Γ\Gamma-convergence analysis of a generalized XYXY model: fractional vortices and string defects

We propose and analyze a generalized two dimensional $XY$ model, whose interaction potential has $n$ weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by $\Gamma$-convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The $\Gamma$-limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings. Our model describes in a simple way several topological singularities arising in Physics and Materials Science. Among them, disclinations and string defects in liquid crystals, fractional vortices and domain walls in micromagnetics, partial dislocations and stacking faults in crystal plasticity

Ground states of a two phase model with cross and self attractive interactions

We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations

Multiscale modeling of synthetic and biological supramolecular systems.

In this thesis, we exploited the synergistic combination of multiscale molecular modeling, molecular dynamics (MD), and enhanced sampling to tackle two complex systems. In the first case study, we investigated the intrinsic dynamic behavior of a Benzene 1,3,5-TricarboxAmide (BTA) supramolecular polymer in water. In the second case study, we inquired about the effect of functionalized amphiphilic gold nanoparticles (Au NPs) on the phase behavior of a multi-component lipid membrane. Through our simulations, we gained a deeper understanding of the structure and dynamics of a class of supramolecular polymers. Additionally, we identified the factors that control the exchange of monomers between the different fibers, which can be used to inform the design of novel supramolecular materials in the future. Our simulations provided insights into the mechanisms underlying the interaction between functionalized nanoparticles and lipid membranes, extrapolating the factors that influence the stability of the membrane phase separation. The acquired knowledge can be applied in drug delivery systems or to create new hybrid materials containing ordered two-dimensional NP lattices. In particular, it is worth noting that in both studies, using coarse-grained models with the proper (sub-molecular) resolution was crucial to overcoming the limitations of classic all-atom force fields while maintaining the needed chemical specificity. Overall, the results of these studies have broad implications for materials science and biophysics and demonstrate the potential of computational modeling to inform the design of novel materials and systems

Semidiscrete Modeling of Systems of Wedge Disclinations and Edge Dislocations via the Airy Stress Function Method

We present a variational theory for lattice defects of rotational and translational type. We focus on finite systems of planar wedge disclinations, disclination dipoles, and edge dislocations, which we model as the solutions to minimum problems for isotropic elastic energies under the constraint of kinematic incompatibility. Operating under the assumption of planar linearized kinematics, we formulate the mechanical equilibrium problem in terms of the Airy stress function, for which we introduce a rigorous analytical formulation in the context of incompatible elasticity. Our main result entails the analysis of the energetic equivalence of systems of disclination dipoles and edge dislocations in the asymptotics of their singular limit regimes. By adopting the regularization approach via core radius, we show that, as the core radius vanishes, the asymptotic energy expansion for disclination dipoles coincides with the energy of finite systems of edge dislocations. This proves that Eshelby's kinematic characterization of an edge dislocation in terms of a disclination dipole is exact also from the energetic standpoint

Audio-vestibular symptoms in systemic autoimmune diseases

Immune-mediated inner ear disease can be primary, when the autoimmune response is against the inner ear, or secondary. The latter is characterized by the involvement of the ear in the presence of systemic autoimmune conditions. Sensorineural hearing loss is the most common audiovestibular symptom associated with systemic autoimmune diseases, although conductive hearing impairment may also be present. Hearing loss may present in a sudden, slowly, rapidly progressive or fluctuating form, and is mostly bilateral and asymmetric. Hearing loss shows a good response to corticosteroid therapy that may lead to near-complete hearing restoration. Vestibular symptoms, tinnitus, and aural fullness can be found in patients with systemic autoimmune diseases; they often mimic primary inner ear disorders such as Menière’s disease and mainly affect both ears simultaneously. Awareness of inner ear involvement in systemic autoimmune diseases is essential for the good response shown to appropriate treatment. However, it is often misdiagnosed due to variable clinical presentation, limited knowledge, sparse evidence, and lack of specific diagnostic tests. The aim of this review is to analyse available evidence, often only reported in the form of case reports due to the rarity of some of these conditions, of the different clinical presentations of audiological and vestibular symptoms in systemic autoimmune diseases

The influence of spatial variability on 2D reactive transport simulations

International audienceIn reactive transport simulations, the effects of the spatial variability of geological media are generally neglected. The impact of this variability is systematically examined here in 2D simulations, with a simple geometry and chemistry with a positive feedback: increase of porosity and of permeability during calcite dissolution. The results highlight the leading role in these conditions of: (i) the correlation length of porosity and of permeability; and (ii) the kinematic dispersivity, whose effects are dominant compared to those of variance and reaction kinetics. The impact of stochastic variability (between several randomdraws) is also significant, as it is of the same order of magnitude as the impact of the range and dispersivity

Equivalent block transmissivity in an irregular 2D polygonal grid for one-phase flow: a sensitivity analysis

International audienceUpscaling is needed to transform the representation of non additive space-dependent variables, such as permeability, from the fine grid of geostatistical simulations (to simulate small scale spatial variability) to the coarser, generally irregular grids for hydrodynamic transport codes. A new renormalisation method is proposed, based on the geometric properties of a Voronoï grid. It is compared to other classic methods by a sensitivity analysis (grid, range and sill of the variogram, random realisation of a simulation); the criterion is the flux of a tracer at the outlet. The effect of the upscaling technique on the results appears to be of second order compared to the spatial discretisation, the choice of variogram, and the realisation