3D Assembly of All‐Inorganic Colloidal Nanocrystals into Gels and Aerogels

We report an efficient approach to assemble a variety of electrostatically stabilized all‐inorganic semiconductor nanocrystals (NCs) by their linking with appropriate ions into multibranched gel networks. These all‐inorganic non‐ordered 3D assemblies benefit from strong interparticle coupling, which facilitates charge transport between the NCs with diverse morphologies, compositions, sizes, and functional capping ligands. Moreover, the resulting dry gels (aerogels) are highly porous monolithic structures, which preserve the quantum confinement of their building blocks. The inorganic semiconductor aerogel made of 4.5 nm CdSe colloidal NCs capped with I^? ions and bridged with Cd²⁺ ions had a large surface area of 146 m² g^?1.     

REAKTIONEN DES PYRIDINIUM-FLUOR-DITHIOPHOSPHORSÄURE-BETAINS

Abstract

Pyridinium-fluor-dithiophosphorsäure-betain (1) reagiert mit Hydrazin unter Bildung von Pyridinium-hydrazin-bis(fluor-dithiophosphate) (3), mit Phenylhydrazin unter Bildung von Pyridinium-phenylhydrazido-fluordithiophosphat (5). 3 und 5 können mit Methyljodid in die entsprechenden S-Methylester 7 und 8 überführt werden. Die Umsetzung der Titelverbindung 1 mit H₂S führt zu Pyridinium-difluor-pentathiodiphosphat (9). Das primäre Hydrolyseprodukt von 1 ist nicht stabil. Mercaptane und 1 reagieren zu den Pyridiniumsalzen der Fluor-trithiophosphorsäure-monoester (10), die durch Umsetzung mit Methyljodid in die Fluor-trithiophosphorsäure-diester (12) umgewandelt werden können. Die Reaktion von Phenyl-t-butyl-phosphan mit 1 hat eine P–P-Verknüpfung zur Folge. Reaktionsprodukt ist Pyridinium-phenyl-t-butyl-phosphido-fluor-dithiophosphat (13).

Pyridinium-fluoro-dithiophosphoric betaine (1) reacts with hydrazine to give pyridinium hydrazine bis(fluoro-dithiophosphate) (3), with phenylhydrazine to give pyridinium phenylhydrazido fluoro-dithiophosphate (5). 3 and 5 can be converted into the corresponding S-methyl esters 7 and 8 by methyl iodide. Reaction of the title compound 1 with H₂S yields pyridinium difluoro pentathiodiphosphate (9). The primary hydrolysis product of 1 is not stable. Mercaptanes and 1 yield pyridinium salts of fluoro trithiophosphoric monoesters (10) which by reaction with methyl iodide can be converted into fluoro trithiophosphoric diesters (12). The reaction of phenyl t-butyl phosphane with 1 results in the formation of a P–P bond. Reaction product is pyridinium phenyl t-butyl phosphido fluoro dithiophosphate (13).     

Nonlinear Instability of the Two-Dimensional Striation Model About Smooth Steady States

The two-dimensional striation model consists of a nonlinear system of PDE's which arises in the modeling of the ionospheric plasma. The local-in-time existence of strong solutions is first proved using Banach's fixed point theorem. Then, under physically relevant assumptions, the system is shown to be nonlinearly unstable as soon as it is linearly unstable. Moreover, the instability occurs before the possible blow-up time of the solution. The proof relies on an earlier work of Hwang and Guo (2003 Hwang , H. J. , Guo , Y. ( 2003 ). On the dynamical Rayleigh–Taylor instability . Arch. of Rat. Mech. Anal. 167 : 235 – 253 .[Crossref], [Web of Science ®] , [Google Scholar]). The first step of the proof is to investigate under which conditions the linearized system is unstable and to prove that its spectrum is bounded, by means of a variational formulation. The second one consists in constructing a family of solutions depending on the parameter δ measuring the smallness of the perturbation to the steady-state. Thanks to the boundedness of the linearized spectrum, this family of solutions is shown to be unstable by means of a power series expansion in δ.     

Modeling,Analysis, and Simulation of Biofilm Formation and Decay

In this article, we give a brief overview of our recent work on continuum mechanical modelling and simulation of microbial films. This comprises some classical tasks of applied mathematics such as computational fluid dynamics, analysis of partial differential equations, and mathematical biology.     

Subsampling effects in neuronal avalanche distributions recorded in vivo

Background  

Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma = 1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task.     

Entropy Optimization,Maxwell–Boltzmann,and Rayleigh Distributions

In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations.