Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

Our aim in this work is to synthesize optimal feeding strategies that maximize, over a time period, the biogas production in a continuously filled bioreactor controlled by its dilution rate. Such an anaerobic process is described by a four-dimensional dynamical system. Instead of modeling the optimization of the biogas production as a Lagrange-type optimal control problem, we propose a slightly different optimal control approach in this paper: We study the minimal time control problem to reach a target point, which is chosen in such a way that it maximizes the biogas production at steady state. Thanks to the Pontryagin maximum principle and the geometric control theory, we provide an optimal feedback control for the minimal time control problem, when the initial conditions are taken within the invariant and attractive manifold of the system. The optimal synthesis exhibits turnpike and anti-turnpike singular arcs and a cut locus.     

Phase locking control in the Circle Map

The phase-locking between two oscillators occurs when the ratio of their frequencies becomes locked in a ratio p/q of integer numbers over some finite domain of parameters values. Due to it, oscillators with some kind of nonlinear coupling may synchronize for certain set of parameters. This phenomenon can be better understood and studied with the use of a well-known paradigm, the Circle Map, and the definition of the winding number. Two diagrams related to this map are especially useful: the ‘Arnold tongues’ and the ‘devil’s staircase’. The synchronization that occurs in this map is described by the ‘Farey Series’. This property is the starting point for the development of control algorithms capable of locking the system under the action of an external excitation into a desired winding number. In this work, we discuss the main characteristics of the phase-locking phenomenon and consider three control algorithms designed to drive and keep the Circle Map into a desired winding number.     

Multiscale modelling of skeletal muscle tissue by incorporating microstructural effects

The macroscopic mechanical response of skeletal muscle tissue is mainly influenced by the properties and arrangement of microstructural elements, such as, for example, sarcomeres and connective tissue. Like for many biological materials, the mechanical properties of skeletal muscle tissue can vary quite significantly between different specimens like, for example, different persons or muscle types. Current state-of-the-art continuum-mechanical muscle models often lack the ability to take into account such variations in a natural way. Further, phenomenological constitutive laws face the challenge that appropriate material parameter sets need to be found for each tissue variation. Thus, the present work aims to identify the microstructural features and parameters governing the overall mechanical response and to incorporate them into a macroscopic material model by applying suitable homogenisation methods. The motivation hereby is that the estimation of material parameters for microstructures, such as collagen fibres, can be done in a more reliable and general way and that fluctuations between specimens are included by, for example, adapting the alignment of the collagen fibres inside the muscle. Moreover, instead of computationally expensive homogenisation methods like FE², this work proceeds from well-founded analytical homogenisation techniques in order to keep the model as simple as possible. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Second-order estimates for the large-deformation response of particle-reinforced rubbersEstimations homogénéisées pour le comportement mécanique des caoutchoucs renforcés en grandes déformations

This paper presents the application of a recently proposed ‘second-order’ homogenization method (J. Mech. Phys. Solids 50 (2002) 737–757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of ‘generalized’ secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin–Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389–1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible. To cite this article: O. Lopez-Pamies, P. Ponte Castañeda, C. R. Mecanique 331 (2003).     

SET-VALUED EXTENSION OF OPERATORS VIA STEINER SELECTIONS (Ⅰ)-THEORETICAL RESULTS

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Effect of pH and added electrolyte on the thermal-induced transitions of egg yolk

Thermally-induced transitions of egg yolk were studied using Differential Scanning Calorimetry (DSC) and temperature-controlled Small Amplitude Oscillatory Shear (SAOS). The influence of composition (pH and electrolyte content and type) was analysed. The results obtained under DSC measurements suggest a continuous evolution in protein denaturation that depends on pH and salt content. Cure experiments performed using SAOS show dramatic increases in viscoelasticity functions. Protein gelation is affected by the pH, ionic strength and salt type. SAOS was also used to obtain the mechanical spectra of egg yolk dispersions and gels as a function of composition. The microstructures of gels were also evaluated by Scanning Electron Microscopy (SEM). SEM results reveal an increase in microstructure homogeneity and a decrease in the size of aggregates at lowered pH. The influence of pH and ionic strength on linear viscoelastic properties and microstructure may be explained in terms of the model for the formation of gel networks of globular proteins. However, the characteristic structure of native yolk must also be considered.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

Protein-based bioplastics: effect of thermo-mechanical processing

Bioplastics based on glycerol and different proteins (wheat gluten, albumen, rice and albumen/gluten blends) have been manufactured to determine the effect that processing and further thermal treatments exert on different thermo-mechanical properties of the bioplastics obtained. Oscillatory shear, modulated differential scanning calorimetry, dynamic mechanical thermal analysis, thermo-gravimetric analysis and water absorption tests were carried out to study the effect of processing on the physical characteristics of the bioplastics. The protein-based bioplastics studied in this work present a high capacity for thermosetting modification because of protein denaturation that may favour the development of a wide variety of materials. The use of albumen or rice protein allows the reduction in both protein concentration and thermosetting temperature, leading to linear viscoelastic moduli values similar to those of synthetic polymers such as LDPE and HDPE. The hygroscopic characteristics of protein-glycerol bioplastics may lead to a decrease in the values of the linear viscoelasticity functions. However, hygroscopic properties depend on the protein nature and may be used for industrial applications where water absorption is required. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.