in the scanner's transmit and receive fields, is the most complete protocol that can be handled by the toolbox. Here we present a dataset acquired with such a full MPM protocol, which is made freely available to be used as a tutorial by following instructions provided on the associated toolbox wiki pages, which can be found at http://hMRI.info, and following the theory described in: hMRI – A toolbox for quantitative MRI in neuroscience and clinical research [1].
- ItemBayesian inference for spectral projectors of the covariance matrix(Ithaca, NY : Cornell University Library, 2018) Silin, Igor; Spokoiny, VladimirLet X1,…,Xn be an i.i.d. sample in Rp with zero mean and the covariance matrix Σ∗. The classical PCA approach recovers the projector P∗J onto the principal eigenspace of Σ∗ by its empirical counterpart ˆPJ. Recent paper [24] investigated the asymptotic distribution of the Frobenius distance between the projectors ∥ˆPJ−P∗J∥2, while [27] offered a bootstrap procedure to measure uncertainty in recovering this subspace P∗J even in a finite sample setup. The present paper considers this problem from a Bayesian perspective and suggests to use the credible sets of the pseudo-posterior distribution on the space of covariance matrices induced by the conjugated Inverse Wishart prior as sharp confidence sets. This yields a numerically efficient procedure. Moreover, we theoretically justify this method and derive finite sample bounds on the corresponding coverage probability. Contrary to [24, 27], the obtained results are valid for non-Gaussian data: the main assumption that we impose is the concentration of the sample covariance ˆΣ in a vicinity of Σ∗. Numerical simulations illustrate good performance of the proposed procedure even on non-Gaussian data in a rather challenging regime.
- ItemScaling limit of ballistic self-avoiding walk interacting with spatial random permutations([Madralin] : EMIS ELibEMS, 2019) Betz, Volker; Taggi, LorenzoWe consider nearest neighbour spatial random permutations on Zd. In this case, the energy of the system is proportional to the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually self-avoiding loops. The constant of proportionality, α, is the order parameter of the model. Our first result is that in a parameter regime of edge weights where it is known that a single self-avoiding loop is weakly space filling, long cycles of spatial random permutations are still exponentially unlikely. For our second result, we embed a self-avoiding walk into a background of spatial random permutations, and condition it to cover a macroscopic distance. For large values of α (where long cycles are very unlikely) we show that this walk collapses to a straight line in the scaling limit, and give bounds on the fluctuations that are almost sufficient for diffusive scaling. For proving our results, we develop the concepts of spatial strong Markov property and iterative sampling for spatial random permutations, which may be of independent interest. Among other things, we use them to show exponential decay of correlations for large values of α in great generality.
- ItemChange-point detection in high-dimensional covariance structure(Ithaca, NY : Cornell University Library, 2018) Avanesov, Valeriy; Buzun, NazarIn this paper we introduce a novel approach for an important problem of break detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process – a problem, which has applications in many areas e.g., neuroimaging and finance. The developed approach is essentially a testing procedure involving a choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. Theoretical study features a result providing guaranties for break detection. All the theoretical results are established in a high-dimensional setting (dimensionality p≫n). Multiscale nature of the approach allows for a trade-off between sensitivity of break detection and localization. The approach can be naturally employed in an on-line setting. Simulation study demonstrates that the approach matches the nominal level of false alarm probability and exhibits high power, outperforming a recent approach.