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Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis…
This work is devoted to the derivation and the matematical study of a new model for water-soluble polymers and metal ions interactions, which are used in chemistry for their wide range of applications. First, we motivate and derive a model…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
Adsorption is a relevant process in many fields, such as product manufacturing or pollution remediation in porous materials. Adsorption takes place at the molecular scale, amenable to be modeled by Lagrangian numerical methods. We have…
Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work…
We construct a coarse-grained effective two-dimensional (2d) hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane.…
The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions,…
Analytical approaches describing non-Fickian diffusion in complex systems are presented. The corresponding methods are applied to the study of statistical properties of pyramidal islands formation with interacting adsorbate at epitaxial…
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in space dimensions $d\ge2$ is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies…
Hypothesis:Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular…
With the aim to characterize the formation and propagation of bulges in cylindrical rubber balloons, we carry out an expansion of the non-linear axisymmetric membrane model assuming slow axial variations. We obtain a diffuse interface model…
We consider the dynamic wetting and dewetting processes of films and droplets of complex liquids on planar surfaces, focusing on the case of colloidal suspensions, where the particle interactions can be sufficiently attractive to cause…
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
An infinite hierarchy of layering transitions exists for model polymers in solution under poor solvent or low temperatures and near an attractive surface. A flat histogram stochastic growth algorithm known as FlatPERM has been used on a…
We propose a theory of the dynamics of polymers in dilute solution, in which the popular Zimm and Rouse models are limiting cases of infinitely large and small draining parameter. The equation of motion for the polymer segments beads) is…
In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion…
A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biot's theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which…
Lagrangian particle-tracking methods are particularly suitable to study solute transport in velocity fields displaying chaotic advection. They can accurately resolve stretching and folding processes, the increase in the solute-solvent…