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International audience; This note addresses mathematical issues raised by congestion constraints in transport equations that arise in the modeling of crowd motion or more general active entities. We address in particular the differences between the microscopic and the macroscopic settings.; Cette note aborde des questions mathématiques liées à la prise en compte de contrainte de congestion pour des équations de transport modélisant les mouvements de foules, ou plus généralement d'entités actives. Nous présentons en particulier les analogies et différences entre les cadres microscopique et macroscopique.

International audience; This note addresses mathematical issues raised by congestion constraints in transport equations that arise in the modeling of crowd motion or more general active entities. We address in particular the differences between the microscopic and the macroscopic settings.; Cette note aborde des questions mathématiques liées à la prise en compte de contrainte de congestion pour des équations de transport modélisant les mouvements de foules, ou plus généralement d'entités actives. Nous présentons en particulier les analogies et différences entre les cadres microscopique et macroscopique.

This paper establishes a link between some space discretization strategies of the Finite Volume type for the Fokker-Planck equation in general meshes (Voronoï tesselations) and gradient flows on the underlying networks of cells, in the framework of discrete Wasserstein distances on graphs recently proposed by Maas [6].

We propose and analyze a natural extension of the Moreau sweeping process: given a family of moving convex sets (C(t))t, we look for the evolution of a probability density ρt, constrained to be supported on C(t). We describe in detail three cases: in the first, particles do not interact with each other and stay at rest unless pushed by the moving boundary; in the second they interact via a maximal density constraint ρ ≤ 1, so that they are not only pushed by the boundary, but also by the other particles; in the third case particles are submitted to Brownian diffusion, reflected along the moving boundary. We prove existence, uniqueness and approximation results by using techniques from optimal transport, and we provide numerical illustrations.

Performance dentistry and equilibration is of the utmost importance for any horse which is ridden or driven. Properly done, with skill and judgment, it permits the horse to better respond to the rider or driver, minimizes fussiness on the bit, and through better mastication, improves nutrition. Every tooth must be addressed. Cheek teeth need to have sharp enamel points removed. Excessively long cheek teeth need to be reduced. Waves and ramps need to be corrected. Bit seats need to be established. Wolf teeth need to be extracted. Canine teeth need to be reduced in height and their margins rounded. Incisors need to be evaluated and corrected if necessary. Careful attention to these needs will help the horse to reach his full potential.

Studies of animal development using a 4Dmicroscopy system generate an immense amount of image data. In order to properly analyze the recorded embryogenesis, a computer-aided systematic process of categorization of cells from the image data should be accomplished. We present a software tool named LTMaker for the systematic semiautomatic identification of embryonic cells centers and also to determine the underlying linage tree. The program saves the generated data to a file so that further analysis of the embryo can be performed with external tools. Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.

The Fat Boundary Method (FBM) is a fictitious domain like method for solving partial differential equations in a domain with holes ? \ B - where B is a collection of smooth open subsets - that consists in splitting the initial problem into two parts to be coupled via Schwartz type iterations: the solution, with a fictitious domain approach, of a problem set in the whole domain ?, for which fast solvers can be used, and the solution of a collection of independent problems defined on narrow strips around the connected components of B, that can be performed fully in parallel. In this work, we give some results on a semi-discrete FBM in the framework of a finite element discretization, and we present some numerical experiments.