Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

A micro-simulation of airport passengers with advanced traits

An approach for modeling passenger flows in airport terminals by a set of devised advanced traits of passengers is proposed. Advanced traits take into account a passenger’s cognitive preferences which would be the underlying motivations of route-choice decisions. Basic traits are the status of passengers such as travel class. Although the activities of passengers are normally regarded as stochastic and sometimes unpredictable, we advise that real scenarios of passenger flows are basically feasible to be compared with virtual simulations in terms of tactical route-choice decision-making by individual personals. Inside airport terminals, passengers are goal-directed and not only use standard processing check points but also behave discretionary activities during the course. In this paper, we integrated discretionary activities in the study to fulfill full-range of passenger flows. In the model passengers are built as intelligent agents who possess a bunch of initial basic traits and then can be categorized into ten distinguish groups in terms of route-choice preferences by inferring the results of advanced traits. An experiment is executed to demonstrate the capability to facilitate predicting passenger flows.

Numerical simulation of red blood cells' deformation using SPH method

A numerical simulation method for the Red Blood Cells’ (RBC) deformation is presented in this study. The two-dimensional RBC membrane is modeled by the spring network, where the elastic stretch/compression energy and the bending energy are considered with the constraint of constant RBC surface area. Smoothed Particle Hydrodynamics (SPH) method is used to solve the Navier-Stokes equation coupled with the Plasma-RBC membrane and Cytoplasm- RBC membrane interaction. To verify the method, the motion of a single RBC is simulated in Poiseuille flow and compared with the results reported earlier. Typical motion and deformation mechanism of the RBC is observed.

Numerical simulation of red blood cells’ motion : a review

The micro-circulation of blood plays an important role in human body by providing oxygen and nutrients to the cells and removing carbon dioxide and wastes from the cells. This process is greatly affected by the rheological properties of the Red Blood Cells (RBCs). Changes in the rheological properties of the RBCs are caused by certain human diseases such as malaria and sickle cell diseases. Therefore it is important to understand the motion and deformation mechanism of RBCs in order to diagnose and treat this kind of diseases. Although, many methods have been developed to explore the behavior of the RBCs in micro-channels, they could not explain the deformation mechanism of the RBCs properly. Recently developed Particle Methods are employed to explain the RBCs’ behavior in micro-channels more comprehensively. The main objective of this study is to critically analyze the present methods, used to model the RBC behavior in micro-channels, in order to develop a computationally efficient particle based model to describe the complete behavior of the RBCs in micro-channels accurately and comprehensively

Simulation of phosphine flow in vertical grain storage : a preliminary numerical study

To fumigate grain stored in a silo, phosphine gas is distributed by a combination of diffusion and fan-forced advection. This initial study of the problem mainly focuses on the advection, numerically modelled as fluid flow in a porous medium. We find satisfactory agreement between the flow predictions of two Computational Fluid Dynamics packages, Comsol and Fluent. The flow predictions demonstrate that the highest velocity (>0.1 m/s) occurs less than 0.2m from the inlet and reduces drastically over one metre of silo height, with the flow elsewhere less than 0.002 m/s or 1% of the velocity injection. The flow predictions are examined to identify silo regions where phosphine dosage levels are likely to be too low for effective grain fumigation.

Large eddy simulation of smoke flow in a real road tunnel fire using FDS

Numerical study is carried out using large eddy simulation to study the heat and toxic gases released from fires in real road tunnels. Due to disasters about tunnel fires in previous decade, it attracts increasing attention of researchers to create safe and reliable ventilation designs. In this research, a real tunnel with 10 MW fire (which approximately equals to the heat output speed of a burning bus) at the middle of tunnel is simulated using FDS (Fire Dynamic Simulator) for different ventilation velocities. Carbone monoxide concentration and temperature vertical profiles are shown for various locations to explore the flow field. It is found that, with the increase of the longitudinal ventilation velocity, the vertical profile gradients of CO concentration and smoke temperature were shown to be both reduced. However, a relatively large longitudinal ventilation velocity leads to a high similarity between the vertical profile of CO volume concentration and that of temperature rise.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type.

Three dimensional simulation of a parabolic trough concentrator thermal collector

Parabolic Trough Concentrators (PTC) are the most proven solar collectors for solar thermal power plants, and are suitable for concentrating photovoltaic (CPV) applications. PV cells are sensitive to spatial uniformity of incident light and the cell operating temperature. This requires the design of CPV-PTCs to be optimised both optically and thermally. Optical modelling can be performed using Monte Carlo Ray Tracing (MCRT), with conjugate heat transfer (CHT) modelling using the computational fluid dynamics (CFD) to analyse the overall designs. This paper develops and evaluates a CHT simulation for a concentrating solar thermal PTC collector. It uses the ray tracing work by Cheng et al. (2010) and thermal performance data for LS-2 parabolic trough used in the SEGS III-VII plants from Dudley et al. (1994). This is a preliminary step to developing models to compare heat transfer performances of faceted absorbers for concentrating photovoltaic (CPV) applications. Reasonable agreement between the simulation results and the experimental data confirms the reliability of the numerical model. The model explores different physical issues as well as computational issues for this particular kind of system modeling. The physical issues include the resultant non-uniformity of the boundary heat flux profile and the temperature profile around the tube, and uneven heating of the HTF. The numerical issues include, most importantly, the design of the computational domain/s, and the solution techniques of the turbulence quantities and the near-wall physics. This simulation confirmed that optical simulation and the computational CHT simulation of the collector can be accomplished independently.

Molecular dynamics simulation of fracture strength and morphology of defective graphene

Different types of defects can be introduced into graphene during material synthesis, and significantly influence the properties of graphene. In this work, we investigated the effects of structural defects, edge functionalisation and reconstruction on the fracture strength and morphology of graphene by molecular dynamics simulations. The minimum energy path analysis was conducted to investigate the formation of Stone-Wales defects. We also employed out-of-plane perturbation and energy minimization principle to study the possi-ble morphology of graphene nanoribbons with edge-termination. Our numerical results show that the fracture strength of graphene is dependent on defects and environmental temperature. However, pre-existing defects may be healed, resulting in strength recovery. Edge functionalization can induce compressive stress and ripples in the edge areas of gra-phene nanoribbons. On the other hand, edge reconstruction contributed to the tensile stress and curved shape in the graphene nanoribbons.

Computer simulation of underground blast response of pile in saturated soil

This paper treats the blast response of a pile foundation in saturated sand using explicit nonlinear finite element analysis, considering complex material behavior of soil and soil–pile interaction. Blast wave propagation in the soil is studied and the horizontal deformation of pile and effective stresses in the pile are presented. Results indicate that the upper part of the pile to be vulnerable and the pile response decays with distance from the explosive. The findings of this research provide valuable information on the effects of underground explosions on pile foundation and will guide future development, validation and application of computer models.

Faster Monte Carlo simulation of radiotherapy geometries

Using Monte Carlo simulation for radiotherapy dose calculation can provide more accurate results when compared to the analytical methods usually found in modern treatment planning systems, especially in regions with a high degree of inhomogeneity. These more accurate results acquired using Monte Carlo simulation however, often require orders of magnitude more calculation time so as to attain high precision, thereby reducing its utility within the clinical environment. This work aims to improve the utility of Monte Carlo simulation within the clinical environment by developing techniques which enable faster Monte Carlo simulation of radiotherapy geometries. This is achieved principally through the use new high performance computing environments and simpler alternative, yet equivalent representations of complex geometries. Firstly the use of cloud computing technology and it application to radiotherapy dose calculation is demonstrated. As with other super-computer like environments, the time to complete a simulation decreases as 1=n with increasing n cloud based computers performing the calculation in parallel. Unlike traditional super computer infrastructure however, there is no initial outlay of cost, only modest ongoing usage fees; the simulations described in the following are performed using this cloud computing technology. The definition of geometry within the chosen Monte Carlo simulation environment - Geometry & Tracking 4 (GEANT4) in this case - is also addressed in this work. At the simulation implementation level, a new computer aided design interface is presented for use with GEANT4 enabling direct coupling between manufactured parts and their equivalent in the simulation environment, which is of particular importance when defining linear accelerator treatment head geometry. Further, a new technique for navigating tessellated or meshed geometries is described, allowing for up to 3 orders of magnitude performance improvement with the use of tetrahedral meshes in place of complex triangular surface meshes. The technique has application in the definition of both mechanical parts in a geometry as well as patient geometry. Static patient CT datasets like those found in typical radiotherapy treatment plans are often very large and present a significant performance penalty on a Monte Carlo simulation. By extracting the regions of interest in a radiotherapy treatment plan, and representing them in a mesh based form similar to those used in computer aided design, the above mentioned optimisation techniques can be used so as to reduce the time required to navigation the patient geometry in the simulation environment. Results presented in this work show that these equivalent yet much simplified patient geometry representations enable significant performance improvements over simulations that consider raw CT datasets alone. Furthermore, this mesh based representation allows for direct manipulation of the geometry enabling motion augmentation for time dependant dose calculation for example. Finally, an experimental dosimetry technique is described which allows the validation of time dependant Monte Carlo simulation, like the ones made possible by the afore mentioned patient geometry definition. A bespoke organic plastic scintillator dose rate meter is embedded in a gel dosimeter thereby enabling simultaneous 3D dose distribution and dose rate measurement. This work demonstrates the effectiveness of applying alternative and equivalent geometry definitions to complex geometries for the purposes of Monte Carlo simulation performance improvement. Additionally, these alternative geometry definitions allow for manipulations to be performed on otherwise static and rigid geometry.

Computer experiment – a case study for modelling and simulation of manufacturing systems

Deterministic computer simulation of physical experiments is now a common technique in science and engineering. Often, physical experiments are too time consuming, expensive or impossible to conduct. Complex computer models or codes, rather than physical experiments lead to the study of computer experiments, which are used to investigate many scientific phenomena. A computer experiment consists of a number of runs of the computer code with different input choices. The Design and Analysis of Computer Experiments is a rapidly growing technique in statistical experimental design. This paper aims to discuss some practical issues when designing a computer simulation and/or experiments for manufacturing systems. A case study approach is reviewed and presented.

Molecular dynamics simulation of structural characteristics in metal cluster deposition on surfaces

The deposition of small metal clusters (Cu, Au and Al) on f.c.c. metals (Cu, Au and Ni) has been studied by molecular dynamics simulation using Finnis–Sinclair (FS) potential. The impact energy varied from 0.01 to 10 eV/atom. First, the deposition of single cluster was simulated. We observed that, even at much lower energy, a small cluster with (Ih) icosahedral symmetry was reconstructed to match the substrate structure (f.c.c.) after deposition. Next, clusters were modeled to drop, one after the other, on the surface. The nanostructure was found by soft landing of Au clusters on Cu with increasing coverage, where interfacial energy dominates. While at relatively higher deposition energy (a few eV), the ordered f.c.c.-like structure was observed in the first adlayer of the film formed by Al clusters depositing on Ni substrate. This characteristic is mainly attributive to the ballistic collision. Our results indicate that the surface morphology synthesized by cluster deposition could be controlled by experimental parameters, which will be helpful for controlled design of nanostructure.