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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.
- 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).
- ItemOn the Complexity of Attacking Elliptic Curve Based Authentication Chips(Amsterdam [u.a.] : Elsevier, 2021) Kabin, Ievgen; Dyka, Zoya; Klann, Dan; Schaeffner, Jan; Langendoerfer, PeterIn this paper we discuss the difficulties of mounting successful attacks against crypto implementations if essential information is missing. We start with a detailed description of our attack against our own design, to highlight which information is needed to increase the success of an attack, i.e. we use it as a blueprint to the following attack against commercially available crypto chips. We would like to stress that our attack against our own design is very similar to what happens during certification e.g. according to the Common Criteria Standard as in those cases the manufacturer needs to provide detailed information. If attacking commercial designs without signing NDAs, we were forced to intensively search the Internet for information about the designs. We were able to reveal information on the processing sequence during the authentication process even as detailed as identifying the clock cycles in which the individual key bits are processed. But we could not reveal the private keys used by the attacked commercial authentication chips 100% correctly. Moreover, as we did not knew the used keys we could not evaluate the success of our attack. To summarize, the effort of such an attack is significantly higher than the one of attacking a well-known implementation.
- ItemOn the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints(Berlin ; Heidelberg : Springer, 2021) Berthold, Holger; Heitsch, Holger; Henrion, René; Schwientek, JanWe present an adaptive grid refinement algorithm to solve probabilistic optimization problems with infinitely many random constraints. Using a bilevel approach, we iteratively aggregate inequalities that provide most information not in a geometric but in a probabilistic sense. This conceptual idea, for which a convergence proof is provided, is then adapted to an implementable algorithm. The efficiency of our approach when compared to naive methods based on uniform grid refinement is illustrated for a numerical test example as well as for a water reservoir problem with joint probabilistic filling level constraints.
- ItemA rigorous derivation and energetics of a wave equation with fractional damping(Basel : Springer, 2021) Mielke, Alexander; Netz, Roland R.; Zendehroud, SinaWe consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water–air interface, which is an experimental setup that is relevant for understanding wave propagation in biological membranes. We study the scaling regime where the relevant horizontal length scale is much larger than the vertical length scale and provide a rigorous limit leading to a fractionally damped wave equation for the membrane. We provide the associated existence results via linear semigroup theory and show convergence of the solutions in the scaling limit. Moreover, based on the energy–dissipation structure for the full model, we derive a natural energy and a natural dissipation function for the fractionally damped wave equation with a time derivative of order 3/2.
- ItemWell-posedness analysis of multicomponent incompressible flow models(Basel : Springer, 2021) Bothe, Dieter; Druet, Pierre-EtienneIn this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the partial mass densities stays constant. In this type of models, the velocity field in the Navier–Stokes equations is not solenoidal and, due to different specific volumes of the species, the pressure remains connected to the densities by algebraic formula. By means of a change of variables in the transport problem, we equivalently reformulate the PDE system as to eliminate positivity and incompressibility constraints affecting the density, and prove two type of results: the local-in-time well-posedness in classes of strong solutions, and the global-in-time existence of solutions for initial data sufficiently close to a smooth equilibrium solution.
- ItemPoisson approximation and connectivity in a scale-free random connection model([Madralin] : EMIS ELibEMS, 2021) Iyer, Srikanth K.; Jhawar, Sanjoy KrFor abstract see PDF
- ItemConnecting Islands: Bridging zbMATH and DLMF with Scholix, a blueprint for connecting expert knowledge systems(Berlin : EMS Press, 2021) Cohl, Howard S.; Teschke, Olaf; Schubotz, MoritzThis paper reports on the recently launched zbMATH Links API. We discuss its potential based on the initial link partner, the National Institute of Standards and Technology Digital Library of Mathematical Functions. As the API provides machine readable data in the links, we show how one can use data from both sources for further analysis. To exemplify the simplicity, we also show how one can use zbMATH’s link data in Jupyter notebooks.
- ItemTransport and continuity equations with (very) rough noise(Cham : Springer International Publishing, 2021) Bellingeri, C.; Djurdjevac, A.; Friz, P. K.; Tapia, N.Existence and uniqueness for rough flows, transport and continuity equations driven by general geometric rough paths are established.
- ItemUncertainty Quantification in Image Segmentation Using the Ambrosio–Tortorelli Approximation of the Mumford–Shah Energy(Dordrecht [u.a.] : Springer Science + Business Media B.V, 2021) Hintermüller, Michael; Stengl, Steven-Marian; Surowiec, Thomas M.The quantification of uncertainties in image segmentation based on the Mumford–Shah model is studied. The aim is to address the error propagation of noise and other error types in the original image to the restoration result and especially the reconstructed edges (sharp image contrasts). Analytically, we rely on the Ambrosio–Tortorelli approximation and discuss the existence of measurable selections of its solutions as well as sampling-based methods and the limitations of other popular methods. Numerical examples illustrate the theoretical findings.