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Stabilization of the inverted pendulum on a skate
No full textIn the classical control theory literature, the inverted pendulum
stabilization problem has been addressed in two ways: as an
application of the vibrational control principle, or by imagining
that the pivot is on a cart moved according to a suitable feedback
law. Several other stabilization methods have been recently
proposed.
In this paper we propose a new approach: the
pendulum is assembled on an ice skate, subject to some
constraints and equipped with a driving device. The upper
equilibrium position is stabilized provided that the speed of the
skate is sufficiently large
Reconstruction of the local contractility of the cardiac muscle from deficient apparent kinematics
Full text linkActive solids are a large class of materials, including both living soft tissues and artificial matter,
that share the ability to undergo strain even in absence of external loads. While in engineered
materials the actuation is typically designed a priori, in natural materials it is an unknown of
the problem. In such a framework, the identification of inactive regions in active materials is of
particular interest. An example of paramount relevance is cardiac mechanics and the assessment
of regions of the cardiac muscle with impaired contractility. The impossibility to measure the
local active forces directly suggests us to develop a novel methodology exploiting kinematic
data from clinical images by a variational approach to reconstruct the local contractility of
the cardiac muscle. By finding the stationary points of a suitable cost functional we recover
the contractility map of the muscle. Numerical experiments, including severe conditions with
added noise to model uncertainties, and data knowledge limited to the boundary, demonstrate
the effectiveness of our approach. Unlike other methods, we provide a spatially continuous
recovery of the contractility map without compromising the computational efficiency
Bifurcation analysis of pressure-induced detachment of a rod adhered to a plate
No full textWe study the lift of an elastica adhering to a flat rigid surface induced by a pressure difference. Adhesion is modelled by a cohesive force that decreases linearly with separation. Using a nonlinear local analysis, we determine the bifurcation diagram that governs the peeling process under quasi-static conditions. We show that the delamination emerges through a discontinuous transition: a normal form of the bifurcation diagram allows us to draw in a simple way the main physical mechanism, elucidating the local validity of the theory at the transition. We predict that the pressure, as a function of the detachment length, undergoes an initial drop followed by an approximately constant behaviour, while the detachment length at the transition is always finite and is roughly proportional to the elasto-adhesion length. This analysis can be the starting point to understand more complex-related problems that arise in fracture mechanics or in biology, such as testing of adhesives in a flowfield and the arterial dissection
Activation of a muscle as a mapping of stress-strain curves
Full text linkThe mathematical modeling of the contraction of a muscle is a crucial problem
in biomechanics. Several different models of muscle activation exist in
literature. A possible approach to contractility is the so-called active
strain: it is based on a multiplicative decomposition of the deformation
gradient into an active contribution, accounting for the muscle activation, and
an elastic one, due to the passive deformation of the body.
We show that the active strain approach does not allow to recover the
experimental stress-stretch curve corresponding to a uniaxial deformation of a
skeletal muscle, whatever the functional form of the strain energy. To overcome
such difficulty, we introduce an alternative model, that we call mixture active
strain approach, where the muscle is composed of two different solid phases and
only one of them actively contributes to the active behavior of the muscle
Strain energy storage and dissipation rate in active cell mechanics
Full text linkWhen living cells are observed at rest on a flat substrate, they can typically exhibit a rounded (symmetric) or an elongated (polarized) shape. Although the cells are apparently at rest, the active stress generated by the molecular motors continuously stretches and drifts the actin network, the cytoskeleton of the cell. In this paper we theoretically compare the energy stored and dissipated in this active system in two geometric configurations of interest: symmetric and polarized. We find that the stored energy is larger for a radially symmetric cell at low activation regime, while the polar configuration has larger strain energy when the active stress is beyond a critical threshold. Conversely, the dissipation of energy in a symmetric cell is always larger than that of a nonsymmetric one. By a combination of symmetry arguments and competition between surface and bulk stress, we argue that radial symmetry is an energetically expensive metastable state that provides access to an infinite number of lower-energy states, the polarized configurations
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