This paper presents a numerical investigation of plaque growth in a diseased artery using the two-way fluid–structural interaction (FSI) technique. An axis-asymmetric 45% stenosis model is used as the base model to start the plaque growth approximation. The blood is modelled as a non-Newtonian fluid described by the Casson model. The artery tissue is assumed to be a nonlinear material. The two-way FSI simulation is carried out in a way that mimics the unsteady blood flow through a diseased artery by using a pulsatile flow condition. After each flow velocity cycle, the numerical results are extracted and used to modify the stenosis geometry based upon critical wall shear stress (WSS) values and an accepted relationship between the concentration of low density lipoprotein and WSS. The simulation procedure is repeated until the growth-updated stenosis morphology reaches 79% severity. The behaviour of the flow velocity is analysed at each growth stage, together with the WSS, to determine the change of plaque morphology due to growth. The effects of WSS and pressure on the artery wall at the final stage (79% severity) of the plaque growth model are also compared with results from the authors’ previous work, to demonstrate the importance of the morphology change in plaque growth modelling.

The vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear free-boundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume.

This paper aims at describing the way Flow machinery may be used in order to deal with Resource Constrained Project Scheduling Problems (RCPSP). In order to do it, it first introduces the Timed Flow Polyhedron related to a RCPSP instance. Next it states several structural results related to connectivity and to cut management. It keeps on with a description of the way this framework gives rise to a generic Insertion operator, which enables programmers to design greedy and local search algorithms. It ends with numerical experiments.

This is a review of thin-body and slender-body theories, with indications of some new applications. Topics discussed include bodies with near-constant surface pressure, subsonic and supersonic aerodynamics, ship hydrodynamics, slender bodies in Stokes flow, slender footings in elastic media, and slender moonpools. Mathematical features of the thin- and slender-body approximations are also discussed, especially nonlocal convolution terms modelling three-dimensionality in the otherwise two-dimensional near field, end effects, and the role of the logarithm of the slenderness ratio. This review was presented by the first author as the IMA Lighthill Memorial Lecture at the British Applied Mathematics Colloquium (BAMC) 2004.

Infecting Aedes aegypti mosquitoes with the bacteria Wolbachia has been proposed as an innovative new strategy to reduce the transmission of dengue fever. Field trials are currently being undertaken in Queensland, Australia. However, few mathematical models have been developed to consider the persistence of Wolbachia-infected mosquitoes in the wild. This paper develops a mathematical model to determine the persistence of Wolbachia-infected mosquitoes by considering the competition between Wolbachia-infected and non-Wolbachia mosquitoes. The model has four steady states that are biologically feasible: all mosquitoes dying out, only non-Wolbachia mosquitoes surviving, and two steady states where non-Wolbachia and Wolbachia-infected mosquitoes coexist. The stability of the steady states is determined with respect to the key parameters in the mosquito life cycle. A global sensitivity analysis of the model is also conducted. The results show that the persistence of Wolbachia-infected mosquitoes is dominated by the reproductive rate, death rate, maturation rate and maternal transmission. For the parameter values where Wolbachia persists, it dominates the population, and hence the introduction of Wolbachia has great potential to reduce dengue transmission.

For a specific query merging the returned results from multiple search engines, in theform of a metasearch aggregation, can provide significant improvement in the quality ofrelevant documents. This paper suggests a minimax linear programming (LP) formulation forfusion of multiple search engines results. The paper proposes a weighting method toinclude the importance weights of the underlying search engines. This is a two-phaseapproach which in the first phase a new method for computing the importance weights of thesearch engines is introduced and in the second stage a minimax LP model for findingrelevant search engines results is formulated. To evaluate the retrieval effectiveness ofthe suggested method, the 50 queries of the 2002 TREC Web track were utilized andsubmitted to three popular Web search engines called Ask, Bing and Google. The returnedresults were aggregated using two exiting approaches, three high-performance commercialWeb metasearch engines and our proposed technique. The efficiency of the generated listswas measured using TREC-Style Average Precision (TSAP). The new findings demonstrate thatthe suggested model improved the quality of merging considerably.

Consider an M/M/1 retrial queue with collisions and working vacation interruption underN-policy. We use a quasi birth and death process to describe the considered system andderive a condition for the stability of the model. Using the matrix-analytic method, weobtain the stationary probability distribution and some performance measures. Furthermore,we prove the conditional stochastic decomposition for the queue length in the orbit.Finally, some numerical examples are presented.

The coupled tasks scheduling problem is a class of scheduling problems introduced forbeam steering software of sophisticated radar devices, called phased arrays. Due toincreasing popularity of such radars, the importance of coupled tasks scheduling isconstantly growing. Unfortunately, most of the coupled tasks problems are NP-hard, andonly a few practically usable algorithms for such problems were found. This paper providesa survey of already known complexity results of various variants of coupled tasksproblems. Then, it complements previous results by providing experimental results of twonew polynomial algorithms for coupled tasks scheduling, which are: an exact algorithm for1|(1,4,1),strictchains|Cmax problem,and a fast heuristic algorithm for more general1|(1,2k, 1), strictchains|Cmaxproblem, where k ∈ ℕ.

In this paper, a batch arrival general bulk service queueing system with interruptedvacation (secondary job) is considered. At a service completion epoch, if the server findsat least ‘a’ customers waiting for service say ξ, heserves a batch of min (ξ, b) customers, whereb ≥ a. On the other hand, if the queue length is atthe most ‘a-1’, the server leaves for a secondary job (vacation) ofrandom length. It is assumed that the secondary job is interrupted abruptly and the serverresumes for primary service, if the queue size reaches ‘a’, during thesecondary job period. On completion of the secondary job, the server remains in the system(dormant period) until the queue length reaches ‘a’. For the proposedmodel, the probability generating function of the steady state queue size distribution atan arbitrary time is obtained. Various performance measures are derived. A cost model forthe queueing system is also developed. To optimize the cost, a numerical illustration isprovided.

Conformal slit maps play a fundamental theoretical role in analytic function theory and potential theory. A lesser-known fact is that they also have a key role to play in applied mathematics. This review article discusses several canonical conformal slit maps for multiply connected domains and gives explicit formulae for them in terms of a classical special function known as the Schottky–Klein prime function associated with a circular preimage domain. It is shown, by a series of examples, that these slit mapping functions can be used as basic building blocks to construct more complicated functions relevant to a variety of applied mathematical problems.

In earlier work we have studied a method for discretization in time of a parabolic problem, which consists of representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite-element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive-definite matrix with a complex shift. We study iterative methods for such systems, considering the basic and preconditioned versions of first the Richardson algorithm and then a conjugate gradient method.

This paper studies outflow of a light fluid from a point source, starting from an initially spherical bubble. This region of light fluid is embedded in a heavy fluid, from which it is separated by a thin interface. A gravitational force directed radially inward toward the mass source is permitted. Because the light inner fluid is pushing the heavy outer fluid, the interface between them may be unstable to small perturbations, in the Rayleigh–Taylor sense. An inviscid model of this two-layer flow is presented, and a linearized solution is developed for early times. It is argued that the inviscid solution develops a point of infinite curvature at the interface within finite time, after which the solution fails to exist. A Boussinesq viscous model is then presented as a means of quantifying the precise effects of viscosity. The interface is represented as a narrow region of large density gradient. The viscous results agree well with the inviscid theory at early times, but the curvature singularity of the inviscid theory is instead replaced by jet formation in the viscous case. This may be of relevance to underwater explosions and stellar evolution.

In a multi server queuing system, buffer size is often larger than the number of servers.This necessitates queuing and waiting for some customers. Customers become impatient whilewaiting for service. Additionally, they may also become impatient if service is notoffered at the desired rate. This paper analyses a finite buffer multi server queuingsystem with the additional restriction that customers may balk as well as renege. Closedform expressions of a number of performance measures are presented. A design problem isdiscussed to demonstrate the results derived.

In this paper, we develop a supply chain network equilibrium model in which electronic commerce in the presence of both B2B (business-to-business) and B2C (business-to-consumer) transactions, multiperiod decision-making and multicriteria decision-making are integrated. The model consists of three tiers of decision-makers (manufacturers, retailers and consumers at demand markets) who compete within a tier but may cooperate between tiers. Both manufacturers and retailers are concerned with maximization of profit as well as minimization of risk, whereas consumers take both the prices charged by manufacturers and retailers, along with the corresponding costs of transacting, in making their consumption decisions. Increasing relationship levels are assumed to decrease costs of transacting as well as risk costs. Establishing and maintaining these relationship levels incur some costs that have to be borne by the various decision-makers. We study the interaction among different tiers of decision-makers, describe their multicriteria decision-making behavior and derive the optimality conditions as well as the equilibrium conditions which are then shown to satisfy a finite-dimensional variational inequality problem. We then establish qualitative properties of the equilibrium model under some reasonable assumptions and illustrate the model with several numerical examples.

The minimum cost network flow problem, (MCNFP) constitutes a wide category of networkflow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) forthe MCNFP has been developed. This algorithm belongs to a special “exterior point simplextype” category. Similar to the classical dual network simplex algorithm (DNSA), thisalgorithm starts with a dual feasible tree-solution and after a number of iterations, itproduces a solution that is both primal and dual feasible, i.e. it isoptimal. However, contrary to the DNSA, the new algorithm does not always maintain a dualfeasible solution. Instead, it produces tree-solutions that can be infeasible for the dualproblem and at the same time infeasible for the primal problem. In this paper, we presentfor the first time, the mathematical proof of correctness of DNEPSA, a detailedcomparative computational study of DNEPSA and DNSA on sparse and dense random probleminstances, a statistical analysis of the experimental results, and finally some newresults on the empirical complexity of DNEPSA. The analysis proves the superiority ofDNEPSA compared to DNSA in terms of cpu time and iterations.