A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Numerical methods and analysis for a class of fractional advection-dispersion models

In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.

Molecular investigation of the mechanical properties of single actin filaments based on vibration analyses

The mechanical vibration properties of single actin filaments from 50 to 288 nm are investigated by the molecular dynamics simulation in this study. The natural frequencies obtained from the molecular simulations agree with those obtained from the analytical solution of the equivalent Euler–Bernoulli beam model. Through the convergence study of the mechanical properties with respect to the filament length, it was found that the Euler–Bernoulli beam model can only be reliably used when the single actin filament is of the order of hundreds of nanometre scale. This molecular investigation not only provides the evidence for the use of the continuum beam model in characterising the mechanical properties of single actin filaments, but also clarifies the criteria for the effective use of the Euler–Bernoulli beam model.

Study of mechanical deformations on tough skinned vegetables during mechanical peeling process

Peeling is an essential phase of post harvesting and processing industry; however undesirable processing losses are unavoidable and always have been the main concern of food processing sector. There are three methods of peeling fruits and vegetables including mechanical, chemical and thermal, depending on the class and type of fruit. By comparison, the mechanical methods are the most preferred; mechanical peeling methods do not create any harmful effects on the tissue and they keep edible portions of produce fresh. The main disadvantage of mechanical peeling is the rate of material loss and deformations. Obviously reducing material losses and increasing the quality of the process has a direct effect on the whole efficiency of food processing industry, this needs more study on technological aspects of these operations. In order to enhance the effectiveness of food industrial practices it is essential to have a clear understanding of material properties and behaviour of tissues under industrial processes. This paper presents the scheme of research that seeks to examine tissue damage of tough skinned vegetables under mechanical peeling process by developing a novel FE model of the process using explicit dynamic finite element analysis approach. A computer model of mechanical peeling process will be developed in this study to stimulate the energy consumption and stress strain interactions of cutter and tissue. The available Finite Element softwares and methods will be applied to establish the model. Improving the knowledge of interactions and involves variables in food operation particularly in peeling process is the main objectives of the proposed study. Understanding of these interrelationships will help researchers and designer of food processing equipments to develop new and more efficient technologies. Presented work intends to review available literature and previous works has been done in this area of research and identify current gap in modelling and simulation of food processes.

Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Characterisation of flexural bond strength in thin bed concrete masonry

This paper presents an experimental investigation of the flexural bond strength of thin bed concrete masonry. Flexural bond strength of masonry depends upon the mortar type, the techniques of dispersion of mortar and the surface texture (roughness) of concrete blocks. There exists an abundance of literature on the conventional masonry bond containing 10mm thick mortar; however, the 2mm polymer flue mortar bond is not yet well researched. This paper reports a study on the examination of the effect of mortar compositions, dispersion methods and unit surface textures to the flexural bond strength of thin bed concrete masonry. Three types of polymer modified glue mortars, three surface textures and four techniques of mortar dispersion have been used in preparing 108 four point flexural test specimens. All mortar joints have been carefully prepared to ensure achievement of 2mm layer polymer mortar thickness on average. The results exhibit the flexural bond strength of thin bed concrete masonry much is higher than that of the conventional masonry; moreover the unit surface texture and the mortar dispersion methods are found to have significant influence on the flexural bond strength.

How important is length? : mechanical testing and measurement of a cemented, polished, tapered femoral implant

Total hip arthroplasty (THA) has a proven clinical record for providing pain relief and return of function to patients with disabling arthritis. There are many successful options for femoral implant design and fixation. Cemented, polished, tapered femoral implants have been shown to have excellent results in national joint registries and long-term clinical series. These implants are usually 150mm long at their lateral aspect. Due to their length, these implants cannot always be offered to patients due to variations in femoral anatomy. Polished, tapered implants as short as 95mm exist, however their small proximal geometry (neck offset and body size) limit their use to smaller stature patients. There is a group of patients in which a shorter implant with a maintained proximal body size would be advantageous. There are also potential benefits to a shorter implant in standard patient populations such as reduced bone removal due to reduced reaming, favourable loading of the proximal femur, and the ability to revise into good proximal bone stock if required. These factors potentially make a shorter implant an option for all patient populations. The role of implant length in determining the stability of a cemented, polished, tapered femoral implant is not well defined by the literature. Before changes in implant design can be made, a better understanding of the role of each region in determining performance is required. The aim of the thesis was to describe how implant length affects the stability of a cemented, polished, tapered femoral implant. This has been determined through an extensive body of laboratory testing. The major findings are that for a given proximal body size, a reduction in implant length has no effect on the torsional stability of a polished, tapered design, while a small reduction in axial stability should be expected. These findings are important because the literature suggests that torsional stability is the major determinant of long-term clinical performance of a THA system. Furthermore, a polished, tapered design is known to be forgiving of cement-implant interface micromotion due to the favourable wear characteristics. Together these findings suggest that a shorter polished, tapered implant may be well tolerated. The effect of a change in implant length on the geometric characteristics of polished, tapered design were also determined and applied to the mechanical testing. Importantly, interface area does play a role in stability of the system; however it is the distribution of the interface and not the magnitude of the area that defines stability. Taper angle (at least in the range of angles seen in this work) was shown not to be a determinant of axial or torsional stability. A range of implants were tested, comparing variations in length, neck offset and indication (primary versus cement-in-cement revision). At their manufactured length, the 125mm implants were similar to their longer 150mm counterparts suggesting that they may be similarly well tolerated in the clinical environment. However, the slimmer cement-in-cement revision implant was shown to have a poorer mechanical performance, suggesting their use in higher demand patients may be hazardous. An implant length of 125mm has been shown to be quite stable and the results suggest that a further reduction to 100mm may be tolerated. However, further work is required. A shorter implant with maintained proximal body size would be useful for the group of patients who are unable to access the current standard length implants due to variations in femoral anatomy. Extending the findings further, the similar function with potential benefits of a shorter implant make their application to all patients appealing.

Experimental study on mechanical properties of pumpkin tissue

Purpose: The purpose of this study was to calculate mechanical properties of tough skinned vegetables as a part of Finite Element Modelling (FEM) and simulation of tissue damage during mechanical peeling of tough skinned vegetables. Design/methodology: There are some previous studies on mechanical properties of fruits and vegetables however, behaviour of tissue under different processing operations will be different. In this study indentation test was performed on Peel, Flesh and Unpeeled samples of pumpkin as a tough skinned vegetable. Additionally, the test performed in three different loading rates for peel: 1.25, 10, 20 mm/min and 20 mm/min for flesh and unpeeled samples respectively. The spherical end indenter with 8mm diameter used for the experimental tests. Samples prepare from defect free and ripped pumpkin purchased from local shops in Brisbane, Australia. Humidity and temperature were 20-55% and 20-250C respectively. Findings: Consequently, force deformation and stress and strain of samples were calculated and shown in presented figures. Relative contribution (%) of skin to different mechanical properties is computed and compared with data available from literature. According the results, peel samples had the highest value of rupture force (291N) and as well as highest value of firmness (1411Nm-1). Research limitations/implications: The proposed study focused on one type of tough skinned vegetables and one variety of pumpkin however, more tests will give better understandings of behaviours of tissue. Additionally, the behaviours of peel, unpeeled and flesh samples in different speed of loading will provide more details of tissue damages during mechanical loading. Originality/value: Mechanical properties of pumpkin tissue calculated using the results of indentation test, specifically the behaviours of peel, flesh and unpeeled samples were explored which is a new approach in Finite Element Modelling (FEM) of food processes. Keywords: Finite Element Modelling (FEM), relative contribution, firmness, toughness and rupture force.

Do thermal agents affect range of movement and mechanical properties in soft tissues? A systematic review

OBJECTIVES: To examine the effect of thermal agents on the range of movement (ROM) and mechanical properties in soft tissue and to discuss their clinical relevance. DATA SOURCES: Electronic databases (Cochrane Central Register of Controlled Trials, MEDLINE, and EMBASE) were searched from their earliest available record up to May 2011 using Medical Subjects Headings and key words. We also undertook related articles searches and read reference lists of all incoming articles. STUDY SELECTION: Studies involving human participants describing the effects of thermal interventions on ROM and/or mechanical properties in soft tissue. Two reviewers independently screened studies against eligibility criteria. DATA EXTRACTION: Data were extracted independently by 2 review authors using a customized form. Methodologic quality was also assessed by 2 authors independently, using the Cochrane risk of bias tool. DATA SYNTHESIS: Thirty-six studies, comprising a total of 1301 healthy participants, satisfied the inclusion criteria. There was a high risk of bias across all studies. Meta-analyses were not undertaken because of clinical heterogeneity; however, effect sizes were calculated. There were conflicting data on the effect of cold on joint ROM, accessory joint movement, and passive stiffness. There was limited evidence to determine whether acute cold applications enhance the effects of stretching, and further evidence is required. There was evidence that heat increases ROM, and a combination of heat and stretching is more effective than stretching alone. CONCLUSIONS: Heat is an effective adjunct to developmental and therapeutic stretching techniques and should be the treatment of choice for enhancing ROM in a clinical or sporting setting. The effects of heat or ice on other important mechanical properties (eg, passive stiffness) remain equivocal and should be the focus of future study.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Mechanical properties of graphene : effects of layer number, temperature and isotope

Herein the mechanical properties of graphene, including Young’s modulus, fracture stress and fracture strain have been investigated by molecular dynamics simulations. The simulation results show that the mechanical properties of graphene are sensitive to the temperature changes but insensitive to the layer numbers in the multilayer graphene. Increasing temperature exerts adverse and significant effects on the mechanical properties of graphene. However, the adverse effect produced by the increasing layer number is marginal. On the other hand, isotope substitutions in graphene play a negligible role in modifying the mechanical properties of graphene.