Inexact uniformization method for computing transient distributions of Markov chains

The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.

Velocity-jump models with crowding effects

Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions 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 distributions 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 magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Insect distributions and sampling protocols for stored commodities

Purpose of review: This review provides an overview on the importance of characterising and considering insect distribution infor- mation for designing stored commodity sampling protocols. Findings: Sampling protocols are influenced by a number of factors including government regulations, management practices, new technology and current perceptions of the status of insect pest damage. The spatial distribution of insects in stored commodities influ- ences the efficiency of sampling protocols; these can vary in response to season, treatment and other factors. It is important to use sam- pling designs based on robust statistics suitable for the purpose. Future research: The development of sampling protocols based on flexible, robust statistics allows for accuracy across a range of spatial distributions. Additionally, power can be added to sampling protocols through the integration of external information such as treatment history and climate. Bayesian analysis provides a coherent and well understood means to achieve this.

Double diffusive magneto-convection fluid flow in a strong cross magnetic field with uniform surface heat and mass flux

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. For smooth integrations the boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation as well as the free variable formulation. The nonsimilar parabolic partial differential equations are integrated numerically for Pr ≪1 that is appropriate for liquid metals against the local Hartmann parameter ξ . Further, asymptotic solutions are obtained near the leading edge using regular perturbation method for smaller values of ξ . Solutions for values of ξ ≫ 1 are also obtained by employing the matched asymptotic technique. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10:0.

Water lubricated bearings

The increasing ecological awareness and stringent requirements for environmental protection have led to the development of water lubricated bearings in many applications where oil was used as the lubricant. The chapter details the theoretical analysis to determine both the static and dynamic characteristics,including the stability (using both the linearised perturbation method and the nonlinear transient analysis) of multiple axial groove water lubricated bearings. Experimental measurements and computational fluid dynamics (CFD) simulations by the Tribology research group at Queensland University of Technology,Australia and Manipal Institute of Technology, India, have highlighted a significant gap in the understanding of the flow phenomena and pressure conditions within the lubricating fluid. An attempt has been made to present a CFD approach to model fluid flow in the bearing with three equi-spaced axial grooves and supplied with water from one end of the bearing. Details of the experimental method used to measure the film pressure in the bearing are outlined. The lubricant is subjected to a velocity induced flow (as the shaft rotates) and a pressure induced flow (as the water is forced from one end of the bearing to the other). Results are presented for the circumferential and axial pressure distribution in the bearing clearance for different loads, speeds and supply pressures. The axial pressure profile along the axial groove located in the loaded part of the bearing is measured. The theoretical analysis shows that smaller the groove angle better will be the load-carrying capacity and stability of these bearings. Results are compared with experimentally measured pressure distributions.

Velocity jump processes with proliferation

Cell invasion involves a population of cells that migrate along a substrate and proliferate to a carrying capacity density. These two processes, combined, lead to invasion fronts that move into unoccupied tissues. Traditional modelling approaches based on reaction–diffusion equations cannot incorporate individual–level observations of cell velocity, as information propagates with infinite velocity according to these parabolic models. In contrast, velocity jump processes allow us to explicitly incorporate individual–level observations of cell velocity, thus providing an alternative framework for modelling cell invasion. Here, we introduce proliferation into a standard velocity–jump process and show that the standard model does not support invasion fronts. Instead, we find that crowding effects must be explicitly incorporated into a proliferative velocity–jump process before invasion fronts can be observed. Our observations are supported by numerical and analytical solutions of a novel coupled system of partial differential equations, including travelling wave solutions, and associated random walk simulations.

Accurate stratospheric particle size distributions from two separate flat-plate collection surfaces

Over the past two decades, flat-plate particle collections have revealed the presence of a remarkable variety of both terrestrial and extraterrestrial material in the stratosphere [1-6]. The ratio of terrestrial to extraterrestrial material and the nature of material collected may vary over observable time scales. Variations in particle number density can be important since the earth’s atmospheric radiation balance, and therefore the earth’s climate, can be influenced by articulate absorption and scattering of radiation from the sun and earth [7-9]. In order to assess the number density of solid particles in the stratosphere, we have examined a representative fraction of the so1id particles from two flat-plate collection surfaces, whose collection dates are separated in time by 5 years.

Grain size distributions of Magneli phases and metallic titanium in chondritic porous interplanetary dust particles

A mineralogical survey of chondritic interplanetary dust particles (IDPs)showed that these micrometeorites differ significantly in form and texture from components of carbonaceous chondrites and contain some mineral assemblages which do not occur in any meteorite class1. Models of chondritic IDP mineral evolution generally ignore the typical (ultra-) fine grain size of consituent minerals which range between 0.002-0.1µm in size2. The chondritic porous (CP) subset of chondritic IDPs is probably debris from short period comets although evidence for a cometary origin is still circumstantial3. If CP IDPs represent dust from regions of the Solar System in which comet accretion occurred, it can be argued that pervasive mineralogical evolution of IDP dust has been arrested due to cryogenic storage in comet nuclei. Thus, preservation in CP IDPs of "unusual meteorite minerals", such as oxides of tin, bismuth and titanium4, should not be dismissed casually. These minerals may contain specific information about processes that occurred in regions of the solar nebula, and early Solar System, which spawned the IDP parent bodies such as comets and C, P and D asteroids6. It is not fully appreciated that the apparent disparity between the mineralogy of CP IDPs and carbonaceous chondrite matrix may also be caused by the choice of electron-beam techniques with different analytical resolution. For example, Mg-Si-Fe distributions of Cl matrix obtained by "defocussed beam" microprobe analyses are displaced towards lower Fe-values when using analytical electron microscope (AEM)data which resolve individual mineral grains of various layer silicates and magnetite in the same matrix6,7. In general, "unusual meteorite minerals" in chondritic IDPs, such as metallic titanium, Tin01-n(Magneli phases) and anatase8 add to the mineral data base of fine-grained Solar System materials and provide constraints on processes that occurred in the early Solar System.

Accurate stratospheric particle-size distributions from a flat-plate collection surface

The first representative chemical, structural, and morphological analysis of the solid particles from a single collection surface has been performed. This collection surface sampled the stratosphere between 17 and 19km in altitude in the summer of 1981, and therefore before the 1982 eruptions of El Chichón. A particle collection surface was washed free of all particles with rinses of Freon and hexane, and the resulting wash was directed through a series of vertically stacked Nucleopore filters. The size cutoff for the solid particle collection process in the stratosphere is found to be considerably less than 1 μm. The total stratospheric number density of solid particles larger than 1μm in diameter at the collection time is calculated to be about 2.7×10−1 particles per cubic meter, of which approximately 95% are smaller than 5μm in diameter. Previous classification schemes are expanded to explicitly recognize low atomic number material. With the single exception of the calcium-aluminum-silicate (CAS) spheres all solid particle types show a logarithmic increase in number concentration with decreasing diameter. The aluminum-rich particles are unique in showing bimodal size distributions. In addition, spheres constitute only a minor fraction of the aluminum-rich material. About 2/3 of the particles examined were found to be shards of rhyolitic glass. This abundant volcanic material could not be correlated with any eruption plume known to have vented directly to the stratosphere. The micrometeorite number density calculated from this data set is 5×10−2 micrometeorites per cubic meter of air, an order of magnitude greater than the best previous estimate. At the collection altitude, the maximum collision frequency of solid particles >5μm in average diameter is calculated to be 6.91×10−16 collisions per second, which indicates negligible contamination of extraterrestrial particles in the stratosphere by solid anthropogenic particles.