Colossal Atomic Force Response in van der Waals Materials Arising From Electronic Correlations

Understanding static and dynamic phenomena in complex materials at different length scales requires reliably accounting for van der Waals (vdW) interactions, which stem from long-range electronic correlations. While the important role of many-body vdW interactions has been extensively documented when it comes to the stability of materials, much less is known about the coupling between vdW interactions and atomic forces. Here we analyze the Hessian force response matrix for a single and two vdW-coupled atomic chains to show that a many-body description of vdW interactions yields atomic force response magnitudes that exceed the expected pairwise decay by 3-5 orders of magnitude for a wide range of separations between the perturbed and the observed atom. Similar findings are confirmed for graphene and carbon nanotubes. This colossal force enhancement suggests implications for phonon spectra, free energies, interfacial adhesion, and collective dynamics in materials with many interacting atoms

From quantum to continuum mechanics in the delamination of atomically-thin layers from substrates

Anomalous proximity effects have been observed in adhesive systems ranging from proteins, bacteria, and gecko feet suspended over semiconductor surfaces to interfaces between graphene and different substrate materials. In the latter case, long-range forces are evidenced by measurements of non-vanishing stress that extends up to micrometer separations between graphene and the substrate. State-of-the-art models to describe adhesive properties are unable to explain these experimental observations, instead underestimating the measured stress distance range by 2–3 orders of magnitude. Here, we develop an analytical and numerical variational approach that combines continuum mechanics and elasticity with quantum many-body treatment of van der Waals dispersion interactions. A full relaxation of the coupled adsorbate/substrate geometry leads us to conclude that wavelike atomic deformation is largely responsible for the observed long-range proximity effect. The correct description of this seemingly general phenomenon for thin deformable membranes requires a direct coupling between quantum and continuum mechanics

Combining polynomial chaos expansions and genetic algorithm for the coupling of electrophysiological models

The number of computational models in cardiac research has grown over the last decades. Every year new models with di erent assumptions appear in the literature dealing with di erences in interspecies cardiac properties. Generally, these new models update the physiological knowledge using new equations which reect better the molecular basis of process. New equations require the fi tting of parameters to previously known experimental data or even, in some cases, simulated data. This work studies and proposes a new method of parameter adjustment based on Polynomial Chaos and Genetic Algorithm to nd the best values for the parameters upon changes in the formulation of ionic channels. It minimizes the search space and the computational cost combining it with a Sensitivity Analysis. We use the analysis of di ferent models of L-type calcium channels to see that by reducing the number of parameters, the quality of the Genetic Algorithm dramatically improves. In addition, we test whether the use of the Polynomial Chaos Expansions improves the process of the Genetic Algorithm search. We conclude that it reduces the Genetic Algorithm execution in an order of 103 times in the case studied here, maintaining the quality of the results. We conclude that polynomial chaos expansions can improve and reduce the cost of parameter adjustment in the development of new models.Peer ReviewedPostprint (author's final draft

Mesh, geometry and boundary conditions for the incompressible Navier-Stokes problem.

<p>Mesh, geometry and boundary conditions for the incompressible Navier-Stokes problem.</p

Elastic bar with stochastic Young’s modulus.

<p>Elastic bar with stochastic Young’s modulus.</p

Mesh, geometry and boundary conditions for the incompressible Navier-Stokes problem.

<p>Mesh, geometry and boundary conditions for the incompressible Navier-Stokes problem.</p

Second sensitivity derivative of the expected value of the strain with respect to the Young’s modulus for the Kelvin-Voigt model.

<p>Comparison between the exact solution solution and the MWS method. The Young’s modulus is modelled with a log-normal distribution. For the MWS method, <i>Z</i> = 10⁷ realisations are performed. Note that the value of <i>Z</i> for the same order of magnitude for the error is higher for the second derivative compared to the first derivative because the variance <i>V</i> in the Malliavin estimator is bigger and we know from the central limit theorem that the error is in .</p

Hyperelastic beam: Mesh and schematic of boundary conditions.

<p>(1) a realisation of the problem where there is a geometric instability (buckling) and (2) another without.</p

Velocity magnitude at time <i>t</i> = 1 s for one realisation of the viscosity.

<p>Velocity magnitude at time <i>t</i> = 1 s for one realisation of the viscosity.</p

Malliavin derivative of the expected value of the strain with respect to the loading <i>σ</i>₀ for the Kelvin-Voigt model with uncertain stress modelled as a Gaussian random variable.

<p>Comparison between the exact solution, the MWS method and the the MWS-steady-state method with a correction using the correlation function to improve the convergence of the MWS method when the system transitions into the steady state. For the MWS method we use <i>Z</i> = 20000 realisations at each time step.</p