Immunity in the ABM-DSGE Framework for Preventing and Controlling Epidemics—Validation of Results

The COVID-19 pandemic has raised many questions on how to manage an epidemiological and economic crisis around the world. Since the beginning of the COVID-19 pandemic, scientists and policy makers have been asking how effective lockdowns are in preventing and controlling the spread of the virus. In the absence of vaccines, the regulators lacked any plausible alternatives. Nevertheless, after the introduction of vaccinations, to what extent the conclusions of these analyses are still valid should be considered. In this paper, we present a study on the effect of vaccinations within the dynamic stochastic general equilibrium model with an agent-based epidemic component. Thus, we validated the results regarding the need to use lockdowns as an efficient tool for preventing and controlling epidemics that were obtained in November 2020.     

Indentation of transversely isotropic power-law hardening materials: computational modelling of the forward and reverse problems

Using a combination of dimensional analysis and large deformation finite element simulations of triple indentations of 120 materials, a framework for capturing the indentation response of transversely isotropic materials is developed. By considering 4800 combinations of material properties within the bounds of the original set of 120 materials, forward algorithms that predict the indentation response of materials and reverse algorithms that predict the materials’ elastic and plastic properties from experimentally measured indentation responses are formulated for both longitudinal and transverse indentations. Issues of accuracy, reversibility, uniqueness and sensitivity within the context of the indentation of transversely isotropic materials are addressed carefully. Using 1400 combinations of material properties, it is demonstrated that there is perfect reversibility between the material properties and their indentation responses as predicted by the forward and reverse algorithms. On average, the differences between the results of the finite element analysis and those predicted by the forward algorithms for longitudinal or transverse indentations are less than 1%, thus demonstrating the high accuracy and uniqueness of the forward analysis. For longitudinal and transverse indentations, the reverse algorithms provide accurate results in most cases with an average error of 3 and 6%, respectively. A sensitivity analysis with a ±2% variation in the material properties in the forward algorithm and ±2% variation in the indentation responses in the reverse algorithms demonstrated the robustness of the algorithms developed in the present study, with the longitudinal indentations providing relatively less sensitivity to variability in indentation responses as compared to the transverse indentations.     

Microgravity droplet combustion: effect of tethering fiber on burning rate and flame structure

Droplets tethering on fibers has become a well established technique for conducting droplet combustion experiments in microgravity conditions. The effects of these supporting fibers are frequently assumed to be negligible and are not considered in the experimental analysis or in numerical simulations. In this work, the effect of supporting fibers on the characteristics of microgravity droplet combustion has been investigated numerically; a priori predictions have then been compared with published experimental data. The simulations were conducted using a transient one-dimensional spherosymmetric droplet combustion model, where the effect of the supporting fiber was implicitly taken into account. The model applied staggered convective flux finite volume method combined with high-order implicit time integration. Thermal radiation was evaluated using a statistical narrow band radiation model. Chemical kinetics and thermophysical properties were represented in rigorous detail. Tether fiber diameter, droplet diameter, ambient pressure and oxygen concentration were varied over a range for n-decane droplets in the simulations. The results of the simulations were compared to previously published experiments conducted in the Japan Microgravity Center (JAMIC) 10 second drop tower and the NASA Glenn Research Center (GRC) 5.2 second drop tower. The model reproduces closely nearly all aspects of tethered n-decane droplet burning phenomena, which included droplet burning history, transient and average burning rate, and flame standoff ratio. The predictions show that the presence of the tethering fiber significantly influences the observed burning rate, standoff ratio, and extinction.     

Large Eddy Simulations of a piloted lean premix jet flame using finite-rate chemistry

A Large Eddy Simulation (LES) model capable of accurately representing finite-rate chemistry effects in turbulent premixed combustion is presented. The LES computations use finite-rate chemistry and implicit LES combustion modelling to simulate an experimentally well-documented lean-premixed jet flame stabilized by a stoichiometric pilot. The validity of the implicit LES assumption is discussed and criteria are expressed in terms of subgrid scale Damköhler and Karlovitz numbers. Simulation results are compared to experimental data for velocity, temperature and species mass fractions of CH₄, CO and OH. The simulation results highlight the validity and capability of the present approach for the flame and in general the combustion regime examined. A sensitivity analysis to the choice of the finite-rate chemistry mechanism is reported, this analysis indicates that the one and two-step global reaction mechanisms evaluated fail to capture the reaction layer with sufficient accuracy, while a 20-species skeletal mechanism reproduces the experimental observations accurately including the key finite-rate chemistry indicators CO and OH. The LES results are shown to be grid insensitive and that the grid resolution within the bounds examined is far less important compared to the sensitivity of the finite-rate chemistry representation. The results are analyzed in terms of the flame dynamics and it is shown that intense small scale mixing (high Karlovitz number) between the pilot and the jet is an important mechanism for the stabilization of the flame.     

Aromatic interactions impact ligand binding and function at serotonin 5-HT2C G protein-coupled receptors: receptor homology modelling,ligand docking,and molecular dynamics results validated by experimental studies

The serotonin (5-hydroxytryptamine, 5-HT) 5-HT₂ G protein-coupled receptor (GPCR) family consists of types 2A, 2B, and 2C that share ～75% transmembrane (TM) sequence identity. Agonists for 5-HT_2C receptors are under development for psychoses; whereas, at 5-HT_2A receptors, antipsychotic effects are associated with antagonists – in fact, 5-HT_2A agonists can cause hallucinations and 5-HT_2B agonists cause cardiotoxicity. It is known that 5-HT_2A TM6 residues W6.48, F6.51, and F6.52 impact ligand binding and function; however, ligand interactions with these residues at the 5-HT_2C receptor have not been reported. To predict and validate molecular determinants for 5-HT_2C-specific activation, results from receptor homology modelling, ligand docking, and molecular dynamics simulation studies were compared with experimental results for ligand binding and function at wild type and W6.48A, F6.51A, and F6.52A point-mutated 5-HT_2C receptors.     

New Relaxation Method for Mathematical Programs with Complementarity Constraints

In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising.     

Children’s use of realistic considerations in problem solving: some English evidence

This is the second of two papers exploring children’s responses to an extended version of a division-with-remainder problem intended to elicit general rather than particular realistic considerations during mathematical problem solving. Responses to two problems are analyzed. The first is a ‘realistically’ contextualised item drawn from national tests in England whose ambiguities have been previously discussed (Cooper, 1992); the second is a version of this problem revised to encourage a wider range of realistic responses. In Cooper and Harries (2002), the responses of children at the end of their first year of secondary schooling were analyzed. Here the responses of children at the end of their primary schooling are analyzed and compared with the previous results. It is shown that many children, given suitable encouragement, are willing and able to enter into an extended form of realistic thinking during problem solving, although the original test item renders this invisible.     

Investigations of Droplet‐Plasma Interaction using Multi‐Dimensional Coupled Model

Recently developed multi‐dimensional coupled fluid‐droplet model is used to investigate the behavior of complex interaction between the liquid precursor droplets and atmospheric pressure plasma (APP). The significance of this droplet‐plasma interaction is not well understood under diverse realm of working conditions in two‐phase flow. In this study, we explain the implication of vaporization of liquid droplets in APP which are subsequently responsible to control major characteristics of surface coating depositions. Coalescence of water droplets is more dominant than Hexamethyldisiloxane (HMDSO) droplets because of its sluggish rate of evaporation. A disparity in the performance of evaporation is identified in two independent mediums, such as gas mixture and discharge plasma using HMDSO precursor. The length of evaporation of droplets is amplified by an increment of gas flow rate indicating with a reduction in the gas temperature and electron mean energy. In particular, the spatio‐temporal density distributions of charged particles show a clear pattern in which the typical nitrogen impurity ions are primarily effective as compared to other helium ionic species along the pulse of droplets in APP. Finally, we contrast the behavior of discharge species in the pure helium and He‐N2 gas mixtures revealing the importance of stepwise and Penning ionization processes. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A nilpotent Roth theorem

Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L ²-norm for any u, v∈L ^∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T _-n A∩S ^{- n} A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L ²(X) for all u, v∈L ^∞(X) if and only if T×S is ergodic on X×X and the group generated by T ^-1 S, T ^-2 S ²,..., T ^-c S ^c acts ergodically on X. Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001     

Bouquet and join theorems for disentanglements

The disentanglement of certain augmentations is shown to be the topological join of a disentanglement and a Milnor fibre. The kth disentanglement of a finite map is defined and for corank 1 maps from ℂ ⁿ to ℂ ^{n +1} it is shown that they are homotopically equivalent to a wedge of spheres. Applications to the Mond conjecture are given. Oblatum 24-VII-2000 & 5-VII-2001?Published online: 12 October 2001