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We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
When a rotor blade encounters reverse flow in edgewise flight at high advance ratio, a strong vortical structure forms on the leeside of the sharp blade edge. This has unexpected effects on blade aerodynamics. A differential onset velocity…
There are two long-standing conjectures in Hamiltonian dynamics concerning Reeb flows on the boundaries of star-shaped domains in $\mathbb{R}^{2n}$ ($n \geq 2$). One conjecture states that such a Reeb flow possesses either $n$ or infinitely…
Coronal jets are observed above minority polarity intrusions throughout the solar corona. Some of the most energetic occur on the periphery of active regions where the magnetic field is strongly inclined. These jets exhibit a non-radial…
The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between…
Recent work on Abelian topological phases with rotational symmetry has raised the question of whether rotational symmetry can protect gapless propagating edge modes. Here we address this issue by considering the coupling of topological…
In the near-Earth asteroid population, binary and triple systems have been discovered with mutual orbits that have significant eccentricities as well as large semi-major axes. All known systems with eccentric orbits and all widely-separated…
Hamiltonian dynamical systems tend to have infinitely many periodic orbits. For example, for a broad class of symplectic manifolds almost all levels of a proper smooth Hamiltonian carry periodic orbits. The Hamiltonian Seifert conjecture is…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…
The presented investigation is motivated by the need to uncover connections between underlying rotor fluid-structure interactions and vortex dynamics to fatigue performance and characterization of flexible rotor blades, their hub, and their…
We use a general circulation model to study the three-dimensional (3-D) flow and temperature distributions of atmospheres on tidally synchronized extrasolar planets. In this work, we focus on the sensitivity of the evolution to the initial…
Active nematics in two dimensions stir themselves efficiently through internally generated chaotic flows, largely driven by motile $+1/2$ disclinations. We investigate how this tendency toward chaotic fluid stirring can, counterintuitively,…
The properties of wave-like helically twisted normal mode structures on steady relativistic jets are summarized. Wave speeds are a function of the wavelength and less than the jet speed. However, normal mode interference can lead to both…
Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime…
Water vortices are known to develop polygon structures inside their cores. The apexes of the polygonal manifestations are the result of satellite vortices attached to the parent vortex. Exploiting the analogy between the shallow water…
In these decades, it has been gradually established that edge modes of a wide class of topologically ordered systems are governed by the bulk-edge correspondence and anyon condensation. The former has been studied many times because it can…
In a numerical investigation, we demonstrate the existence and curious evolution of vortices in a ladder-type three-level nonlinear atomic vapor with linear, cubic, and quintic susceptibilities considered simultaneously with the dressing…
Flexible filaments moving in viscous fluids are ubiquitous in the natural microscopic world. For example, the swimming of bacteria and spermatozoa as well as important physiological functions at organ-level, such as the cilia-induced motion…
The flow condition at the leading edge governs the dynamics of the leading-edge vortex, which is crucial for understanding the separated flow over an airfoil at high angle of attack. Furthermore, with extensive applications in biomimetic…
The evolution of a large-scale poloidal magnetic field in an accretion disc is an important problem because it determines the launching of winds and the feasibility of the magnetorotational instability to generate turbulence or channel…