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- ItemRevealing the co-action of viscous and multistability hysteresis in an adhesive, nominally flat punch: A combined numerical and experimental study([Erscheinungsort nicht ermittelbar] : arXiv, 2022) Christian Müller, Manar Samri, René Hensel, Eduard Arzt, Martin H. MüserViscoelasticity is well known to cause a significant hysteresis of crack closure and opening when an elastomer is brought in and out of contact with a flat, rigid counterface. In contrast, the idea that adhesive hysteresis can also result under quasi-static driving due to small-scale, elastic multistability is relatively new. Here, we study a system in which both mechanisms act concurrently. Specifically, we compare the simulated and experimentally measured time evolution of the interfacial force and the real contact area between a soft elastomer and a rigid, flat punch, to which small-scale, single-sinusoidal roughness is added. To this end, we further the Green's function molecular dynamics method and extend recently developed imaging techniques to elucidate the rate- and preload-dependence of the pull-off process. Our results reveal that hysteresis is much enhanced when the saddle points of the topography come into contact, which, however, is impeded by viscoelastic forces and may require sufficiently large preloads. A similar coaction of viscous- and multistability effects is expected to occur in macroscopic polymer contacts and be relevant, e.g., for pressure-sensitive adhesives and modern adhesive gripping devices.
- ItemElectron beam induced dehydrogenation of MgH2 studied by VEELS(Cham : Springer International Publishing AG, 2016) Surrey, Alexander; Schultz, Ludwig; Rellinghaus, BerndNanosized or nanoconfined hydrides are promising materials for solid-state hydrogen storage. Most of these hydrides, however, degrade fast during the structural characterization utilizing transmission electron microscopy (TEM) upon the irradiation with the imaging electron beam due to radiolysis. We use ball-milled MgH2 as a reference material for in-situ TEM experiments under low-dose conditions to study and quantitatively understand the electron beam-induced dehydrogenation. For this, valence electron energy loss spectroscopy (VEELS) measurements are conducted in a monochromated FEI Titan3 80–300 microscope. From observing the plasmonic absorptions it is found that MgH2 successively converts into Mg upon electron irradiation. The temporal evolution of the spectra is analyzed quantitatively to determine the thickness-dependent, characteristic electron doses for electron energies of both 80 and 300 keV. The measured electron doses can be quantitatively explained by the inelastic scattering of the incident high-energy electrons by the MgH2 plasmon. The obtained insights are also relevant for the TEM characterization of other hydrides.
- ItemA function space framework for structural total variation regularization with applications in inverse problems(Bristol [u.a.] : Inst., 2018) Hintermüller, Michael; Holler, Martin; Papafitsoros, KostasIn this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.
- ItemSimple, accurate, and efficient implementation of 1-electron atomic time-dependent Schrödinger equation in spherical coordinates(Amsterdam : North Holland Publ. Co., 2015) Patchkovskii, Serguei; Müller, Harm GeertModelling atomic processes in intense laser fields often relies on solving the time-dependent Schrödinger equation (TDSE). For processes involving ionisation, such as above-threshold ionisation (ATI) and high-harmonic generation (HHG), this is a formidable task even if only one electron is active. Several powerful ideas for efficient implementation of atomic TDSE were introduced by H.G. Muller some time ago (Muller, 1999), including: separation of Hamiltonian terms into tri-diagonal parts; implicit representation of the spatial derivatives; and use of a rotating reference frame. Here, we extend these techniques to allow for non-uniform radial grids, arbitrary laser field polarisation, and non-Hermitian terms in the Hamiltonian due to the implicit form of the derivatives (previously neglected). We implement the resulting propagator in a parallel Fortran program, adapted for multi-core execution. Cost of TDSE propagation scales linearly with the problem size, enabling full-dimensional calculations of strong-field ATI and HHG spectra for arbitrary field polarisations on a standard desktop PC.
- ItemNumerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains(Heidelberg : Springer, 2022) Eigel, Martin; Gruhlke, Robert; Moser, Dieter; Grasedyck, LarsA fuzzy arithmetic framework for the efficient possibilistic propagation of shape uncertainties based on a novel fuzzy edge detection method is introduced. The shape uncertainties stem from a blurred image that encodes the distribution of two phases in a composite material. The proposed framework employs computational homogenisation to upscale the shape uncertainty to a effective material with fuzzy material properties. For this, many samples of a linear elasticity problem have to be computed, which is significantly sped up by a highly accurate low-rank tensor surrogate. To ensure the continuity of the underlying mapping from shape parametrisation to the upscaled material behaviour, a diffeomorphism is constructed by generating an appropriate family of meshes via transformation of a reference mesh. The shape uncertainty is then propagated to measure the distance of the upscaled material to the isotropic and orthotropic material class. Finally, the fuzzy effective material is used to compute bounds for the average displacement of a non-homogenized material with uncertain star-shaped inclusion shapes.
- ItemNTMpy: An open source package for solving coupled parabolic differential equations in the framework of the three-temperature model(Amsterdam : North Holland Publ. Co., 2021) Alber, Lukas; Scalera, Valentino; Unikandanunni, Vivek; Schick, Daniel; Stefano BonettiThe NTMpy code package allows for simulating the one-dimensional thermal response of multilayer samples after optical excitation, as in a typical pump-probe experiment. Several Python routines are combined and optimized to solve coupled heat diffusion equations in one dimension, on arbitrary piecewise homogeneous material stacks, in the framework of the so-called three-temperature model. The energy source deposited in the material is modelled as a light pulse of arbitrary cross-section and temporal profile. A transfer matrix method enables the calculation of realistic light absorption in presence of scattering interfaces as in multilayer samples. The open source code is fully object-oriented to enable a user-friendly and intuitive interface for adjusting the physically relevant input parameters. Here, we describe the mathematical background of the code, we lay out the workflow, and we validate the functionality of our package by comparing it to commercial software, as well as to experimental transient reflectivity data recorded in a pump-probe experiment with femtosecond light pulses.
- ItemLab::Measurement—A portable and extensible framework for controlling lab equipment and conducting measurements(Amsterdam : North Holland Publ. Co., 2019) Reinhardt, S.; Butschkow, C.; Geissler, S.; Dirnaichner, A.; Olbrich, F.; Lane, C.E.; Schröer, D.; Hüttel, A.K.Lab::Measurement is a framework for test and measurement automatization using Perl 5. While primarily developed with applications in mesoscopic physics in mind, it is widely adaptable. Internally, a layer model is implemented. Communication protocols such as IEEE 488 [1], USB Test & Measurement [2], or, e.g., VXI-11 [3] are addressed by the connection layer. The wide range of supported connection backends enables unique cross-platform portability. At the instrument layer, objects correspond to equipment connected to the measurement PC (e.g., voltage sources, magnet power supplies, multimeters, etc.). The high-level sweep layer automates the creation of measurement loops, with simultaneous plotting and data logging. An extensive unit testing framework is used to verify functionality even without connected equipment. Lab::Measurement is distributed as free and open source software. Program summary: Program Title: Lab::Measurement 3.660 Program Files doi: http://dx.doi.org/10.17632/d8rgrdc7tz.1 Program Homepage: https://www.labmeasurement.de Licensing provisions: GNU GPL v23 Programming language: Perl 5 Nature of problem: Flexible, lightweight, and operating system independent control of laboratory equipment connected by diverse means such as IEEE 488 [1], USB [2], or VXI-11 [3]. This includes running measurements with nested measurement loops where a data plot is continuously updated, as well as background processes for logging and control. Solution method: Object-oriented layer model based on Moose [4], abstracting the hardware access as well as the command sets of the addressed instruments. A high-level interface allows simple creation of measurement loops, live plotting via GnuPlot [5], and data logging into customizable folder structures. [1] F. M. Hess, D. Penkler, et al., LinuxGPIB. Support package for GPIB (IEEE 488) hardware, containing kernel driver modules and a C user-space library with language bindings. http://linux-gpib.sourceforge.net/ [2] USB Implementers Forum, Inc., Universal Serial Bus Test and Measurement Class Specification (USBTMC), revision 1.0 (2003). http://www.usb.org/developers/docs/devclass_docs/ [3] VXIbus Consortium, VMEbus Extensions for Instrumentation VXIbus TCP/IP Instrument Protocol Specification VXI-11 (1995). http://www.vxibus.org/files/VXI_Specs/VXI-11.zip [4] Moose—Apostmodern object system for Perl 5. http://moose.iinteractive.com [5] E. A. Merritt, et al., Gnuplot. An Interactive Plotting Program. http://www.gnuplot.info/ © 2018 The Author(s)