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Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to established properties of transitional turbulence. A…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
Continuum hydrodynamic models of active liquid crystals have been used to describe dynamic self-organising systems such as bacterial swarms and cytoskeletal gels. A key prediction of such models is the existence of self-stabilising kink…
Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive…
It has been conjectured that every stable manifold arising from a holomorphic automorphism, that acts hyperbolically on a compact invariant set, is biholomorphic to complex Euclidean space. Such stable manifolds are known to be…
In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…
Focusing a finite amount of energy dynamically into a vanishingly small amount of material requires that the initial condition be perfectly symmetric. In reality, imperfections are always present and cut-off the approach towards the…
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
It is shown that low Reynolds number fluid flows can cause suspended particles to respond as though they were in an equilibrium system with an effective potential. This general result follows naturally from the fact that different methods…
Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a…
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to…
Two generically different but universal dynamical quantum many-body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite/long range inter-particle interactions. We use…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
Simulations show that when a phase-separated binary AB fluid is driven to flow past chemically patterned substrates in a microchannel, the fluid exhibits unique morphological instabilities. For the pattern studied, these instabilities give…
We consider the dynamics of monodisperse bubbly fluid confined by two plane solid walls and subjected to small-amplitude high-frequency transversal oscillations. The frequency these oscillations is assumed to be high in comparison with…
Emergent phenomena share the fascinating property of not being obvious consequences of the design of the system in which they appear. This characteristic is no less relevant when attempting to simulate such phenomena, given that the outcome…
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to…
We consider a pendulum with vertically oscillating support and time-dependent damping coefficient which varies until reaching a finite final value. The sizes of the corresponding basins of attraction are found to depend strongly on the full…
Fundamental limits to predictability are central to our understanding of many physical and computational systems. Here we show that, despite its remarkable capabilities, deep learning exhibits such fundamental limits rooted in the fractal,…