Related papers: A Deflation Technique for Detecting Multiple Liqui…
Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterise convection but are still too coarse to fully resolve it. Recently, numerical solutions of…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
Extreme and isolated eigenvalues are known to be harmful to the convergence of an iterative solver. These eigenvalues can be produced by strong heterogeneity in the underlying physics. We can improve the quality of the spectrum by…
Microgrids are recognized as a relevant tool to absorb decentralized renewable energies in the energy mix. However, the sequential handling of multiple stochastic productions and demands, and of storage, make their management a delicate…
We develop a flux-conservative formalism for a Newtonian multi-fluid system, including dissipation and entrainment (i.e. allowing the momentum of one fluid to be a linear combination of the velocities of all fluids). Maximum use is made of…
A thorough backward stability analysis of Hotelling's deflation, an explicit external deflation procedure through low-rank updates for computing many eigenpairs of a symmetric matrix, is presented. Computable upper bounds of the loss of the…
Research on transport, self-assembly and defect dynamics within confined, flowing liquid crystals requires versatile and computationally efficient mesoscopic algorithms to account for fluctuating nematohydrodynamic interactions. We present…
We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence…
This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on the results of [14] for…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem can be solved, in principle, using real quantifier…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
We study a deflation method to reduce and to solve linear dfferential-algebraic equations (DAEs). It consists to define a sequence of DAEs with index reduction of one unit by step. This is simultaneously performed by substitution and…
Deflation techniques are typically used to shift isolated clusters of small eigenvalues in order to obtain a tighter distribution and a smaller condition number. Such changes induce a positive effect in the convergence behavior of Krylov…
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…
Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the…
When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a…
Arclength continuation and branch switching are enormously successful algorithms for the computation of bifurcation diagrams. Nevertheless, their combination suffers from three significant disadvantages. The first is that they attempt to…
We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…
An ongoing problem in the study of a classical many-body system is the characterization of its equilibrium behaviour by theory or numerical simulation. For purely repulsive particles, locating the melting line in the pressure-temperature…