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- Item1D symmetry for semilinear pdes from the limit interface of the solution(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Farina, Alberto; Valdinoci, EnricoWe study bounded, entire, monotone solutions of the Allen-Cahn equation. We prove that under suitable assumptions on the limit interface and on the energy growth, the solution is 1D. In particular, differently from the previous literature, the solution is not assumed to have minimal properties. We think that this approach could be fruitful in concrete situations, where one can observe the phase separation at a large scale and whishes to deduce the values of the state parameter in the vicinity of the interface. As a simple example of the results obtained with this point of view, we mention that monotone solutions with energy bounds, whose limit interface does not contain a vertical line through the origin, are 1D, at least up to dimension 4.
- Item2-Minimal subgroups in classical groups: Linear and unitary groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Parker, Chris; Rowley, Peter[no abstract available]
- ItemA 3-Local characterization of Co2(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2008) Parker, Christopher; Rowley, PeterConway's second largest simple group, Co2, is characterized by the centralizer of an element of order 3 and certain fusion data.
- ItemA 3-local identification of the alternating group of degree 8, the McLaughlin simple group and their automorphism groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2007) Parker, Christopher; Rowley, PeterIn this article we give 3-local characterizations of the alternating and symmetric groups of degree 8 and use these characterizations to recognize the sporadic simple group discovered by McLaughlin from its 3-local subgroups.
- Item3D boundary recovery by constrained Delaunay tetrahedralization(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Si, Hang; Gärtner, KlausThree-dimensional boundary recovery is a fundamental problem in mesh generation. In this paper, we propose a practical algorithm for solving this problem. Our algorithm is based on the construction of a it constrained Delaunay tetrahedralization (CDT) for a set of constraints (segments and facets). The algorithm adds additional points (so-called Steiner points) on segments only. The Steiner points are chosen in such a way that the resulting subsegments are Delaunay and their lengths are not unnecessarily short. It is theoretically guaranteed that the facets can be recovered without using Steiner points. The complexity of this algorithm is analyzed. The proposed algorithm has been implemented. Its performance is reported through various application examples
- Item3D electrothermal simulations of organic LEDs showing negative differential resistance(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Liero, Matthias; Fuhrmann, Jürgen; Glitzky, Annegret; Koprucki, Thomas; Fischer, Axel; Reineke, SebastianOrganic semiconductor devices show a pronounced interplay between temperature-activated conductivity and self-heating which in particular causes inhomogeneities in the brightness of large-area OLEDs at high power. We consider a 3D thermistor model based on partial differential equations for the electrothermal behavior of organic devices and introduce an extension to multiple layers with nonlinear conductivity laws, which also take the diode-like behavior in recombination zones into account. We present a numerical simulation study for a red OLED using a finite-volume approximation of this model. The appearance of S-shaped current-voltage characteristics with regions of negative differential resistance in a measured device can be quantitatively reproduced. Furthermore, this simulation study reveals a propagation of spatial zones of negative differential resistance in the electron and hole transport layers toward the contact.
- Item3D numerical simulations of THz generation by two-color laser filaments(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Bergé, Luc; Skupin, Stefan; Köhler, Christian; Babushkin, Ihar; Herrmann, JoachimTerahertz (THz) radiation produced by the filamentation of two-color pulses over long distances in argon is numerically investigated using a comprehensive model in full spacetime resolved geometry. We show that the dominant physical mechanism for THz generation in the filamentation regime at clamping intensity is based on quasi-dc plasma currents. The calculated THz spectra for different pump pulse energies and pulse durations are in agreement with previously reported experimental observations. For the same pulse parameters, near-infrared pump pulses at 2 m are shown to generate a more than one order of magnitude larger THz yield than pumps centered at 800 nm.
- ItemThe 3D transient semiconductor equations with gradient-dependent and interfacial recombination(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Disser, Karoline; Rehberg, JoachimWe establish the well-posedness of the transient van Roosbroeck system in three space dimensions under realistic assumptions on the data: non-smooth domains, discontinuous coefficient functions and mixed boundary conditions. Moreover, within this analysis, recombination terms may be concentrated on surfaces and interfaces and may not only depend on chargecarrier densities, but also on the electric field and currents. In particular, this includes Avalanche recombination. The proofs are based on recent abstract results on maximal parabolic and optimal elliptic regularity of divergence-form operators.
- Item3D-Simulation von Halbleiterdetektoren : Schlussbericht(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2001) Gajewski, Herbert[no abstract available]
- Item4-dimensional Manifolds(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2001) Kronheimer, Peter B.; Stern, Ronald J.[no abstract available]
- ItemAbelian theorems for stochastic volatility models with application to the estimation of jump activity of volatility(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Belomestny, Denis; Panov, VladimirIn this paper, we prove a kind of Abelian theorem for a class of stochastic volatility models $(X, V)$, where both the state process $X$ and the volatility process $V$ may have jumps. Our results relate the asymptotic behavior of the characteristic function of $X_Delta$ for some $Delta > 0$ in a stationary regime to the Blumenthal-Getoor indexes of the Lévy processes driving the jumps in $X$ and $V$ . The results obtained are used to construct consistent estimators for the above Blumenthal-Getoor indexes based on low-frequency observations of the state process $X$. We derive the convergence rates for the corresponding estimator and prove that these rates can not be improved in general.
- ItemAbrupt transitions in time series with uncertainties(London : Nature Publishing Group, 2018) Goswami, B.; Boers, N.; Rheinwalt, A.; Marwan, N.; Heitzig, J.; Breitenbach, S.F.M.; Kurths, J.Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.
- ItemAbsence of percolation in graphs based on stationary point processes with degrees bounded by two(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Jahnel, Benedikt; Tóbiás, AndrásWe consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for SINR graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional $k$-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for k=2.
- ItemAbsence of percolation in graphs based on stationary point processes with degrees bounded by two(New York, NY [u.a.] : Wiley, 2022) Jahnel, Benedikt; Tóbiás, AndrásWe consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for signal-to-interference ratio graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional k-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for k=2.
- ItemAbsolute stability and absolute hyperbolicity in systems with discrete time-delays(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Yanchuk, Serhiy; Wolfrum, Matthias; Pereira, Tiago; Turaev, DmitryAn equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete timedelays. In the case of a single delay, the absolute stability is shown to be equivalent to asymptotic stability for sufficiently large delays. Similarly, for multiple delays, the absolute stability is equivalent to asymptotic stability for hierarchically large delays. Additionally, we give necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays. The latter conditions are crucial for determining whether a system can have stabilizing or destabilizing bifurcations by varying time delays.
- ItemAbsorbing boundary condition for hyperbolic systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Erhardt, MatthiasThis paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.
- ItemAbstract bivariant Cuntz semigroups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Antoine, Ramon; Perera, Francesc; Thiel, HannesWe show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups S and T, there is another Cuntz semigroup JS, TK playing the role of morphisms from S to T. Applied to C*-algebras A and B, the semigroup JCu(A),Cu(B)K should be considered as the target in analogues of the UCT for bivariant theories of Cuntz semigroups. Abstract bivariant Cuntz semigroups are computable in a number of interesting cases. We explore its behaviour under the tensor product with the Cuntz semigroup of strongly self-absorbing C*-algebras and the Jacelon-Razak algebra. We also show that order-zero maps between C*-algebras naturally define elements in the respective bivariant Cuntz semigroup.
- ItemAbundance of 3-planes on real projective hypersurfaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Finashin, S.; Kharlamov, V.We show that a generic real projective n-dimensional hypersurface of odd degree d , such that 4(n - 2) = (d + 3 3), contains "many" real 3-planes, namely, in the logarithmic scale their number has the same rate of growth, d3 log d, as the number of complex 3-planes. This estimate is based on the interpretation of a suitable signed count of the 3-planes as the Euler number of an appropriate bundle.
- ItemAccelerated rogue solitons triggered by background radiation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Morgner, Uwe; Steinmeyer, Günter[no abstract available]
- ItemAccelerated variance-reduced methods for saddle-point problems(Amsterdam : Elsevier, 2022) Borodich, Ekaterina; Tominin, Vladislav; Tominin, Yaroslav; Kovalev, Dmitry; Gasnikov, Alexander; Dvurechensky, PavelWe consider composite minimax optimization problems where the goal is to find a saddle-point of a large sum of non-bilinear objective functions augmented by simple composite regularizers for the primal and dual variables. For such problems, under the average-smoothness assumption, we propose accelerated stochastic variance-reduced algorithms with optimal up to logarithmic factors complexity bounds. In particular, we consider strongly-convex-strongly-concave, convex-strongly-concave, and convex-concave objectives. To the best of our knowledge, these are the first nearly-optimal algorithms for this setting.