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In the present article, we research the existence of the positive periodic solutions for a mathematical model that describes the propagation dynamics of a pathogen living within a vector population over a plant population. We propose a generalized compartment model of the susceptible–infected–susceptible (SIS) type. This model is derived primarily based on four assumptions: (i) the plant population is subdivided into healthy plants, which are susceptible to virus infection, and infected plants; (ii) the vector population is categorized into non-infectious and infectious vectors; (iii) the dynamics of pathogen propagation follow the standard susceptible–infected–susceptible pattern; and (iv) the rates of pathogen propagation are time-dependent functions. The main contribution of this paper is the introduction of a sufficient condition for the existence of positive periodic solutions in the model. The proof of our main results relies on a priori estimates of system solutions and the application of coincidence degree theory. Additionally, we present some numerical examples that demonstrate the periodic behavior of the system. [ABSTRACT FROM AUTHOR]

During the last years, mathematical modelling has been entering the field of engineering education because it is a bridge between mathematics and industry that also promotes the development of skills that require the engineer of the twenty-first century. Nevertheless, the modelling process is involved and requires the deployment of cognitive skills of superior level, particularly metacognitive skills. This contribution presents the results of a multiple qualitative case study on metacognitive strategies used by groups of engineering students associated with each transition of the mathematical modelling process. During the development of the course, observations and retrospective interviews were carried out, which evidenced the use of metacognitive planning strategies from simplification to interpretation; metacognitive monitoring strategies throughout the modelling process, metacognitive regulation strategies from mathematization to mathematical work and metacognitive evaluation strategies during simplification, mathematization and validation. The results expand the classification framework of metacognitive strategies for engineering students. [ABSTRACT FROM AUTHOR]

In this contribution we consider the problem of flux identification in a scalar conservation law modelling the phenomenon of sedimentation. The experimental observation data used for the calibration consist of a solid concentration profile at a fixed time. The identification problem is formulated as an optimization one, where the distance between the profiles of the model simulation and observation data is minimized by a least squares cost function. The direct problem is approximated by a monotone finite volume scheme. The numerical solution of the calibration problem is obtained by a continuous genetic algorithm. Numerical results are presented in order to validate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper analyses a continuum model of the sedimentation of polydisperse suspensions, where the volume concentrations of the solids species are the sought unknowns. This leads to systems of conservation laws which are non-genuinely nonlinear (“non-convex”) in the sense that they are only piecewise genuinely nonlinear. The solution of a Riemann problem is represented as a concatenation of elementary waves, where the linear degeneracy requires using the Liu entropy condition. After a general description of the composition of elementary waves, an algorithm for the computational construction is given. The solution of the Riemann problem is then utilized as a problem-adapted building block of a front tracking method. For the model of bidisperse suspensions, Riemann problems are classified by the location of the left and right state in the phase space of unknown variables. The front tracking method is applied to solve the initial value problem of a first-order hyperbolic 2 × 2 system of conservation laws describing the settling of a bidisperse suspension. The solution obtained by front tracking is compared with results obtained by an experiment and a finite difference scheme. [ABSTRACT FROM AUTHOR]

Abstract: The well-known Masliyah–Lockett–Bassoon (MLB) model for sedimentation of small particles is extended to fluidization of polydisperse suspensions. For N particle species that differ in size and density, this model leads to a first-order system of N conservation laws, which in general is of mixed (in the case N=2, hyperbolic–elliptic) type. By a simple algebraic steady-state analysis, we derive necessary compatibility conditions on the size and density parameters that admit the formation of stationary fluidized beds. We then proceed to determine the composition of polydisperse fluidized beds of given compatible species by varying the fluidization velocity and the initial composition of the suspensions, and prove that, within the framework of the MLB model combined with the Richardson–Zaki formula, the constructed bidisperse beds always cause the equations to be hyperbolic. This means that these states are always predicted to be stable. The transient behaviour of the MLB model applied to fluidization is illustrated by three numerical examples, in which the system of conservation laws is solved for N=2, N=3 and N=5, respectively. These examples illustrate the effects of bed expansion and layer inversion caused by successively increasing the applied fluidization velocity and show that the predicted fluidized states are indeed attained. [Copyright &y& Elsevier]

Examines how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a theory of the sedimentation processes of polydisperse suspensions forming compressible sediments. Characteristic polynomials of the Jacobian of the convective flux vector and the diffusion matrix.