A finite element solution scheme for an elastic–viscoplastic soil model

A Newton–Raphson solution scheme with a stress point algorithm is presented for the implementation of an elastic–viscoplastic soilmodel in a finite element program. Viscoplastic strain rates are calculated using the stress and volumetric states of the soil. Sub-incrementsof time are defined for each iterative calculation of elastic–viscoplastic stress changes so that their sum adds up to the time incrementfor the load step. This carefully defined ‘iterative time’ ensures that the correct amount of viscoplastic straining is accumulated overthe applied load step. The algorithms and assumptions required to implement the solution scheme are provided. Verification of the solutionscheme is achieved by using it to analyze typical boundary value problems.

2D-drop model applied to the calculation of step formation energies on a (111) substrate

A model is presented for obtaining the step formation energy for metallic islands on (1 1 1) surfaces from Monte Carlo simulations. This model is applied to homo (Cu/Cu(1 1 1), Ag/Ag(1 1 1)) and heteroepitaxy (Ag/Pt(1 1 1)) systems. The embedded atom method is used to represent the interaction between the particles of the system, but any other type of potential could be used as well. The formulation can also be employed to consider the case of other single crystal surfaces, since the higher barriers for atom motion on other surfaces are not a hindrance for the simulation scheme proposed.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.

A probabilistic modelling scheme for analysis of long-term failure of cemented femoral joint replacements

Reliable prediction of long-term medical device performance using computer simulation requires consideration of variability in surgical procedure, as well as patient-specific factors. However, even deterministic simulation of long-term failure processes for such devices is time and resource consuming so that including variability can lead to excessive time to achieve useful predictions. This study investigates the use of an accelerated probabilistic framework for predicting the likely performance envelope of a device and applies it to femoral prosthesis loosening in cemented hip arthroplasty.
A creep and fatigue damage failure model for bone cement, in conjunction with an interfacial fatigue model for the implant–cement interface, was used to simulate loosening of a prosthesis within a cement mantle. A deterministic set of trial simulations was used to account for variability of a set of surgical and patient factors, and a response surface method was used to perform and accelerate a Monte Carlo simulation to achieve an estimate of the likely range of prosthesis loosening. The proposed framework was used to conceptually investigate the influence of prosthesis selection and surgical placement on prosthesis migration.
Results demonstrate that the response surface method is capable of dramatically reducing the time to achieve convergence in mean and variance of predicted response variables. A critical requirement for realistic predictions is the size and quality of the initial training dataset used to generate the response surface and further work is required to determine the recommendations for a minimum number of initial trials. Results of this conceptual application predicted that loosening was sensitive to the implant size and femoral width. Furthermore, different rankings of implant performance were predicted when only individual simulations (e.g. an average condition) were used to rank implants, compared with when stochastic simulations were used. In conclusion, the proposed framework provides a viable approach to predicting realistic ranges of loosening behaviour for orthopaedic implants in reduced timeframes compared with conventional Monte Carlo simulations.

The analysis of large-scale turbulence characteristics in the Indonesian seas derived from a regional model based on the Princeton Ocean Model

Turbulence characteristics in the Indonesian seas on the horizontal scale of order of 100 km were calculated with a regional model of the Indonesian seas circulation in the area based on the Princeton Ocean Model (POM). As is well known, the POM incorporates the Mellor–Yamada turbulence closure scheme. The calculated characteristics are: twice the turbulence kinetic energy per unit mass, <i>q</i>²; the turbulence master scale, &ell;; mixing coefficients of momentum, <i>K</i>_M; and temperature and salinity, <i>K</i>_H; etc. The analyzed turbulence has been generated essentially by the shear of large-scale ocean currents and by the large-scale wind turbulence. We focused on the analysis of turbulence around important topographic features, such as the Lifamatola Sill, the North Sangihe Ridge, the Dewakang Sill, and the North and South Halmahera Sea Sills. In general, the structure of turbulence characteristics in these regions turned out to be similar. For this reason, we have carried out a detailed analysis of the Lifamatola Sill region because dynamically this region is very important and some estimates of mixing coefficients in this area are available. <br><br> Briefly, the main results are as follows. The distribution of <i>q</i>² is quite adequately reproduced by the model. To the north of the Lifamatola Sill (in the Maluku Sea) and to the south of the Sill (in the Seram Sea), large values of <i>q</i>² occur in the deep layer extending several hundred meters above the bottom. The observed increase of <i>q</i>² near the very bottom is probably due to the increase of velocity shear and the corresponding shear production of <i>q</i>² very close to the bottom. The turbulence master scale, &ell;, was found to be constant in the main depth of the ocean, while &ell; rapidly decreases close to the bottom, as one would expect. However, in deep profiles away from the sill, the effect of topography results in the &ell; structure being unreasonably complicated as one moves towards the bottom. Values of 15 to 20 × 10^&minus;4 m² s^-1 were obtained for <i>K</i>_M and <i>K</i>_H in deep water in the vicinity of the Lifamatola Sill. These estimates agree well with basin-scale averaged values of 13.3 × 10^&minus;4 m² s^-1 found diagnostically for <i>K</i>_H in the deep Banda and Seram Seas (Gordon et al., 2003) and a value of 9.0 × 10^&minus;4 m² s^-1 found diagnostically for <i>K</i>_H for the deep Banda Sea system (van Aken et al., 1988). The somewhat higher simulated values can be explained by the presence of steep topography around the sill.

Detached-Eddy Simulation of a Louver-Cooling Scheme for Turbine Blades

The performance of a louver-cooling scheme on a flat plate was analyzed using a detached-eddy-simulation turbulence model. It was assumed that the louver-cooling scheme was tested in a wind tunnel with the mainstream flow velocity of 20 m/s, equivalent to a Reynolds number of 16,200, based on the jet diameter. Turbulence closure was achieved by a realizable k-e-based detached-eddy-simulation turbulence model. Solutions of two blowing ratios of 0.5 and 1 were successfully obtained by running parallel on 16 nodes on a computer cluster. The flowfields were found to be highly unsteady and oscillatory in nature, with the maximum fluctuation of the adiabatic effectiveness as high as 15% of the time-averaged value. It is shown that the fluctuations in the adiabatic effectiveness are mainly caused by the spanwise fluctuation of the coolant jet and the unsteady vortical structures created by the interaction of the jet and the mainstream.

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Shape corrections to the standard approximate Kohn-Sham exchange-correlation (xc) potentials are considered with the aim to improve the excitation energies (especially for higher excitations) calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection (GRAC) of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends (LB) are seamlessly connected to the (shifted) xc potential of Becke and Perdew (BP) with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N-2, CO, CH2O, C2H4, C5NH5, C6H6, Li-2, Na-2, K-2. The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of (model) orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, which in quite a few cases approach the benchmark accuracy of 0.1 eV for the electronic spectra. Based on these results, the potential BP-GRAC-LB is proposed for molecular response calculations, which is a smooth potential and a genuine "local" density functional with an analytical representation. (C) 2001 American Institute of Physics.

Universal tight binding model for chemical reactions in solution and at surfaces. III. Stoichiometric and reduced surfaces of titania and the adsorption of water

We demonstrate a model for stoichiometric and reduced titanium dioxide intended for use in molecular dynamics and other atomistic simulations and based in the polarizable ion tight binding theory. This extends the model introduced in two previous papers from molecular and liquid applications into the solid state, thus completing the task of providing a comprehensive and unified scheme for studying chemical reactions, particularly aimed at problems in catalysis and electrochemistry. As before, experimental results are given priority over theoretical ones in selecting targets for model fitting, for which we used crystal parameters and band gaps of titania bulk polymorphs, rutile and anatase. The model is applied to six low index titania surfaces, with and without oxygen vacancies and adsorbed water molecules, both in dissociated and non-dissociated states. Finally, we present the results of molecular dynamics simulation of an anatase cluster with a number of adsorbed water molecules and discuss the role of edge and corner atoms of the cluster. (C) 2014 AIP Publishing LLC.

Universal tight binding model for chemical reactions in solution and at surfaces. I. Organic molecules

As is now well established, a first order expansion of the Hohenberg-Kohn total energy density functional about a trial input density, namely, the Harris-Foulkes functional, can be used to rationalize a non self consistent tight binding model. If the expansion is taken to second order then the energy and electron density matrix need to be calculated self consistently and from this functional one can derive a charge self consistent tight binding theory. In this paper we have used this to describe a polarizable ion tight binding model which has the benefit of treating charge transfer in point multipoles. This admits a ready description of ionic polarizability and crystal field splitting. It is necessary in constructing such a model to find a number of parameters that mimic their more exact counterparts in the density functional theory. We describe in detail how this is done using a combination of intuition, exact analytical fitting, and a genetic optimization algorithm. Having obtained model parameters we show that this constitutes a transferable scheme that can be applied rather universally to small and medium sized organic molecules. We have shown that the model gives a good account of static structural and dynamic vibrational properties of a library of molecules, and finally we demonstrate the model's capability by showing a real time simulation of an enolization reaction in aqueous solution. In two subsequent papers, we show that the model is a great deal more general in that it will describe solvents and solid substrates and that therefore we have created a self consistent quantum mechanical scheme that may be applied to simulations in heterogeneous catalysis.

A Cross-Layer Optimized Scheme and Its Application in Mobile Multimedia Networks with QoS Provision

To cope with the rapid growth of multimedia applications that requires dynamic levels of quality of service (QoS), cross-layer (CL) design, where multiple protocol layers are jointly combined, has been considered to provide diverse QoS provisions for mobile multimedia networks. However, there is a lack of a general mathematical framework to model such CL scheme in wireless networks with different types of multimedia classes. In this paper, to overcome this shortcoming, we therefore propose a novel CL design for integrated real-time/non-real-time traffic with strict preemptive priority via a finite-state Markov chain. The main strategy of the CL scheme is to design a Markov model by explicitly including adaptive modulation and coding at the physical layer, queuing at the data link layer, and the bursty nature of multimedia traffic classes at the application layer. Utilizing this Markov model, several important performance metrics in terms of packet loss rate, delay, and throughput are examined. In addition, our proposed framework is exploited in various multimedia applications, for example, the end-to-end real-time video streaming and CL optimization, which require the priority-based QoS adaptation for different applications. More importantly, the CL framework reveals important guidelines as to optimize the network performance

A Revised Disrupted Langmuir-Adsorption Model of Photocatalysis

The increasingly popular disrupted Langmuir–adsorption (DLA) kinetic model of photocatalysis does not contain an explicit function for the dependence of rate on the irradiance, ρ, but instead has a term αρθ, where, α is a constant of the system, and θ is also a constant equal to 1 or 0.5 at low or high ρ values, respectively. Several groups have recently replaced the latter term with an explicit function of the form χ1(−1 + (1 + χ2ρ)1/2), where χ1 and χ2, are constants that can be related to a proposed reaction scheme. Here the latter schemes are investigated, and revised to create a more credible form by assuming an additional hole trapping step. The latter may be the oxidation of water or a surface saturated with O2–. Importantly, this revision suggests that it is only applicable for low quantum yield/efficiency processes. The revised disrupted Langmuir–adsorption model is used to provide good fits to the kinetic data reported for a number of different systems including the photocatalytic oxidation of nitric oxide (NO), phenol (PhOH), and formic acid (FA).