Related papers: Fisher equation with turbulence in one dimension
We consider the fractional unforced Burgers equation in the one-dimensional space-periodic setting: $$\partial u/\partial t+(f(u))_x +\nu \Lambda^{\alpha} u= 0, t \geq 0,\ \mathbb{x} \in \mathbb{T}^d=(\mathbb{R}/\mathbb{Z})^d.$$ Here $f$ is…
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
A viscous instability in shearing laminar axisymmetric hydrodynamic flows around a gravitating center is described. In the linearized hydrodynamic equations written in the Boussinesq approximation with microscopic molecular transport…
Run-and-tumble is a basic model of persistent motion and a motility strategy widespread in micro-organisms and individual cells. In many natural settings, movement occurs in the presence of confinement. While accumulation at the surface has…
In this Letter, we study the collective behaviour of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedently large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We…
We study the radial distribution of pressure, density, temperature and flow velocity fields at different times in a two dimensional hard sphere gas that is initially at rest and disturbed by injecting kinetic energy in a localized region…
Single-body diffusion and two-body dispersion are fundamental processes in classical turbulence, governing particle mixing and transport. However, their behaviors in superfluid turbulence remain largely unexplored. In this study, we…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
Chaotic flows drive mixing and efficient transport in fluids, as well as the associated beautiful complex patterns familiar to us from our every day life experience. Generating such flows at small scales where viscosity takes over is highly…
The transport of self-propelled particles such as bacteria and phoretic swimmers through crowded heterogeneous environments is relevant to many natural and engineering processes, from biofilm formation and contamination processes to…
Turbulent puffs are ubiquitous in everyday life phenomena. Understanding their dynamics is important in a variety of situations ranging from industrial processes to pure and applied science. In all these fields, a deep knowledge of the…
Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in…
The inviscid limit of the stochastic Burgers equation is discussed in terms of the level surfaces of the minimising Hamilton-Jacobi function, the classical mechanical caustic and the Maxwell set and their algebraic pre-images under the…
The aim of this paper is to show how a weakly dispersive perturbation of the inviscid Burgers equation improve (enlarge) the space of resolution of the local Cauchy problem. More generally we will review several problems arising from weak…
Many chemotactic bacteria inhabit environments in which chemicals appear as localized pulses and evolve by processes such as diffusion and mixing. We show that, in such environments, physical limits on the accuracy of temporal gradient…
Many fluid-dynamical systems met in nature are quasi-two-dimensional: they are constrained to evolve in approximately two dimensions with little or no variation along the third direction. This has a drastic effect in the flow evolution…
In the present work we simulate the basic two-dimensional dynamics of swarming E. coli bacteria on the surface of a moderately soft agar plate. Individual bacteria are modelled by self-propelled ridged bodies (agents), which interact with…
Particle dynamics are investigated in plasma turbulence, using self-consistent kinetic simulations, in two dimensions. In steady state, the trajectories of single protons and proton-pairs are studied, at different values of plasma "beta"…
Memory effects in transport require, for their incorporation into reaction diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is…
We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the…