Related papers: To the problem of turbulence in quantitative easin…
Chaotic dynamics have emerged as a versatile resource for neuromorphic and probabilistic computing, enabling high-dimensional nonlinear processing and classical analogues of quantum randomness. Exploiting chaos for computation requires…
Incompressible fluids in microfluidic networks with non-rigid channels can exhibit flow rate oscillations analogous to electric current oscillations in RLC circuits. This is due to the elastic deformation of channel walls that can store and…
In this work, we quantify the time scales and information flow associated with multiscale energy transfer in a weakly turbulent system. This is done through a greedy optimization algorithm which finds the maximum conditional-mutual…
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
According to a recent theory \cite{Li14}, when the Reynolds number is large, fully developed turbulence is caused by short term unpredictability (rough dependence upon initial data); when the Reynolds number is moderate, often transient…
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…
The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world turbulent systems. Although there have been several mathematical studies, the occurrence of abrupt transitions in real-world systems such as…
The nonlinear robustness of laminar plane Couette flow is considered under the action of in-phase spanwise wall oscillations by computing properties of the edge of chaos, i.e., the boundary of its basin of attraction. Three measures are…
It is now established that subcritical mechanisms play a crucial role in the transition to turbulence of non-rotating plane shear flows. The role of these mechanisms in rotating channel flow is examined here in the linear and nonlinear…
We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks.…
Analytical non-perturbative study of the three-dimensional nonlinear stochastic partial differential equation with additive thermal noise, analogous to that proposed by V.N. Nikolaevskii [1]-[5]to describe longitudinal seismic waves, is…
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…
Contrasting with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become…
Abrupt transition to turbulence may occur in pipe and channel flows at moderate flow rates, an unexpected event according to linear stability theory, and has been an open problem in fluid dynamics for more than a century. Extensive…
We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference…
Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…