Related papers: A Blob Method for the Aggregation Equation
The question of energy concentration in approximate solution sequences $u^\epsilon$, as $\epsilon \to 0$, of the two-dimensional incompressible Euler equations with vortex-sheet initial data is revisited. Building on a novel identity for…
We present a new Eulerian framework for the computation of turbulent compressible multiphase channel flows, specifically to assess turbulence modulation by dispersed particulate matter in dilute concentrations but with significant mass…
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles and preserves the…
A coarse-grained multi-blob description of polymer solutions is presented, based on soft, transferable effective interactions between bonded and non-bonded blobs. The number of blobs is chosen such that the blob density does not exceed…
We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…
In recent years, an abundance of feature attribution methods for explaining neural networks have been developed. Especially in the field of computer vision, many methods for generating saliency maps providing pixel attributions exist.…
The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such…
We report experimental measurements of Lagrangian accelerations in the bulk of intense turbulent flows of dilute polymer solutions by following tracer particles with a high-speed optical tracking system. We observed a significant decrease…
Similarly-charged polyelectrolytes are known to attract each other and aggregate into bundles when the charge density of the polymers exceeds a critical value that depends on the valency of the counterions. The dynamics of aggregation of…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a…
We introduce a numerical method for solving Grad's moment equations or regularized moment equations for arbitrary order of moments. In our algorithm, we do not need explicitly the moment equations. As an instead, we directly start from the…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
In the problem of planetary formation one seeks a mechanism to gather small solid particles together into larger accumulations of solid matter. Here we describe a scenario in which turbulence mediates this process by aggregating particles…
A numerical method is presented to simulate gas-liquid-solid flows with bubble-particle interaction, including particle collision, sliding, and attachment. Gas-liquid flows are simulated in an Eulerian framework using a volume-of-fluid…
This paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called…
We consider the compressible Euler system for ideal gas flow in the absence of any forces except the internal thermodynamic pressure. In this setting, and in dimensions higher 1, it is known that wave-focusing can drive Euler solutions to…
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from $O(N^2)$ per time step to…
Anderson Acceleration is a well-established method that allows to speed up or encourage convergence of fixed-point iterations. It has been successfully used in a variety of applications, in particular within the Self-Consistent Field (SCF)…
Collocation boundary element methods for integral equations are easier to implement than Galerkin methods because the elements of the discretization matrix are given by lower-dimensional integrals. For that same reason, the matrix assembly…