Search Results
A logistic equation with nonlocal interactions
We 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.
An asymptotic analysis for a generalized Cahn--Hilliard system with fractional operators
In a recent paper the same authors have proved existence, uniqueness and regularity results for a class of viscous and nonviscous Cahn--Hilliard systems of two operator equations in which nonlinearities of double-well type, like regular or logarithmic potentials, as well as nonsmooth potentials with indicator functions, were admitted. The operators appearing in the system equations are fractional powers in the spectral sense of general linear operators, which are densely defined, unbounded, selfadjoint, and monotone in the Hilbert space of square-integrable functions on a bounded and smooth three-dimensional domain, and have compact resolvents. Here, for the case of the viscous system, we analyze the asymptotic behavior of the solution as the fractional power coefficient of the second operator tends to zero. We prove convergence to a phase relaxation problem at the limit, and we also investigate this limiting problem, in which an additional term containing the projection of the phase variable on the kernel of the second operator appears.
Ring-Closure Mechanisms Mediated by Laccase to Synthesize Phenothiazines, Phenoxazines, and Phenazines
The green and environmentally friendly synthesis of highly valuable organic substances is one possibility for the utilization of laccases (EC 1.10.3.2). As reactants for the herein described syntheses, different o-substituted arylamines or arylthiols and 2,5-dihydroxybenzoic acid and its derivatives were used. In this way, the formation of phenothiazines, phenoxazines, and phenazines was achieved in aqueous solution mediated by the laccase of Pycnoporus cinnabarinus in the presence of oxygen. Two types of phenothiazines (3-hydroxy- and 3-oxo-phenothiazines) formed in one reaction assay were described for the first time. The cyclization reactions yielded C–N, C–S, or C–O bonds. The syntheses were investigated with regard to the substitution pattern of the reaction partners. Differences in C–S and C–N bond formations without cyclization are discussed.
Synthesis and crystal structure of a one-dimensional chain-like strontium(II) coordination polymer built of N-methyldiethanolamine and isobutyrate ligands
The one-dimensional coordination polymer (I) [Sr(ib)2 (H2mda)]n (Hib = isobutyric acid, C4H8O2, and H2mda = N-methyldiethanolamine, C5H13NO2), namely, catena-poly[[(N-methyldiethanolamine-k3O, N, O')strontium(II)]-di-μ2- isobutyrato-K3O, O':O;K3O:O, O'], was prepared by the one-pot aerobic reaction of [Zr6O4 (OH)4 (ib)12 (H2O)].3Hib with Sr(NO3)2 and H2mda in the presence of MnCl2 and Et3N in acetonitrile. The use of MnCl2 is key to the isolation of I as high-quality colorless crystals in good yield. The molecular solid-state structure of I was determined by single-crystal X-ray diffraction. Compound I crystallizes in the monoclinic space group P21/c and shows a one-dimensional polymeric chain structure. Each monomeric unit of this coordination polymer consists of a central SrII ion in the NO8 coordination environment of two deprotonated ib- ligands and one fully protonated H2mda ligand. The C and O atoms of the H2mda ligand were refined as disordered over two sets of sites with site occupancies of 0.619 (3) and 0.381 (3). Compound I shows thermal stability up to 130°C in air. © 2021 International Union of Crystallography. All rights reserved.
Mini-Workshop: Gibbs Measures for Nonlinear Dispersive Equations
In 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.
Microfluidic colloid filtration
Filtration 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.
Trend detection in river flow indices in Poland
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.
Graph properties for nonlocal minimal surfaces
In 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.
Knowledge Graphs - Working Group Charter (NFDI section-metadata) (1.2)
Knowledge Graphs are a key technology for implementing the FAIR principles in data infrastructures by ensuring interoperability for both humans and machines. The Working Group "Knowledge Graphs" in Section "(Meta)data, Terminologies, Provenance" of the German National Research Data Infrastructure (Nationale Forschungsdateninfrastruktur (NFDI) e.V.) aims to promote the use of knowledge graphs in all NFDI consortia, to facilitate cross-domain data interlinking and federation following the FAIR principles, and to contribute to the joint development of tools and technologies that enable transformation of structured and unstructured data into semantically reusable knowledge across different domains.
Synthesis and Characterization of Oxide Chloride Sr2VO3Cl, a Layered S = 1 Compound
The mixed-anion compound with composition Sr2VO3Cl has been synthesized for the first time, using the conventional high-temperature solid-state synthesis technique in a closed silica ampule under inert conditions. This compound belongs to the known Sr2TmO3Cl (Tm = Sc, Mn, Fe, Co, Ni) family, but with Tm = V. All homologues within this family can be described with the tetragonal space group P4/nmm (No. 129); from a Rietveld refinement of powder X-ray diffraction data on the Tm = V homologue, the unit cell parameters were determined to a = 3.95974(8) and c = 14.0660(4) Å, and the atomic parameters in the crystal structure could be estimated. The synthesized powder is black, implying that the compound is a semiconductor. The magnetic investigations suggest that Sr2VO3Cl is a paramagnet at high temperatures, exhibiting a μeff = 2.0 μB V-1 and antiferromagnetic (AFM) interactions between the magnetic vanadium spins (θCW = −50 K), in line with the V-O-V advantageous super-exchange paths in the V-O layers. Specific heat capacity studies indicate two small anomalies around 5 and 35 K, which however are not associated with long-range magnetic ordering. 35Cl ss-NMR investigations suggest a slow spin freezing below 4.2 K resulting in a glassy-like spin ground state.