01955nas a2200145   4500008004100000245009100041210006900132260006400201520139800265100002701663700002201690700002101712700002501733856005101758       2014                        en  d00aAn effective model for nematic liquid crystal composites with ferromagnetic inclusions0 aeffective model for nematic liquid crystal composites with ferro  bSociety for Industrial and Applied Mathematics Publications3 aMolecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature.1 aCalderer, Maria, Carme1 aDeSimone, Antonio1 aGolovaty, Dmitry1 aPanchenko, Alexander  uhttp://urania.sissa.it/xmlui/handle/1963/3494001548nas a2200157   4500008004300000245008600043210006900129260005100198300001400249490000800263520101800271100002101289700002201310700002201332856003601354       2011                        en_Ud  00aAn Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers0 aExistence and Uniqueness Result for the Motion of SelfPropelled   bSociety for Industrial and Applied Mathematics  a1345-13680 v 433 a<p>We present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.</p>1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco  uhttp://hdl.handle.net/1963/389401258nas a2200145   4500008004300000245008600043210006900129260001700198520078200215100002300997700001801020700002201038700001601060856003601076       2004                        en_Ud  00aEnergetics and switching of quasi-uniform states in small ferromagnetic particles0 aEnergetics and switching of quasiuniform states in small ferroma  bEDP Sciences3 aWe present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size.1 aAlouges, François1 aConti, Sergio1 aDeSimone, Antonio1 aPokern, Ivo  uhttp://hdl.handle.net/1963/2999