We consider a geometric motion associated with the minimization of a curvature dependent functional, which is related to the Willmore functional. Such a functional arises in connection with the image segmentation problem in computer vision theory. We show by using formal asymptotics that the geometric motion can be approximated by the evolution of the zero level set of the solution of a nonlinear fourth-order equation related to the Cahn-Hilliard and Allen-Cahn equations.

Objective: Customization of the rate of drug delivered based on individual patient requirements is of paramount importance in the design of drug delivery devices. Advances in manufacturing may enable multilayer drug delivery devices with different initial drug distributions in each layer. However, a robust mathematical understanding of how to optimize such capabilities is critically needed. The objective of this work is to determine the initial drug distribution needed in a spherical drug delivery device such as a capsule in order to obtain a desired drug release profile.

The dynamics and rheology of a vesicle confined in a channel under shear flow are studied at finite temperature. The effect of finite temperature on vesicle motion and system viscosity is investigated. A two-dimensional numerical model, which includes thermal fluctuations and is based on a combination of molecular dynamics and mesoscopic hydrodynamics, is used to perform a detailed analysis in a wide range of the Peclet numbers (the ratio of the shear rate to the rotational diffusion coefficient).

We present LBcuda, a GPU accelerated version of LBsoft, our open-source MPI-based software for the simulation of multi-component colloidal flows. We describe the design principles, the optimization and the resulting performance as compared to the CPU version, using both an average cost GPU and high-end NVidia GPU cards (V100 and the latest A100). The results show a substantial acceleration for the fluid solver reaching up to 200 GLUPS (Giga Lattice Updates Per Second) on a cluster made of 512 A100 NVIDIA cards simulating a grid of eight billion lattice points.

A suspension of nanoparticles with very low volume fraction is found to assemble into a macroscopic cellular phase that is composed of particle-rich walls and particle-free voids under the collective influence of AC and DC voltages. Systematic study of this phase transition shows that it was the result of electrophoretic assembly into a two-dimensional configuration followed by spinodal decomposition into particle-rich walls and particle-poor cells mediated principally by electrohydrodynamic flow.

We study some properties of a nonconvex variational problem. The infimum of the functional that has to be minimized fails to be attained. Instead, minimizing sequences develop gradient oscillations which allow them to decrease the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original non perturbed problem is analyzed numerically.

Drug-coated balloons (DCBs) are used commonly for delivering drug into diseased arteries. When applied on the inner surface of an artery, drug is transported from the balloon into the multilayer arterial wall through diffusion and advection, where it is ultimately absorbed through binding reactions. Mathematical modeling of these mass transport processes has the potential to help understand and optimize balloon-based drug delivery, thereby ensuring both safety and efficacy.

In this paper we propose a modeling setting and a numerical Riemann problem solver at the junction of one dimensional shallow-water channel networks. The junction conditions take into account the angles with which the channels intersect and include the possibility of channels with different sections. The solver is illustrated with several numerical tests which underline the importance of the angle dependence to obtain reliable solutions.

In this perspective we take stock of the current state of the art of computational models for droplets microfluidics and we suggest some strategies which may open the way to the full-scale simulation of microfluidic phenomena with interfaces, from near-contact interactions to the device operational lengths.

We report new dynamical modes in confined soft granular flows, such as stochastic jetting and dripping, with no counterpart in continuum viscous fluids. The new modes emerge as a result of the propagation of the chaotic behavior of individual grains - here, monodisperse emulsion droplets - to the level of the entire system as the emulsion is focused into a narrow orifice by an external viscous flow. We observe avalanching dynamics and the formation of remarkably stable jets - single-file granular chains - which occasionally break, resulting in a non-Gaussian distribution of cluster sizes.