Improving the approximation of the probability density function of random nonautonomous logistic‐type differential equations

In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P^′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t₀,T], P(t₀,ω)=P₀(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P₀ to approximate the density function f₁(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P₀, and the density of P₀, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L²([t₀,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P₀, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f₁(p,t) pointwise. Numerical examples illustrate our theoretical results.     

Monitoring dendrimer conformational transition using 19F and 1H2O NMR

The conformational transition of a fluorinated amphiphilic dendrimer is monitored by the ¹H signal from water, alongside the ¹⁹F signal from the dendrimer. High-field NMR data (chemical shift δ, self-diffusion coefficient D, longitudinal relaxation rate R₁, and transverse relaxation rate R₂) for both dendrimer (¹⁹F) and water (¹H) match each other in detecting the conformational transition. Among all parameters for both nuclei, the water proton transverse-relaxation rate R₂(¹H₂O) displays the highest relative scale of change upon conformational transition of the dendrimer. Hydrogen/deuterium-exchange mass spectrometry reveals that the compact form of the dendrimer has slower proton exchange with water than the extended form. This result suggests that the sensitivity of R₂(¹H₂O) toward dendrimer conformation originates, at least partially, from the difference in proton exchange efficiency between different dendrimer conformations. Finally, we also demonstrated that this conformational transition could be conveniently monitored using a low-field benchtop NMR spectrometer via R₂(¹H₂O). The ¹H₂O signal thus offers a simple way to monitor structural changes of macromolecules using benchtop time-domain NMR.     

Electrochemical and Scalable Dehydrogenative C(sp3)−H Amination via Remote Hydrogen Atom Transfer in Batch and Continuous Flow

A hydrogen atom transfer-directed electrochemical intramolecular C−H amination has been developed in which the N-radical species are generated at the anode, and the base required for the reaction is generated at the cathode. A broad range of valuable pyrrolidines were prepared in good yields and with high chemoselectivity. The reaction was easily scaled up in both batch and continuous flow systems.     

An Analytical Model for Flow of Seawater Adjacent to an Igneous Wall

Transport in Porous Media - We develop an analytical model describing the flow of NaCl– $$\hbox {H}_2\hbox {O}$$ in a saturated porous medium adjacent to a hot vertical wall and apply the...     

Discovering patterns in time-varying graphs: a triclustering approach

This paper introduces a novel technique to track structures in time varying graphs. The method uses a maximum a posteriori approach for adjusting a three-dimensional co-clustering of the source vertices, the destination vertices and the time, to the data under study, in a way that does not require any hyper-parameter tuning. The three dimensions are simultaneously segmented in order to build clusters of source vertices, destination vertices and time segments where the edge distributions across clusters of vertices follow the same evolution over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make any a priori quantization. Experiments conducted on artificial data illustrate the good behavior of the technique, and a study of a real-life data set shows the potential of the proposed approach for exploratory data analysis.     

Adsorption‐Induced Restructuring and Early Stages of Carbon‐Nanotube Growth on Ni Nanoparticles

Carbon adsorption on various Ni surfaces is investigated as a function of coverage via a combination of first‐principles simulations and field emission microscope experiments. It is found that carbon can be efficiently stored as subsurface carbides, but with different energetics on differently oriented surfaces depending on their compactness and density of adsorption sites. In the resulting morphological reshaping, {113} facets are predicted to grow at the expense of {111} and {100} facets, in excellent agreement with experimental observations. Moreover, at high coverage on the {113} surface the carbon adsorption energy passes through a maximum after which a structural crossover is realized such that carbon atoms tend to ascend to the surface to form one‐dimensional chains (which are the precursors of graphitic nanostructures). This rationalizes the experimental observation of an incubation time between carbon storage and the beginning of catalytic growth, and provides insight into the early stages (nucleation mechanism) of carbon nanotubes on Ni nanoparticles.