In-situ combustion synthesis of ultrafine TiB2 particles reinforced Cu matrix composite

Due to the lower strength of pure copper (Cu), ceramic particulate or whisker reinforced Cu matrix composites have attracted wide interest in recent years [1–3]. These materials exhibit a combination of excellent thermal and electrical conductivities, high strength retention at elevated temperatures, and high microstructural stability [3]. The potential applications include various electrodes, electrical switches, and X-ray tube components [4].

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.

Oxygen transport in a three-dimensional microvascular network incorporated with early tumour growth and preexisting vessel cooption: Numerical simulation study

We propose a dynamic mathematical model of tissue oxygen transport by a preexisting three-dimensional microvascular network which provides nutrients for an in situ cancer at the very early stage of primary microtumour growth. The expanding tumour consumes oxygen during its invasion to the surrounding tissues and cooption of host vessels. The preexisting vessel cooption, remodelling and collapse are modelled by the changes of haemodynamic conditions due to the growing tumour. A detailed computational model of oxygen transport in tumour tissue is developed by considering (a) the time-varying oxygen advection diffusion equation within the microvessel segments, (b) the oxygen flux across the vessel walls, and (c) the oxygen diffusion and consumption with in the tumour and surrounding healthy tissue. The results show the oxygen concentration distribution at different time points of early tumour growth. In addition, the influence of preexisting vessel density on the oxygen transport has been discussed. The proposed model not only provides a quantitative approach for investigating the interactions between tumour growth and oxygen delivery, but also is extendable to model other molecules or chemotherapeutic drug transport in the future study.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Examination of gaze behaviors under in situ and video simulation task constraints reveals differences in information pickup for perception and action

Gaze and movement behaviors of association football goalkeepers were compared under two video simulation conditions (i.e., verbal and joystick movement responses) and three in situ conditions (i.e., verbal, simplified body movement, and interceptive response). The results showed that the goalkeepers spent more time fixating on information from the penalty kick taker’s movements than ball location for all perceptual judgment conditions involving limited movement (i.e., verbal responses, joystick movement, and simplified body movement). In contrast, an equivalent amount of time was spent fixating on the penalty taker’s relative motions and the ball location for the in situ interception condition, which required the goalkeepers to attempt to make penalty saves. The data suggest that gaze and movement behaviors function differently, depending on the experimental task constraints selected for empirical investigations. These findings highlight the need for research on perceptual— motor behaviors to be conducted in representative experimental conditions to allow appropriate generalization of conclusions to performance environments.

Numerical simulation of flow in a photocatalytic reactor containing baffles

In this study a new immobilized flat plate photocatalytic reactor for wastewater treatment has been investigated using computational fluid dynamics (CFD). The reactor consists of a reactor inlet, a reactive section where the catalyst is coated, and outlet parts. For simulation, the reactive section of the reactor was modelled with an array of baffles. In order to optimize the fluid mixing and reactor design, this study attempts to investigate the influence of baffles with differing heights on the flow field of the flat plate reactor. The results obtained from the simulation of a baffled flat plate reactor hydrodynamics for differing baffle heights for certain positions are presented. Under the conditions simulated, the qualitative flow features, such as the distribution of local stream lines, velocity contours, and high shear region, boundary layers separation, vortex formation, and the underlying mechanism are examined. At low and high Re numbers, the influence of baffle heights on the distribution of species mass fraction of a model pollutant are also highlighted. The simulation of qualitative and quantitative properties of fluid dynamics in a baffled reactor provides valuable insight to fully understand the effect of baffles and their role on the flow pattern, behaviour, and features of wastewater treatment using a photocatalytic reactor.

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 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.

Nanosphere monolayer-templated, ion-assisted nanofeature etching in dielectric materials : a numerical simulation of nanoscale ion flux topography

The results of numerical simulations of nanometer precision distributions of microscopic ion fluxes in ion-assisted etching of nanoscale features on the surfaces of dielectric materials using a self-assembled monolayer of spherical nanoparticles as a mask are presented. It is shown that the ion fluxes to the substrate and nanosphere surfaces can be effectively controlled by the plasma parameters and the external bias applied to the substrate. By proper adjustment of these parameters, the ion flux can be focused onto the areas uncovered by the nanospheres. Under certain conditions, the ion flux distributions feature sophisticated hexagonal patterns, which may lead to very different nanofeature etching profiles. The results presented are generic and suggest viable ways to overcome some of the limitations of the existing plasma-assisted nanolithography.

Numerical simulation of self-organized nano-islands in plasma-based assembly of quantum dot arrays

This work presents the details of the numerical model used in simulation of self-organization of nano-islands on solid surfaces in plasma-assisted assembly of quantum dot structures. The model includes the near-substrate non-neutral layer (plasma sheath) and a nanostructured solid deposition surface and accounts for the incoming flux of and energy of ions from the plasma, surface temperature-controlled adatom migration about the surface, adatom collisions with other adatoms and nano-islands, adatom inflow to the growing nano-islands from the plasma and from the two-dimensional vapour on the surface, and particle evaporation to the ambient space and the two-dimensional vapour. The differences in surface concentrations of adatoms in different areas within the quantum dot pattern significantly affect the self-organization of the nano-islands. The model allows one to formulate the conditions when certain islands grow, and certain ones shrink or even dissolve and relate them to the process control parameters. Surface coverage by selforganized quantum dots obtained from numerical simulation appears to be in reasonable agreement with the available experimental results.

Numerical simulation of nanoparticle-generating electronegative plasmas in the PECVD of nanostructured silicon film

The results of numerical simulation of the equilibrium parameters of a low pressure nanopowder-generating discharge in silane for the plasma enhanced chemical vapor deposition (PECVD) of nanostructured silicon-based films are presented. It is shown that a low electron temperature and a low density of negative SiH3 - ions are favorable for the PECVD process. This opens a possibility to predict the main parameters of the reactive plasma and plasma-nucleated nanoparticles, and hence, to control the quality of silicon nanofilms.