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- ItemA logistic equation with nonlocal interactions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Caffarelli, Luis; Dipierro, Serena; Outrata, Jir̆íWe consider here a logistic equation, modeling processes of nonlocal character both in the diffusion and proliferation terms. More precisely, for populations that propagate according to a Levy process and can reach resources in a neighborhood of their position, we compare (and find explicit threshold for survival) the local and nonlocal case. As ambient space, we can consider: bounded domains, periodic environments, transition problems, where the environment consists of a block of infinitesimal diffusion and an adjacent nonlocal one. In each of these cases, we analyze the existence/nonexistence of solutions in terms of the spectral properties of the domain. In particular, we give a detailed description of the fact that nonlocal populations may better adapt to sparse resources and small environments.
- ItemMini-Workshop: Gibbs Measures for Nonlinear Dispersive Equations(Zürich : EMS Publ. House, 2018) Schlein, Benjamin; Sohinger, VedranIn this mini-workshop we brought together leading experts working on the application of Gibbs measures to the study of nonlinear PDEs. This framework is a powerful tool in the probabilistic study of solutions to nonlinear dispersive PDEs, in many ways alternative or complementary to deterministic methods. Among the special topics discussed were the construction of the measures, applications to dynamics, as well as the microscopic derivation of Gibbs measures from many-body quantum mechanics.
- ItemGraph properties for nonlocal minimal surfaces(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Dipierro, Serena; Savin, Ovidiu; Valdinoci, EnricoIn this paper we show that a nonlocal minimal surface which is a graph outside a cylinder is in fact a graph in the whole of the space. As a consequence, in dimension 3, we show that the graph is smooth. The proofs rely on convolution techniques and appropriate integral estimates which show the pointwise validity of an Euler-Lagrange equation related to the nonlocal mean curvature.
- ItemMicrofluidic colloid filtration([London] : Macmillan Publishers Limited, part of Springer Nature, 2016) Linkhorst, John; Beckmann, Torsten; Go, Dennis; Kuehne, Alexander J. C.; Wessling, MatthiasFiltration of natural and colloidal matter is an essential process in today’s water treatment processes. The colloidal matter is retained with the help of micro- and nanoporous synthetic membranes. Colloids are retained in a “cake layer” – often coined fouling layer. Membrane fouling is the most substantial problem in membrane filtration: colloidal and natural matter build-up leads to an increasing resistance and thus decreasing water transport rate through the membrane. Theoretical models exist to describe macroscopically the hydrodynamic resistance of such transport and rejection phenomena; however, visualization of the various phenomena occurring during colloid retention is extremely demanding. Here we present a microfluidics based methodology to follow filter cake build up as well as transport phenomena occuring inside of the fouling layer. The microfluidic colloidal filtration methodology enables the study of complex colloidal jamming, crystallization and melting processes as well as translocation at the single particle level.
- ItemTrend detection in river flow indices in Poland(Heidelberg : Springer, 2018) Piniewski, Mikołaj; Marcinkowski, Paweł; Kundzewicz, Zbigniew W.The issue of trend detection in long time series of river flow records is of vast theoretical interest and considerable practical relevance. Water management is based on the assumption of stationarity; hence, it is crucial to check whether taking this assumption is justified. The objective of this study is to analyse long-term trends in selected river flow indices in small- and medium-sized catchments with relatively unmodified flow regime (semi-natural catchments) in Poland. The examined indices describe annual and seasonal average conditions as well as annual extreme conditions—low and high flows. The special focus is on the spatial analysis of trends, carried out on a comprehensive, representative data set of flow gauges. The present paper is timely, as no spatially comprehensive studies (i.e. covering the entire Poland or its large parts) on trend detection in time series of river flow have been done in the recent 15 years or so. The results suggest that there is a strong random component in the river flow process, the changes are weak and the spatial pattern is complex. Yet, the results of trend detection in different indices of river flow in Poland show that there exists a spatial divide that seems to hold quite generally for various indices (annual, seasonal, as well as low and high flow). Decreases of river flow dominate in the northern part of the country and increases usually in the southern part. Stations in the central part show mostly ‘no trend’ results. However, the spatial gradient is apparent only for the data for the period 1981–2016 rather than for 1956–2016. It seems also that the magnitude of increases of river flow is generally lower than that of decreases.
- Item2-hydroxyethylammonium iodide(Chester : International Union of Crystallography, 2014) Kohrt, C.; Spannenberg, A.; Werner, T.In the crystal structure of the title salt, C2H 8NO+·I-, N-H⋯O, N-H⋯I and O-H⋯I hydrogen bonds lead to the formation of layers staggered along the c axis.
- ItemCrystal structure of diethyl (E)-2-[(benzofuran-2-yl)methylidene]succinate(Chester : International Union of Crystallography, 2015) Schirmer, Marie-Luis; Spannenberg, Anke; Werner, ThomasThe title compound, C17H18O5, was synthesized by a base-free catalytic Wittig reaction. The molecule consists of a diethyl itaconate unit, which is connected via the C=C double bond to a benzofuran moiety. The benzofuran ring system (r.m.s. deviation = 0.007 Å) forms dihedral angles of 79.58 (4) and 12.12 (10)° with the mean planes through the cis and trans ethoxycarbonyl groups, respectively. An intramolecular C-H...O hydrogen bond involving the O atom of the benzofuran moiety is observed. In the crystal, molecules are linked into ribbons running parallel to the b axis by C-H...O hydrogen bonds.
- ItemIntermolecular hydrogen bonding in isostructural pincer complexes [OH-(t-BuPOCOPt-Bu)MCl] (M = Pd and Pt)(Chester : International Union of Crystallography, 2019) Joksch, M.; Spannenberg, A.; Beweries, T.In the crystal structure of the isostructural title compounds, namely {2,6-bis[(di-tert-butylphosphanyl)oxy]-4-hydroxyphenyl}chloridopalladium(II), [Pd(C22H39O3P2)Cl], 1, and {2,6-bis[(di-tert-butylphosphanyl)oxy]-4-hydroxyphenyl}chloridoplatinum(II), [Pt(C22H39O3P2)Cl], 2, the metal centres are coordinated in a distorted square-planar fashion by the POCOP pincer fragment and the chloride ligand. Both complexes form strong hydrogen-bonded chain structures through an interaction of the OH group in the 4-position of the aromatic POCOP backbone with the halide ligand.
- Item(Cyanido-κC)(2,2-diphenylacetamido-κ2 N,O)bis(η5-pentamethylcyclopentadienyl)zirconium(IV)(Chester : International Union of Crystallography, 2014) Becker, L.; Spannenberg, A.; Arndt, P.; Rosenthal, U.In the title compound, [Zr(C10H15)2(C14H12NO)(CN)], the ZrIV atom is coordinated by two pentamethylcyclopentadienyl ligands, the amidate ligand via the N and O atoms, and an additional C N ligand. The four-membered metallacycle is nearly planar (r.m.s. deviation = 0.008Å). In the crystal, the molecules are connected into centrosymmetric dimers via pairs of N - HN hydrogen bonds.
- ItemChanges of snow cover in Poland(Heidelberg : Springer, 2017) Szwed, Małgorzata; Pin´skwar, Iwona; Kundzewicz, Zbigniew W.; Graczyk, Dariusz; Mezghani, AbdelkaderThe present paper examines variability of characteristics of snow cover (snow cover depth, number of days with snow cover and dates of beginning and end of snow cover) in Poland. The study makes use of a set of 43 long time series of observation records from the stations in Poland, from 1952 to 2013. To describe temporal changes in snow cover characteristics, the intervals of 1952–1990 and of 1991–2013 are compared and trends in analysed data are sought (e.g., using the Mann–Kendall test). Observed behaviour of time series of snow-related variables is complex and not easy to interpret, for instance because of the location of the research area in the zone of transitional moderate climate, where strong variability of climate events is one of the main attributes. A statistical link between the North Atlantic Oscillation (NAO) index and the snow cover depth, as well as the number of snow cover days is found.