arXiv subjects

Alessandro Musesti

Publications and source records attributed to Alessandro Musesti.

8 recordsLinked to original sources

arXiv2024

Thermal convection in a higher velocity gradient and higher temperature gradient fluid

We analyse a model for thermal convection in a class of generalized Navier-Stokes equations containing fourth order spatial derivatives of the velocity and of the temperature. The work generalises the isothermal model of A. Musesti. We derive critical Rayleigh and wavenumbers for the onset of convective fluid motion paying careful attention to the variation of coefficients of the highest derivatives. In addition to linear instability theory we include an analysis of fully nonlinear stability theory. The theory analysed possesses a bi-Laplacian term for the velocity field and also for the temperature field. It was pointed out by E. Fried and M. Gurtin that higher order terms represent micro-length effects and these phenomena are very important in flows in microfluidic situations. We introduce temperature into the theory via a Boussinesq approximation where the density of the body force term is allowed to depend upon temperature to account for buoyancy effects which arise due to expansion of the fluid when this is heated. We analyse a meaningful set of boundary conditions which are introduced by Fried and Gurtin as conditions of strong adherence, and these are crucial to understand the effect of the higher order derivatives upon convective motion in a microfluidic scenario where micro-length effects are paramount. The basic steady state is the one of zero velocity, but in contrast to the classical theory the temperature field is nonlinear in the vertical coordinate. This requires care especially dealing with nonlinear theory and also leads to some novel effects.

physics.flu-dyn↗

arXiv2018

Strain-dependent internal parameters in hyperelastic biological materials

The behavior of hyperelastic energies depending on an internal parameter, which is a function of the deformation gradient, is discussed. As an example, the analysis of two models where the parameter describes the activation of a tetanized skeletal muscle tissue is presented. In those models, the activation parameter depends on the strain and it is shown the importance of considering the derivative of the parameter with respect to the strain in order to capture the proper stress-strain relations.

q-bio.TO↗

arXiv2017

A comparison between active strain and active stress in transversely isotropic hyperelastic materials

Active materials are media for which deformations can occur in absence of loads, given an external stimulus. Two approaches to the modeling of such materials are mainly used in literature, both based on the introduction of a new tensor: an additive stress $\mathsf{P}_\text{act}$ in the active stress case and a multiplicative strain $\mathsf{F}_a$ in the active strain one. Aim of this paper is the comparison between the two approaches on simple shears. Considering an incompressible and transversely isotropic material, we design constitutive relations for $\mathsf{P}_\text{act}$ and $\mathsf{F}_a$ so that they produce the same results for a uniaxial deformation along the symmetry axis. We then study the two approaches in the case of a simple shear deformation. In a hyperelastic setting, we show that the two approaches produce different stress components along a simple shear, unless some necessary conditions on the strain energy density are fulfilled. However, such conditions are very restrictive and rule out the usual elastic strain energy functionals. Active stress and active strain therefore produce different results in shear, even if they both fit uniaxial data. Our results show that experimental data on the stress-stretch response on uniaxial deformations are not enough to establish which activation approach can capture better the mechanics of active materials. We conclude that other types of deformations, beyond the uniaxial one, should be taken into consideration in the modeling of such materials.

cond-mat.soft↗

arXiv2017

A continuum model of skeletal muscle tissue with loss of activation

We present a continuum model for the mechanical behavior of the skeletal muscle tissue when its functionality is reduced due to aging. The loss of ability of activating is typical of the geriatric syndrome called sarcopenia. The material is described by a hyperelastic, polyconvex, transverse isotropic strain energy function. The three material parameters appearing in the energy are fitted by least square optimization on experimental data, while incompressibility is assumed through a Lagrange multiplier representing the hydrostatic pressure. The activation of the muscle fibers, which is related to the contraction of the sarcomere, is modeled by the so called active strain approach. The loss of performance of an elder muscle is then obtained by lowering of some percentage the active part of the stress. The model is implemented numerically and the obtained results are discussed and graphically represented.

q-bio.TO↗

arXiv2016

A nonlinear Korn inequality based on the Green-Saint Venant strain tensor

A nonlinear Korn inequality based on the Green-Saint Venant strain tensor is proved, whenever the displacement is in the Sobolev space $W^{1,p}$, $p\geq 2$, under Dirichlet conditions on a part of the boundary. The inequality can be useful in proving the coercivity of a nonlinear elastic energy.

math-ph↗

arXiv2015

An optimal bound on the number of moves for open Mancala

We determine the optimal bound for the maximum number of moves required to reach a periodic configuration of open mancala (also called open owari), inspired by a popular African game. A mancala move can be interpreted as a map from the set of compositions of a given integer in itself, thus relating our result to the study of the corresponding finite dynamical system.

math.CO↗

arXiv2014

Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number

The paper is devoted to the study of the motion of one-dimensional rigid bodies during a free fall in a quasi-Newtonian hyperviscous fluid at low Reynolds number. We show the existence of a steady solution and furnish sufficient conditions on the geometry of the body in order to get purely translational motions. Such conditions are based on a generalized version of the so-called Reciprocal Theorem for fluids.

math-ph↗

arXiv2014

Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids

We consider the free fall of slender rigid bodies in a viscous incompressible fluid. We show that the dimensional reduction (DR), performed by substituting the slender bodies with one-dimensional rigid objects, together with a hyperviscous regularization (HR) of the Navier--Stokes equation for the three-dimensional fluid lead to a well-posed fluid-structure interaction problem. In contrast to what can be achieved within a classical framework, the hyperviscous term permits a sound definition of the viscous force acting on the one-dimensional immersed body. Those results show that the DR/HR procedure can be effectively employed for the mathematical modeling of the free fall problem in the slender-body limit.

math-ph↗