13 results
Search Results
Now showing 1 - 10 of 13
- ItemRobust homoclinic orbits in planar systems with Preisach hysteresis operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Pimenov, Alexander; Rachinskii, DmitriiWe construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically.
- ItemImproving accuracy and temporal resolution of learning curve estimation for within- and across-session analysis(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Deliano, Matthias; Tabelow, Karsten; König, Reinhard; Polzehl, JörgEstimation of learning curves is ubiquitously based on proportions of correct responses within moving trial windows. In this approach, it is tacitly assumed that learning performance is constant within the moving windows, which, however, is often not the case. In the present study we demonstrate that violations of this assumption lead to systematic errors in the analysis of learning curves, and we explored the dependency of these errors on window size, different statistical models, and learning phase. To reduce these errors for single subjects as well as on the population level, we propose adequate statistical methods for the estimation of learning curves and the construction of confidence intervals, trial by trial. Applied to data from a shuttle-box avoidance experiment with Mongolian gerbils, our approach revealed performance changes occurring at multiple temporal scales within and across training sessions which were otherwise obscured in the conventional analysis. The proper assessment of the behavioral dynamics of learning at a high temporal resolution clarified and extended current descriptions of the process of avoidance learning. It further disambiguated the interpretation of neurophysiological signal changes recorded during training in relation to learning.
- ItemElectrical, mechanical, and glass transition behavior of polycarbonate-based nanocomposites with different multi-walled carbon nanotubes(Oxford : Elsevier Science, 2011) Castillo, Frank Yepez; Socher, Robert; Krause, Beate; Headrick, Robert; Grady, Brian P.; Prada-Silvy, Ricardo; Pötschke, PetraFive commercially available multi-walled carbon nanotubes (MWNTs), with different characteristics, were melt mixed with polycarbonate (PC) in a twin-screw micro compounder to obtain nanocomposites containing 0.25-3.0 wt.% MWNT. The electrical properties of the composites were assessed using bulk electrical conductivity measurements, the mechanical properties of the composites were evaluated using tensile tests and dynamic mechanical analysis (DMA), and the thermal properties of the composites were investigated using differential scanning calorimetry (DSC). Electrical percolation thresholds (pcs) were observed between 0.28 wt.% and 0.60 wt.%, which are comparable with other well-dispersed melt mixed materials. Based on measurements of diameter and length distributions of unprocessed tubes it was found that nanotubes with high aspect ratios exhibited lower pcs, although one sample did show higher pc than expected (based on aspect ratio) which was attributed to poorer dispersion achieved during mixing. The stress-strain behavior of the composites is only slightly altered with CNT addition; however, the strain at break is decreased even at low loadings. DMA tests suggest the formation of a combined polymer-CNT continuous network evidenced by measurable storage moduli at temperatures above the glass transition temperature (T g), consistent with a mild reinforcement effect. The composites showed lower glass transition temperatures than that of pure PC. Lowering of the height of the tanδ peak from DMA and reductions in the heat capacity change at the glass transition from DSC indicate that MWNTs reduced the amount of polymer material that participates in the glass transition of the composites, consistent with immobilization of polymer at the nanotube interface. © 2011 Elsevier Ltd. All rights reserved.
- ItemInfluence of cell shape, inhomogeneities and diffusion barriers in cell polarization models(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Giese, Wolfgang; Eigel, Martin; Westerheide, Sebastian; Engwer, Christian; Klipp, EddaIn silico experiments bear the potential to further the understanding of biological transport processes by allowing a systematic modification of any spatial property and providing immediate simulation results for the chosen models. We consider cell polarization and spatial reorganization of membrane proteins which are fundamental for cell division, chemotaxis and morphogenesis. Our computational study is motivated by mating and budding processes of S. cerevisiae. In these processes a key player during the initial phase of polarization is the GTPase Cdc42 which occurs in an active membrane-bound form and an inactive cytosolic form. We use partial differential equations to describe the membrane-cytosol shuttling of Cdc42 during budding as well as mating of yeast. The membrane is modeled as a thin layer that only allows lateral diffusion and the cytosol is modeled as a volume. We investigate how cell shape and diffusion barriers like septin structures or bud scars influence Cdc42 cluster formation and subsequent polarization of the yeast cell. Since the details of the binding kinetics of cytosolic proteins to the membrane are still controversial, we employ two conceptual models which assume different binding kinetics. An extensive set of in silico experiments with different modeling hypotheses illustrate the qualitative dependence of cell polarization on local membrane curvature, cell size and inhomogeneities on the membrane and in the cytosol. We examine that spatial inhomogenities essentially determine the location of Cdc42 cluster formation and spatial properties are crucial for the realistic description of the polarization process in cells. In particular, our computer simulations suggest that diffusion barriers are essential for the yeast cell to grow a protrusion.
- ItemAn updated micromechanical model based on morphological characterization of carbon nanotube nanocomposites(Oxford [u.a.] : Elsevier, 2017) Talò, Michela; Krause, Beate; Pionteck, Jürgen; Lanzara, Giulia; Lacarbonara, WalterBy leveraging on extensive morphological analysis of carbon nanotube nanocomposites, an update of the Eshelby-Mori-Tanaka method is proposed for a more accurate estimation of the nanocomposites effective elastic response. The experimental results are employed to overcome the main modeling limitations inherent in most common micromechanical theories, such as the perfect dispersion of the nanofiller and the uniformity of the nanofiller's aspect ratio within the nanocomposite. The actual variability of the CNTs aspect ratio and the CNTs degree of dispersion are experimentally measured and introduced in the proposed model by averaging the Eshelby tensor over the actual CNT lengths distribution and by accounting for the effective CNT volume fraction. The effects of the nanofiller morphology on the mechanical response of three different thermoplastic nanocomposites with low- and high-aspect ratio CNTs are explored, and monotonic tensile tests are performed to validate the predictions of the proposed model. A good agreement is found between the predicted nanocomposites elastic moduli and the experimental data.
- ItemMinimization of a fractional perimeter-Dirichlet integral functional(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Caffarelli, Luis; Savin, Ovidiu; Valdinoci, EnricoWe consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set. We obtain regularity results for the minimizers and for their free boundaries using blow-up analysis, density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems.
- ItemMethods to characterize the dispersability of carbon nanotubes and their length distribution(Weinheim : Wiley-VCH Verl., 2012) Krause, Beate; Mende, Mandy; Petzold, Gudrun; Boldt, Regine; Pötschke, PetraTwo main properties of carbon nanotube (CNT) materials are discussed in this contribution. First, a method to characterize the dispersability of CNT materials in aqueous surfactant solutions in presented, which also allows conclusions towards the dispersability in other media, like polymer melts. On the other hand it is shown, how the length of CNTs before and after processing, e.g., after melt mixing with thermoplastics, can be quantified. Both methods are illustrated with examples and the practical relevance is shown. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
- ItemError estimates for nonlinear reaction-diffusion systems involving different diffusion length scales(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Reichelt, SinaWe derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms, and we allow for different diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1, other species may diffuse much slower, namely, with order of the characteristic microstructure-length scale. We consider an effective system, which is rigorously obtained via two-scale convergence, and we prove that the error of its solution to the original solution is of order 1/2.
- ItemSimultaneous statistical inference for epigenetic data(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Schildknecht, Konstantin; Olek, Sven; Dickhaus, ThorstenEpigenetic research leads to complex data structures. Since parametric model assumptions for the distribution of epigenetic data are hard to verify we introduce in the present work a nonparametric statistical framework for two-group comparisons. Furthermore, epigenetic analyses are often performed at various genetic loci simultaneously. Hence, in order to be able to draw valid conclusions for specific loci, an appropriate multiple testing correction is necessary. Finally, with technologies available for the simultaneous assessment of many interrelated biological parameters (such as gene arrays), statistical approaches also need to deal with a possibly unknown dependency structure in the data. Our statistical approach to the nonparametric comparison of two samples with independent multivariate observables is based on recently developed multivariate multiple permutation tests. We adapt their theory in order to cope with families of hypotheses regarding relative effects. Our results indicate that the multivariate multiple permutation test keeps the pre-assigned type I error level for the global null hypothesis. In combination with the closure principle, the family-wise error rate for the simultaneous test of the corresponding locus/parameter-specific null hypotheses can be controlled. In applications we demonstrate that group differences in epigenetic data can be detected reliably with our methodology.
- ItemHausdorff metric BV discontinuity of sweeping processes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Klein, Olaf; Recupero, VincenzoSweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of emphrate independent operator containing as a particular case the so called emphplay operator which is widely used in hysteresis. The continuity properties of these operators were studied in several works. In this note we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide a counterexample showing that the solution operator of the sweeping process is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1-topology. This is at variance with the case of the play operator which instead is continuous in this sense.