Temperature distributions recorded by thermocouples in a solid body (slab) subject to surface heating are used in a mathematical model of two-dimensional heat conduction. The corresponding Dirichlet problem for a holomorphic function (complex potential), involving temperature and a heat stream function, is solved in a strip. The Zhukovskii function is reconstructed through singular integrals, involving an auxiliary complex variable. The complex potential is mapped onto an auxiliary half-plane. The flow net (orthogonal isotherms and heat lines) of heat conduction is compared with the known Carslaw–Jaeger solution and shows a puzzling topology of three regimes of energy fluxes for temperature boundary conditions common in passive thermal insulation. The simplest regime is realized if cooling of a shaded zone is mild and heat flows in a slightly distorted “resistor model” flow tube. The second regime emerges when cooling is stronger and two disconnected separatrices demarcate the back-flow of heat from a relatively hot segment of the slab surface to the atmosphere through relatively cold parts of this surface. The third topological regime is characterized by a single separatrix with a critical point inside the slab, where the thermal gradient is nil. In this regime the back-suction of heat into the atmosphere is most intensive. The closed-form solutions obtained can be used in assessment of efficiency of thermal protection of buildings.

A theoretical investigation of the unsteady flow of a Newtonian fluid through a channel is presented using an alternative boundary condition to the standard no-slip condition, namely the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter called the slip length, and the most general case of a constant but different slip length on each channel wall is studied. An analytical solution for the velocity distribution through the channel is obtained via a Fourier series, and is used as a benchmark for numerical simulations performed utilizing a finite element analysis modified with a penalty method to implement the slip boundary condition. Comparison between the analytical and numerical solution shows excellent agreement for all combinations of slip lengths considered.

Selective withdrawal of a two-layer fluid is considered. The fluid layers are weakly compressible, miscible and viscous and therefore flow rotationally. The lower, denser fluid flows with constant velocity out through one or more drain holes in the bottom of a rectangular tank. The drain is opened impulsively and the subsequent draw-down produces waves in the interface which travel outward to the edges of the tank and are reflected back with a $18{0}^{\circ } $ change of phase. The points on the interface that have the highest absolute gradient form regions of high vorticity in the tank, enabling mixing of the fluids. An inviscid linearized interface is computed and compared to contour plots of density for the viscous solution. The two agree closely at early times in the withdrawal process, but as time increases, nonlinear and viscous effects take over. The time at which the lighter fluid starts to flow out of the tank is dependent on the number of drains, their width, and the fluid flow rate and density, and is investigated here.

We develop a computational method for solving an optimal control problem governed by a switched impulsive dynamical system with time delay. At each time instant, only one subsystem is active. We propose a computational method for solving this optimal control problem where the time spent by the state in each subsystem is treated as a new parameter. These parameters and the jump strengths of the impulses are decision parameters to be optimized. The gradient formula of the cost function is derived in terms of solving a number of delay differential equations forward in time. Based on this, the optimal control problem can be solved as an optimization problem.

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Increased frequency and severity of stressors associated with climate change are drastically altering ecosystems. Caribbean coral reefs differ markedly from just 30 years ago, with much restructuring attributable to infectious disease outbreaks. Using a classic epidemiological approach, we demonstrate how density-dependent demographic rates serve as a mechanism for intrinsic coral resilience to population perturbations arising from disturbances such as disease. We explore the impact of allowing infection status to influence demographic rates and ascertain outbreak thresholds that are corroborated by epizootic patterns observed in the field. We discuss how our threshold calculations may provide metrics of coral epizootic early warning systems. Integrating our infection model with equations describing the interspecific competition for space between coral and macroalgae, we provide new mechanistic understanding of the influence that coral life history dynamism and infectious disease have on the changing face of these threatened ecosystems.

Random networks were first used to model epidemic dynamics in the 1950s, but in the last decade it has been realized that scale-free networks more accurately represent the network structure of many real-world situations. Here we give an analytical and a Monte Carlo method for approximating the basic reproduction number ${R}_{0} $ of an infectious agent on a network. We investigate how final epidemic size depends on ${R}_{0} $ and on network density in random networks and in scale-free networks with a Pareto exponent of 3. Our results show that: (i) an epidemic on a random network has the same average final size as an epidemic in a well-mixed population with the same value of ${R}_{0} $; (ii) an epidemic on a scale-free network has a larger average final size than in an equivalent well-mixed population if ${R}_{0} \lt 1$, and a smaller average final size than in a well-mixed population if ${R}_{0} \gt 1$; (iii) an epidemic on a scale-free network spreads more rapidly than an epidemic on a random network or in a well-mixed population.

For solving linear complementarity problems LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting. But up to now, no paper has discussed the effect of preconditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and we use a class of preconditioners with generalized Accelerated Overrelaxation (GAOR) methods and analyze the convergence of these methods for LCP. Furthermore, Comparison between our methods and other non-preconditioned methods for the studied problem shows a remarkable agreement and reveals that our models are superior in point of view of convergence rate and computing efficiency. Besides, by choosing the appropriate parameters of these methods, we derive same results as the other iterative methods such as AOR, JOR, SOR etc. Finally the method is tested by some numerical experiments.

This work studies a new strategic game called delegation game. A delegation game isassociated to a basic game with a finite number of players where each player has a finiteinteger weight and her strategy consists in dividing it into several integer parts andassigning each part to one subset of finitely many facilities. In the associateddelegation game, a player divides her weight into several integer parts, commits each partto an independent delegate and collects the sum of their payoffs in the basic game playedby these delegates. Delegation equilibrium payoffs, consistent delegation equilibriumpayoffs and consistent chains inducing these ones in a delegation game are defined.Several examples are provided.

This paper considers the problem of scheduling n jobs on a singlemachine. A fixed processing time and an execution interval are associated with each job.Preemption is not allowed. The objective is to find a feasible job sequence that minimizesthe number of tardy jobs. On the basis of an original mathematical integer programmingformulation, this paper shows how good-quality lower and upper bounds can be computed.Numerical experiments are provided for assessing the proposed approach.

This note is concerned with the bicriteria scheduling problem on a series-batchingmachine to minimize maximum cost and makespan. AnO(n5) algorithm has been establishedpreviously. Here is an improved algorithm which solves the problem inO(n3) time.

This paper describes an unreliable server batch arrival retrial queue with two types ofrepair and second optional service. The server provides preliminary first essentialservice (FES) to the primary arriving customers or customers from retrial group. Onsuccessful completion of FES, the customer may opt for second optional service (SOS) withprobability α. The server is subject to active break downs. The customerunder FES (or SOS) during the failure decides, with probability q, tojoin the orbit(impatientcustomer) and, with complementary probabilityp, to remain in the server for repair in order to conclude hisremaining service (patientcustomer). Both service and repair times areassumed to have general distribution. It is considered that the repair time of serverduring the presence of patient customer and the repair time of the server while thecustomer (impatientcustomer) joining the orbit due to failure, aredifferent. For this queueing system, the orbit and system size distributions are obtained.Reliability of the proposed model is analysed. Some particular cases are also discussed.Other performance measures are also obtained. The effects of several parameters on thesystem are analysed numerically.

We consider the scheduling of an interval order precedence graph of unit execution time tasks with communication delays, release dates and deadlines. Tasks must be executed by a set of processors partitioned into K classes; each task requires one processor from a fixed class. The aim of this paper is to study the extension of the Leung–Palem–Pnueli (in short LPP) algorithm to this problem. The main result is to prove that the LPP algorithm can be extended to dedicated processors and monotone communication delays. It is also proved that the problem is NP–complete for two dedicated processors if communication delays are non monotone. Lastly, we show that list scheduling algorithm cannot provide a solution for identical processors.