Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Toward assessing the effects of aerosols on deep convection: a numerical study using the WRF-Chemistry model

As the formative agents of cloud droplets, aerosols play an undeniably important role in the development of clouds and precipitation. Few meteorological models have been developed or adapted to simulate aerosols and their contribution to cloud and precipitation processes. The Weather Research and Forecasting model (WRF) has recently been coupled with an atmospheric chemistry suite and is jointly referred to as WRF-Chem, allowing atmospheric chemistry and meteorology to influence each other’s evolution within a mesoscale modeling framework. Provided that the model physics are robust, this framework allows the feedbacks between aerosol chemistry, cloud physics, and dynamics to be investigated. This study focuses on the effects of aerosols on meteorology, specifically, the interaction of aerosol chemical species with microphysical processes represented within the framework of the WRF-Chem. Aerosols are represented by eight size bins using the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) sectional parameterization, which is linked to the Purdue Lin bulk microphysics scheme. The aim of this study is to examine the sensitivity of deep convective precipitation modeled by the 2D WRF-Chem to varying aerosol number concentration and aerosol type. A systematic study has been performed regarding the effects of aerosols on parameters such as total precipitation, updraft/downdraft speed, distribution of hydrometeor species, and organizational features, within idealized maritime and continental thermodynamic environments. Initial results were obtained using WRFv3.0.1, and a second series of tests were run using WRFv3.2 after several changes to the activation, autoconversion, and Lin et al. microphysics schemes added by the WRF community, as well as the implementation of prescribed vertical levels by the author. The results of WRFv3.2 runs contrasted starkly with WRFv3.0.1 runs. The WRFv3.0.1 runs produced a propagating system resembling a developing squall line, whereas the WRFv3.2 runs did not. The response of total precipitation, updraft/downdraft speeds, and system organization to increasing aerosol concentrations were opposite between runs with different versions of WRF. Results of the WRFv3.2 runs, however, were in better agreement in timing and magnitude of vertical velocity and hydrometeor content with a WRFv3.0.1 run using single-moment Lin et al. microphysics, than WRFv3.0.1 runs with chemistry. One result consistent throughout all simulations was an inhibition in warm-rain processes due to enhanced aerosol concentrations, which resulted in a delay of precipitation onset that ranged from 2-3 minutes in WRFv3.2 runs, and up to 15 minutes in WRFv.3.0.1 runs. This result was not observed in a previous study by Ntelekos et al. (2009) using the WRF-Chem, perhaps due to their use of coarser horizontal and vertical resolution within their experiment. The changes to microphysical processes such as activation and autoconversion from WRFv3.0.1 to WRFv3.2, along with changes in the packing of vertical levels, had more impact than the varying aerosol concentrations even though the range of aerosol tested was greater than that observed in field studies. In order to take full advantage of the input of aerosols now offered by the chemistry module in WRF, the author recommends that a fully double-moment microphysics scheme be linked, rather than the limited double-moment Lin et al. scheme that currently exists. With this modification, the WRF-Chem will be a powerful tool for studying aerosol-cloud interactions and allow comparison of results with other studies using more modern and complex microphysical parameterizations.

Hamburg model basin : numerical and experimental investigations on the dependence of the fluctuations of thrust and torque on the blade area ratio of four-blade ship-propellers /

Contract no. N 62558-2223.

Numerical and analytical study of an atherosclerosis inflammatory disease model

We study a reaction–diffusion mathematical model for the evolution of atherosclerosis as an inflammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction–diffusion system and lead to the complete characterisation of the ωω-limit for every initial condition. Qualitative properties of the solution are rigorously proved, some of them hinted at by the numerical study

Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deteriorating—Part II : Model updating and verification

This paper is a continuation of the paper titled “Concurrent multi-scale modeling of civil infrastructure for analyses on structural deteriorating—Part I: Modeling methodology and strategy” with the emphasis on model updating and verification for the developed concurrent multi-scale model. The sensitivity-based parameter updating method was applied and some important issues such as selection of reference data and model parameters, and model updating procedures on the multi-scale model were investigated based on the sensitivity analysis of the selected model parameters. The experimental modal data as well as static response in terms of component nominal stresses and hot-spot stresses at the concerned locations were used for dynamic response- and static response-oriented model updating, respectively. The updated multi-scale model was further verified to act as the baseline model which is assumed to be finite-element model closest to the real situation of the structure available for the subsequent arbitrary numerical simulation. The comparison of dynamic and static responses between the calculated results by the final model and measured data indicated the updating and verification methods applied in this paper are reliable and accurate for the multi-scale model of frame-like structure. The general procedures of multi-scale model updating and verification were finally proposed for nonlinear physical-based modeling of large civil infrastructure, and it was applied to the model verification of a long-span bridge as an actual engineering practice of the proposed procedures.

Groundwater flow model of the Logan river alluvial aquifer system Josephville, South East Queensland

The study focuses on an alluvial plain situated within a large meander of the Logan River at Josephville near Beaudesert which supports a factory that processes gelatine. The plant draws water from on site bores, as well as the Logan River, for its production processes and produces approximately 1.5 ML per day (Douglas Partners, 2004) of waste water containing high levels of dissolved ions. At present a series of treatment ponds are used to aerate the waste water reducing the level of organic matter; the water is then used to irrigate grazing land around the site. Within the study the hydrogeology is investigated, a conceptual groundwater model is produced and a numerical groundwater flow model is developed from this. On the site are several bores that access groundwater, plus a network of monitoring bores. Assessment of drilling logs shows the area is formed from a mixture of poorly sorted Quaternary alluvial sediments with a laterally continuous aquifer comprised of coarse sands and fine gravels that is in contact with the river. This aquifer occurs at a depth of between 11 and 15 metres and is overlain by a heterogeneous mixture of silts, sands and clays. The study investigates the degree of interaction between the river and the groundwater within the fluvially derived sediments for reasons of both environmental monitoring and sustainability of the potential local groundwater resource. A conceptual hydrogeological model of the site proposes two hydrostratigraphic units, a basal aquifer of coarse-grained materials overlain by a thick semi-confining unit of finer materials. From this, a two-layer groundwater flow model and hydraulic conductivity distribution was developed based on bore monitoring and rainfall data using MODFLOW (McDonald and Harbaugh, 1988) and PEST (Doherty, 2004) based on GMS 6.5 software (EMSI, 2008). A second model was also considered with the alluvium represented as a single hydrogeological unit. Both models were calibrated to steady state conditions and sensitivity analyses of the parameters has demonstrated that both models are very stable for changes in the range of ± 10% for all parameters and still reasonably stable for changes up to ± 20% with RMS errors in the model always less that 10%. The preferred two-layer model was found to give the more realistic representation of the site, where water level variations and the numerical modeling showed that the basal layer of coarse sands and fine gravels is hydraulically connected to the river and the upper layer comprising a poorly sorted mixture of silt-rich clays and sands of very low permeability limits infiltration from the surface to the lower layer. The paucity of historical data has limited the numerical modelling to a steady state one based on groundwater levels during a drought period and forecasts for varying hydrological conditions (e.g. short term as well as prolonged dry and wet conditions) cannot reasonably be made from such a model. If future modelling is to be undertaken it is necessary to establish a regular program of groundwater monitoring and maintain a long term database of water levels to enable a transient model to be developed at a later stage. This will require a valid monitoring network to be designed with additional bores required for adequate coverage of the hydrogeological conditions at the Josephville site. Further investigations would also be enhanced by undertaking pump testing to investigate hydrogeological properties in the aquifer.

Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, FE simulations to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson’s ratio =0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27m to 0.11m with a von Mises model, and from 0.09m to 0.02m with Drucker-Prager plasticity. We conclude that it is important to include friction in nanoindentation simulations of bone.

Study of wheel-rail impact at insulated rail joint through experimental and numerical methods

As part of an ongoing research on the development of a longer life insulated rail joint (IRJ), this paper reports a field experiment and a simplified 2D numerical modelling for the purpose of investigating the behaviour of rail web in the vicinity of endpost in an insulated rail joint (IRJ) due to wheel passages. A simplified 2D plane stress finite element model is used to simulate the wheel-rail rolling contact impact at IRJ. This model is validated using data from a strain gauged IRJ that was installed in a heavy haul network; data in terms of the vertical and shear strains at specific positions of the IRJ during train passing were captured and compared with the results of the FE model. The comparison indicates a satisfactory agreement between the FE model and the field testing. Furthermore, it demonstrates that the experimental and numerical analyses reported in this paper provide a valuable datum for developing further insight into the behaviour of IRJ under wheel impacts.