175 results
Search Results
Now showing 1 - 10 of 175
- ItemWeak-strong uniqueness for the general Ericksen-Leslie system in three dimensions(Springfield, Mo. : American Institute of Mathematical Sciences, 2018) Emmrich, Etienne; Lasarzik, RobertWe study the Ericksen-Leslie system equipped with a quadratic free energy functional. The norm restriction of the director is incorporated by a standard relaxation technique using a double-well potential. We use the relative energy concept, often applied in the context of compressible Euler- or related systems of fluid dynamics, to prove weak-strong uniqueness of solutions. A main novelty, not only in the context of the Ericksen-Leslie model, is that the relative energy inequality is proved for a system with a nonconvex energy.
- ItemSynchronization of a Class of Memristive Stochastic Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays via Sampled-Data Control(London : Hindawi Limited, 2018) Yuan, M.; Wang, W.; Luo, X.; Ge, C.; Li, L.; Kurths, J.; Zhao, W.The paper addresses the issue of synchronization of memristive bidirectional associative memory neural networks (MBAMNNs) with mixed time-varying delays and stochastic perturbation via a sampled-data controller. First, we propose a new model of MBAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying distributed delays and discrete delays. Second, we design a new method of sampled-data control for the stochastic MBAMNNs. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the methods are carefully designed to confirm the synchronization processes are suitable for the feather of the memristor. Third, sufficient criteria guaranteeing the synchronization of the systems are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.
- ItemImplications of possible interpretations of ‘greenhouse gas balance’ in the Paris Agreement(London : The Royal Society, 2018) Fuglestvedt, J.; Rogelj, J.; Millar, R. J.; Allen, M.; Boucher, O.; Cain, M.; Forster, P. M.; Kriegler, E.; Shindell, D.The main goal of the Paris Agreement as stated in Article 2 is ‘holding the increase in the global average temperature to well below 2°C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5°C’. Article 4 points to this long-term goal and the need to achieve ‘balance between anthropogenic emissions by sources and removals by sinks of greenhouse gases'. This statement on ‘greenhouse gas balance’ is subject to interpretation, and clarifications are needed to make it operational for national and international climate policies. We study possible interpretations from a scientific perspective and analyse their climatic implications. We clarify how the implications for individual gases depend on the metrics used to relate them. We show that the way in which balance is interpreted, achieved and maintained influences temperature outcomes. Achieving and maintaining net-zero CO2-equivalent emissions conventionally calculated using GWP100 (100-year global warming potential) and including substantial positive contributions from short-lived climate-forcing agents such as methane would result in a sustained decline in global temperature. A modified approach to the use of GWP100 (that equates constant emissions of short-lived climate forcers with zero sustained emission of CO2) results in global temperatures remaining approximately constant once net-zero CO2-equivalent emissions are achieved and maintained. Our paper provides policymakers with an overview of issues and choices that are important to determine which approach is most appropriate in the context of the Paris Agreement.
- ItemClimate extremes, land–climate feedbacks and land-use forcing at 1.5°C(London : The Royal Society, 2018) Seneviratne, Sonia I.; Wartenburger, Richard; Guillod, Benoit P.; Hirsch, Annette L.; Vogel, Martha M.; Brovkin, Victor; van Vuuren, Detlef P.; Schaller, Nathalie; Boysen, Lena; Calvin, Katherine V.; Doelman, Jonathan; Greve, Peter; Havlik, Petr; Humpenöder, Florian; Krisztin, Tamas; Mitchell, Daniel; Popp, Alexander; Riahi, Keywan; Rogelj, Joeri; Schleussner, Carl-Friedrich; Sillmann, Jana; Stehfest, ElkeThis article investigates projected changes in temperature and water cycle extremes at 1.5°C of global warming, and highlights the role of land processes and land-use changes (LUCs) for these projections. We provide new comparisons of changes in climate at 1.5°C versus 2°C based on empirical sampling analyses of transient simulations versus simulations from the ‘Half a degree Additional warming, Prognosis and Projected Impacts’ (HAPPI) multi-model experiment. The two approaches yield similar overall results regarding changes in climate extremes on land, and reveal a substantial difference in the occurrence of regional extremes at 1.5°C versus 2°C. Land processes mediated through soil moisture feedbacks and land-use forcing play a major role for projected changes in extremes at 1.5°C in most mid-latitude regions, including densely populated areas in North America, Europe and Asia. This has important implications for low-emissions scenarios derived from integrated assessment models (IAMs), which include major LUCs in ambitious mitigation pathways (e.g. associated with increased bioenergy use), but are also shown to differ in the simulated LUC patterns. Biogeophysical effects from LUCs are not considered in the development of IAM scenarios, but play an important role for projected regional changes in climate extremes, and are thus of high relevance for sustainable development pathways.
- ItemFrom Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data(New York, NY : Springer, 2018) Koltai, Péter; Renger, D.R. MichielOne way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the “best” approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.
- 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.
- ItemSpectral Theory of Infinite Quantum Graphs(Cham (ZG) : Springer International Publishing AG, 2018) Exner, Pavel; Kostenko, Aleksey; Malamud, Mark; Neidhardt, HagenWe investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection together with spectral theory of (unbounded) discrete Laplacians on infinite graphs, we prove a number of new results on spectral properties of quantum graphs. Namely, we prove several self-adjointness results including a Gaffney-type theorem. We investigate the problem of lower semiboundedness, prove several spectral estimates (bounds for the bottom of spectra and essential spectra of quantum graphs, CLR-type estimates) and study spectral types.
- ItemLocalization of the principal Dirichlet eigenvector in the heavy-tailed random conductance model([Madralin] : EMIS ELibEMS, 2018) Flegel, FranziskaWe study the asymptotic behavior of the principal eigenvector and eigenvalue of the random conductance Laplacian in a large domain of Zd (d≥2) with zero Dirichlet condition. We assume that the conductances w are positive i.i.d. random variables, which fulfill certain regularity assumptions near zero. If γ=sup{q≥0:E[w−q]<∞}<1/4, then we show that for almost every environment the principal Dirichlet eigenvector asymptotically concentrates in a single site and the corresponding eigenvalue scales subdiffusively. The threshold γc=1/4 is sharp. Indeed, other recent results imply that for γ>1/4 the top of the Dirichlet spectrum homogenizes. Our proofs are based on a spatial extreme value analysis of the local speed measure, Borel-Cantelli arguments, the Rayleigh-Ritz formula, results from percolation theory, and path arguments.
- ItemA semismooth Newton method with analytical path-following for the H1-projection onto the Gibbs simplex(Oxford : Oxford Univ. Press, 2018) Adam, L.; Hintermüller, M.; Surowiec, T.M.An efficient, function-space-based second-order method for the H1-projection onto the Gibbs simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau–Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first- and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits mesh-independent behavior.
- ItemExtremal decomposition for random Gibbs measures: from general metastates to metastates on extremal random Gibbs measures([Madralin] : EMIS ELibEMS, 2018) Cotar, Codina; Jahnel, Benedikt; Külske, ChristofThe concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in the strong-coupling regime. We consider the general issue of the extremal decomposition for Gibbsian specifications which depend measurably on a parameter that may describe a whole random environment in the infinite volume. Given a random Gibbs measure, as a measurable map from the environment space, we prove measurability of its decomposition measure on pure states at fixed environment, with respect to the environment. As a general corollary we obtain that, for any metastate, there is an associated decomposition metastate, which is supported on the extremes for almost all environments, and which has the same barycenter.