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This paper presents AquaMILR+, an untethered limbless robot designed for agile navigation in complex aquatic environments. The robot features a bilateral actuation mechanism that models musculoskeletal actuation in many anguilliform swimming organisms which propagates a moving wave from head to tail allowing open fluid undulatory swimming. This actuation mechanism employs mechanical intelligence, enhancing the robot's maneuverability when interacting with obstacles. AquaMILR+ also includes a compact depth control system inspired by the swim bladder and lung structures of eels and sea snakes. The mechanism, driven by a syringe and telescoping leadscrew, enables depth and pitch control-capabilities that are difficult for most anguilliform swimming robots to achieve. Additional structures, such as fins and a tail, further improve stability and propulsion efficiency. Our tests in both open water and indoor 2D and 3D heterogeneous aquatic environments highlight AquaMILR+'s capabilities and suggest a promising system for complex underwater tasks such as search and rescue and deep-sea exploration.

The one-dimensional spin-$s$ ${\rm SU}(2)$ ferromagnetic Heisenberg model, as a paradigmatic example for spontaneous symmetry breaking (SSB) with type-B Goldstone modes (GMs), is expected to exhibit an abstract fractal underlying the ground state subspace. This intrinsic abstract fractal is here revealed from a systematic investigation into the entanglement entropy for a linear combination of factorized (unentangled) ground states on a fractal decomposable into a set of the Cantor sets. The entanglement entropy scales logarithmically with the block size, with the prefactor being half the fractal dimension of a fractal, as long as the norm for the linear combination scales as the square root of the number of the self-similar building blocks kept at each step $k$ for a fractal, under an assumption that the maximum absolute value of the coefficients in the linear combination is chosen to be around one, and the coefficients in the linear combination are almost constants within the building blocks. Actually, the set of the fractal dimensions for all the Cantor sets forms a {\it dense} subset in the interval $[0,1]$. As a consequence, the ground state subspace is separated into a disjoint union of countably infinitely many regions, each of which is labeled by a decomposable fractal. Hence, the interpretation of the prefactor as half the fractal dimension is valid for any support beyond a fractal, which in turn leads to the identification of the fractal dimension with the number of type-B GMs for the orthonormal basis states. Our argument may be extended to any quantum many-body systems undergoing SSB with type-B GMs., Comment: 23 pages, 8 figures

Leveraging background fluid flows for propulsion has the potential to enhance the range and speed of autonomous aerial and underwater vehicles. In this work, we demonstrate experimentally a fully autonomous strategy for exploiting vortex rings for energy-efficient propulsion. First, an underwater robot used an onboard inertial measurement unit (IMU) to sense the motion induced by the passage of a vortex ring generated by a thruster in a 13,000-liter water tank. In response to the sensed acceleration, an impulsive maneuver entrained the robot into the material boundary of the vortex ring. After entrainment, the robot was propelled across the tank without expending additional energy or control effort. By advecting with the vortex ring, the robot achieved a near five-fold reduction in the energy required to traverse the tank. Using the controlled finite-time Lyapunov exponent field and corresponding Lagrangian coherent structures, we analyze and explain the initial entrainment process and the sensitivity to the starting time and position of the surfing maneuver. Additionally, linear acceleration as sensed by the onboard IMU was found to correspond with the pressure gradient of the background flow, and rotational acceleration is suggested as a method for measuring the vorticity of the vortex ring. This study serves as a proof-of-concept demonstration of the potential for onboard inertial measurements to enable efficient interaction with background fluid flows.

The unsteady flow physics of wind-turbine wakes under dynamic forcing conditions are critical to the modeling and control of wind farms for optimal power density. Unsteady forcing in the streamwise direction may be generated by unsteady inflow conditions in the atmospheric boundary layer, dynamic induction control of the turbine, or streamwise surge motions of a floating offshore wind turbine due to floating-platform oscillations. This study seeks to identify the dominant flow mechanisms in unsteady wakes forced by a periodic upstream inflow condition. A theoretical framework for the problem is derived, which describes traveling-wave undulations in the wake radius and streamwise velocity. These dynamics encourage the aggregation of tip vortices into large structures that are advected along in the wake. Flow measurements in the wake of a periodically surging turbine were obtained in an optically accessible towing-tank facility, with an average diameter-based Reynolds number of 300,000 and with surge-velocity amplitudes of up to 40% of the mean inflow velocity. Qualitative agreement between trends in the measurements and model predictions is observed, supporting the validity of the theoretical analyses. The experiments also demonstrate large enhancements in the recovery of the wake relative to the steady-flow case, with wake-length reductions of up to 46.5% and improvements in the available power at 10 diameters downstream of up to 15.7%. These results provide fundamental insights into the dynamics of unsteady wakes and serve as additional evidence that unsteady fluid mechanics can be leveraged to increase the power density of wind farms.

We report direct measurements of the magnetic field screening at the limits of the Meissner phase for two superconducting Nb samples. The samples are processed with two different surface treatments that have been developed for superconducting radio-frequency cavity applications -- a "baseline" treatment and an oxygen-doping ("O-doping") treatment. The measurements show: 1) that the screening length is significantly longer in the "O-doping" sample compared to the "baseline" sample; 2) that the screening length near the limits of the Meissner phase increases with applied field; 3) the evolution of the screening profile as the material transitions from the Meissner phase to the mixed phase; and 4) a demonstration of the absence of any screening profile for the highest applied field, indicative of the full flux entering the sample. Measurements are performed utilizing the $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) technique that allows depth resolved studies of the local magnetic field within the first 100 nm of the surface. The study takes advantage of the $\beta$-SRF beamline, a new facility at TRIUMF, Canada, where field levels up to 200 mT are available parallel to the sample surface to replicate radio frequency (RF) fields near the Meissner breakdown limits of Nb.

Hydrodynamic interactions among swimming or flying organisms can lead to complex flows on the scale of the group. These emergent fluid dynamics are often more complex than a linear superposition of individual organism flows, especially at intermediate Reynolds numbers. This paper presents an approach to estimate the flow induced by multiple swimmer wakes in proximity using an analytical model that conserves mass and momentum in the aggregation. This analytical model was informed by and validated with empirical measurements of induced vertical migrations of brine shrimp, $\textit{Artemia salina}$. The response of individual swimmers to ambient background flow and light intensity was evaluated. In addition, the time-resolved three-dimensional spatial configuration of the swimmers was measured using a recently developed laser scanning system. Computational experiments using the analytical model found that the induced flow at the front of the aggregation was insensitive to the presence of downstream swimmers, with the induced flow reaching an asymptote beyond a threshold aggregation length. Closer swimmer spacing led to higher induced flow, in some cases leading to model predictions of induced flow exceeding swimmer speeds required to maintain a stable spatial configuration. This result was reconciled by comparing two different models for the near-wake of each swimmer. Our results demonstrate that aggregation-scale flows result from a complex, yet predictable interplay amongst organism-scale wake structure, swimmer spacing and configuration, and aggregation size.

Autonomous ocean-exploring vehicles have begun to take advantage of onboard sensor measurements of water properties such as salinity and temperature to locate oceanic features in real time. Such targeted sampling strategies enable more rapid study of ocean environments by actively steering towards areas of high scientific value. Inspired by the ability of aquatic animals to navigate via flow sensing, this work investigates hydrodynamic cues for accomplishing targeted sampling using a palm-sized robotic swimmer. As proof-of-concept analogy for tracking hydrothermal vent plumes in the ocean, the robot is tasked with locating the center of turbulent jet flows in a 13,000-liter water tank using data from onboard pressure sensors. To learn a navigation strategy, we first implemented Reinforcement Learning (RL) on a simulated version of the robot navigating in proximity to turbulent jets. After training, the RL algorithm discovered an effective strategy for locating the jets by following transverse velocity gradients sensed by pressure sensors located on opposite sides of the robot. When implemented on the physical robot, this gradient following strategy enabled the robot to successfully locate the turbulent plumes at more than twice the rate of random searching. Additionally, we found that navigation performance improved as the distance between the pressure sensors increased, which can inform the design of distributed flow sensors in ocean robots. Our results demonstrate the effectiveness and limits of flow-based navigation for autonomously locating hydrodynamic features of interest.

Recall that $\alpha=(a_1,a_2,\ldots,a_n)\in[n]^n$ is a parking function if its nondecreasing rearrangement $\beta=(b_1,b_2,\ldots,b_n)$ satisfies $b_i\leq i$ for all $1\leq i\leq n$. In this article, we study parking functions based on their ascents (indices at which $a_ia_{i+1}$), and ties (indices at which $a_i=a_{i+1}$). By utilizing multiset Eulerian polynomials, we give a generating function for the number of parking functions of length $n$ with $i$ descents. We present a recursive formula for the number of parking functions of length $n$ with descents at a specified subset of $[n-1]$. We establish that the number of parking functions of length $n$ with descents at $I\subset[n-1]$ and descents at $J=\{n-i:i\in I\}$ are equinumerous. As a special case, we show that the number of parking functions of length $n$ with descents at the first $k$ indices is given by $f(n, n-k-1)=\frac{1}{n}\binom{n}{k}\binom{2n-k}{n-k-1}$. We prove this by bijecting to the set of standard Young tableaux of shape $((n-k)^2,1^k)$, which are enumerated by $f(n,n-k-1)$. We also study peaks of parking functions, which are indices at which $a_{i-1}a_{i+1}$. We show that the set of parking functions with no peaks and no ties is enumerated by the Catalan numbers. We conclude our study by characterizing when a parking function is uniquely determined by their statistic encoding; a word indicating what indices in the parking function are ascents, descents, and ties. We provide open problems throughout., Comment: 17 pages, 2 figures, 5 tables, version 2 provides a new proof of Theorem 3.8

The vast majority of the ocean's volume remains unexplored, in part because of limitations on the vertical range and measurement duration of existing robotic platforms. In light of the accelerating rate of climate change impacts on the physics and biogeochemistry of the ocean, the need for new tools that can measure more of the ocean on faster timescales is becoming pressing. Robotic platforms inspired or enabled by aquatic organisms have the potential to augment conventional technologies for ocean exploration. Recent work demonstrated the feasibility of directly stimulating the muscle tissue of live jellyfish via implanted microelectronics. We present a biohybrid robotic jellyfish that leverages this external electrical swimming control, while also using a 3D printed passive mechanical attachment to streamline the jellyfish shape, increase swimming performance, and significantly enhance payload capacity. A six-meter-tall, 13,600-liter saltwater facility was constructed to enable testing of the vertical swimming capabilities of the biohybrid robotic jellyfish over distances exceeding 35 body diameters. We found that the combination of external swimming control and the addition of the mechanical forebody resulted in an increase in swimming speeds to 4.5 times natural jellyfish locomotion. Moreover, the biohybrid jellyfish carried a payload volume up to 105% of the jellyfish body volume. The added payload decreased the intracycle acceleration of the biohybrid robots relative to natural jellyfish, which could facilitate more precise measurements by onboard sensors. In contrast with existing robotic exploration tools, this platform is inexpensive, highly efficient, and benefits from the widespread natural habitats of jellyfish. The demonstrated performance of these biohybrid robots suggests an opportunity to expand the set of robotic tools for comprehensive monitoring of the changing ocean.

The semantic segmentation of pelvic organs via MRI has important clinical significance. Recently, deep learning-enabled semantic segmentation has facilitated the three-dimensional geometric reconstruction of pelvic floor organs, providing clinicians with accurate and intuitive diagnostic results. However, the task of labeling pelvic floor MRI segmentation, typically performed by clinicians, is labor-intensive and costly, leading to a scarcity of labels. Insufficient segmentation labels limit the precise segmentation and reconstruction of pelvic floor organs. To address these issues, we propose a semi-supervised framework for pelvic organ segmentation. The implementation of this framework comprises two stages. In the first stage, it performs self-supervised pre-training using image restoration tasks. Subsequently, fine-tuning of the self-supervised model is performed, using labeled data to train the segmentation model. In the second stage, the self-supervised segmentation model is used to generate pseudo labels for unlabeled data. Ultimately, both labeled and unlabeled data are utilized in semi-supervised training. Upon evaluation, our method significantly enhances the performance in the semantic segmentation and geometric reconstruction of pelvic organs, Dice coefficient can increase by 2.65% averagely. Especially for organs that are difficult to segment, such as the uterus, the accuracy of semantic segmentation can be improved by up to 3.70%.

The world's oceans are in constant motion, transporting the sun's heat from the equator to the poles, bringing marine life fresh supplies of oxygen and nutrients, and sequestering nearly half of our carbon dioxide emissions since the Industrial Revolution. Within this dynamic aquatic milieu exists another type of motion: the perpetual teeming of trillions of swimming animals. Are these organisms simply along for the ride, carried by the prevailing ocean currents and occasionally using their powers of locomotion to explore their surroundings; or could their propulsion result in dynamical feedbacks that influence the physical and biogeochemical structure of the ocean itself?, Comment: Invited article, in review

Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities that could be sufficient to explain turbulence transition. In many cases, the near-wall behavior of the discovered instabilities is empirically indistinguishable from the classical no-slip condition. The ability of these alternative boundary conditions to predict linear instabilities that are consistent with turbulence transition suggests that the no-slip condition may be an overly simplified model of fluid-solid interface physics, particularly as a description of the flow perturbations that lead to turbulence transition in wall-bounded flows., Comment: Accepted in Journal of Fluid Mechanics

Accurate measurements of atmospheric flows at meter-scale resolution are essential for a broad range of sustainability applications, including optimal design of wind and solar farms, safe and efficient urban air mobility, monitoring of environmental phenomena such as wildfires and air pollution dispersal, and data assimilation into weather and climate models. Measurement of the relevant microscale wind flows is inherently challenged by the optical transparency of the wind. This review explores new ways in which physics can be leveraged to "see" environmental flows non-intrusively, that is, without the need to place measurement instruments directly in the flows of interest. Specifically, while the wind itself is transparent, its effect can be visually observed in the motion of objects embedded in the environment and subjected to wind -- swaying trees and flapping flags are commonly encountered examples. We describe emerging efforts to accomplish visual anemometry, the task of quantitatively inferring local wind conditions based on the physics of observed flow-structure interactions. Approaches based on first-principles physics as well as data-driven, machine learning methods will be described, and remaining obstacles to fully generalizable visual anemometry will be discussed., Comment: Revised with expanded bibliography