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- ItemDistribution of Cracks in a Chain of Atoms at Low Temperature(Cham (ZG) : Springer International Publishing AG, 2021) Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, FlorianWe consider a one-dimensional classical many-body system with interaction potential of Lennard–Jones type in the thermodynamic limit at low temperature 1/β∈(0,∞). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of Nexp(−βesurf/2) with esurf>0 a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.
- ItemDifferentiability Properties for Boundary Control of Fluid-Structure Interactions of Linear Elasticity with Navier-Stokes Equations with Mixed-Boundary Conditions in a Channel(New York, NY : Springer, 2023) Hintermüller, Michael; Kröner, AxelIn this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from (Lasiecka et al. in Nonlinear Anal 44:54–85, 2018). An elastic body surrounded by a liquid in a rectangular domain is deformed by the flow which can be controlled by the Dirichlet boundary condition at the inlet. On the walls along the channel homogeneous Dirichlet boundary conditions and on the outflow boundary do-nothing conditions are prescribed. We recall existence results for the nonlinear system from that reference and analyze the control to state mapping generalizing the results of (Wollner and Wick in J Math Fluid Mech 21:34, 2019) to the setting of the nonlinear Navier-Stokes equation for the fluid and the situation of mixed boundary conditions in a domain with corners.
- ItemLocal Well-Posedness of Strong Solutions to the Three-Dimensional Compressible Primitive Equations(Berlin ; Heidelberg : Springer, 2021) Liu, Xin; Titi, Edriss S.This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, are unique, and depend continuously on the initial data, for a short time in two cases: with gravity but without vacuum, and with vacuum but without gravity. © 2021, The Author(s).
- ItemRevealing all states of dewetting of a thin gold layer on a silicon surface by nanosecond laser conditioning(Amsterdam : Elsevier, 2021) Ernst, Owen C.; Uebel, David; Kayser, Stefan; Lange, Felix; Teubner, Thomas; Boeck, TorstenDewetting is a ubiquitous phenomenon which can be applied to the laser synthesis of nanoparticles. A classical spinodal dewetting process takes place in four successive states, which differ from each other in their morphology. In this study all states are revealed by interaction of pulsed nanosecond UV laser light with thin gold layers with thicknesses between 1 nm and 10 nm on (100) silicon wafers. The specific morphologies of the dewetting states are discussed with particular emphasis on the state boundaries. The main parameter determining which state is formed is not the duration for which the gold remains liquid, but rather the input energy provided by the laser. This shows that each state transition has a separate measurable activation energy. The temperature during the nanosecond pulses and the duration during which the gold remains liquid was determined by simulation using the COMSOL Multiphysics® software package. Using these calculations, an accurate local temperature profile and its development over time was simulated. An analytical study of the morphologies and formed structures was performed using Minkowski measures. With aid of this tool, the laser induced structures were compared with thermally annealed samples, with perfectly ordered structures and with perfectly random structures. The results show that both, structures of the laser induced and the annealed samples, strongly resemble the perfectly ordered structures. This reveals a close relationship between these structures and suggests that the phenomenon under investigation is indeed a spinodal dewetting generated by an internal material wave function. The purposeful generation of these structures and the elucidation of the underlying mechanism of dewetting by short pulse lasers may assist the realisation of various technical elements such as nanowires in science and industry. © 2020
- ItemWeak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models(Boston, Mass. : De Gruyter, 2022) Eiter, Thomas; Hopf, Katharina; Lasarzik, RobertWe study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and a symmetric deviatoric stress tensor. This stress tensor is transported via the Zaremba-Jaumann rate, and it is subject to two dissipation processes: one induced by a nonsmooth convex potential and one by stress diffusion. We show short-time existence of strong solutions as well as their uniqueness in a class of Leray-Hopf-type weak solutions satisfying the tensorial component in the sense of an evolutionary variational inequality. The global-in-time existence of such generalized solutions has been established in a previous work. We further study the limit when stress diffusion vanishes. In this case, the above notion of generalized solutions is no longer suitable, and we introduce the concept of energy-variational solutions, which is based on an inequality for the relative energy. We derive general properties of energy-variational solutions and show their existence by passing to the nondiffusive limit in the relative energy inequality satisfied by generalized solutions for nonzero stress diffusion.
- ItemOn the Differential Capacitance and Potential of Zero Charge of Au(111) in Some Aprotic Solvents(Weinheim : Wiley-VCH, 2021) Shatla, Ahmed S.; Landstorfer, Manuel; Baltruschat, HelmutVoltammetric and Gouy-Chapman capacitance minimum measurements were conducted on Au(111) and roughened Au(111) electrodes in aprotic electrolytes in the absence and presence of specifically adsorbed ions for concentrations ranging from 0.001 to 0.5 M. Negative of the point of zero charge (pzc), the capacitance maximum increases in the order Ca2+
- ItemAxisymmetric diffusion kurtosis imaging with Rician bias correction: A simulation study(New York, NY : Wiley-Liss, 2022) Oeschger, Jan Malte; Tabelow, Karsten; Mohammadi, SiawooshPurpose: To compare the estimation accuracy of axisymmetric diffusion kurtosis imaging (DKI) and standard DKI in combination with Rician bias correction (RBC). Methods: Axisymmetric DKI is more robust against noise-induced variation in the measured signal than standard DKI because of its reduced parameter space. However, its susceptibility to Rician noise bias at low signal-to-noise ratios (SNR) is unknown. Here, we investigate two main questions: first, does RBC improve estimation accuracy of axisymmetric DKI?; second, is estimation accuracy of axisymmetric DKI increased compared to standard DKI? Estimation accuracy was investigated on the five axisymmetric DKI tensor metrics (AxTM): the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor, using a noise simulation study based on synthetic data of tissues with varying fiber alignment and in-vivo data focusing on white matter. Results: RBC mainly increased accuracy for the parallel AxTM in tissues with highly to moderately aligned fibers. For the perpendicular AxTM, axisymmetric DKI without RBC performed slightly better than with RBC. However, the combination of axisymmetric DKI with RBC was the overall best performing algorithm across all five AxTM in white matter and axisymmetric DKI itself substantially improved accuracy in axisymmetric tissues with low fiber alignment. Conclusion: Combining axisymmetric DKI with RBC facilitates accurate DKI parameter estimation at unprecedented low SNRs ((Formula presented.)) in white matter, possibly making it a valuable tool for neuroscience and clinical research studies where scan time is a limited resource. The tools used here are available in the open-source ACID toolbox for SPM.
- ItemInverse learning in Hilbert scales(Dordrecht [u.a.] : Springer Science + Business Media B.V, 2023) Rastogi, Abhishake; Mathé, PeterWe study linear ill-posed inverse problems with noisy data in the framework of statistical learning. The corresponding linear operator equation is assumed to fit a given Hilbert scale, generated by some unbounded self-adjoint operator. Approximate reconstructions from random noisy data are obtained with general regularization schemes in such a way that these belong to the domain of the generator. The analysis has thus to distinguish two cases, the regular one, when the true solution also belongs to the domain of the generator, and the ‘oversmoothing’ one, when this is not the case. Rates of convergence for the regularized solutions will be expressed in terms of certain distance functions. For solutions with smoothness given in terms of source conditions with respect to the scale generating operator, then the error bounds can then be made explicit in terms of the sample size.
- ItemInversion-recovery MR elastography of the human brain for improved stiffness quantification near fluid-solid boundaries(New York, NY [u.a.] : Wiley-Liss, 2021) Lilaj, Ledia; Herthum, Helge; Meyer, Tom; Shahryari, Mehrgan; Bertalan, Gergely; Caiazzo, Alfonso; Braun, Jürgen; Fischer, Thomas; Hirsch, Sebastian; Sack, IngolfPurpose: In vivo MR elastography (MRE) holds promise as a neuroimaging marker. In cerebral MRE, shear waves are introduced into the brain, which also stimulate vibrations in adjacent CSF, resulting in blurring and biased stiffness values near brain surfaces. We here propose inversion-recovery MRE (IR-MRE) to suppress CSF signal and improve stiffness quantification in brain surface areas. Methods: Inversion-recovery MRE was demonstrated in agar-based phantoms with solid-fluid interfaces and 11 healthy volunteers using 31.25-Hz harmonic vibrations. It was performed by standard single-shot, spin-echo EPI MRE following 2800-ms IR preparation. Wave fields were acquired in 10 axial slices and analyzed for shear wave speed (SWS) as a surrogate marker of tissue stiffness by wavenumber-based multicomponent inversion. Results: Phantom SWS values near fluid interfaces were 7.5 ± 3.0% higher in IR-MRE than MRE (P =.01). In the brain, IR-MRE SNR was 17% lower than in MRE, without influencing parenchymal SWS (MRE: 1.38 ± 0.02 m/s; IR-MRE: 1.39 ± 0.03 m/s; P =.18). The IR-MRE tissue–CSF interfaces appeared sharper, showing 10% higher SWS near brain surfaces (MRE: 1.01 ± 0.03 m/s; IR-MRE: 1.11 ± 0.01 m/s; P <.001) and 39% smaller ventricle sizes than MRE (P <.001). Conclusions: Our results show that brain MRE is affected by fluid oscillations that can be suppressed by IR-MRE, which improves the depiction of anatomy in stiffness maps and the quantification of stiffness values in brain surface areas. Moreover, we measured similar stiffness values in brain parenchyma with and without fluid suppression, which indicates that shear wavelengths in solid and fluid compartments are identical, consistent with the theory of biphasic poroelastic media. © 2021 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals LLC on behalf of International Society for Magnetic Resonance in Medicine
- ItemNonlinear dynamical properties of frequency swept fiber-based semiconductor lasers(Bristol : IOP Publishing, 2021) Slepneva, Svetlana; Pimenov, AlexanderWe investigate dynamics of semiconductor lasers with fiber-based unidirectional ring cavity that can be used as frequency swept sources. We identify key factors behind the reach dynamical behavior of such lasers using state-of-the-art experimental and analytical methods. Experimentally, we study the laser in static, quasi-static and synchronization regimes. We apply experimental methods such as optical heterodyne or electric field reconstruction in order to characterize these regimes or study the mechanisms of transition between them. Using a delay differential equation model, we demonstrate that the presence of chromatic dispersion can lead to destabilization of the laser modes through modulational instability, which results in undesirable chaotic emission. We characterize the instability threshold both theoretically and experimentally, and demonstrate deterioration of the Fourier domain mode locking regime near the threshold.