Amabile Tatone

Crawling motility through the analysis of model locomotors: two case studies.

AbstractWe study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.

Nonstandard Models for Thin-Walled Beams With a View to Applications

A direct theory of a one-dimensional structured continuum is introduced in order to study the postbuckling behavior of thin-walled beams. A simply supported beam bent by end couples is analyzed showing that, in the case of nonsymmetric cross sections, lateral buckling gives rise to imperfection sensitivity. Then an axially loaded beam is studied taking also into account the interaction between torsional and flexural buckling. The results obtained prove that in this case imperfection sensitivity, though slighter than in the previous case, arises also for symmetric cross sections.

Symbolic manipulation in buckling and postbuckling analysis

Abstract A perturbation procedure for the buckling and postbuckling analysis of elastic structures is shown to be well suited to be implemented as an automatic symbolic manipulation procedure. The postbuckling analysis of a circular arch is considered as an example, and the asymptotic description of the bifurcated equilibrium path is given. The main purposes of the automatic procedure are to generate the representation of the Frechet operator for the strain field and to perform integration by parts. This allows the manipulation of correct expressions of the basic relationships, as the strain-displacement one, without introducing any simplifying assumption or restriction. The perturbation equations are automatically generated and a solution procedure leads to parametric expressions for the coefficients of the asymptotic expansion of the bifurcated path. The symbolic manipulation system used is REDUCE.

Traction on the retina induced by saccadic eye movements in the presence of posterior vitreous detachment

Posterior vitreous detachment is a fairly common condition in elderly people. Tractions exerted by the detached vitreous on the retina may result in retinal tears and detachments. We studied how these tractions can arise from saccadic eye movements. Numerical simulations have been performed on a two-dimensional model of the vitreous chamber within a rigid spherical sclera, subjected to prescribed finite-amplitude rotations about a vertical axis. The vitreous chamber was assumed to be split into two regions: one occupied by the detached vitreous, modeled as an elastic viscous solid, and the other occupied by the separated liquefied vitreous, modeled as a Newtonian fluid. At the interface between the two phases, we also considered the presence of the vitreous cortex, modeled as an elastic membrane. We tested several different configurations of the interface. In all cases, we found that eye rotations generate large tractions on the retina close to the attachment points of the membrane. Comparing them, we identified configurations of the vitreous detachment that exhibit higher tractions. We also investigated how the response to saccadic movements depends on some physical parameters, in particular on the rheological properties of the solid phase and the membrane. The numerical simulations show that the generated tractions may be of the same order of magnitude as the adhesive force between the retina and the pigment epithelium. Therefore, the model provides a sound physical justification for the hypothesis that saccadic movements, in the presence of posterior vitreous detachment, could be responsible for high tractions on the retina, which may trigger retinal tear formation.

Vibration Damping Using CCII-Based Inductance Simulators

In this paper, we present an application of second- generation current-conveyor (CCII)-based active inductance simulators to mechanical vibration damping. The oscillation amplitude of a metallic beam, which is near some resonant frequencies, can be reduced by converting mechanical energy into electrical energy through a piezoelectric transducer that is bonded to the beam. An electric circuit, which is made up of the piezoelectric transducer, a resistance, and an inductance, accomplishes the task of dissipating the energy. To this end, the natural frequency of the circuit should be close to the natural frequency of interest of the mechanical system. The high value that is requested for the inductance (thousands of Henrys) can only be achieved through an inductance-simulator circuit. In the literature, the circuit implementations of the inductance simulators are typically based on operational amplifiers, such as the Antoniou circuit. In this paper, we make use of the CCIIs, which allow us to obtain both grounded and floating equivalent inductances that work within a regulated frequency range from three to four decades. The effectiveness of the traditional inductance simulators and CCII-based simulators is discussed, comparing the responses of an experimental mechanical-electrical system, with different circuit implementations, through experimental results. The use of series-resistance compensation, which is obtained through the use of a suitable topology based on the CCIIs, in the implementation of the equivalent inductance, allows one to obtain the best vibration damping, as confirmed by measurements, for all the natural mechanical frequencies of the realized system.

Bifurcation analysis of a circular arch under hydrostatic pressure

SommarioNel presente lavoro si studia la biforcazione di un arco circolare soggetto a pressione idrostatica nel campo elastico facendo uso di un modello di trave cinematicamente esatto. Le corrispondenti equazioni di campo nonlineari vengono risolte utilizzando una tecnica perturbativa. Vengono riportati in diagramma una serie di risultati numerici riguardanti la dipendenza del carico critico e del parametro di carico del secondo ordine dai parametri geometrici e meccanici.SummaryIn this paper the bifurcation analysis of a circular arch under hydrostatic pressure in the elastic postbuckling range is performed by means of a geometrically exact beam model. The relevant nonlinear field equations are solved by utilizing a perturbation technique. A number of numerical results regarding the dependence of the critical load and the second order load parameter on the geometric and mechanical parameters are plotted in diagrams.

Concentration wave of a solute in an artery: the influence of curvature

Mass transport and diffusion phenomena in the arterial lumen are studied through a mathematical model. Blood flow is described by the unsteady Navier–Stokes equation and solute dynamics by an advection–diffusion equation, the convective field being provided by the fluid velocity. A linearization procedure over the steady state solution is carried out and an asymptotic analysis is used to study the effect of a small curvature with respect to the straight tube. Analytical and numerical solutions are found: the results show the characteristics of the long wave propagation and the role played by the geometry on the solute distribution and demonstrate the strong influence of curvature induced by the fluid dynamics.

Using Symbolic Computation in Buckling Analysis

Asymptotic buckling analysis of elastic structures can be considered a well established procedure (Budiansky, 1974) . It consists in bifurcation analysis of a system of oneparameter differential equations: balance, compatibility and constitutive equations . The aim of this work was to experiment with the use of automatic symbolic computation in the asymptotic bifurcation analysis of elastic beams . To this end an application of the system REDUCE (Hearn, 1971) has been devised in particular for (a) the generation of the formal perturbation equations and (b) the construction of a procedure for solving a specific problem . Further details can be found in Rizzi & Tatone (1985) . A first assessment of the use of symbolic computation systems in structural mechanics can be found in Noor & Andersen (1979), while another application to the solution of perturbation problems is in Noor & Balch (1984) .

Dynamics of a Soft Contractile Body on a Hard Support

The motion of a soft and contractile body on a hard support is described by fields of short range contact forces. Besides repulsion these forces are able to describe also viscous friction, damping and adhesion allowing the body to have complex motions which look rather realistic. The contractility is used to make the body behave like a living body with some basic locomotion capabilities. The simulated motions, showing jumping or crawling, are driven either by a contraction or by a contractile couple. Although only homogeneous deformations are allowed, the model arises from a general theory of remodeling in finite elasticity. The body is made of a viscoelastic incompressible neo-Hookean material.

One-dimensional model for multilayered planar beams

A 1D model for multilayered planar beams is defined by joining 1D beam models a la Cosserat together. An interlaminar stress arises naturally from the expression of the inner working, and its singular part at the boundary as well. Local and boundary balance equations are derived from an assumed expression for the working.