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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.
- ItemTime-Warping Invariants of Multidimensional Time Series(Dordrecht [u.a.] : Springer Science + Business Media B.V., 2020) Diehl, Joscha; Ebrahimi-Fard, Kurusch; Tapia, NikolasIn data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants. We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties. © 2020, The Author(s).
- 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
- ItemLongtime behavior for a generalized Cahn-Hilliard system with fractional operators(Messina : Accademia Peloritana dei Pericolanti, 2020) Colli, Pierluigi; Gilardi, Gianni; Sprekels, JürgenIn this contribution, we deal with the longtime behavior of the solutions to the fractional variant of the Cahn-Hilliard system, with possibly singular potentials, that we have recently investigated in the paper Well-posedness and regularity for a generalized fractional Cahn-Hilliard system. More precisely, we study the ω-limit of the phase parameter y and characterize it completely. Our characterization depends on the first eigenvalues λ1≥0 of one of the operators involved: if λ1>0, then the chemical potential μ vanishes at infinity and every element yω of the ω-limit is a stationary solution to the phase equation; if instead λ1=0, then every element yω of the ω-limit satisfies a problem containing a real function μ∞ related to the chemical potential μ. Such a function μ∞ is nonunique and time dependent, in general, as we show by an example. However, we give sufficient conditions for μ∞ to be uniquely determined and constant.
- 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+
- ItemExistence, iteration procedures and directional differentiability for parabolic QVIs(Berlin ; Heidelberg : Springer, 2020) Alphonse, Amal; Hintermüller, Michael; Rautenberg, Carlos N.We study parabolic quasi-variational inequalities (QVIs) of obstacle type. Under appropriate assumptions on the obstacle mapping, we prove the existence of solutions of such QVIs by two methods: one by time discretisation through elliptic QVIs and the second by iteration through parabolic variational inequalities. Using these results, we show the directional differentiability (in a certain sense) of the solution map which takes the source term of a parabolic QVI into the set of solutions, and we relate this result to the contingent derivative of the aforementioned map. We finish with an example where the obstacle mapping is given by the inverse of a parabolic differential operator.
- 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.
- 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