Finite dynamic deformations of a hyperelastic,anisotropic, incompressible and prestressed tube. Applications to in vivo arteries

In this paper, we study the mechanical behavior of a prestressed tube subjected to finite dynamic deformations. The tube is assumed to be made of a hyperelastic, anisotropic and incompressible material. The analysis is carried out by using a Mooney–Rivlin stored energy function augmented with fiber reinforcements in four unidimensional orientations. A semi-analytical solution is proposed to study the radial dynamic mechanical response of an artery by using in vivo data. The optimal model parameters describing the mechanical characteristics of arterial wall microconstituents are obtained by minimizing the difference between computed and measured inner pressures over the cardiac cycle using a nonlinear regression. Theoretical and experimental results on rat carotid elastic arteries are compared in order to assess the validity of the approach by estimating differences of the model parameters and wall stresses with aging.     

Multi-scale Modeling of Vision-Guided Remodeling and Age-Dependent Growth of the Tree Shrew Sclera During Eye Development and Lens-Induced Myopia

The sclera uses unknown mechanisms to match the eye’s axial length to its optics during development, producing eyes with good focus (emmetropia). A myopic eye is too long for its own optics. We propose a multi-scale computational model to simulate eye development based on the assumption that scleral growth is controlled by genetic factors while scleral remodeling is driven by genetic factors and the eye’s refractive error. We define growth as a mechanism that changes the tissue volume and mass while remodeling involves internal micro-deformations that are volume-preserving at the macro-scale. The model was fitted against longitudinal refractive measurements in tree shrews of different ages and exposed to three different visual conditions: (i) normal development; (ii) negative lens wear to induce myopia; and (iii) recovery from myopia by removing the negative lens. The model was able to replicate the age- and vision-dependent response of the tree shrew experiments. Scleral growth ceased at younger age than scleral remodeling. The remodeling rate decreased as the eye emmetropized but increased at any age when a negative lens was put on. The predictive power of the model was investigated by calculating the susceptibility to scleral remodeling and the response to form deprivation myopia in tree shrews. Both predictions were in good agreement with experimental data that were not used to fit the model. We propose the first model that distinguishes scleral growth from remodeling. The good agreement of our results with experimental data supports the notion that scleral growth and scleral remodeling are two independently controlled mechanisms during eye development.     

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.     

Solutions analytiques globales de problèmes linéaires avec argument absorbant

The aim of this work is the study of the Cauchy problem for a large class of linear operators, non-necessarily kowalevskian, with shrinking argument. We prove the well posedness of this problem in the space of analytic functions with respect to time and Gevrey class with respect to spatial variable. Our tools are based on formal norms of Leray and Waelbroeck [J. Leray, L. Waelbroeck, Norme formelle d'une fonction composée (Préliminaire à l'étude des systèmes non linéaires, hyperboliques non stricts), in: Colloque de Liège, CBRM, 1964, pp. 145-152. [23]], already used in [Cl. Wagschal, Le problème de Goursat non linéaire, J. Math. Pure Appl. 58 (1979) 309-337; D. Gourdin, M. Mechab, Solution globale d'un problème de Cauchy linéaire, J. Funct. Anal. 202 (2003) 123-146].     

Pharmazeutische Pr?parate

Ohne Zusammenfassung     

NMR and DSC investigations of the miscibility of blends of cis-1,4-polyisoprene with polybutadienes of different microstructures

Differential scanning calorimetry and torsional braid analysis investigations of the phase diagram of cis-1,4-polyisoprene/polybutadiene blends as a function of the polybutadiene microstructure were reported by several authors. Polybutadienes containing a high vinyl content were shown to be miscible with cis-1,4-polyisoprene on the DSC spatial scale, whereas polybutadienes containing a low vinyl content were immiscible. In this article, we used variable-temperature determinations of ¹H NMR free induction decays and low-temperature, high-resolution solid-state ¹³C NMR measurements of proton spin-lattice relaxation times in the rotating frame to probe the phase behavior of the cis-1,4-polyisoprene/polybutadiene blends at the smaller spatial scale of the NMR technique. Blends of cis-1,4-polyisoprene with a polybutadiene having a large number of vinyl 1,2 linkages appeared to be miscible on the molecular scale, in spite of small regions in which the polybutadiene component is not uniformily dispersed in the other polymer. On the contrary, blends in which the polybutadiene has a low content of vinyl 1,2 sequences were phase separated over the whole temperature range considered and no intermixed regions could be detected. The limiting case was observed with the polybutadiene containing 33 wt % vinyl 1,2 units, for which miscibility on a molecular scale is highly dependent on the blend composition. © 1995 John Wiley & Sons, Inc.     

Polymerization-induced Phase Separation: Phase Behavior Developments and Hydrodynamic Interaction

The process of polymer synthesis based on polymerization-induced phase separation (PIPS) is revisited from the theoretical point of view. Cahn–Hilliard–Cook theories for spinodal decomposition are adapted to describe the kinetics of phase separation and deduce the time-resolved scattering function, while the double reaction model is used to describe the kinetics of polymerization. Coupling of these two kinetics is provided by the Carother's equation relating the fraction of reacted monomers to the degree of polymerization at time t, denoted N(t). It is argued that the approach to criticality is governed by a critical parameter, χ_c, that is different from the usual parameter for spinodal decomposition, χ_s, deduced from the second derivative of the free energy. While the latter parameter depends on the reciprocal degree of polymerization N^?1(t), the former one depends on its time integral. This leads to significant consequences on the phase behavior developments during the PIPS process. Hydrodynamic interactions are found to speed up the emergence of instability modes. Although the qualitative trends remain similar to those of the Rouse dynamics, important quantitative changes are found due to the long-range viscous flow effects.     

Transmissions of quantum entangled states in anisotropic depolarizing channels

We investigate the effect of an anisotropic depolarizing channel on the classical transmission of quantum entangled states. We calculate numerically mutual information between honest parts as a function of the degree of anisotropy of the depolarizing channel. In contrast to the case of isotropic channels, we found that the mutual information depends on both the degree of anisotropy and the degree of entanglement. It increases with increase in the degree of entanglement for a quantum channel with sufficiently large depolarizing anisotropy and decreases with increase in the entanglement.