Dynamic Covalent Synthesis of Crystalline Porous Graphitic Frameworks

Porous graphitic framework (PGF) is a two-dimensional (2D) material that has emerging energy applications. An archetype contains stacked 2D layers, the structure of which features a fully annulated aromatic skeleton with embedded heteroatoms and periodic pores. Due to the lack of a rational approach in establishing in-plane order under mild synthetic conditions, the structural integrity of PGF has remained elusive and ultimately limited its material performance. Here, we report the discovery of the unusual dynamic character of the C=N bonds in the aromatic pyrazine ring system under basic aqueous conditions, which enables the successful synthesis of a crystalline porous nitrogenous graphitic framework with remarkable in-plane order, as evidenced by powder X-ray diffraction studies and direct visualization using high-resolution transmission electron microscopy. The crystalline framework displays superior performance as a cathode material for lithium-ion batteries, outperforming the amorphous counterparts in terms of capacity and cycle stability. Insertion of well-defined, evenly spaced nanoscale pores into the two-dimensional (2D) layers of graphene invokes exciting properties due to the modulation of its electronic band gaps and surface functionalities. A bottom-up synthesis approach to such porous graphitic frameworks (PGFs) is appealing but also remains a great challenge. The current methods of building covalent organic frameworks rely on a small collection of thermodynamically reversible reactions. Such reactions are, however, inadequate in generating a fully annulated aromatic skeleton in PGFs. With the discovery of dynamic pyrazine formation, we succeeded in applying this linking chemistry to obtain a crystalline PGF material, which has displayed high electrical conductivity and remarkable performance as a cathode material for lithium-ion batteries. We envision that the demonstrated success will open the door to a wide array of fully annulated 2D porous frameworks, which hold immense potential for clean energy applications. We report the unusual dynamic characteristics of the C=N bonds in the pyrazine ring promoted under basic aqueous conditions, which enables the successful synthesis of two-dimensional porous graphitic frameworks (PGFs) featuring fully annulated aromatic skeletons and periodic pores. The PGF displayed high electrical conductivity and remarkable performance as a cathode material for lithium-ion batteries, far outperforming the amorphous counterparts in terms of capacity and cycle stability

Expectation thinning operators based on linear fractional probability generating functions

We introduce a two-parameter expectation thinning operator based on a linear fractional probability generating function. The operator is then used to define a first-order integer-valued autoregressive \inar1 process. Distributional properties of the \inar1 process are described. We revisit the Bernoulli-geometric \inar1 process of Bourguignon and Wei{\ss} (2017) and we introduce a new stationary \inar1 process with a compound negative binomial distribution. Lastly, we show how a proper randomization of our operator leads to a generalized notion of monotonicity for distributions on \bzp

Gluon Polarization from Correlated High-p_T Hadron Pairs in Polarized l - N Scattering

We propose to access the gluon polarization $\Delta G$ by measuring the cross section spin-asymmetry in semi-inclusive polarized lepton -- nucleon scattering. The photon-gluon fusion sub-process will be tagged by detecting high-$p_T$ correlated hadron pairs in the forward hemisphere. Selecting oppositely charged kaon pairs will allow to suppress the background coming from gluon radiation.Comment: 6 pages, 3 eps figures, aipproc.cls and aipproc.sty include

Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times

Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server's capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capacity that depends on both the number of waiting customers and their classes. The service times are generally distributed and class-dependent. These features complicate the analysis in a non-trivial way. We tackle it by examining the system state at embedded points, and studying the resulting Markov Chain. We first establish the joint probability generating function (pgf) of the service capacity and the number of customers left behind in the queue immediately after service initiation epochs. From this joint pgf, we extract the pgf for the number of customers in the queue and in the system respectively at service initiation epochs and departure epochs, and the pgf of the actual server capacity. Combined with additional techniques, we also obtain the pgf of the queue and system content at customer arrival epochs and random slot boundaries, and the pgf of the delay of a random customer. In the numerical experiments, we focus on the impact of correlation between the classes of consecutive customers, and on the influence of different service time distributions on the system performance. (C) 2019 Elsevier B.V. All rights reserved

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics

Exact results for fixation probability of bithermal evolutionary graphs

One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats exchanging individuals among each other and can be modeled by an evolutionary graph (EG), where directed links weight the probability for the offspring of one individual to replace another individual in the community. Very few exact analytical results are known for EGs. We show here how by using the techniques of the fixed point of Probability Generating Function, we can uncover a large class of of graphs, which we term bithermal, for which the exact fixation probability can be simply computed