Optimal Control of Population Dynamics

This paper studies the role of projection algorithms in conditional set membership estimation. These algorithms are known to be suboptimal in terms of the worst-case estimation error. A tight upper bound on the error of central projection estimators and interpolatory projection estimators is computed as a function of the conditional radius of information. Since the radius of information represents the minimum achievable error, the derived bound provides a measure of the reliability level of the suboptimal algorithms. The results are derived in a general deterministic setting, which allows the consideration of linearly parametrized approximations of a compact set of feasible problem elements.     

Rigid-rod liquid crystalline polyesters based on n-alkoxyterephthalic acid and 4,4′-dihydroxybiphenyl

The synthesis and the characterization of a set of polymers obtained by polycondensation of n-alkoxyterephthalic acid (n = 1, 3, 5, 7) and 4,4′-dihydroxybiphenyl are reported. The n-alkoxy insertion promotes the processability of the material by lowering the melting temperature. All polymers show the nematic phase at about 300°C, almost independently of the length of lateral substituent. The isotropization is not observed up to 450°C, where thermal decomposition occurs. The temperature of glass transition decreases with increasing n, ranging from 170°C (n = 5) to 220°C (n = 1). © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 263–267, 1998     

Averaging for switched DAEs

Switched differential-algebraic equations (switched DAEs) are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an average non-switching system. It is well known that for a quite general class of switched ordinary differential equations (ODEs) this is the case. For switched DAEs, due the presence of the so-called consistency projectors, it is possible that the limit of trajectories for faster and faster switching does not exist. Under certain assumptions on the consistency projectors a result concerning the averaging for switched DAEs is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global boundedness of the solutions to a Gurtin-MacCamy system

This paper is concerned with the analysis of a generalized Gurtin-MacCamy model describing the evolution of an age-structured population. The problem of global boundedness is studied. Namely we ask whether there are simple general assumptions that one can make on the vital rates in order to have boundedness of the solution. Next a fully implicit finite difference scheme along the characteristic is considered to approximate the solution of the system. Global boundedness of the numerical solutions is investigated. The optimal rate of convergence of the scheme is obtained in the maximum norm. Numerical examples are presented.     

Selective microwave-accelerated synthesis and polymerization of chiral methacrylamide directly from methacrylic acid and (R)-1-phenyl-ethylamine

The chiral (R)-N-(1-phenyl-ethyl)-methacrylamide was synthesized directly from methacrylic acid and (R)-1-phenyl-ethylamine through microwave irradiation in a solvent-free medium. Kinetic comparison between reactions carried out either under microwaves (MW) or conventional thermal heating evidenced the higher selectivity of the MW accelerated reaction. Under the MW applied conditions, the desired amidation is clearly preferred to the Michael side-reactions. The addition of a radical initiator to the starting mixture leads, in one step, to the formation of an optically active polymer containing both methacrylamide and imide moieties.     

Analysis of a nonlinear model of the vibrating string

A nonlinear model of the vibrating string is studied under the assumption that the motion is transversal and existence and uniqueness theorems are given for the Cauchy-Dirichlet problems. Some numerical experiments are also described, illustrating the behaviour of this model with respect to the nonlinear Kirchhoff model and the classical linear model of D'Alembert.The research has been supported by MURST 40% and 60% Research Contracts     

Analysis of the local truncation error in the pressure‐free projection method for incompressible flows: a new accurate expression of the intermediate boundary conditions

The numerical integration of the Navier–Stokes equations for incompressible flows demands efficient and accurate solution algorithms for pressure–velocity splitting. Such decoupling was traditionally performed by adopting the Fractional Time‐Step Method that is based on a formal separation between convective–diffusive momentum terms from the pressure gradient term. This idea is strictly related to the fundamental theorem on the Helmholtz–Hodge orthogonal decomposition of a vector field in a finite domain, from which the name projection methods originates. The aim of this paper is to provide an original evaluation of the local truncation error (LTE) for analysing the actual accuracy achieved by solving the de‐coupled system. The LTE sources are formally subdivided in two categories: errors intrinsically due to the splitting of the original system and errors due to the assignment of the boundary conditions. The main goal of the present paper consists in both providing the LTE analysis and proposing a remedy for the inaccuracy of some types of intermediate boundary conditions associated with the prediction equation. Such evaluations will be directly performed in the physical space for both the time continuous formulation and the finite volume discretization along with the discrete Adams–Bashforth/Crank–Nicolson time integration. A new proposal for a boundary condition expression, congruent with the discrete prediction equation is herein derived, fulfilling the goal of accomplishing the closure of the problem with fully second order accuracy. In our knowledge, this procedure is new in the literature and can be easily implemented for confined flows. The LTE is clearly highlighted and many computations demonstrate that our proposal is efficient and accurate and the goal of adopting the pressure‐free method in a finite domain with fully second order accuracy is reached. Copyright © 2003 John Wiley & Sons, Ltd.     

Harvesting Control for an Age-Structured Population in a Multilayered Habitat

This paper continues previous works concerning the dynamics of an age-structured population spreading in a spatially heterogeneous habitat. Our model takes into account two important features of the population, namely its spatial diffusion and its age structure. Within this context we consider the harvesting of the population, occurring in a different way in the layers and establish a specific strategy aimed to maximizing the yield and keeping the population at an optimal level in the habitat.