Related papers: From directed percolation to patterned turbulence
The present work discusses about a possible physical interpretation of the occurrence of turbulence in a dynamic fluid with mathematical modeling and computer simulation. Here turbulence is defined to be a phenomenon of random velocity…
Interacting systems driven far from equilibrium tend to evolve to steady states exhibiting large-scale structure and order. In two-dimensional turbulent flow the seemingly random swirling motion of a fluid can evolve towards persistent…
Natural convection is usually complicated by additional factors such as rotation, shear, radiative transfer, compressibility and electromagnetic fields (in the case of electro-conductive fluids). It is shown, using results of numerical…
A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…
Perturbed plane Couette flow containing a thin spanwise-oriented ribbon undergoes a subcritical bifurcation at Re = 230 to a steady 3D state containing streamwise vortices. This bifurcation is followed by several others giving rise to a…
Chaotic systems are characterised by exponential separation between close-by trajectories, which in particular leads to deterministic unpredictability over an infinite time-window. It is now believed, that such butterfly effect is not fully…
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific…
The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The transition to turbulence in pipes is characterized by a coexistence of laminar and turbulent states. At the lower end of the transition, localized turbulent pulses, called puffs, can be excited. Puffs can decay when rare fluctuations…
This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…
Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
Recent progress in the understanding of star formation is summarized. A consistent picture is emerging where molecular clouds form with turbulent velocity fields and clumpy substructure, imprinted already during their formation. The clouds…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
A liquid drop containing a long fiber is a complex system whose configuration is determined by an interplay of elastic stresses in the fiber and capillary forces due to the liquid. We study the morphological evolution of fibers that are…
The dynamical behavior of propagating structures, determined from a Karhunen-Lo`eve decomposition, in turbulent pipe flow undergoing reverse transition to laminar flow is investigated. The turbulent flow data is generated by a direct…