In this work lipid ordering phase changes arising in planar membrane bilayers is investigated bot... more In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only (Deseri and Zurlo, 2013). As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations (Espinosa et al., 2011) show a power-law in-plane viscous behavior of lipid structures allowing for an effective viscoelastic behavior of lipid membranes, which falls in the framework of Fractional Hereditariness. A suitable generalization of the variational principle invoked for the elasticity is applied in this case, and the corresponding Euler–Lagrange equation is found together with a set of boundary and initial conditions. Separation of variables allows for showing how Fractional Hereditariness owes bifurcated modes with a larger number of spatial oscillations than the corresponding elastic analog. Indeed, the available range of areal stresses for material instabilities is found to increase with respect to the purely elastic case. Nevertheless, the time evolution of the perturbations solving
ABSTRACT New finite-element models for curved beam vibration analysis are derived from classical ... more ABSTRACT New finite-element models for curved beam vibration analysis are derived from classical complementary variational principles of elastodynamics. The use of a spline approximation of the axis line (as previously introduced by the writers in the static case) allows for the a priori satisfaction of the dynamic differential equilibrium equations in a simple and effective way. More precisely, starting from the Hellinger-Reissner principle and making use of a linear interpolation of displacements and momentum fields, a very simple hybrid-mixed model is obtained that can be easily linked with general-purpose finite element packages. Alternatively, fully equilibrated models are derived from the complementary energy principle assuming as unknowns either the momentum or the stress resultant fields; in both cases highly accurate finite element models are obtained for which upper and lower bounds on eigenvalue estimates are readily available. Several examples are worked out that are capable of showing the efficiency and the wide spectrum of applicability of the proposed method. The comparison with two general-purpose finite element packages of large diffusion let us assess the high level of performance of the complementary energy models for curved elements.
Coherent angular rotation of epithelial cells is thought to contribute to many vital physiologica... more Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed, remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements.
Elasticity is viewed here as a starting point in the description of in- elastic behavior. The two... more Elasticity is viewed here as a starting point in the description of in- elastic behavior. The two-scale geometry provided by structured defor- mations and a fleld theory of elastic bodies undergoing disarrangements (non-smooth geometrical changes) and dissipation are used to formulate and illustrate a concept of "submacroscopically stable conflguration." A body in a submacroscopically stable equilibrium conflguration resists ad- ditional
In this work lipid ordering phase changes arising in planar membrane bilayers is investigated bot... more In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only (Deseri and Zurlo, 2013). As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations (Espinosa et al., 2011) show a power-law in-plane viscous behavior of lipid structures allowing for an effective viscoelastic behavior of lipid membranes, which falls in the framework of Fractional Hereditariness. A suitable generalization of the variational principle invoked for the elasticity is applied in this case, and the corresponding Euler–Lagrange equation is found together with a set of boundary and initial conditions. Separation of variables allows for showing how Fractional Hereditariness owes bifurcated modes with a larger number of spatial oscillations than the corresponding elastic analog. Indeed, the available range of areal stresses for material instabilities is found to increase with respect to the purely elastic case. Nevertheless, the time evolution of the perturbations solving
ABSTRACT New finite-element models for curved beam vibration analysis are derived from classical ... more ABSTRACT New finite-element models for curved beam vibration analysis are derived from classical complementary variational principles of elastodynamics. The use of a spline approximation of the axis line (as previously introduced by the writers in the static case) allows for the a priori satisfaction of the dynamic differential equilibrium equations in a simple and effective way. More precisely, starting from the Hellinger-Reissner principle and making use of a linear interpolation of displacements and momentum fields, a very simple hybrid-mixed model is obtained that can be easily linked with general-purpose finite element packages. Alternatively, fully equilibrated models are derived from the complementary energy principle assuming as unknowns either the momentum or the stress resultant fields; in both cases highly accurate finite element models are obtained for which upper and lower bounds on eigenvalue estimates are readily available. Several examples are worked out that are capable of showing the efficiency and the wide spectrum of applicability of the proposed method. The comparison with two general-purpose finite element packages of large diffusion let us assess the high level of performance of the complementary energy models for curved elements.
Coherent angular rotation of epithelial cells is thought to contribute to many vital physiologica... more Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed, remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements.
Elasticity is viewed here as a starting point in the description of in- elastic behavior. The two... more Elasticity is viewed here as a starting point in the description of in- elastic behavior. The two-scale geometry provided by structured defor- mations and a fleld theory of elastic bodies undergoing disarrangements (non-smooth geometrical changes) and dissipation are used to formulate and illustrate a concept of "submacroscopically stable conflguration." A body in a submacroscopically stable equilibrium conflguration resists ad- ditional
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Papers by Luca Deseri