Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Radiation effects on natural convection laminar flow from a horizontal circular cylinder

The effect of radiation on natural convection flow from an isothermal circular cylinder has been investigated numerically in this study. The governing boundary layer equations of motion are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are reduced to convenient boundary layer equations, which are then solved numerically by two distinct efficient methods namely: (i) implicit finite differencemethod or the Keller-Box Method (KBM) and (ii) Straight Forward Finite Difference Method (SFFD). Numerical results are presented by velocity and temperature distribution of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of surface heating parameter and radiation-conduction parameter. Due to the effects of the radiation the skin-friction coefficients as well as the rate of heat transfer increased and consequently the momentum and thermal boundary layer thickness enhanced.

Radiation effect on free convection laminar flow along a vertical flat plate with streamwise sinusoidal surface temperature

The effect of thermal radiation on a steady two-dimensional natural convection laminar flow of viscous incompressible optically thick fluid along a vertical flat plate with streamwise sinusoidal surface temperature has been investigated in this study. Using the appropriate variables; the basic governing equations are transformed to convenient form and then solved numerically employing two efficient methods, namely, Implicit finite difference method (IFD) together with Keller box scheme and Straight forward finite difference (SFFD) method. Effects of the variation of the physical parameters, for example, conduction-radiation parameter (Planck number), surface temperature parameter, and the amplitude of the surface temperature, are shown on the skin friction and heat transfer rate quantitatively are shown numerically. Velocity and temperature profiles as well as streamlines and isotherms are also presented and discussed for the variation of conduction-radiation parameter. It is found that both skin-friction and rate of heat transfer are enhanced considerably by increasing the values of conduction radiation parameter, Rd.

The effect of temperature dependent viscosity on MHD natural convection flow from an isothermal sphere

Laminar magnetohydrodynamic (MHD) natural convection flow from an isothermal sphere immersed in a fluid with viscosity proportional to linear function of temperature has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are reduced to convenient form which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distribution, streamlines and isotherms of the fluid as well as heat transfer characteristics, namely the local skin-friction coefficients and the local heat transfer rate for a wide range of magnetohydrodynamic paramagnet and viscosity-variation parameter.

Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media

We present here a numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium. The governing equations of mass, momentum, energy and species are non-dimensionalized. These equations have been solved by using an implicit finite difference method and local non-similarity method. The results show many interesting aspects of complex interaction of the two buoyant mechanisms that have been shown in both the tabular as well as graphical form.

Large-Eddy Simulation of physiological pulsatile non-newtonian flow in a channel with double constriction

Physiological pulsatile flow in a 3D model of arterial double stenosis, using the modified Power-law blood viscosity model, is investigated by applying Large Eddy Simulation (LES) technique. The computational domain has been chosen is a simple channel with biological type stenoses. The physiological pulsation is generated at the inlet of the model using the first four harmonics of the Fourier series of the physiological pressure pulse. In LES, a top-hat spatial grid-filter is applied to the Navier-Stokes equations of motion to separate the large scale flows from the subgrid scale (SGS). The large scale flows are then resolved fully while the unresolved SGS motions are modelled using the localized dynamic model. The flow Reynolds numbers which are typical of those found in human large artery are chosen in the present work. Transitions to turbulent of the pulsatile non-Newtonian along with Newtonian flow in the post stenosis are examined through the mean velocity, wall shear stress, mean streamlines as well as turbulent kinetic energy and explained physically along with the relevant medical concerns.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

Effect of cold water immersion on repeated cycling performance and limb blood flow

The purpose of the present study was to compare the effects of cold water immersion (CWI) and active recovery (ACT) on resting limb blood flow, rectal temperature and repeated cycling performance in the heat. Ten subjects completed two testing sessions separated by 1 week; each trial consisted of an initial all-out 35-min exercise bout, one of two 15-min recovery interventions (randomised: CWI or ACT), followed by a 40-min passive recovery period before repeating the 35-min exercise bout. Performance was measured as the change in total work completed during the exercise bouts. Resting limb blood flow, heart rate, rectal temperature and blood lactate were recorded throughout the testing sessions. There was a significant decline in performance after ACT (mean (SD) −1.81% (1.05%)) compared with CWI where performance remained unchanged (0.10% (0.71%)). Rectal temperature was reduced after CWI (36.8°C (1.0°C)) compared with ACT (38.3°C (0.4°C)), as was blood flow to the arms (CWI 3.64 (1.47) ml/100 ml/min; ACT 16.85 (3.57) ml/100 ml/min) and legs (CW 4.83 (2.49) ml/100 ml/min; ACT 4.83 (2.49) ml/100 ml/min). Leg blood flow at the end of the second exercise bout was not different between the active (15.25 (4.33) ml/100 ml/min) and cold trials (14.99 (4.96) ml/100 ml/min), whereas rectal temperature (CWI 38.1°C (0.3°C); ACT 38.8°C (0.2°C)) and arm blood flow (CWI 20.55 (3.78) ml/100 ml/min; ACT 23.83 (5.32) ml/100 ml/min) remained depressed until the end of the cold trial. These findings indicate that CWI is an effective intervention for maintaining repeat cycling performance in the heat and this performance benefit is associated with alterations in core temperature and limb blood flow.