Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.     

Transmission of macroeconomic shocks to risk parameters: Their uses in stress testing

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk parameters. We propose the use of an extensive family of models, called General Transfer Function Models, which condense well the characteristics of the transmission described by the impact measures. The procedure for estimating the parameters of these models is described employing the Bayesian approach and using the prior information provided by the impact measures. In addition, we illustrate the use of the estimated models from the credit risk data of a portfolio.     

A review of mobility metrics for next generation vehicle mobility models

In the United States, the NATO Reference Mobility Model (NRMM) has been used for evaluating military ground vehicle mobility and the Vehicle Cone Index (VCI) has been selected as a mobility metric. VCI represents the minimum soil strength required for a vehicle to consistently make a specific number of passes, usually one or fifty passes. In the United Kingdom, the Mean Maximum Pressure (MMP) has been adopted as a metric for assessing military vehicle cross-country mobility. MMP is the mean value of the maxima occurring under all the wheel stations of a vehicle. Both VCI and MMP are empirically based. This paper presents a review of the basis upon which VCI and MMP were developed, as well as their applications to evaluating vehicle mobility in practice. With the progress in terramechanics and in modelling and simulation techniques in recent years, there is a growing desire to develop physics-based mobility metrics for next generation vehicle mobility models. Based on the review, criteria for selecting physics-based mobility metrics are proposed. Following these criteria, metrics for characterizing military vehicle traction limits and traversability on a given operating area are recommended.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.     

Cover Feature: Mechanism of Oxidative Activation of Fluorinated Aromatic Compounds by N-Bridged Diiron-Phthalocyanine: What Determines the Reactivity? (Chem. Eur. J. 63/2019)

The biodegradation of compounds with C−F bonds is challenging due to the fact that these bonds are stronger than the C−H bond in methane. In this work, results on the unprecedented reactivity of a biomimetic model complex that contains an N-bridged diiron-phthalocyanine are presented; this model complex is shown to react with perfluorinated arenes under addition of H₂O₂ effectively. To get mechanistic insight into this unusual reactivity, detailed density functional theory calculations on the mechanism of C₆F₆ activation by an iron(IV)-oxo active species of the N-bridged diiron phthalocyanine system were performed. Our studies show that the reaction proceeds through a rate-determining electrophilic C−O addition reaction followed by a 1,2-fluoride shift to give the ketone product, which can further rearrange to the phenol. A thermochemical analysis shows that the weakest C−F bond is the aliphatic C−F bond in the ketone intermediate. The oxidative defluorination of perfluoroaromatics is demonstrated to proceed through a completely different mechanism compared to that of aromatic C−H hydroxylation by iron(IV)-oxo intermediates such as cytochrome P450 Compound I.     

NMR analysis and triad sequence distributions of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

Polyhydroxyalkanoates (PHAs) are considered promising “green” alternatives to synthetic polymers because they are bio-derived, biodegradable and biocompatible. The properties of bacterial PHA copolymers depend on their microstructures, which can be modified with the use of different fermentation processes and feed materials. Thus, it is desirable to have an improved testing method for the determination of PHA microstructures. In this work, a detailed NMR analysis of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) microstructure was made. Previously only two of the hydroxyvalerate ¹³C NMR peaks have been assigned at the triad level. In this work, three of the ¹³C hydroxyvalerate peaks and two of the hydroxybutyrate peaks were found to be split into four peaks each due to comonomer sequence effects. Using eight copolymer samples with a wide compositional range, we were able to assign all these peaks to B-centered and V-centered triad sequences. Through curve deconvolution, the triad intensities were determined. These triad sequence intensities can then be analyzed via both the first-order Markovian and two-component Bernoullian models to obtain more in-depth information on copolymer composition and comonomer reactivities.     

Screening gas-phase chemical kinetic models: Collision limit compliance and ultrafast timescales

Detailed gas-phase chemical kinetic models are widely used in combustion research, and many new mechanisms for different fuels and reacting conditions are developed each year. Recent works have highlighted the need for error checking when preparing such models, but a useful community tool to perform such analysis is missing. In this work, we present a simple online tool to screen chemical kinetic mechanisms for bimolecular reactions exceeding collision limits. The tool is implemented on a user-friendly website, cloudflame.kaust.edu.sa, and checks three different classes of bimolecular reactions; (ie, pressure independent, pressure-dependent falloff, and pressure-dependent PLOG). In addition, two other online modules are provided to check thermodynamic properties and transport parameters to help kinetic model developers determine the sources of errors for reactions that are not collision limit compliant. Furthermore, issues related to unphysically fast timescales can remain an issue even if all bimolecular reactions are within collision limits. Therefore, we also present a procedure to screen ultrafast reaction timescales using computational singular perturbation. For demonstration purposes only, three versions of the rigorously developed AramcoMech are screened for collision limit compliance and ultrafast timescales, and recommendations are made for improving the models. Larger models for biodiesel surrogates, tetrahydropyran, and gasoline surrogates are also analyzed for exemplary purposes. Numerical simulations with updated kinetic parameters are presented to show improvements in wall-clock time when resolving ultrafast timescales.     

AEIV结合AHSI用于饱和脂肪酮类物质的13C NMR谱模拟

应用一种反映分子局部微环境描述子--原子电性相互作用矢量（vector of atomic electronegative interaction,AEIV）和原子杂化状态指数（Atomic Hybridation State Index, AHSI）对饱和脂肪酮类化合物的55种分子中的153个¹³C NMR谱建模模拟,应用多元线性回归方法得到定量结构波谱关系(QSSR)模型的复相关系数R_MM=0.997, 标准偏差为SD_MM=7.155. 采用留一法交互检验的结果是R_CV=0.993,SD_CV=10.195. 并随机抽出三部分分子进行检验,得到的相关系数分别是R_MM1=0.996,R_MM2=0.996,R_MM3=0.999. 研究结果表明使用AEIV和AHSI所建模型预测能力是相当稳定的.