Numerical study of turbulent fluid flow and heat transfer in lateral perforated extended surfaces

Numerical study has been performed in this study to investigate the turbulent convection heat transfer on a rectangular plate mounted over a flat surface. Thermal and fluid dynamic performances of extended surfaces having various types of lateral perforations with square, circular, triangular and hexagonal cross sections are investigated. RANS (Reynolds averaged Navier–Stokes) based modified k–ω turbulence model is used to calculate the fluid flow and heat transfer parameters. Numerical results are compared with the results of previously published experimental data and obtained results are in reasonable agreement. Flow and heat transfer parameters are presented for Reynolds numbers from 2000 to 5000 based on the fin thickness.

Revisiting borehole stresses in anisotropic elastic media : comparison of analytical versus numerical solutions

We present a rigorous validation of the analyticalAmadei solution for the stress concentration around arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients β11 and β55 are not equal. It is shown from theoretical considerations and published experimental data that the β11 and β55 are not equal for realistic rocks. Second, we develop a 3D finite-element elastic model within a hybrid analyticalnumerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic and transverse isotropic symmetries. It is concluded that the analytical Amadei solution is valid with no restrictions on the borehole orientation or elastic anisotropy symmetry.

Effects of strain artefacts arising from a pre-defined callus domain in models of bone healing mechanobiology

Iterative computational models have been used to investigate the regulation of bone fracture healing by local mechanical conditions. Although their predictions replicate some mechanical responses and histological features, they do not typically reproduce the predominantly radial hard callus growth pattern observed in larger mammals. We hypothesised that this discrepancy results from an artefact of the models’ initial geometry. Using axisymmetric finite element models, we demonstrated that pre-defining a field of soft tissue in which callus may develop introduces high deviatoric strains in the periosteal region adjacent to the fracture. These bone-inhibiting strains are not present when the initial soft tissue is confined to a thin periosteal layer. As observed in previous healing models, tissue differentiation algorithms regulated by deviatoric strain predicted hard callus forming remotely and growing towards the fracture. While dilatational strain regulation allowed early bone formation closer to the fracture, hard callus still formed initially over a broad area, rather than expanding over time. Modelling callus growth from a thin periosteal layer successfully predicted the initiation of hard callus growth close to the fracture site. However, these models were still susceptible to elevated deviatoric strains in the soft tissues at the edge of the hard callus. Our study highlights the importance of the initial soft tissue geometry used for finite element models of fracture healing. If this cannot be defined accurately, alternative mechanisms for the prediction of early callus development should be investigated.

Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying

Dried plant food products are increasing in demand in the consumer market, leading to continuing research to develop better products and processing techniques. Plant materials are porous structures, which undergo large deformations during drying. For any given food material, porosity and other cellular parameters have a direct influence on the level of shrinkage and deformation characteristics during drying, which involve complex mechanisms. In order to better understand such mechanisms and their interrelationships, numerical modelling can be used as a tool. In contrast to conventional grid-based modelling techniques, it is considered that meshfree methods may have a higher potential for modelling large deformations of multiphase problem domains. This work uses a meshfree based microscale plant tissue drying model, which was recently developed by the authors. Here, the effects of porosity have been newly accounted for in the model with the objective of studying porosity development during drying and its influence on shrinkage at the cellular level. For simplicity, only open pores are modelled and in order to investigate the influence of different cellular parameters, both apple and grape tissues were used in the study. The simulation results indicated that the porosity negatively influences shrinkage during drying and the porosity decreases as the moisture content reduces (when open pores are considered). Also, there is a clear difference in the deformations of cells, tissues and pores, which is mainly influenced by the cell wall contraction effects during drying.

Learning the learning rate for prediction with expert advice

Most standard algorithms for prediction with expert advice depend on a parameter called the learning rate. This learning rate needs to be large enough to fit the data well, but small enough to prevent overfitting. For the exponential weights algorithm, a sequence of prior work has established theoretical guarantees for higher and higher data-dependent tunings of the learning rate, which allow for increasingly aggressive learning. But in practice such theoretical tunings often still perform worse (as measured by their regret) than ad hoc tuning with an even higher learning rate. To close the gap between theory and practice we introduce an approach to learn the learning rate. Up to a factor that is at most (poly)logarithmic in the number of experts and the inverse of the learning rate, our method performs as well as if we would know the empirically best learning rate from a large range that includes both conservative small values and values that are much higher than those for which formal guarantees were previously available. Our method employs a grid of learning rates, yet runs in linear time regardless of the size of the grid.

Superpixel-based appearance change prediction for long-term navigation across seasons

Changing environments pose a serious problem to current robotic systems aiming at long term operation under varying seasons or local weather conditions. This paper is built on our previous work where we propose to learn to predict the changes in an environment. Our key insight is that the occurring scene changes are in part systematic, repeatable and therefore predictable. The goal of our work is to support existing approaches to place recognition by learning how the visual appearance of an environment changes over time and by using this learned knowledge to predict its appearance under different environmental conditions. We describe the general idea of appearance change prediction (ACP) and investigate properties of our novel implementation based on vocabularies of superpixels (SP-ACP). Our previous work showed that the proposed approach significantly improves the performance of SeqSLAM and BRIEF-Gist for place recognition on a subset of the Nordland dataset under extremely different environmental conditions in summer and winter. This paper deepens the understanding of the proposed SP-ACP system and evaluates the influence of its parameters. We present the results of a large-scale experiment on the complete 10 h Nordland dataset and appearance change predictions between different combinations of seasons.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical simulation of anomalous infiltration in porous media

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order timefractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

Prediction of GMA welding characteristic parameter by artificial neural network system

Nowadays, demand for automated Gas metal arc welding (GMAW) is growing and consequently need for intelligent systems is increased to ensure the accuracy of the procedure. To date, welding pool geometry has been the most used factor in quality assessment of intelligent welding systems. But, it has recently been found that Mahalanobis Distance (MD) not only can be used for this purpose but also is more efficient. In the present paper, Artificial Neural Networks (ANN) has been used for prediction of MD parameter. However, advantages and disadvantages of other methods have been discussed. The Levenberg–Marquardt algorithm was found to be the most effective algorithm for GMAW process. It is known that the number of neurons plays an important role in optimal network design. In this work, using trial and error method, it has been found that 30 is the optimal number of neurons. The model has been investigated with different number of layers in Multilayer Perceptron (MLP) architecture and has been shown that for the aim of this work the optimal result is obtained when using MLP with one layer. Robustness of the system has been evaluated by adding noise into the input data and studying the effect of the noise in prediction capability of the network. The experiments for this study were conducted in an automated GMAW setup that was integrated with data acquisition system and prepared in a laboratory for welding of steel plate with 12 mm in thickness. The accuracy of the network was evaluated by Root Mean Squared (RMS) error between the measured and the estimated values. The low error value (about 0.008) reflects the good accuracy of the model. Also the comparison of the predicted results by ANN and the test data set showed very good agreement that reveals the predictive power of the model. Therefore, the ANN model offered in here for GMA welding process can be used effectively for prediction goals.

Experimental and numerical investigation of strain-rate dependent mechanical properties of single living cells

The objective of this project is to investigate the strain-rate dependent mechanical behaviour of single living cells using both experimental and numerical techniques. The results revealed that living cells behave as porohyperlastic materials and that both solid and fluid phases within the cells play important roles in their mechanical responses. The research reported in this thesis provides a better understanding of the mechanisms underlying the cellular responses to external mechanical loadings and of the process of mechanical signal transduction in living cells. It would help us to enhance knowledge of and insight into the role of mechanical forces in supporting tissue regeneration or degeneration.