How superfluid vortex knots untie

Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in the Gross-Pitaevskii equation. Without exception, we find that the knots untie efficiently and completely, and do so within a predictable time range. We also observe that the centerline helicity -- a measure of knotting and writhing -- is partially preserved even as the knots untie. Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal 2D knot diagrams, and tend to concentrate in states along specific maximally chiral pathways.Comment: 5 figures and a supplemental PD

The Life of a Vortex Knot

The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessential example of a knotted flow is a knotted vortex filament, however, owing to experimental difficulties, it has not been possible until recently to directly generate knotted vortices in real fluids. Using 3D printed hydrofoils and high-speed laser scanning tomography, we generate vortex knots and links and measure their subsequent evolution. In both cases, we find that the vortices deform and stretch until a series of vortex reconnections occurs, eventually resulting several disjoint vortex rings. This article accompanies a fluid dynamics video entered into the Gallery of Fluid Motion at the 66th Annual Meeting of the APS Division of Fluid Dynamics.Comment: Videos are included; this submission is part of the DFD Gallery of Fluid Motio

Formation of Colloidal Chains and Driven Clusters with Optical Binding

We study the effects of the optical binding force on wavelength sized colloidal particles free to move in a counter-propagating beam. This work is motivated by the concept of using optical binding to direct the assembly of large numbers of colloidal particles; previous work has used small numbers of particles and/or 1D or 2D restricted geometries. Utilizing a novel experimental scheme, we describe the general static and dynamic self-organization behaviors for 20--100 particles free to move in 3-dimensional space. We observe the self-organization of the colloids into large optically bound structures along with the formation of driven particle clusters. Furthermore we show that the structure and behavior of these optically bound systems can be tuned using the refractive index of the particles and properties of the binding light. In particular, we show that the driven behavior originates from $N$-body interactions, which has significant implications for future work on optically bound clusters of more than 2 particles

Topological mechanics of gyroscopic metamaterials

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial -- comprised of coupled gyroscopes on a lattice -- that breaks time-reversal symmetry. The vibrational spectrum of these novel structures displays a sonic gap populated by topologically protected edge modes which propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We envision applications of these edges modes to the design of loss-free, one-way, acoustic waveguides and demonstrate this functionality in experiment

Creating and Verifying a Quantum Superposition in a Micro-optomechanical System

Micro-optomechanical systems are central to a number of recent proposals for realizing quantum mechanical effects in relatively massive systems. Here we focus on a particular class of experiments which aim to demonstrate massive quantum superpositions, although the obtained results should be generalizable to similar experiments. We analyze in detail the effects of finite temperature on the interpretation of the experiment, and obtain a lower bound on the degree of non-classicality of the cantilever. Although it is possible to measure the quantum decoherence time when starting from finite temperature, an unambiguous demonstration of a quantum superposition requires the mechanical resonator to be in or near the ground state. This can be achieved by optical cooling of the fundamental mode, which also provides a method to measure the mean phonon number in that mode. We also calculate the rate of environmentally induced decoherence and estimate the timescale for gravitational collapse mechanisms as proposed by Penrose and Diosi. In view of recent experimental advances, practical considerations for the realization of the described experiment are discussed.Comment: 19 pages, 8 figures, published in New J. Phys. 10 095020 (2008); minor revisions to improve clarity; fixed possibly corrupted figure

Retention of rising droplets in density stratification

In this study, we present results from experiments on the retention of single oil droplets rising through a two-layer density stratification. These experiments confirm the significant slowdown observed in past literature of settling and rising particles and droplets in stratification, and are the first experiments to study single liquid droplets as opposed to solid particles. By tracking the motion of the droplets as they rise through a stratified fluid, we identify two timescales which quantitatively describe this slowdown: an entrainment timescale, and a retention timescale. The entrainment timescale is a measure of the time that a droplet spends below its upper-layer terminal velocity and relates to the length of time over which the droplet's rise is affected by entrained dense fluid. The retention time is a measure of the time that the droplet is delayed from reaching an upper threshold far from the density transition. Both timescales are found to depend on the Froude and Reynolds numbers of the system, Fr $=U_u/(Nd)$ and Re $=\rho_u U_u d/\nu$. We find that both timescales are only significantly large for Fr $\lesssim1$, indicating that trapping dynamics in a relatively sharp stratification arise from a balance between drop inertia and buoyancy. Finally, we present a theoretical formulation for the drag enhancement $\Gamma$, the ratio between the maximum stratification force and the corresponding drag force on the droplet, based on a simple force balance at the point of the velocity minimum. Using our experimental data, we find that our formulation compares well with recent theoretical and computational work by Zhang et al. [J. Fluid Mech. 875, 622-656 (2019)] on the drag enhancement on a solid sphere settling in a stratified fluid, and provides the first experimental data supporting their approach

Retention of Rising Oil Droplets in Density Stratification

In this study, we present results from experiments on the retention of single oil droplets rising through a two-layer density stratification, with the goal of quantifying and parametrizing the impact of stratification on timescales that describe the delay in rising. These experiments confirm the significant slowdown observed in past literature of settling and rising particles and droplets in stratification, and these are the first experiments to study single liquid droplets as opposed to solid particles or bubbles. By tracking the motion of the droplets as they rise through a stratified fluid, we identify two new timescales which quantitatively describe this slowdown: an entrainment timescale and a retention timescale. These timescales measure dynamics that were not captured in previous timescale discussions, which primarily focused on the timescale to the velocity minimum (Umin). The entrainment timescale is a measure of the time that a droplet spends below its upper-layer terminal velocity and relates to the duration over which the droplet\u27s rise is affected by entrained dense fluid. The retention time is a measure of the time that the droplet is delayed from reaching an upper threshold far from the density transition. These two timescales are interconnected by the magnitude of the slowdown (Uu−Umin) relative to the upper-layer terminal velocity (Uu), as well as a constant that reflects the approximately universal form of the recovery of a droplet\u27s velocity from Uminto Uu. Both timescales are found to depend on the Froude and Reynolds numbers of the system, Fr =Uu/(Nd) and Re =ρuUud/ν. We find that both timescales are only significantly large for Fr ≲1, indicating that trapping dynamics in a relatively sharp stratification arise from a balance between drop inertia and buoyancy. Finally, we present a theoretical formulation for the force enhancement Γ, the ratio between the maximum stratification-induced force and the corresponding drag force on the droplet, based on a simple force balance at the point of the velocity minimum. Using our experimental data, we find that our formulation compares well with recent theoretical and computational work by Zhang et al. [J. Fluid Mech. 875, 622 (2019)] on the force enhancement on a solid sphere settling in a stratified fluid, and provides the first experimental data supporting their approach