New experimental evidence of self-motion a confined active suspension is presented. Depositing fresh semen sample in an annular shaped microfluidic chip leads to spontaneous vortex state the fluid at sufficiently large sperm concentration. The rotation occurs unpredictably clockwise or counterclockwise and robust stable. Furthermore, for highly concentrated semen, richer dynamics can occur such as self-sustained damped oscillations. Experimental results obtained with systematic dilution...

For the thin obstacle problem, we develop a unified approach that leads to rates of convergence blow-up profiles at contact points with integer frequencies. these points, also obtain stratification result.

We design and analyze up to third order accurate discontinuous Galerkin (DG) methods satisfying a strict maximum principle for Fokker--Planck equations. A procedure is established identify an effective test set in each computational cell ensure the desired bounds of numerical averages during time evolution. This achievable by taking advantage two parameters flux novel decomposition weighted averages. Based on this result, scaling limiter DG method with first Euler forward discretization...

Myxobacteria are social bacteria, that can glide in two dimensions and form counter-propagating, interacting waves. Here, we present a novel age-structured, continuous macroscopic model for the movement of myxobacteria. The derivation is based on microscopic interaction rules be formulated as particle-based set within Self-Organized Hydrodynamics (SOH) framework. strength this combined approach knowledge or data incorporated easily into particle model, whilst allows easy numerical analysis...

For the obstacle problem involving a convex fully nonlinear elliptic operator, we show that singular set in free boundary stratifies. The top stratum is locally covered by C^{1,\alpha} manifold, and lower strata are C^{1,\log^\varepsilon} manifolds. This recovers some of recent regularity results due to Colombo–Spolaor–Velichkov (2018) Figalli–Serra (2019) when operator Laplacian.

A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists introducing hydrodynamic scaling the corresponding mean field kinetic equation. resulting perturbation problem solved thanks to concept generalized collision invariants. It yields hyperbolic but non-conservative system equations direction flow and densities flowing parallel or anti-parallel this direction. Diffusive terms are...

In this paper, we propose an entropy satisfying conservative method to solve the Fokker–Planck equation of finitely extensible nonlinear elastic dumbbell model for polymers, subject homogeneous fluids. Both semidiscrete and fully discrete schemes satisfy all three desired properties—(i) mass conservation, (ii) positivity preserving, (iii) satisfying—in sense that these inequalities both physical quadratic entropy. These ensure computed solution is a probability density are stable preserve...

Abstract We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is coupled Vicsek–Stokes system. Vicsek model describes agents interacting through alignment. It provides phenomenological description of hydrodynamic interactions between at high density. Stokes equations describe low Reynolds number These two are by the interaction and fluid contributes to rotating Jeffery’s equation. Particle self-propulsion induces force dipole on After coarse-graining we...

For $0<p<+\infty$, we prove a global $W^{2,p}$-estimate for potentials of optimal transport maps between convex domains in the plane. Among tools developed that purpose are obliqueness general and estimates growth eccentricity sections potentials.

We develop a new moving-water equilibria preserving numerical scheme for the Saint-Venant system. The is designed in two major steps. First, geometric source term incorporated into discharge flux, which results hyperbolic system with global flux. Second, equation relaxed so that nonlinearity moved stiff right-hand side of added auxiliary equation. main advantages are (i) no special treatment required, and (ii) nonlinear (cubic) equations should be solved to obtain point values water depth...

Abstract We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when free boundary is graph of a continuous function, solution half-plane solution. This answers, in salient analogue Bernstein’s for minimal surfaces. As an application, also classify monotone semilinear equations with bump-type nonlinearity.

We study global solutions to the thin obstacle problem with at most quadratic growth infinity. show that every ellipsoid can be realized as contact set of such a solution. On other hand, if solution has compact set, we it must an ellipsoid.

The Self-Organized Hydrodynamics model of collective behavior is studied on an annular domain. A modal analysis the linearized around a perfectly polarized steady-state conducted. It shows that has only pure imaginary modes in countable number and hence stable. Numerical computations low-order are provided. fully non-linear numerically solved nonlinear mode-coupling then analyzed. Finally, efficiency decomposition to analyze complex features demonstrated.

Connectivity plays an crucial role in measuring the fault tolerance of a multiprocessor system case vertices failures. Extra connectivity is important indicator network's ability for diagnosis and tolerance. In this paper, we analyse n,k-dimensional enhanced hypercube, well-known interconnection network denoted by Qn,k proposed systems, establish {1,2,3}-extra Qn,k.

ABSTRACT A reverse flow diverter (RFD) is a key fluidic component in RFD pumps, which are air‐powered, low‐maintenance devices used for transferring hazardous liquids. Despite several decades of practical application, no clear characteristic numbers exist the suction ratio q = 1.0 and peak value , nor there dimensionless performance curves reverse‐flow portion pumping cycle. We experimentally investigated effects gap length nozzle exit diameter on pressure under condition diffuser entrance...