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The problem of a rigid disk rolling down a ramp is a classic problem given to students in introductory mechanics courses. In contrast, systematic studies on the rolling behavior of an ellipse have only recently emerged. Unlike a rolling disk, here the geometric center remains at a constant height from the floor, the center of a rotating ellipse changes nonlinearly due to its eccentric shape. This eccentricity introduces new modes of motion beyond rolling, including rocking and hopping. Leveraging this multi-motion behavior, we design an ellipsoidal actuator which exhibits both rolling and hopping behaviors in response to changes in the applied angular velocity. Using a simple geometric framework, we successfully capture the motion of the actuator as a force-driven rigid ellipsoid on a non-slip flat surface, and identify the critical angular velocity for the rolling-to-hopping transition. Furthermore, by adding deformability to the actuator, we unlock new functionalities, enabling soft actuators that can climb slopes and work together to collectively ascend stairs.

Evaporation profiles have a strong effect on tear film thinning and breakup (TBU), a key factor in dry eye disease (DED). In experiments, TBU is typically seen to occur in patterns that locally can be circular (spot), linear (streak), or intermediate . We investigate a two-dimensional (2D) model of localized TBU using a Fourier spectral collocation method to observe how the evaporation distribution affects the resulting dynamics of tear film thickness and osmolarity, among other variables. We find that the dynamics are not simply an addition of individual 1D solutions of independent TBU events, and we show how the TBU quantities of interest vary continuously from spots to streaks for the shape of the evaporation distribution. We also find a significant speedup by using a proper orthogonal decomposition to reduce the dimension of the numerical system. The speedup will be especially useful for future applications of the model to inverse problems, allowing the clinical observation at scale of quantities that are thought to be important to DED but not directly measurable in vivo within TBU locales.

We study the Lie algebra of physical states associated with certain vertex operator algebras of central charge 24. By applying the no-ghost theorem from string theory we express the corresponding Lie brackets in terms of vertex algebra operations. In the special case of the Moonshine module this result answers a question of Borcherds, posed in his paper on the Monstrous moonshine conjecture., Comment: 18 pages

Polymer gels are comprised of a three-dimensional, cross-linked network that can typically withstand the mechanical deformation associated with both swelling and de-swelling. Thus, gels can be designed with smart behaviors that require both stress generation and dissipation, making them well-suited to many applications including membrane technology, water capture devices, and drug delivery systems. In contrast to the fully swelled equilibrium state, limited research characterizes the unsteady-state swelling regime prior to equilibrium. It is in this regime where unique surface deformations can occur. Here we show how internal network constraints and external diffusive pressure can be leveraged to manipulate swelling kinetics and surface deformations in poly(ethylene glycol) gels during unconstrained, three-dimensional swelling. We find that increasing cross-linker molecular weight and swelling in ethanol, as opposed to water, are both effective routes to increase the time it takes to reach equilibrium but do so through different mechanisms. Networks with fewer internal constraints, manipulated via cross-linker chain-length, imbibe more solvent over a longer time. In contrast, swelling in ethanol reduces the amount of solvent imbibed by the network while increasing the time to reach equilibrium. Measurements of surface patterns during swelling establishes that an immediate, fast relaxation at the surface occurs during the first five minutes of swelling. However, the density and persistence of these features varies with solvent quality. These results serve establish a framework for how soft materials undergo dynamic deformation. Engineering transient surface properties while mitigating unwanted instabilities opens the door for emerging technologies such as smart anti-fouling and sensors.

A near memory hardware accelerator, based on a novel direct path computational model, for real-time emulation of radio frequency systems is demonstrated. Our evaluation of hardware performance uses both application-specific integrated circuits (ASIC) and field programmable gate arrays (FPGA) methodologies: 1). The ASIC testchip implementation, using TSMC 28nm CMOS, leverages distributed autonomous control to extract concurrency in compute as well as low latency. It achieves a $518$ MHz per channel bandwidth in a prototype $4$-node system. The maximum emulation range supported in this paradigm is $9.5$ km with $0.24$ $\mu$s of per-sample emulation latency. 2). The FPGA-based implementation, evaluated on a Xilinx ZCU104 board, demonstrates a $9$-node test case (two Transmitters, one Receiver, and $6$ passive reflectors) with an emulation range of $1.13$ km to $27.3$ km at $215$ MHz bandwidth.

In this paper we consider the problem of developing a computational model for emulating an RF channel. The motivation for this is that an accurate and scalable emulator has the potential to minimize the need for field testing, which is expensive, slow, and difficult to replicate. Traditionally, emulators are built using a tapped delay line model where long filters modeling the physical interactions of objects are implemented directly. For an emulation scenario consisting of $M$ objects all interacting with one another, the tapped delay line model's computational requirements scale as $O(M^3)$ per sample: there are $O(M^2)$ channels, each with $O(M)$ complexity. In this paper, we develop a new ``direct path" model that, while remaining physically faithful, allows us to carefully factor the emulator operations, resulting in an $O(M^2)$ per sample scaling of the computational requirements. The impact of this is drastic, a $200$ object scenario sees about a $100\times$ reduction in the number of per sample computations. Furthermore, the direct path model gives us a natural way to distribute the computations for an emulation: each object is mapped to a computational node, and these nodes are networked in a fully connected communication graph. Alongside a discussion of the model and the physical phenomena it emulates, we show how to efficiently parameterize antenna responses and scattering profiles within this direct path framework. To verify the model and demonstrate its viability in hardware, we provide several numerical experiments produced using a cycle level C++ simulator of a hardware implementation of the model.

Active components incorporated in materials generate motion by inducing conformational changes in response to external fields. Magnetic fields are particularly interesting as they can actuate materials remotely. Millimeter-sized ferrofluid droplets placed on a solid surface, surrounded by an ambient gas phase, are shown here to migrate under a rotating magnetic field due to the periodic deformation of the liquid-gas interface. This interface wobbling leads to droplet migration with speeds that increase as the amplitude and frequency of the magnetic field increase. In addition to migrating in a controlled manner, we demonstrate the ability of magnetic droplets to clean surface impurities and transport cargo.

High quality random numbers are necessary in the modern world. Ranging from encryption keys in cyber security to models and simulations for scientific use: it's important that these random numbers are of high quality and quickly attainable. One common solution to the generation of random numbers is that of pseudo-random number generators, or PRNGs. PRNGs generate random numbers by first quantifying some unpredictable phenomena into a number or string and feeding it into an algorithm which yields numbers randomly based on that seed. Easy places to find seeds include the user's mouse movements or the machine's uptime. These are only pseudorandom, however, as if given the same seed twice, the PRNG would generate the same 'random' output. This is great for games like Minecraft, but not so great for cybersecurity encryption key generation. By using a hardware random number generator (HRNG), random numbers that are not susceptible to the flaws found in PRNGs can be attained at a high rate., Comment: Presented at College of STEM SYmposium, Clayton State University

A wide range of real-world applications can be formulated as Multi-Agent Path Finding (MAPF) problem, where the goal is to find collision-free paths for multiple agents with individual start and goal locations. State-of-the-art MAPF solvers are mainly centralized and depend on global information, which limits their scalability and flexibility regarding changes or new maps that would require expensive replanning. Multi-agent reinforcement learning (MARL) offers an alternative way by learning decentralized policies that can generalize over a variety of maps. While there exist some prior works that attempt to connect both areas, the proposed techniques are heavily engineered and very complex due to the integration of many mechanisms that limit generality and are expensive to use. We argue that much simpler and general approaches are needed to bring the areas of MARL and MAPF closer together with significantly lower costs. In this paper, we propose Confidence-based Auto-Curriculum for Team Update Stability (CACTUS) as a lightweight MARL approach to MAPF. CACTUS defines a simple reverse curriculum scheme, where the goal of each agent is randomly placed within an allocation radius around the agent's start location. The allocation radius increases gradually as all agents improve, which is assessed by a confidence-based measure. We evaluate CACTUS in various maps of different sizes, obstacle densities, and numbers of agents. Our experiments demonstrate better performance and generalization capabilities than state-of-the-art MARL approaches with less than 600,000 trainable parameters, which is less than 5% of the neural network size of current MARL approaches to MAPF., Comment: Accepted to AAMAS 2024

We present measurements and theoretical modeling demonstrating the capability of Doppler Broadened annihilation gamma Spectroscopy (DBS) to provide element-specific information from the topmost atomic layer of surfaces that are either clean or covered with adsorbates or thin films. Our measurements show that the energy spectra of Doppler-shifted annihilation gamma photons emitted following the annihilation of positrons from the topmost atomic layers of clean gold (Au) and copper (Cu) differ significantly. With the aid of the positron annihilation-induced Auger electron spectroscopy (PAES) performed simultaneously with DBS, we show that measurable differences between the Doppler broadened gamma spectra from Au and Cu surfaces in the high energy region of the gamma spectra can be used for the quantification of surface chemical composition. Modeling the measured Doppler spectra from clean Au and Cu surfaces using gamma spectra obtained from ab initio calculations after considering the detector energy resolution and surface positronium formation pointed to an increase in the relative contribution of gamma from positron annihilation with valence shell electrons. The fit result also suggests that the surface-trapped positrons predominantly annihilated with the delocalized valence shell (s and p) electrons that extended into the vacuum as compared to the highly localized d electrons. Simultaneous DBS and PAES measurements from adsorbate (sulfur, oxygen, carbon) or thin film (selenium (Se), graphene) covered Cu surface showed that it is possible to distinguish and quantify the surface adsorbate and thin-film composition just based on DBS. DBS of elemental surfaces presents a promising avenue for developing a characterization tool that can be used to probe external and internal surfaces that are inaccessible by conventional surface science techniques.

We classify reflective automorphic products of singular weight under certain regularity assumptions. Using obstruction theory we show that there are exactly 11 such functions. They are naturally related to certain conjugacy classes in Conway's group $\text{Co}_0$. The corresponding modular varieties have a very rich geometry. We establish a bijection between their $1$-dimensional type-$0$ cusps and the root systems in Schellekens' list. We also describe a $1$-dimensional cusp along which the restriction of the automorphic product is given by the eta product of the corresponding class in $\text{Co}_0$. Finally we apply our results to give a complex-geometric proof of Schellekens' list., Comment: 71 pages

There has been huge recent interest in the potential of making operational weather forecasts using machine learning techniques. As they become a part of the weather forecasting toolbox, there is a pressing need to understand how well current machine learning models can simulate high-impact weather events. We compare forecasts of Storm Ciar\'an, a European windstorm that caused sixteen deaths and extensive damage in Northern Europe, made by machine learning and numerical weather prediction models. The four machine learning models considered (FourCastNet, Pangu-Weather, GraphCast and FourCastNet-v2) produce forecasts that accurately capture the synoptic-scale structure of the cyclone including the position of the cloud head, shape of the warm sector and location of warm conveyor belt jet, and the large-scale dynamical drivers important for the rapid storm development such as the position of the storm relative to the upper-level jet exit. However, their ability to resolve the more detailed structures important for issuing weather warnings is more mixed. All of the machine learning models underestimate the peak amplitude of winds associated with the storm, only some machine learning models resolve the warm core seclusion and none of the machine learning models capture the sharp bent-back warm frontal gradient. Our study shows there is a great deal about the performance and properties of machine learning weather forecasts that can be derived from case studies of high-impact weather events such as Storm Ciar\'an.

The interaction between passive and active/driven particles has introduced a new way to control colloidal suspension properties from particle aggregation to crystallization. Here, we focus on the hydrodynamic interaction between a single rotational driven particle and a suspension of passive particles near the floor. Using experiments and Stokesian dynamics simulations that account for near-field lubrication, we demonstrate that the flow induced by the driven particle can induce long-ranged rearrangement in a passive suspension. We observe an accumulation of passive particles in front of the driven particle and a depletion of passive particles behind the driven particle. This restructuring generates a pattern that can span a range more than $10$ times of the driven particle's radius. We further show that size scale of the pattern is only a function of the particle's height above the floor., Comment: S.-Y.C. and H.L-R. contributed equally

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counter-intuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfv\'en waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, $\alpha=2$ as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed $>$600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: pre-flare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that $\alpha = 1.63 \pm 0.03$. This is below the critical threshold, suggesting that Alfv\'en waves are an important driver of coronal heating., Comment: 1,002 authors, 14 pages, 4 figures, 3 tables, published by The Astrophysical Journal on 2023-05-09, volume 948, page 71

We demonstrate a new temperature record for image-current mediated sympathetic cooling of a single proton in a cryogenic Penning trap by laser-cooled $^9$Be$^+$. An axial mode temperature of 170 mK is reached, which is a 15-fold improvement compared to the previous best value. Our cooling technique is applicable to any charged particle, so that the measurements presented here constitute a milestone towards the next generation of high-precision Penning-trap measurements with exotic particles., Comment: 7 pages, 4 figures

Super-Earths span a wide range of bulk densities, indicating a diversity in interior conditions beyond that seen in the solar system. In particular, an emerging population of low-density super-Earths may be explained by volatile-rich interiors. Among these, low-density lava worlds have dayside temperatures high enough to evaporate their surfaces, providing a unique opportunity to probe their interior compositions and test for the presence of volatiles. In this work, we investigate the atmospheric observability of low-density lava worlds. We use a radiative-convective model to explore the atmospheric structures and emission spectra of these planets, focusing on three case studies with high observability metrics and sub-stellar temperatures spanning $\sim$1900-2800 K: HD 86226c, HD 3167b and 55 Cnce. Given the possibility of mixed volatile and silicate interior compositions for these planets, we consider a range of mixed volatile and rock vapor atmospheric compositions. This includes a range of volatile fractions and three volatile compositions: water-rich (100% H$_2$O), water with CO$_2$ (80% H$_2$O+20% CO$_2$), and a desiccated O-rich scenario (67% O$_2$+33%CO$_2$). We find that spectral features due to H$_2$O, CO$_2$, SiO and SiO$_2$ are present in the infrared emission spectra as either emission or absorption features, depending on dayside temperature, volatile fraction and volatile composition. We further simulate JWST secondary eclipse observations for each of the three case studies, finding that H$_2$O and/or CO$_2$ could be detected with as few as $\sim$5 eclipses. Detecting volatiles in these atmospheres would provide crucial independent evidence that volatile-rich interiors exist among the super-Earth population., Comment: Accepted for publication in ApJ. 26 pages, 12 figures, 2 tables

A model of electric energization of the Solar Wind and Corona is developed, including electro-magnetic (EM) particle effects precluded by traditional magneto-hydro (MHD) assumptions. Using standard 1-D radial Solar models for particle density and temperature, the Core gravito-electric field is calculated; and the range of possible Photospheric photoelectric fields is estimated. The extant DC field apparently arises from about 460.Coulombs of charge displacement, mainly caused by the immense Solar energy flux pushing electrons outward. Energetically, this electric field can accelerate surface protons out of the 2.keV gravity well and up to the 4. keV energies observed in the Fast Solar Wind. The electrical energy is released in pervasive, persistent "proton lightning jets", which are proton beams, charge-neutralized by co-propagating electrons. The jets are formed by pinched "avalanche breakdown" of the weakly ionized Photosphere, probably initiated on the down-welling edges of Solar surface granulations. These energetic jets will glow as discrete filamentary surface spicules, and will be observed in reflect solar light as the diffuse K-Corona. Significantly, the total charge displacement and observed Fast Wind Speed (FWS) are quantitatively predicted by a novel "virial limit": the (positive) electrical potential energy at r=0 is limited in magnitude to the 10.keV gravitational well at r=0., Comment: 24 pages, 6 figures