02343nas a2200241   4500008004100000020001400041245008300055210006900138260001500207490000800222520159500230653002401825653002601849653002201875653002101897653001901918653002501937100002601962700002901988700002202017700002502039856003702064       2022                        eng d  a0170-421400aMathematical modelling of oscillating patterns for chronic autoimmune diseases0 aMathematical modelling of oscillating patterns for chronic autoi  c2022/04/010 vn/a3 a<p>Many autoimmune diseases are chronic in nature, so that in general, patients experience periods of recurrence and remission of the symptoms characterizing their specific autoimmune ailment. In order to describe this very important feature of autoimmunity, we construct a mathematical model of kinetic type describing the immune system cellular interactions in the context of autoimmunity exhibiting recurrent dynamics. The model equations constitute a nonlinear system of integro-differential equations with quadratic terms that describe the interactions between self-antigen presenting cells, self-reactive T cells, and immunosuppressive cells. We consider a constant input of self-antigen presenting cells, due to external environmental factors that are believed to trigger autoimmunity in people with predisposition for this condition. We also consider the natural death of all cell populations involved in our model, caused by their interaction with cells of the host environment. We derive the macroscopic analogue and show positivity and well-posedness of the solution and then we study the equilibria of the corresponding dynamical system and their stability properties. By applying dynamical system theory, we prove that steady oscillations may arise due to the occurrence of a Hopf bifurcation. We perform some numerical simulations for our model, and we observe a recurrent pattern in the solutions of both the kinetic description and its macroscopic analogue, which leads us to conclude that this model is able to capture the chronic behaviour of many autoimmune diseases.</p>10aautoimmune diseases10acellular interactions10aDynamical systems10aHopf bifurcation10akinetic theory10amathematical biology1 aDella Marca, Rossella1 aRamos, Maria, da Piedade1 aRibeiro, Carolina1 aSoares, Ana, Jacinta  uhttps://doi.org/10.1002/mma.822902026nas a2200205   4500008004100000022001400041245009500055210006900150300001100219520136500230653002001595653002401615653001701639653002101656100002501677700002701702700002201729700002201751856004701773       2019                        eng d  a0022-509600aNutations in growing plant shoots: The role of elastic deformations due to gravity loading0 aNutations in growing plant shoots The role of elastic deformatio  a1037023 a<p>The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.</p>10aCircumnutations10aFlutter instability10aGravitropism10aHopf bifurcation1 aAgostinelli, Daniele1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio  uhttps://doi.org/10.1016/j.jmps.2019.103702