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Massive star formation involves significant ionization in the innermost regions near the central object, such as gravitationally trapped H II regions, jets, ionized disks, or winds. Resolved observations of the associated continuum and recombination line emission are crucial for guiding theory. The next-generation Very Large Array (ngVLA) will enable unprecedented observations of thermal emission with 1 mas resolution, providing a new perspective on massive star formation at scales down to a few astronomical units at kiloparsec distances. This work presents synthetic interferometric ngVLA observations of the free-free continuum (93-GHz band), $\mathrm{H41\alpha}$, and $\mathrm{H38\alpha}$ recombination lines from ionized jets and disks around massive protostars. Using the sf3dmodels Python package, we generate gas distributions based on analytical models, which are then processed through the RADMC-3D radiative transfer code. Our results indicate that the ngVLA can easily resolve, both spatially and spectrally, the ionized jet from a 15 $\mathrm{M_\odot}$ protostar at 700 pc, distinguishing between collimated jets and wide-angle winds, and resolving their launching radii, widths, and any substructure down to a few astronomical units. Detailed studies of radio jets launched by massive protostars will be feasible up to distances of $\sim 2$ kpc. Furthermore, ngVLA will be able to study in detail the ionized disks around massive ($> 10~\mathrm{M_\odot}$) protostars up to distances from 4 to 12 kpc, resolving their kinematics and enabling the measurement of their central masses across the Galaxy. These observations can be conducted with on-source integrations of only a few hours., Comment: Accepted for publication in ApJ

The last decade has witnessed remarkable advances in the characterization of the (sub-)millimeter emission from planet-forming disks. Instead, the study of the (sub-)centimeter emission has made more limited progress, to the point that only a few exceptional disk-bearing objects have been characterized in the centimeter regime. This work takes a broad view of the centimeter emission from a large sample with VLA observations that is selected from previous ALMA surveys of more representative disks in brightness and extent. We report on the detection and characterization of flux at centimeter wavelengths from 21 sources in the Taurus star-forming region. Complemented by literature and archival data, the entire photometry from 0.85 mm to 6 cm is fitted by a two-component model that determines the ubiquitous presence of free-free emission entangled with the dust emission. The flux density of the free-free emission is found to scale with the accretion rate but is independent of the outer disk morphology depicted by ALMA. The dust emission at 2 cm is still appreciable, and offers the possibility to extract an unprecedented large set of dust spectral indices in the centimeter regime. A pronounced change between the median millimeter indices (2.3) and centimeter indices (2.8) suggests that a large portion of the disk emission is optically thick up to 3 mm. The comparison of both indices and fluxes with the ALMA disk extent indicates that this portion can be as large as 40 au, and suggests that the grain population within this disk region that emits the observed centimeter emission is similar in disks with different size and morphology. All these results await confirmation and dedicated dust modeling once facilities like ngVLA or SKA-mid are able to resolve the centimeter emission from planet-forming disks and disentangle the various components., Comment: Accepted for publication by A&A

The opaque nature of transformer-based models, particularly in applications susceptible to unethical practices such as dark-patterns in user interfaces, requires models that integrate uncertainty quantification to enhance trust in predictions. This study focuses on dark-pattern detection, deceptive design choices that manipulate user decisions, undermining autonomy and consent. We propose a differential fine-tuning approach implemented at the final classification head via uncertainty quantification with transformer-based pre-trained models. Employing a dense neural network (DNN) head architecture as a baseline, we examine two methods capable of quantifying uncertainty: Spectral-normalized Neural Gaussian Processes (SNGPs) and Bayesian Neural Networks (BNNs). These methods are evaluated on a set of open-source foundational models across multiple dimensions: model performance, variance in certainty of predictions and environmental impact during training and inference phases. Results demonstrate that integrating uncertainty quantification maintains performance while providing insights into challenging instances within the models. Moreover, the study reveals that the environmental impact does not uniformly increase with the incorporation of uncertainty quantification techniques. The study's findings demonstrate that uncertainty quantification enhances transparency and provides measurable confidence in predictions, improving the explainability and clarity of black-box models. This facilitates informed decision-making and mitigates the influence of dark-patterns on user interfaces. These results highlight the importance of incorporating uncertainty quantification techniques in developing machine learning models, particularly in domains where interpretability and trustworthiness are critical.

Humanoid robots rely on multi-contact planners to navigate a diverse set of environments, including those that are unstructured and highly constrained. To synthesize stable multi-contact plans within a reasonable time frame, most planners assume statically stable motions or rely on reduced order models. However, these approaches can also render the problem infeasible in the presence of large obstacles or when operating near kinematic and dynamic limits. To that end, we propose a new multi-contact framework that leverages recent advancements in relaxing collision-free path planning into a convex optimization problem, extending it to be applicable to humanoid multi-contact navigation. Our approach generates near-feasible trajectories used as guides in a dynamic trajectory optimizer, altogether addressing the aforementioned limitations. We evaluate our computational approach showcasing three different-sized humanoid robots traversing a high-raised naval knee-knocker door using our proposed framework in simulation. Our approach can generate motion plans within a few seconds consisting of several multi-contact states, including dynamic feasibility in joint space., Comment: Accepted for publication in IEEE-RAS International Conference of Humanoid Robots (Humanoids 2024)

This paper presents an open-source, lightweight, yet comprehensive software framework, named RPC, which integrates physics-based simulators, planning and control libraries, debugging tools, and a user-friendly operator interface. RPC enables users to thoroughly evaluate and develop control algorithms for robotic systems. While existing software frameworks provide some of these capabilities, integrating them into a cohesive system can be challenging and cumbersome. To overcome this challenge, we have modularized each component in RPC to ensure easy and seamless integration or replacement with new modules. Additionally, our framework currently supports a variety of model-based planning and control algorithms for robotic manipulators and legged robots, alongside essential debugging tools, making it easier for users to design and execute complex robotics tasks. The code and usage instructions of RPC are available at https://github.com/shbang91/rpc., Comment: 7pages, 4 figures

In 2017, the next generation Very Large Array (ngVLA) Science Advisory Council, together with the international astronomy community, developed a set of five Key Science Goals (KSGs) to inform, prioritize and refine the technical capabilities of a future radio telescope array for high angular resolution operation from 1.2 - 116 GHz with 10 times the sensitivity of the Jansky VLA and ALMA. The resulting KSGs, which require observations at centimeter and millimeter wavelengths that cannot be achieved by any other facility, represent a small subset of the broad range of astrophysical problems that the ngVLA will be able address. This document presents an update to the original ngVLA KSGs, taking account of new results and progress in the 7+ years since their initial presentation, again drawing on the expertise of the ngVLA Science Advisory Council and the broader community in the ngVLA Science Working Groups. As the design of the ngVLA has also matured substantially in this period, this document also briefly addresses initial expectations for ngVLA data products and processing that will be needed to achieve the KSGs. The original ngVLA KSGs endure as outstanding problems of high priority. In brief, they are: (1) Unveiling the Formation of Solar System Analogues; (2) Probing the Initial Conditions for Planetary Systems and Life with Astrochemistry; (3) Charting the Assembly, Structure, and Evolution of Galaxies from the First Billion Years to the Present; (4) Science at the Extremes: Pulsars as Laboratories for Fundamental Physics; (5) Understanding the Formation and Evolution of Stellar and Supermassive Black Holes in the Era of Multi-Messenger Astronomy., Comment: 29 pages, 9 figures, ngVLA memo 125. arXiv admin note: text overlap with arXiv:1711.09960

Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations of protoplanetary disks in the millimeter continuum have shown a variety of radial gaps, cavities, and spiral features. These substructures may be signposts for ongoing planet formation, and therefore these systems are promising targets for direct imaging planet searches in the near-infrared. To this end, we present results from a deep imaging survey in the $L'$-band (3.8 $\mu$m) with the Keck/NIRC2 vortex coronagraph to search for young planets in 43 disks with resolved features in the millimeter continuum or evidence for gaps/central cavities from their spectral energy distributions. Although we do not detect any new point sources, using the vortex coronagraph allows for high sensitivity to faint sources at small angular separations (down to ${\sim}$0$^{\prime\prime}$.1), allowing us to place strong upper limits on the masses of potential gas giant planets. We compare our mass sensitivities to the masses of planets derived using ALMA observations, and while we are sensitive to $\sim$1 M$_{Jup}$ planets in the gaps in some of our systems, we are generally not sensitive to planets of the masses expected from the ALMA observations. In addition to placing upper limits on the masses of gas giant planets that could be interacting with the dust in the disks to form the observed millimeter substructures, we are also able to map the micron-sized dust as seen in scattered light for 8 of these systems. Our large sample of systems also allows us to investigate limits on planetary accretion rates and disk viscosities., Comment: 23 pages, 14 figures, 3 tables, accepted for publication in AJ

This paper proposes a novel control framework for agile and robust bipedal locomotion, addressing model discrepancies between full-body and reduced-order models. Specifically, assumptions such as constant centroidal inertia have introduced significant challenges and limitations in locomotion tasks. To enhance the agility and versatility of full-body humanoid robots, we formalize a Model Predictive Control (MPC) problem that accounts for the variable centroidal inertia of humanoid robots within a convex optimization framework, ensuring computational efficiency for real-time operations. In the proposed formulation, we incorporate a centroidal inertia network designed to predict the variable centroidal inertia over the MPC horizon, taking into account the swing foot trajectories -- an aspect often overlooked in ROM-based MPC frameworks. By integrating the MPC-based contact wrench planning with our low-level whole-body controller, we significantly improve the locomotion performance, achieving stable walking at higher velocities that are not attainable with the baseline method. The effectiveness of our proposed framework is validated through high-fidelity simulations using our full-body bipedal humanoid robot DRACO 3, demonstrating dynamic behaviors., Comment: 8pages, 6figures

Synthesized beam (PSF) synthetic observations with and without the antennas in Mexico are analyzed. For a simple continuum observing setup, we generated visibility files and their associated PSF images for a grid of parameters (robust weighting, tapering, and declination). The tests were done for both the MID and MID+Spiral+Core configurations and their cropped versions without antennas in Mexico. We show that the performance of the Array, in terms of the beam properties, is in general significantly better when both the MID array antennas are present in Northern Mexico and observations target southern sources. At a declination of -40 deg, there are increments in the ellipticity of at least ~1.3X and 1.2X for a tapering of 3.0 and 4.0 mas, if the antennas in Mexico are not included. For the parameter space tested, the changes in ellipticity of the MID and MID+Spiral+Core configurations differ by ~10%. Larger tapering values help to reduce the ellipticity for cropped configurations at all declinations, but it will impose more constraints in terms of angular resolution., Comment: 10 pages, 8 figures

We investigate the planetary migration of low-mass planets ($M_p\in[1,15]M_\oplus$, here $M_\oplus$ is the Earth mass) in a gaseous disc containing a previously formed gap. We perform high-resolution 3D simulations with the FARGO3D code. To create the gap in the surface density of the disc, we use a radial viscosity profile with a bump, which is maintained during the entire simulation time. We find that when the gap is sufficiently deep, the spiral waves excited by the planet trigger the Rossby wave instability, forming cyclonic (underdense) vortices at the edges of the gap. When the planet approaches the gap, it interacts with the vortices, which produce a complex flow structure around the planet. Remarkably, we find a widening of the horseshoe region of the planet produced by the vortex at the outer edge of the gap, which depending on the mass of the planet differs by at least a factor of two with respect to the standard horseshoe width. This inevitably leads to an increase in the corotation torque on the planet and produces an efficient trap to halt its inward migration. In some cases, the planet becomes locked in corotation with the outer vortex. Under this scenario, our results could explain why low-mass planets do not fall towards the central star within the lifetime of the protoplanetary disc. Lastly, the development of these vortices produces an asymmetric temporal evolution of the gap, which could explain the structures observed in some protoplanetary discs., Comment: 17 pages, 20 figures, accepted for publication in MNRAS

Aims. To comprehend the efficiency of dust evolution within protoplanetary disks, it is crucial to conduct studies of these disks using high-resolution observations at multiple wavelengths with the Atacama Large Millimeter/submillimeter Array (ALMA). Methods. In this work, we present high-frequency ALMA observations of the HL Tau disk using its Band 9 centered at a wavelength of 0.45 mm. These observations achieve the highest angular resolution in a protoplanetary disk to date, 12 milliarcseconds (mas), allowing the study of the dust emission at scales of 2 au. We use these data to extend the previously published multi-wavelength analysis of the HL Tau disk. Results. Our new 0.45 mm data traces mainly optically thick emission, providing a tight constraint to the dust temperature profile. We derive maximum particle sizes of $\sim$1 cm from the inner disk to $\sim$60 au. Beyond this radius, we find particles between 300 $\mu$m and 1 mm. Moreover, an intriguing asymmetry is observed at 32 au in the northeast inner part of the HL Tau disk at 0.45 mm. We propose that this asymmetry is the outcome of a combination of factors including the optically thick nature of the emission, the orientation of the disk, and a relatively large dust scale height of the grains. To validate this, we conducted a series of radiative transfer models using the RADMC-3D software. If this scenario is correct, our measured dust mass within 32 au would suggest a dust scale height H/R> 0.08 for the inner disk. Finally, the unprecedented resolution allowed us to probe for the first time the dust emission down to a few au scales. We observed an increase in brightness temperature inside the estimated water snowline and speculate whether it could indicate the presence of a traffic jam effect in the inner disk. Abridge, Comment: Accepted for publication in A&A, 13 pages, 8 figures

Generative Artificial Intelligence (AI) models can propose solutions to scientific problems beyond human capability. To truly make conceptual contributions, researchers need to be capable of understanding the AI-generated structures and extracting the underlying concepts and ideas. When algorithms provide little explanatory reasoning alongside the output, scientists have to reverse-engineer the fundamental insights behind proposals based solely on examples. This task can be challenging as the output is often highly complex and thus not immediately accessible to humans. In this work we show how transferring part of the analysis process into an immersive Virtual Reality (VR) environment can assist researchers in developing an understanding of AI-generated solutions. We demonstrate the usefulness of VR in finding interpretable configurations of abstract graphs, representing Quantum Optics experiments. Thereby, we can manually discover new generalizations of AI-discoveries as well as new understanding in experimental quantum optics. Furthermore, it allows us to customize the search space in an informed way - as a human-in-the-loop - to achieve significantly faster subsequent discovery iterations. As concrete examples, with this technology, we discover a new resource-efficient 3-dimensional entanglement swapping scheme, as well as a 3-dimensional 4-particle Greenberger-Horne-Zeilinger-state analyzer. Our results show the potential of VR for increasing a human researcher's ability to derive knowledge from graph-based generative AI that, which is a common abstract data representation used in diverse fields of science., Comment: 12 pages, 6 figures, comments welcome

Polarized (sub)millimeter emission from dust grains in circumstellar disks was initially thought to be due to grains aligned with the magnetic field. However, higher resolution multi-wavelength observations along with improved models found that this polarization is dominated by self-scattering at shorter wavelengths (e.g., 870 $\mu$m) and by grains aligned with something other than magnetic fields at longer wavelengths (e.g., 3 mm). Nevertheless, the polarization signal is expected to depend on the underlying substructure, and observations hitherto have been unable to resolve polarization in multiple rings and gaps. HL Tau, a protoplanetary disk located 147.3 $\pm$ 0.5 pc away, is the brightest Class I or Class II disk at millimeter/submillimeter wavelengths. Here we show deep, high-resolution 870 $\mu$m polarization observations of HL Tau, resolving polarization in both the rings and gaps. We find that the gaps have polarization angles with a significant azimuthal component and a higher polarization fraction than the rings. Our models show that the disk polarization is due to both scattering and emission from aligned effectively prolate grains. The intrinsic polarization of aligned dust grains is likely over 10%, which is much higher than what was expected in low resolution observations (~1%). Asymmetries and dust features are revealed in the polarization observations that are not seen in non-polarimetric observations., Comment: Published in Nature

Recent laboratory experiments have revealed that destructive collisions of icy dust particles may occur at much lower velocities than previously believed. These low fragmentation velocities push down the maximum grain size in collisional growth models. Motivated by the smooth radial distribution of pebble sizes inferred from ALMA/VLA multi-wavelength continuum analysis, we propose a concise model to explain this feature and aim to constrain the turbulence level at the midplane of protoplanetary disks. Our approach is built on the assumption that the fragmentation threshold is the primary barrier limiting pebble growth within pressure maxima. Consequently, the grain size at the ring location can provide direct insights into the turbulent velocity governing pebble collisions and, by extension, the turbulence level at the disk midplane. We validate this method using the Dustpy code, which simulates dust transport and coagulation. We apply our method to 7 disks, TW Hya, IM Lup, GM Aur, AS 209, HL Tau, HD 163296, and MWC 480, for which grain sizes have been measured from multi-wavelength continuum analysis. A common feature emerges from our analysis, with an overall low turbulence coefficient of $\alpha\sim10^{-4}$ observed in five out of seven disks when taking fragmentation velocity $v_{\rm frag} = 1{\rm \,m\,s}^{-1}$. A higher fragmentation velocity would imply a turbulence coefficient significantly larger than the current observational constraints. IM Lup stands out with a relatively higher coefficient of $10^{-3}$. Notably, HL Tau exhibits an increasing trend in $\alpha$ with distance, which supports enhanced turbulence at its outer disk region, possibly associated with the infalling streamer onto HL~Tau. The current (sub)mm pebble size constrained in disks implies low levels of turbulence, as well as fragile pebbles consistent with recent laboratory measurements., Comment: 11 pages, 8 figures, 2 tables, Accepted for publication in A&A

We have carried out ALMA observations of the massive star-forming region W75N(B), which contains the massive protostars VLA1, VLA2, and VLA3. Particularly, VLA2 is an enigmatic protostar associated with a wind-driven H$_2$O maser shell, which has evolved from an almost isotropic outflow to a collimated one in just 20 years. The shell expansion seemed to be halted by an obstacle located to the northeast of VLA2. Here we present our findings from observing the 1.3 mm continuum and H$_2$CO and SiO emission lines. Within a region of $\sim 30"$ ($\sim 39,000$ au) diameter, we have detected 40 compact mm-continuum sources, three of them coinciding with VLA1, VLA2, and VLA3. While the H$_2$CO emission is mainly distributed in a fragmented structure around the three massive protostars, but without any of the main H$_2$CO clumps spatially coinciding with them, the SiO is highly concentrated on VLA2, indicating the presence of very strong shocks generated near this protostar. The SiO emission is clearly resolved into an elongated structure ($\sim 0.6"\times0.3"$; $\sim 780$ au$\times$390 au) perpendicular to the major axis of the wind-driven maser shell. The structure and kinematics of the SiO emission are consistent with a toroid and a wide-angle outflow surrounding a central mass of $\sim 10$ M$_{\odot}$, thus supporting previous theoretical predictions regarding the evolution of the outflow. Additionally, we have identified the expected location and estimated the gas density of the obstacle that is hindering the expansion of the maser shell., Comment: To be published in The Astrophysical Journal Letters. Sixteen pages, seven figures. Updated metadata

Polarization is a unique tool to study the properties of dust grains of protoplanetary disks and detail the initial conditions of planet formation. Polarization around HL Tau was previously imaged using the Atacama Large Millimeter/submillimeter Array (ALMA) at Bands 3 (3.1 mm), 6 (1.3 mm), and 7 (0.87 mm), showing that the polarization orientation changes across wavelength $\lambda$. The polarization morphology at Band 7 is predominantly parallel to the disk minor axis but appears azimuthally oriented at Band 3, with the morphology at Band 6 in between the two. We present new ~0.2" (29 au) polarization observations at Q-Band (7.0 mm) using the Karl G. Jansky Very Large Array (VLA) and at Bands 4 (2.1 mm), 5 (1.5 mm), and 7 using ALMA, consolidating HL Tau's position as the protoplanetary disk with the most complete wavelength coverage in dust polarization. The polarization patterns at Bands 4 and 5 continue to follow the morphological transition with wavelength previously identified in Bands 3, 6, and 7. Based on the azimuthal variation, we decompose the polarization into contributions from scattering ($s$) and thermal emission ($t$). We find that $s$ decreases slowly with increasing $\lambda$, and $t$ increases more rapidly with $\lambda$ which are expected from optical depth effects of toroidally aligned, scattering prolate grains. The relatively weak $\lambda$ dependence of $s$ is consistent with large, porous grains. The sparse polarization detections from the Q-band image are also consistent with toroidally aligned prolate grains., Comment: 22 pages, 13 figures, submitted to MNRAS

Despite their promise to facilitate new scientific discoveries, the opaqueness of neural networks presents a challenge in interpreting the logic behind their findings. Here, we use a eXplainable-AI (XAI) technique called $inception$ or $deep$ $dreaming$, which has been invented in machine learning for computer vision. We use this technique to explore what neural networks learn about quantum optics experiments. Our story begins by training deep neural networks on the properties of quantum systems. Once trained, we "invert" the neural network -- effectively asking how it imagines a quantum system with a specific property, and how it would continuously modify the quantum system to change a property. We find that the network can shift the initial distribution of properties of the quantum system, and we can conceptualize the learned strategies of the neural network. Interestingly, we find that, in the first layers, the neural network identifies simple properties, while in the deeper ones, it can identify complex quantum structures and even quantum entanglement. This is in reminiscence of long-understood properties known in computer vision, which we now identify in a complex natural science task. Our approach could be useful in a more interpretable way to develop new advanced AI-based scientific discovery techniques in quantum physics., Comment: Modified Figure 2. Fixed minor typos

We tackle the problem of developing humanoid loco-manipulation skills with deep imitation learning. The difficulty of collecting task demonstrations and training policies for humanoids with a high degree of freedom presents substantial challenges. We introduce TRILL, a data-efficient framework for training humanoid loco-manipulation policies from human demonstrations. In this framework, we collect human demonstration data through an intuitive Virtual Reality (VR) interface. We employ the whole-body control formulation to transform task-space commands by human operators into the robot's joint-torque actuation while stabilizing its dynamics. By employing high-level action abstractions tailored for humanoid loco-manipulation, our method can efficiently learn complex sensorimotor skills. We demonstrate the effectiveness of TRILL in simulation and on a real-world robot for performing various loco-manipulation tasks. Videos and additional materials can be found on the project page: https://ut-austin-rpl.github.io/TRILL., Comment: Accepted to Humanoids 2023

In the context of Industry 4.0, the use of artificial intelligence (AI) and machine learning for anomaly detection is being hampered by high computational requirements and associated environmental effects. This study seeks to address the demands of high-performance machine learning models with environmental sustainability, contributing to the emerging discourse on 'Green AI.' An extensive variety of machine learning algorithms, coupled with various Multilayer Perceptron (MLP) configurations, were meticulously evaluated. Our investigation encapsulated a comprehensive suite of evaluation metrics, comprising Accuracy, Area Under the Curve (AUC), Recall, Precision, F1 Score, Kappa Statistic, Matthews Correlation Coefficient (MCC), and F1 Macro. Simultaneously, the environmental footprint of these models was gauged through considerations of time duration, CO2 equivalent, and energy consumption during the training, cross-validation, and inference phases. Traditional machine learning algorithms, such as Decision Trees and Random Forests, demonstrate robust efficiency and performance. However, superior outcomes were obtained with optimised MLP configurations, albeit with a commensurate increase in resource consumption. The study incorporated a multi-objective optimisation approach, invoking Pareto optimality principles, to highlight the trade-offs between a model's performance and its environmental impact. The insights derived underscore the imperative of striking a balance between model performance, complexity, and environmental implications, thus offering valuable directions for future work in the development of environmentally conscious machine learning models for industrial applications., Comment: 29 references, 8 figures, 9 tables, 18 pages

Dust particle sizes constrained from dust continuum and polarization observations by radio interferometry are inconsistent by at least an order of magnitude. Motivated by porous dust observed in small Solar System bodies (e.g., from the Rosetta mission), we explore how the dust particle's porosity affects the estimated particle sizes from these two methods. Porous particles have lower refractive indices, which affect both opacity and polarization fraction. With weaker Mie interference patterns, the porous particles have lower opacity at mm wavelengths than the compact particles if the particle size exceeds several hundred microns. Consequently, the inferred dust mass using porous particles can be up to a factor of six higher. The most significant difference between compact and porous particles is their scattering properties. The porous particles have a wider range of particle sizes with high linear polarization from dust self-scattering, allowing mm-cm-sized particles to explain polarization observations. With a Bayesian approach, we use porous particles to fit HL Tau disk's multi-wavelength continuum and mm-polarization observations from ALMA and VLA. The moderately porous particles with sizes from 1 mm-1 m can explain both continuum and polarization observations, especially in the region between 20-60 au. If the particles in HL Tau are porous, the porosity should be from 70% to 97% from current polarization observations. We also predict that future observations of the self-scattering linear polarization at longer wavelengths (e.g., ALMA B1 and ngVLA) have the potential to further constrain the particle's porosity and size., Comment: 39 pages, 18 figures, 1 table, accepted to be published in The Astrophysical Journal