The ASBM-SA turbulence closure: Taking advantage of structure-based modeling in current engineering CFD codes

Structure-based turbulence models (SBM) carry information about the turbulence structure that is needed for the prediction of complex non-equilibrium flows. SBM have been successfully used to predict a number of canonical flows, yet their adoption rate in engineering practice has been relatively low, mainly because of their departure from standard closure formulations, which hinders easy implementation in existing codes. Here, we demonstrate the coupling between the Algebraic Structure-Based Model (ASBM) and the one-equation Spalart–Allmaras (SA) model, which provides an easy route to bringing structure information in engineering turbulence closures. As the ASBM requires correct predictions of two turbulence scales, which are not taken into account in the SA model, Bradshaw relations and numerical optimizations are used to provide the turbulent kinetic energy and dissipation rate. Attention is paid to the robustness and accuracy of the hybrid model, showing encouraging results for a number of simple test cases. An ASBM module in Fortran-90 is provided along with the present paper in order to facilitate the testing of the model by interested readers.     

Ill-posedness of the Camassa–Holm and related equations in the critical space

We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space $H^{3/2}$ and even in the Besov space $B_{p,r}^{1+1/p}$ for $p\in [1,\infty ],r\in (1,\infty ]$. Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ([5], [14], [16]).     

Stochastic delay foraging arena predator–prey system with Markov switching

Abstract

In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.     

A health insurance pricing model based on prevalence rates: Application to critical illness insurance

The Italian health insurance market is currently undersized. The paucity of assured data and the discontinuous statistical surveys carried out by the National Institute of Statistics (ISTAT) represent one of the main obstacles to the insurance market development. The paper sets forth a parametric model to estimate technical basis for health insurance policies when data are limited and only aggregated information on mortality and morbidity is available. The probabilistic framework is based on a multiple state continuous and time inhomogeneous Markov model. We provide an estimate of transition intensities from the healthy state to the sickness state when only prevalence rates of sickness are available, according to an extension and modification of the methodology proposed in Olivieri (1996) for Long Term Care insurance. We assume that mortality intensity of both healthy and sick lives is modelled by two independent Gompertz–Makeham models.     

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.     

Thermodynamic description of the viscosity of liquid solder alloys with minor Co impurities

Because of the increasing complexity and cost of experiments carried out, the data for the multi-component alloy systems have frequently been obtained by numerical modelling. It is clear that the related calculations require reliable data dealing with the pure components and binary alloy systems. Selecting the reliable data concerning the pure components from the literature, the viscosities for the SAC and (SAC)_1?x Co_x solder alloys have been calculated using different viscosity models (geometric and physical). The viscosity decreases as the amount of tin content increases in the SAC387 alloy while the addition of the cobalt to SAC387 solder results in the increasing of the viscosity. Moreover, by computing the root mean square values between theoretical and experimental viscosities, it can be concluded that the lowest value among all models is that of obtained by Kaptay equation.     

The incorporation behavior of arsenic and antimony in GaAsSb/GaAs grown by solid source molecular beam epitaxy

GaAsSb ternary epitaxial layers were grown on GaAs (0 0 1) substrate in various Sb₄/As₂ flux ratios by solid source molecular beam epitaxy. The alloy compositions of GaAs_1−ySb_y were inferred using high-resolution X-ray symmetric (0 0 4) and asymmetric (2 2 4) glance exit diffraction. The non-equilibrium thermodynamic model is used to explain the different incorporation behavior between the Sb₄ and As₂ under the assumption that one incident Sb₄ molecule produces one active Sb₂ molecule. It is inferred that the activation energy of Sb₄ dissociation is about 0.46 eV. The calculated results for the incorporation efficiency of group V are in good agreement with the experimental data.     

Surface growth mechanisms and structural faulting in the growth of large single and spherulitic titanosilicate ETS-4 crystals

Morphological, surface and crystallographic analyses of titanosilicate ETS-4 products, with diverse habits ranging from spherulitic particles composed of submicron crystallites to large single crystals, are presented. Pole figures revealed that crystal surfaces with a-, b- and c- axes corresponded to 110, 010 and 001 directions, respectively. Thus, technologically important 8-membered ring pores and titania chains in ETS-4 run along the b-axis of single crystals and terminate at the smallest crystal face. Height of the spiral growth steps observed on 1 0 0 and 0 0 1 surfaces corresponded to the interplanar spacings associated with their crystallographic orientation, and is equivalent to the thickness of building units that form the ETS-4 framework. Data suggest that the more viscous synthesis mixtures, with a large driving force for growth, increased the two- and three-dimensional nucleation, while limiting the transport of nutrients to the growth surface. These conditions increase the tendency for stacking fault formation on 1 0 0 surfaces and small angle branching, which eventually results in spherulitic growth. The growth of high quality ETS-4 single crystals (from less viscous synthesis mixtures) occurred at lower surface nucleation rates. Data suggest that these high quality, large crystals grew due to one-dimensional nucleation at spiral hillocks, and indicate that under these conditions un-faulted growth is preferred.     

Revised mechanism of carboxylation of ribulose‐1,5‐biphosphate by rubisco from large scale quantum chemical calculations

Here, we describe a computational approach for studying enzymes that catalyze complex multi‐step reactions and apply it to Ribulose 1,5‐bisphosphate carboxylase–oxygenase (Rubisco), the enzyme that fixes atmospheric carbon dioxide within photosynthesis. In the 5‐step carboxylase reaction, the substrate Ribulose‐1,5‐bisphosphate (RuBP) first binds Rubisco and undergoes enolization before binding the second substrate, CO₂. Hydration of the RuBP.CO₂ complex is followed by C C bond scission and stereospecific protonation. However, details of the roles and protonation states of active‐site residues, and sources of protons and water, remain highly speculative. Large‐scale computations on active‐site models provide a means to better understand this complex chemical mechanism. The computational protocol comprises a combination of hybrid semi‐empirical quantum mechanics and molecular mechanics within constrained molecular dynamics simulations, together with constrained gradient minimization calculations using density functional theory. Alternative pathways for hydration of the RuBP.CO₂ complex and associated active‐site protonation networks and proton and water sources were investigated. The main findings from analysis of the resulting energetics advocate major revision to existing mechanisms such that: hydration takes place anti to the CO₂; both hydration and C C bond scission require early protonation of CO₂ in the RuBP.CO₂ complex; C C bond scission and stereospecific protonation reactions are concerted and, effectively, there is only one stable intermediate, the C3‐gemdiolate complex. Our main conclusions for interpreting enzyme kinetic results are that the gemdiolate may represent the elusive Michaelis–Menten‐like complex corresponding to the empirical K_m (=K_c) with turnover to product via bond scission concerted with stereospecific protonation consistent with the observed catalytic rate. © 2018 Wiley Periodicals, Inc.