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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).
- ItemNovel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients(Springfield, MO : AIMS Press, 2020) Wei, Ruoyu; Cao, Jinde; Kurths, JürgenIn this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixed-time control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results. © 2020 the Author(s), licensee AIMS Press.
- 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.
- 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.
- ItemCorrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains(Chichester, West Sussex : Wiley, 2020) Kovtunenko, Victor A.; Reichelt, Sina; Zubkova, Anna V.This paper is devoted to the homogenization of a nonlinear transmission problem stated in a two-phase domain. We consider a system of linear diffusion equations defined in a periodic domain consisting of two disjoint phases that are both connected sets separated by a thin interface. Depending on the field variables, at the interface, nonlinear conditions are imposed to describe interface reactions. In the variational setting of the problem, we prove the homogenization theorem and a bidomain averaged model. The periodic unfolding technique is used to obtain the residual error estimate with a first-order corrector. © 2019 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.
- 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.
- ItemDynamic probabilistic constraints under continuous random distributions(Berlin ; Heidelberg : Springer, 2020) González Grandón, T.; Henrion, R.; Pérez-Aros, P.The paper investigates analytical properties of dynamic probabilistic constraints (chance constraints). The underlying random distribution is supposed to be continuous. In the first part, a general multistage model with decision rules depending on past observations of the random process is analyzed. Basic properties like (weak sequential) (semi-) continuity of the probability function or existence of solutions are studied. It turns out that the results differ significantly according to whether decision rules are embedded into Lebesgue or Sobolev spaces. In the second part, the simplest meaningful two-stage model with decision rules from L2 is investigated. More specific properties like Lipschitz continuity and differentiability of the probability function are considered. Explicitly verifiable conditions for these properties are provided along with explicit gradient formulae in the Gaussian case. The application of such formulae in the context of necessary optimality conditions is discussed and a concrete identification of solutions presented. © 2020, The Author(s).
- ItemTime resolution and power consumption of a monolithic silicon pixel prototype in SiGe BiCMOS technology(London : Inst. of Physics, 2020) Paolozzi, L.; Cardarelli, R.; Débieux, S.; Favre, Y.; Ferrère, D.; Gonzalez-Sevilla, S.; Iacobucci, G.; Kaynak, M.; Martinelli, F.; Nessi, M.; Rücker, H.; Sanna, I.; Sultan, D.M.S.; Valerio, P.; Zaffaroni, E.SiGe BiCMOS technology can be used to produce ultra-fast, low-power silicon pixel sensors that provide state-of-the-art time resolution even without internal gain. The development of such sensors requires the identification and control of the main factors that may degrade the timing performance as well as the characterisation of the dependance of the sensor time resolution on the amplifier power consumption. Measurements with a 90Sr source of a prototype sensor produced in SG13G2 technology from IHP Microelectronics shows a time resolution of 140 ps at an amplifier current of 7 µA and 45 ps at a power consumption of 150 µA. The resolution on the measurement of the signal time-over-threshold, which is used to correct for time walk, is the main factor affecting the timing performance of this prototype. c 2020 CERN. Published by IOP Publishing Ltd on behalf of Sissa Medialab.