Related papers: Fisher equation with turbulence in one dimension
An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature…
The dynamics of particles in turbulence when the particle-size is larger than the dissipative scale of the carrier flow is studied. Recent experiments have highlighted signatures of particles finiteness on their statistical properties,…
One of simplest examples of navigation found in nature is run-and-tumble chemotaxis. Tumbles reorient cells randomly, and cells can drift toward attractants or away from repellents by biasing the frequency of these events. The post-tumble…
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers,…
Self-propelled microorganisms, such as unicellular algae or bacteria, swim along their director relative to the fluid velocity. Under a steady shear flow the director rotates in close orbit, a periodic structure that is preserved under an…
Flagellated bacteria are hydrodynamically attracted to rigid walls, yet past work shows a 'hovering' state where they swim stably at a finite height above surfaces. We use numerics and theory to reveal the physical origin of hovering.…
Mechanical effects that span multiple physical scales -- such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions -- play a critical role in real fluid systems. The spin angular…
A dissipation rate, which grows faster than any power of the wave number in Fourier space, may be scaled to lead a hydrodynamic system {\it actually} or {\it potentially} converge to its Galerkin truncation. Actual convergence we name for…
We analyze the dynamics of a tracer particle embedded in a bath of hard spheres confined in a channel of varying section. By means of Brownian dynamics simulations we apply a constant force on the tracer particle and discuss the dependence…
Motion in a one-dimensional (1D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row, and due to their hydrodynamic interactions spacing between these droplets oscillates with a wave-like…
Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the…
We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi two-dimensional reaction-diffusion equation can be reduced…
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…
We present a position Langevin equation for overdamped particle motion on rough two-dimensional surfaces. A Brownian Dynamics algorithm is suggested to evolve this equation numerically, allowing for the prediction of effective (projected)…
We investigate the effects of strong number fluctuations on traveling waves in the Fisher-Kolmogorov reaction-diffusion system. Our findings are in stark contrast to the commonly used deterministic and weak-noise approximations. We compute…
We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…
Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure,…
Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of…
We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A self-similar scaling regime is detected when the…
We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon\textgreater{}0$), and proliferate according to a reaction…