Related papers: Nonlinear Dynamics and Chaos: Applications in Atmo…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and therefore the statistical normal distribution with implicit assumption of independence, fixed mean and…
Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. The macroscale atmospheric flow structure behaves as a unified whole quantum system, where, the superimposition of a continuum of eddies results…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
Low-order climate models can play an important role in understanding low-frequency variability in the atmospheric circulation and how forcing consistent with anthropogenic climate change may affect this variability. Here, we study a…
Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing…
Flow instabilities play important roles in a wide range of engineering, geophysical, and astrophysical flows, ranging from supernova explosion in crab nebula, formation of clouds in sky, waves on ocean, to inertial confinement fusion…
This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres,…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
Understanding the dynamics of material objects advected by turbulent flows is a long standing question in fluid dynamics. In this perspective article we focus on the characterization of the statistical properties of non-interacting…
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
Waves propagating through weakly disordered smooth linear media undergo a universal phenomenon called branched flow. Branched flow has been observed and studied experimentally in various systems by considering coherent waves. Recent…
Understanding the physics of nonequilibrium systems remains as one of the major challenges of theoretical physics. This problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…