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The streaming instability (SI) is a leading mechanism for concentrating solid particles into regions dense enough to form planetesimals. Its efficiency in clumping particles depends primarily on the dimensionless stopping time ($\tau_s$, a proxy for particle size) and dust-to-gas surface density ratio ($Z$). Previous simulations identified a critical $Z$ ($Z_{\rm{crit}}$) above which strong clumping occurs, where particle densities exceed the Hill density (thus satisfying a condition for gravitational collapse), over a wide range of $\tau_s$. These works found that for $\tau_s \leq 0.01$, $Z_{\rm{crit}}$ was above the ISM value $(\sim 0.01)$. In this work, we reexamine the clumping threshold using 2D axisymmetric, stratified simulations at high resolution and with relatively large (compared to many previous simulations) domain sizes. Our main results are as follows: First, when $\tau_s = 0.01$, strong clumping occurs even at $Z \lesssim 0.01$, lower than $Z_{\rm{crit}}$ found in all previous studies. Consequently, we revise a previously published fit to the $Z_{\rm{crit}}$ curve to account for this updated $Z_{\rm{crit}}$. Second, higher resolution results in a thicker dust layer, which may result from other instabilities manifesting, such as the vertical shearing streaming instability. Third, despite this thicker layer, higher resolution can lead to strong clumping even with lower midplane dust-to-gas density ratios (which results from the thicker particle layer) so long as $Z \gtrsim Z_{\rm{crit}}$. Our results demonstrate the efficiency of the SI in clumping small particles at $Z \sim 0.01$, which is a significant refinement of the conditions for planetesimal formation by the SI., Comment: 25 pages, 12 figures, submitted to the Astrophysical Journal

In this paper, we give improved bounds on the Hausdorff dimension of pinned distance sets of planar sets with dimension strictly less than one. As the planar set becomes more regular (i.e., the Hausdorff and packing dimension become closer), our lower bound on the Hausdorff dimension of the pinned distance set improves. Additionally, we prove the existence of small universal sets for pinned distances. In particular, we show that, if a Borel set $X\subseteq\mathbb{R}^2$ is weakly regular ($\dim_H(X) = \dim_P(X)$), and $\dim_H(X) > 1$, then \begin{equation*} \sup\limits_{x\in X}\dim_H(\Delta_x Y) = \min\{\dim_H(Y), 1\} \end{equation*} for every Borel set $Y\subseteq\mathbb{R}^2$. Furthermore, if $X$ is also compact and Alfors-David regular, then for every Borel set $Y\subseteq\mathbb{R}^2$, there exists some $x\in X$ such that \begin{equation*} \dim_H(\Delta_x Y) = \min\{\dim_H(Y), 1\}. \end{equation*}, Comment: 31 pages

Spacecraft detumbling with magnetic torque coils is an inherently underactuated control problem. Contemporary and classical magnetorquer detumbling methods do not adequately consider this underactuation, and suffer from poor performance as a result. These controllers can get stuck on an uncontrollable manifold, resulting in long detumbling times and high power consumption. This work presents a novel detumble controller based on a non-monotonic Lyapunov function that predicts the future magnetic field along the satellite's orbit and avoids uncontrollable configurations. In comparison to other controllers in the literature, our controller detumbles a satellite in significantly less time while also converging to lower overall angular momentum. We provide a derivation and proof of convergence for our controller as well as Monte-Carlo simulation results demonstrating its performance in representative use cases.

Ionization drives important chemical and dynamical processes within protoplanetary disks, including the formation of organics and water in the cold midplane and the transportation of material via accretion and magneto-hydrodynamic (MHD) flows. Understanding these ionization-driven processes is crucial for understanding disk evolution and planet formation. We use new and archival ALMA observations of HCO+, H13CO+, and N2H+ to produce the first forward-modeled 2D ionization constraints for the DM Tau protoplanetary disk. We include ionization from multiple sources and explore the disk chemistry under a range of ionizing conditions. Abundances from our 2D chemical models are post-processed using non-LTE radiative transfer, visibility sampling, and imaging, and are compared directly to the observed radial emission profiles. The observations are best fit by a modestly reduced CR ionization rate ($\zeta_{CR}$ ~ 10$^{-18}$ s$^{-1}$) and a hard X-ray spectrum (hardness ratio [HR] = 0.3), which we associate with stellar flaring conditions. Our best-fit model under-produces emission in the inner disk, suggesting that there may be an additional mechanism enhancing ionization in DM Tau's inner disk. Overall, our findings highlight the complexity of ionization in protoplanetary disks and the need for high resolution multi-line studies., Comment: 18 pages, 12 figures, accepted to be published in The Astrophysical Journal (June 25, 2024)

Disk vortices, seen in numerical simulations of protoplanetary disks and found observationally in ALMA and VLA images of these objects, are promising sites for planet formation given their pebble trapping abilities. Previous works have shown strong concentration of pebbles in vortices, but gravitational collapse has only been shown in low-resolution, two-dimensional, global models. In this letter, we aim to study the pebble concentration and gravitational collapse of pebble clouds in vortices via high-resolution, three-dimensional, local models. We performed simulations of the dynamics of gas and solids in a local shearing box where the gas is subject to convective overstability, generating a persistent giant vortex. We find that the vortex produces objects of Moon and Mars mass, with mass function of power law $d\ln N/d\ln M=-1.6\pm 0.3$. The protoplanets grow rapidly, doubling in mass in about 5 orbits, following pebble accretion rates. The mass range and mass doubling rate are in broad agreement with previous low resolution global models. We conclude that Mars-mass planetary embryos are the natural outcome of planet formation inside the disk vortices seen in millimeter and radio images of protoplanetary disks., Comment: 9 pages, 5 figures, accepted for publication in ApJ letters

We propose a time-resolved optical measurement scheme for sampling transient charge and spin currents in a bulk centrosymmetric semiconductor. The technique relies on emission of second harmonic light triggered by a pulsed below-gap optical excitation and a spontaneous intraband polarization arising from spin or charge motion, mediated by a $\chi^(3)$-based nonlinear optical process. Our proposal uses homodyne amplification to boost the weak second harmonic signal, making it detectable with conventional electronics, calculated for charge current in a room temperature GaAs semiconductor. This all-optical technique requires neither electrical contact nor bias fields and the signal is estimated at a few percent relative to the shot noise of the probe. This proposal motivates a novel method for exploring thermal and quantum fluctuations in the solid state in a non-invasive manner., Comment: 7 pages, 2 figures

The amount of turbulence in protoplanetary discs around young stars is critical for determining the efficiency, timeline, and outcomes of planet formation. It is also difficult to measure. Observations are still limited, but direct measurements of the non-thermal, turbulent gas motion are possible with the Atacama Large Millimeter/submillimeter Array (ALMA). Using CO(2-1)/$^{13}$CO(2-1)/C$^{18}$O(2-1) ALMA observations of the disc around IM Lup at ~0.4" (~60 au) resolution we find evidence of significant turbulence, at the level of $\delta v_{\rm turb}=(0.18-0.30)$c$_s$. This result is robust against systematic uncertainties (e.g., amplitude flux calibration, midplane gas temperature, disc self-gravity). We find that gravito-turbulence as the source of the gas motion is unlikely based on the lack of an imprint on the rotation curve from a massive disc, while magneto-rotational instabilities and hydrodynamic instabilities are still possible, depending on the unknown magnetic field strength and the cooling timescale in the outer disc., Comment: Accepted by MNRAS, 17 pages, 12 figures

This article is a study guide for ``On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" by Orponen and Shmerkin. We begin by introducing Furstenberg set problem and exceptional set of projections and provide a summary of the proof with the core ideas., Comment: 23 pages, 5 figures, Study guide written at the UPenn Study Guide Writing Workshop 2023

It is generally accepted that the Moon accreted from the disk formed by an impact between the proto-Earth and impactor, but its details are highly debated. Some models suggest that a Mars-sized impactor formed a silicate melt-rich (vapor-poor) disk around Earth, whereas other models suggest that a highly energetic impact produced a silicate vapor-rich disk. Such a vapor-rich disk, however, may not be suitable for the Moon formation, because moonlets, building blocks of the Moon, of 100 m-100 km may experience strong gas drag and fall onto Earth on a short timescale, failing to grow further. This problem may be avoided if large moonlets ($\gg 100$ km) form very quickly by streaming instability, which is a process to concentrate particles enough to cause gravitational collapse and rapid formation of planetesimals or moonlets. Here, we investigate the effect of the streaming instability in the Moon-forming disk for the first time and find that this instability can quickly form $\sim 100$ km-sized moonlets. However, these moonlets are not large enough to avoid strong drag and they still fall onto Earth quickly. This suggests that the vapor-rich disks may not form the large Moon, and therefore the models that produce vapor-poor disks are supported. This result is applicable to general impact-induced moon-forming disks, supporting the previous suggestion that small planets ($<1.6 R_\oplus$) are good candidates to host large moons because their impact-induced disks would be likely vapor-poor. We find a limited role of streaming instability in a satellite formation in an impact-induced disk, whereas it plays a key role during planet formation., Comment: Accepted for Publication in PSJ

Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq \mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's line segment extension conjecture posits that the Hausdorff dimension of $F$ should equal that of $E$. Working in $\mathbb{R}^2$, we use effective methods to prove a strong packing dimension variant of this conjecture, from which the generalized Kakeya conjecture for packing dimension immediately follows. This is followed by several doubling estimates in higher dimensions and connections to related problems., Comment: 24 pages, 1 figure. Referee comments incorporated. Proof of Theorem 1.3 simplified. Several typos corrected

Given the important role turbulence plays in the settling and growth of dust grains in protoplanetary disks, it is crucial that we determine whether these disks are turbulent and to what extent. Protoplanetary disks are weakly ionized near the mid-plane, which has led to a paradigm in which largely laminar magnetic field structures prevail deeper in the disk, with angular momentum being transported via magnetically launched winds. Yet, there has been little exploration on the precise behavior of the gas within the bulk of the disk. We carry out 3D, local shearing box simulations that include all three low-ionization effects (Ohmic diffusion, ambipolar diffusion, and the Hall effect) to probe the nature of magnetically driven gas dynamics 1-30 AU from the central star. We find that gas turbulence can persist with a generous yet physically motivated ionization prescription (order unity Elsasser numbers). The gas velocity fluctuations range from 0.03-0.09 of the sound speed $c_s$ at the disk mid-plane to $\sim c_s$ near the disk surface, and are dependent on the initial magnetic field strength. However, the turbulent velocities do not appear to be strongly dependent on the field polarity, and thus appear to be insensitive to the Hall effect. The mid-plane turbulence has the potential to drive dust grains to collision velocities exceeding their fragmentation limit, and likely reduces the efficacy of particle clumping in the mid-plane, though it remains to be seen if this level of turbulence persists in disks with lower ionization levels., Comment: 23 pages, 19 figures, 2 tables, submitted to ApJ

Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric setting, such an energy norm is non-existent. For this reason, convergence of AMG for nonsymmetric systems of equations remains an open area of research. A particular aspect missing from theory of nonsymmetric and indefinite AMG is the incorporation of general relaxation schemes. In the SPD setting, the classical form of optimal AMG interpolation provides a useful insight in determining the best possible two-grid convergence rate of a method based on an arbitrary symmetrized relaxation scheme. In this work, we discuss a generalization of the optimal AMG convergence theory targeting nonsymmetric problems, using a certain matrix-induced orthogonality of the left and right eigenvectors of a generalized eigenvalue problem relating the system matrix and relaxation operator. We show that using this generalization of the optimal convergence theory, one can obtain a measure of the spectral radius of the two grid error transfer operator that is mathematically equivalent to the derivation in the SPD setting for optimal interpolation, which instead uses norms. In addition, this generalization of the optimal AMG convergence theory can be further extended for symmetric indefinite problems, such as those arising from saddle point systems so that one can obtain a precise convergence rate of the resulting two-grid method based on optimal interpolation. We provide supporting numerical examples of the convergence theory for nonsymmetric advection-diffusion problems, two-dimensional Dirac equation motivated by $\gamma_5$-symmetry, and the mixed Darcy flow problem corresponding to a saddle point system., Comment: 20 pages, 5 figures, submitted for publication in the SIAM journal on scientific computing, copper mountain special section, iterative methods, 2024

Kuiper belt objects show an unexpected trend, whereby large bodies have increasingly higher densities, up to five times greater than their smaller counterparts. Current explanations for this trend assume formation at constant composition, with the increasing density resulting from gravitational compaction. However, this scenario poses a timing problem to avoid early melting by decay of $^{26}$Al. We aim to explain the density trend in the context of streaming instability and pebble accretion. Small pebbles experience lofting into the atmosphere of the disk, being exposed to UV and partially losing their ice via desorption. Conversely, larger pebbles are shielded and remain more icy. We use a shearing box model including gas and solids, the latter split into ices and silicate pebbles. Self-gravity is included, allowing dense clumps to collapse into planetesimals. We find that the streaming instability leads to the formation of mostly icy planetesimals, albeit with an unexpected trend that the lighter ones are more silicate-rich than the heavier ones. We feed the resulting planetesimals into a pebble accretion integrator with a continuous size distribution, finding that they undergo drastic changes in composition as they preferentially accrete silicate pebbles. The density and masses of large KBOs are best reproduced if they form between 15 and 22\,AU. Our solution avoids the timing problem because the first planetesimals are primarily icy, and $^{26}$Al is mostly incorporated in the slow phase of silicate pebble accretion. Our results lend further credibility to the streaming instability and pebble accretion as formation and growth mechanisms., Comment: 24 pages, 13 figures, accepted to The Planetary Science Journal

The streaming instability (SI) is a leading candidate for planetesimal formation, which can concentrate solids through two-way aerodynamic interactions with the gas. The resulting concentrations can become sufficiently dense to collapse under particle self-gravity, forming planetesimals. Previous studies have carried out large parameter surveys to establish the critical particle to gas surface density ratio ($Z$), above which SI-induced concentration triggers planetesimal formation. The threshold $Z$ depends on the dimensionless stopping time ($\tau_s$, a proxy for dust size). However, these studies neglected both particle self-gravity and external turbulence. Here, we perform 3D stratified shearing box simulations with both particle self-gravity and turbulent forcing, which we characterize via $\alpha_D$ that measures turbulent diffusion. We find that forced turbulence, at amplitudes plausibly present in some protoplanetary disks, can increase the threshold $Z$ by up to an order of magnitude. For example, for $\tau_s = 0.01$, planetesimal formation occurs when $Z \gtrsim 0.06$, $\gtrsim 0.1$, and $\gtrsim 0.2$ at $\alpha_D = 10^{-4}$, $10^{-3.5}$, and $10^{-3}$, respectively. We provide a single fit to the critical $Z$ as a function of $\alpha_D$ and $\tau_s$ required for the SI to work (though limited to the range $\tau_s = 0.01$--0.1). Our simulations also show that planetesimal formation requires a mid-plane particle-to-gas density ratio that exceeds unity, with the critical value being independent of $\alpha_D$. Finally, we provide the estimation of particle scale height that accounts for both particle feedback and external turbulence., Comment: 27 pages, 13 figures, submitted to The Astrophysical Journal

Silicon photonics has many attractive features but faces a major issue: inefficient and slow photodetection in the telecom range. New metal-semiconductor Schottky photodetectors based on intraband absorption address this problem, but their efficiency remains low. We suggest that by creating a junction between silicon and a transparent oxide with appropriate doping, which results in a real permittivity close to zero (known as the epsilon near zero or ENZ regime), detection efficiency could increase by more than tenfold. Using Aluminum Zinc Oxide (AZO) as an example, we design an optimized AZO/Si slot photonic waveguide detector that could potentially reach an efficiency of several tens of percent, in contrast to a few percent for a metal/Si Schottky detector. This increase is primarily due to the lower density of states in AZO compared to metal, along with superior coupling efficiency and strong absorption within a 10 nm slot., Comment: 14 pages, 6 figures

We prove that if $E\subseteq \R^2$ is analytic and $1

This work develops a novel all-at-once space-time preconditioning approach for resistive magnetohydrodynamics (MHD), with a focus on model problems targeting fusion reactor design. We consider parallel-in-time due to the long time domains required to capture the physics of interest, as well as the complexity of the underlying system and thereby computational cost of long-time integration. To ameliorate this cost by using many processors, we thus develop a novel approach to solving the whole space-time system that is parallelizable in both space and time. We develop a space-time block preconditioning for resistive MHD, following the space-time block preconditioning concept first introduced by Danieli et al. in 2022 for incompressible flow, where an effective preconditioner for classic sequential time-stepping is extended to the space-time setting. The starting point for our derivation is the continuous Schur complement preconditioner by Cyr et al. in 2021, which we proceed to generalise in order to produce, to our knowledge, the first space-time block preconditioning approach for the challenging equations governing incompressible resistive MHD. The numerical results are promising for the model problems of island coalescence and tearing mode, with the overhead computational cost associated with space-time preconditioning versus sequential time-stepping being modest and primarily in the range of 2x-5x, which is low for parallel-in-time schemes in general. Additionally, the scaling results for inner (linear) and outer (nonlinear) iterations are flat in the case of fixed time-step size and only grow very slowly in the case of time-step refinement., Comment: 25 pages, 4 figures, 3 tables

The ability to manipulate the refractive index is a fundamental principle underlying numerous photonic devices. Various techniques exist to modify the refractive index across diverse materials, making performance comparison far from straightforward. In evaluating these methods, power consumption emerges as a key performance characteristic, alongside bandwidth and footprint. Here I undertake a comprehensive comparison of the energy and power requirements for the most well-known index change schemes. The findings reveal that while the energy per volume for index change remains within the same order of magnitude across different techniques and materials, the power consumption required to achieve switching, 100% modulation, or 100% frequency conversion can differ significantly, spanning many orders of magnitude. As it turns out, the material used has less influence on power reduction than the specific resonant or traveling wave scheme employed to enhance the interaction time between light and matter. Though this work is not intended to serve as a design guide, it does establish the limitations and trade-offs involved in index modulation, thus providing valuable insights for photonics practitioners.

The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently. We consider two models for many particle diffusion -- one treats each particle as independent simple random walkers while the other treats them as coupled to a common space-time random forcing field that biases particles nearby in space and time in similar ways. The first passage time of a single diffusing particle under both of these models show the same statistics and scaling behavior. However, for many particle diffusions, the first passage time among all particles (the `extreme first passage time') is very different between the two models, effected in the latter case by the randomness of the common forcing field. We develop an asymptotic (in the number of particles and location where first passage is being probed) theoretical framework to separate out the impact of the random environment with that of sampling trajectories within it. We identify a new power-law describing the impact to the extreme first passage time variance of the environment. Through numerical simulations we verify that the predictions from this asymptotic theory hold even for systems with widely varying numbers of particles, all the way down to 100 particles. This shows that measurements of the extreme first passage time for many-particle diffusions provide an indirect measurement of the underlying environment in which the diffusion is occurring.

Fully CMOS-compatible photonic memory holding devices hold a potential in a development of ultrafast artificial neural networks. Leveraging the benefits of photonics such as high-bandwidth, low latencies, low-energy interconnect and high speed they can overcome the existing limits of the electronic processing. To satisfy all these requirements a new photonic platform is proposed that combines low-loss nitride-rich silicon as a guide and low-loss transparent conductive oxides as an active material that can provide high nonlinearity and bistability under both electrical and optical signals., Comment: 13 pages, 8 figures

Photonics integrated circuits have a huge potential to serve as a framework for a new class of information processing machines and can enable ultrafast artificial neural networks. They can overcome the existing speed and power limits of the electronic processing elements and provide additional benefits of photonics such as high-bandwidth, sub-nanosecond latencies and low-energy interconnect credentials leading to a new paradigm called neuromorphic photonics. The main obstacle to realize such a task is a lack of proper material platform that imposes serious requirements on the architecture of the network. Here we suggest and justify that transparent conductive oxides can be an excellent candidate for such a task as they provide a nonlinearity and bistability under both optical and electrical inputs., Comment: 13 pages, 7 figures

This paper focuses on developing a reduction-based algebraic multigrid method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based algebraic multigrid (AMG) approach, $\ell$AIR (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion dominated problems in two or three dimensions. Motivated by the success of $\ell$AIR in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy minimization AMG methods with the local approximation of ideal operators used in $\ell$AIR. The resulting constrained $\ell$AIR (C$\ell$AIR) algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that has been previously difficult for reduction-based methods., Comment: Revised form published in the SIAM Journal on Scientific computing (SPECIAL SECTION Copper Mountain 2023), 22 pages, 7 Figures

In this work, we achieve propellantless control of both cross-track and along-track separation of a satellite formation by manipulating atmospheric drag. Increasing the differential drag of one satellite with respect to another directly introduces along-track separation, while cross-track separation can be achieved by taking advantage of higher-order terms in the Earth's gravitational field that are functions of altitude. We present an algorithm for solving an n-satellite formation flying problem based on linear programming. We demonstrate this algorithm in a receeding-horizon control scheme in the presence of disturbances and modeling errors in a high-fidelity closed-loop orbital dynamics simulation. Our results show that separation distances of hundreds of kilometers can be achieved by a small-satellite formation in low-Earth orbit over a few months.

Photonic Time crystals (PTC) arise in time-modulated media when the frequency of modulation of permittivity is on the order of twice the frequency of light and are manifested by the generation and amplification of so-called time reversed waves propagating in the direction opposite to the incoming light. Superficially, the observed phenomenon bears resemblance to the widely known phenomena of optical parametric generation (OPG) and amplification (OPA) using second or third order optical nonlinearities. I show that while indeed the same physical mechanism underpins both PTC and OPA , the difference arises from the boundary conditions. Thus , while dispersion for both PTC and OPA exhibit the same bandgap in momentum space, only in the case of PTC can one have propagation in that bandgap with exponential amplification. I also show that PTC can be engineered with both second and third order nonlinearities, and that rather unexpectedly, modulating permittivity on the ultrafast (few fs) rate is not a necessity, and that one can emulate all the PTC features using materials with a few picoseconds response time commensurate with the propagation time through the medium.

Magnetic skyrmions are promising for next-generation information storage and processing owing to their potential advantages in data storage density, robustness, and energy efficiency. The magnetic multilayers consisting of Pt, Co, and a third metal element $X$ provide an ideal platform to study the skyrmions due to their highly tunable magnetic properties. Here, we report the observation of room-temperature bubble-like N\'eel skyrmions in epitaxial Pt/Co/Cu multilayers in samples with multidomain states in zero field. The magneto-optic Kerr effect (MOKE) and superconducting quantum interference device (SQUID) magnetometry are applied to investigate the shapes of the hysteresis loops, the magnetic anisotropy, and the saturation magnetization. By tuning the Co thickness and the number of periods, we achieve perpendicular and in-plane magnetized states and multidomain states that are identified by a wasp-waisted hysteresis loop. Skyrmions are directly imaged by magnetic force microscopy (MFM) and Lorentz transmission electron microscopy (LTEM). The development of room-temperature skyrmions in Pt/Co/Cu multilayers may lead to advances in skyrmion-related research and applications., Comment: 11 pages, 6 Figures

In this chapter, we review the processes involved in the formation of planetesimals and comets. We will start with a description of the physics of dust grain growth and how this is mediated by gas-dust interactions in planet-forming disks. We will then delve into the various models of planetesimal formation, describing how these planetesimals form as well as their resulting structure. In doing so, we focus on and compare two paradigms for planetesimal formation: the gravitational collapse of particle over-densities (which can be produced by a variety of mechanisms) and the growth of particles into planetesimals via collisional and gravitational coagulation. Finally, we compare the predictions from these models with data collected by the Rosetta and New Horizons missions and that obtained via observations of distant Kuiper Belt Objects., Comment: Planetesimal Formation Review accepted for publication in Comets III

Optical isolators are indispensable components of optical networks. Magneto-optic isolators have excellent operating characteristics, including low-to-no power consumption, but are not well suited for on-chip integration. The technique of temporal modulation of dielectric constant offers an alternative way to achieve isolation without magnetic field but is not without its own drawbacks. In this work I examine diverse methods of optical isolation via temporal modulation and show that independent on whether modulation is achieved by carrier injection, Pockels and acousto-optic effects, or any other conceivable method, there is essentially the same set of constraints on footprint, modulation frequency, and, most important, on power consumption required to achieve full isolation without excessive insertion loss. This power is estimated to be on the order of at least a hundred of milliwatts and whether this requirement is acceptable will depend on ongoing progress of both magneto-optic and time modulated integrated technologies.

As CPU clock speeds have stagnated and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes can be a significant bottleneck, as many types of simulations require large numbers of time-steps which must be computed sequentially. Parallel in Time schemes, such as the Multigrid Reduction in Time (MGRIT) method, remedy this by parallelizing across time-steps, and have shown promising results for parabolic problems. However, chaotic problems have proved more difficult, since chaotic initial value problems (IVPs) are inherently ill-conditioned. MGRIT relies on a hierarchy of successively coarser time-grids to iteratively correct the solution on the finest time-grid, but due to the nature of chaotic systems, small inaccuracies on the coarser levels can be greatly magnified and lead to poor coarse-grid corrections. Here we introduce a modified MGRIT algorithm based on an existing quadratically converging nonlinear extension to the multigrid Full Approximation Scheme (FAS), as well as a novel time-coarsening scheme. Together, these approaches better capture long-term chaotic behavior on coarse-grids and greatly improve convergence of MGRIT for chaotic IVPs. Further, we introduce a novel low memory variant of the algorithm for solving chaotic PDEs with MGRIT which not only solves the IVP, but also provides estimates for the unstable Lyapunov vectors of the system. We provide supporting numerical results for the Lorenz system and demonstrate parallel speedup for the chaotic Kuramoto- Sivashinsky partial differential equation over a significantly longer time-domain than in previous works., Comment: 24 pages, 10 figures. arXiv admin note: text overlap with arXiv:2201.10441

Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in almost linear time, that is with an O(n) complexity, where n is the problem size. This capability is crucial at the present, where the increasing availability of massive HPC platforms pushes for the solution of very large problems. The key for a rapidly converging AMG method is a good interplay between the smoother and the coarse-grid correction, which in turn requires the use of an effective prolongation. From a theoretical viewpoint, the prolongation must accurately represent near kernel components and, at the same time, be bounded in the energy norm. For challenging problems, however, ensuring both these requirements is not easy and is exactly the goal of this work. We propose a constrained minimization procedure aimed at reducing prolongation energy while preserving the near kernel components in the span of interpolation. The proposed algorithm is based on previous energy minimization approaches utilizing a preconditioned restricted conjugate gradients method, but has new features and a specific focus on parallel performance and implementation. It is shown that the resulting solver, when used for large real-world problems from various application fields, exhibits excellent convergence rates and scalability and outperforms at least some more traditional AMG approaches., Comment: 24 pages, 4 figures

Photonic time-varying systems have attracted significant attention owing to their rich physics and potential opportunities for new and enhanced functionalities. In this context, the duality of space and time in wave physics has been particularly fruitful to uncover interesting physical effects in the temporal domain, such as reflection/refraction at temporal interfaces and momentum-bandgaps in time crystals. However, the characteristics of the temporal/frequency dimension, particularly its relation to causality and energy conservation ($\hbar \omega$ is energy, whereas $\hbar \boldsymbol{k}$ is momentum), create challenges and constraints that are unique to time-varying systems and are not present in their spatially varying counterparts. Here, we overview two key physical aspects of time-varying photonics that have only received marginal attention so far, namely temporal dispersion and external power requirements, and explore their implications. We discuss how temporal dispersion, an inherent property of any causal material, makes the fields evolve continuously at sharp temporal interfaces and may limit the strength of fast temporal modulations and of various resulting effects. Furthermore, we show that changing the refractive index in time always involves large amounts of energy. We derive power requirements to observe a time-crystal response in one of the most popular material platforms in time-varying photonics, i.e., transparent conducting oxides, and we argue that these effects are almost always obscured by less exotic nonlinear phenomena. These observations and findings shed light on the physics and constraints of time-varying photonics, and may guide the design and implementation of future time-modulated photonic systems., Comment: 14 pages, 3 figures

I present a simple view of nonlinear optcal phenomena as being determined mostly by the length of interaction time between photons and matter. This may explain why in the last decades the progress in developing better nonlinear materials has not been as rapid as wished. A few tentative routes towards possible improvements in the efficiency of nonlinear optical phenomena are suggested.

Monolayer transition metal dichalcogenides (TMDCs), like MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, feature direct bandgaps, strong spin-orbit coupling, and exciton-polariton interactions at the atomic scale, which could be harnessed for efficient light emission, valleytronics, and polaritonic lasing, respectively. Nevertheless, to build next-generation photonic devices that make use of these features, it is first essential to model the all-optical control mechanisms in TMDCs. Herein, a simple model is proposed to quantify the performance of a 35$\,$\textmu m long Si$_3$N$_4$ waveguide-integrated all-optical MoSe$_2$ modulator. Using this model, a switching energy of 14.6$\,$pJ is obtained for a transverse-magnetic (TM) and transverse-electric (TE) polarised pump signals at $\lambda =\,$480$\,$nm. Moreover, maximal extinction ratios of 20.6$\,$dB and 20.1$\,$dB are achieved for a TM and TE polarised probe signal at $\lambda =\,$500$\,$nm, respectively, with an ultra-low insertion loss of $<0.3\,$dB. Moreover, the device operates with an ultrafast recovery time of 50$\,$ps, while maintaining a high extinction ratio for practical applications. These findings facilitate modeling and designing novel TMDC-based photonic devices., Comment: \copyright 2022 Optica Publishing Group. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited

"Digital Divide: How Technology Access Impacts Community Colleges Across the United States During a Pandemic" looks at the current state of the digital divide in the United States and how it is affecting community college students during the COVID-19 pandemic. Leaders at community colleges in Spokane, Washington, Los Angeles, California, and on the Navajo Reservation were interviewed to show what the digital divide looks like in an urban, a suburban, and a rural community and how it is affecting each college's students. While all colleges are faced with different circumstances, similarities emerge as the digital divide impacts students across the country. The paper also looks at how the Coronavirus Aid, Relief, and Economic Security (CARES) Act impacted the digital divide within the community college sector.

In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of Einstein's treatment of single-particle diffusion, has each particle taking independent homogeneous random walks. This, however, neglects the fact that all particles diffuse in a common and often inhomogeneous environment that can affect their motion. A more sophisticated model treats this common environment as a space-time random biasing field which influences each particle's independent motion. While the bulk (or typical particle) behavior of these two models has been found to match to high degree, recent theoretical work of Barraquand, Corwin and Le Doussal on a one-dimensional exactly solvable version of this random environment model suggests that the extreme behavior is quite different between the two models. We transform these asymptotic (in system size and time) results into physically applicable predictions. Using high precision numerical simulations we reconcile different asymptotic phases in a manner that matches numerics down to realistic system sizes, amenable to experimental confirmation. We characterize the behavior of extreme diffusion in the random environment model by the presence of a new phase with anomalous fluctuations related to the Kardar-Parisi-Zhang universality class and equation.

We present evidence that it is unlikely that the streaming instability (SI) can form planetesimals from mm grains inside axisymmetric pressure bumps. We conducted the largest simulation of the SI so far (7 million CPU hours), consisting of a large slice of the disk with mm grains, a solar-like dust-to-gas ratio ($Z = 0.01$), and the largest pressure bump that does not cause gravitational instability (GI) in the particle layer. We used a high resolution of $1000/H$ to resolve as many SI unstable modes as possible. The simulation produced a long-lived particle over-density far exceeding the SI criteria (i.e., a critical solid abundance to headwind parameter ratio $Z/\Pi$) where strong clumping would occur if these conditions were present over an extended region of the disk; yet we observed none. The likely reason is that the time it takes particles to cross the high-$Z/\Pi$ region ($t_{\rm cross}$) is shorter than the growth timescale of the SI ($t_{\rm grow}$). We propose an added criterion for planetesimal formation by the SI -- that $t_{\rm cross} > t_{\rm grow}$. We show that any bump larger than the one in this run would form planetesimals by the GI instead of the SI. Our results significantly restrict the pathways to planet formation: Either protoplanetary disks regularly form grains larger than 1~mm, or planetesimals do not form by the SI in axisymmetric pressure bumps. Since bumps large enough to induce the GI are likely Rossby-wave unstable, we propose that mm grains may only form planetesimals in vortices., Comment: 13 pages, 8 figures, accepted to ApJL. Updated with minor changes to improve clarity with respect to prior works

Permanent dipole moments of electronics states in non-centro-symmetric materials play pivotal role in many phenomena. Correctly evaluating them presents an arduous task and usually requires full knowledge of the band structure as well as understanding the intricate concepts of Berry curvature. Here we show that in a few cases (e.g. zinc blende and wurtzite) a rather facile first-principle analytical derivation of the permanent dipole moments using L Hopital rule can be performed, and the values and dispersion of these dipoles near high symmetry points can be found using just a couple of widely available material parameters. The results will hopefully contribute to better understanding of shift currents, optical rectification and other electro-optical phenomena.

Layered van der Waals materials offer a unique platform for creating atomic-void channels with sub-nanometer dimensions. Coupling light into these channels may further advance sensing, quantum information, and single molecule chemistries. Here we examine limits of light guiding in atomic-void channels and show that van der Waals materials exhibiting strong resonances - excitonic and polaritonic - are ideally suited for deeply subwavelength light guiding. We demonstrate that excitonic transition metal dichalcogenides can squeeze > 70% of optical power in just < {\lambda}/100 thick channel in the visible and near-infrared. We also show that polariton resonances of hexagonal boron nitride allow deeply subwavelength (< {\lambda}/500) guiding in the mid-infrared. We further reveal effects of natural material anisotropy and discuss the influence of losses. Our analysis shows van der Waals channel waveguides while offering extreme optical confinement exhibit significantly lower loss compared to plasmonic counterparts. Such atomic void waveguides pave the way to low loss and deeply subwavelength optics., Comment: 17 pages, 5 figures

The Benjamin-Bona-Mahony (BBM) equation has proven to be a good approximation for the unidirectional propagation of small amplitude long waves in a channel where the crosswise variation can be safely ignored. The Benjamin-Bona-Mahony-Kadomtsev-Petviashvili (BBM-KP) equation is the regularized version of the Kadomtsev-Petviashvili equation which arises in various modeling scenarios corresponding to nonlinear dispersive waves that propagate principally along the $x$-axis with weak dispersive effects undergone in the direction parallel to the $y$-axis and normal to the primary direction of propagation. There is much literature on mathematical studies regarding these well known equations, however the relationship between the solutions of their underlying pure initial value problems is not fully understood. In this work, it is shown that the solution of the Cauchy problem for the BBM-KP equation converges to the solution of the Cauchy problem for the BBM equation in a suitable function space, provided that the initial data for both equations are close as the transverse variable $y \rightarrow \pm \infty$.

Graphene has emerged as an ultrafast photonic material for on-chip all-optical modulation. However, its atomic thickness limits its interaction with guided optical modes, which results in a high switching energy per bit or low modulation efficiencies. Nonetheless, it is possible to enhance the interaction of guided light with graphene by nanophotonic means. Herein, we present a practical design of an all-optical modulator that is based on graphene and hexagonal boron nitride (hBN) heterostructures that are hybrid integrated into silicon slot waveguides. Using this device, a high extinction ratio (ER) of 7.3 dB, an ultralow insertion loss (IL) of <0.6 dB, and energy-efficient switching (<0.33 pJ/bit) are attainable for a 20{\mu}m long modulator with double layer graphene. In addition, the device performs ultrafast switching with a recovery time of <600 fs, and could potentially be employed as a high-performance all-optical modulator with an ultra-high bandwidth in the hundreds of GHz. Moreover, the modulation efficiency of the device is further enhanced by stacking additional layers of graphene-hBN heterostructures, while theoretically maintaining an ultrafast response. The proposed device exhibits highly promising performance metrics, which are expected to serve the needs of next-generation photonic computing systems., Comment: Accepted for publication in the IEEE Journal of Selected Topics in Quantum Electronics

Planet induced sub-structures, like annular gaps, observed in dust emission from protoplanetary disks provide a unique probe to characterize unseen young planets. While deep learning based model has an edge in characterizing the planet's properties over traditional methods, like customized simulations and empirical relations, it lacks in its ability to quantify the uncertainty associated with its predictions. In this paper, we introduce a Bayesian deep learning network "DPNNet-Bayesian" that can predict planet mass from disk gaps and provides uncertainties associated with the prediction. A unique feature of our approach is that it can distinguish between the uncertainty associated with the deep learning architecture and uncertainty inherent in the input data due to measurement noise. The model is trained on a data set generated from disk-planet simulations using the \textsc{fargo3d} hydrodynamics code with a newly implemented fixed grain size module and improved initial conditions. The Bayesian framework enables estimating a gauge/confidence interval over the validity of the prediction when applied to unknown observations. As a proof-of-concept, we apply DPNNet-Bayesian to dust gaps observed in HL Tau. The network predicts masses of $ 86.0 \pm 5.5 M_{\Earth} $, $ 43.8 \pm 3.3 M_{\Earth} $, and $ 92.2 \pm 5.1 M_{\Earth} $ respectively, which are comparable to other studies based on specialized simulations., Comment: 14 pages, 6 figures, submitted to ApJ

As CPU clock speeds have stagnated, and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes are a significant bottleneck, as many types of simulations require large numbers of time-steps which must be computed sequentially. Parallel in Time schemes, such as the Multigrid Reduction in Time (MGRIT) method, remedy this by parallelizing across time-steps, and have shown promising results for parabolic problems. However, chaotic problems have proved more difficult, since chaotic initial value problems are inherently ill-conditioned. MGRIT relies on a hierarchy of successively coarser time-grids to iteratively correct the solution on the finest time-grid, but due to the nature of chaotic systems, subtle inaccuracies on the coarser levels can lead to poor coarse-grid corrections. Here we propose a modification to nonlinear FAS multigrid, as well as a novel time-coarsening scheme, which together better capture long term behavior on coarse grids and greatly improve convergence of MGRIT for chaotic initial value problems. We provide supporting numerical results for the Lorenz system model problem.

Electro optic modulators being key for many signal processing systems must adhere to requirements given by both electrical and optical constrains. Distinguishing between charge driven (CD) and field driven (FD) designs, we answer the question of whether fundamental performance benefits can be claimed of modulators based on emerging electro-optic materials. Following primary metrics, we compare the performance of emerging electro-optic and electro-absorption modulators such as graphene, transparent conductive oxides, and Si, based on charge injection with that of the legacy FD modulators, such as those based on lithium niobate and quantum confined Stark effect. We show that for rather fundamental reasons, FD modulators always outperform CD ones in the conventional wavelength scale waveguides. However, for waveguide featuring a sub-wavelength optical mode, such as those assisted by plasmonics, the emerging CD devices are indeed highly competitive.

Electro-optic modulators provide a key function in optical transceivers and increasingly in photonic programmable Application Specific Integrated Circuits (ASICs) for machine learning and signal processing. However, both foundry ready silicon based modulators and conventional material based devices utilizing Lithium niobate fall short in simultaneously providing high chip packaging density and fast speed. Current driven ITO based modulators have the potential to achieve both enabled by efficient light matter interactions. Here, we introduce micrometer compact Mach Zehnder Interferometer (MZI) based modulators capable of exceeding 100 GHz switching rates. Integrating ITO thin films atop a photonic waveguide, spectrally broadband, and compact MZI phase shifter. Remarkably, this allows integrating more than 3500 of these modulators within the same chip area as only one single silicon MZI modulator. The modulator design introduced here features a holistic photonic, electronic, and RF-based optimization and includes an asymmetric MZI tuning step to optimize the Extinction Ratio (ER) to Insertion Loss (IL) and dielectric thickness sweep to balance the tradeoffs between ER and speed. Driven by CMOS compatible bias voltage levels, this device is the first to address next generation modulator demands for processors of the machine intelligence revolution, in addition to the edge and cloud computing demands as well as optical transceivers alike., Comment: 14 pages, 7 figures

Landau Damping (LD) mechanism of the Localized Surface Plasmon (LSP) decay is studied for the hybrid nanoplasmonic (metal core/dielectric shell) structures. It is shown that LD in hybrid structures is strongly affected by permittivity and electron effective mass in the dielectric shell in accordance with previous observations by Kreibig, and the strength of LD can be enhanced by an order of magnitude for some combinations of permittivity and effective mass. The physical reason for this effect is identified as electron spillover into the dielectric where electric field is higher than in the metal and the presence of quasi-discrete energy levels in the dielectric. The theory indicates that the transition absorption at the interface metal-dielectric is a dominant contribution to LD in such hybrid structures. Thus, by judicious selection of dielectric material and its thickness one can engineer decay rates and hot carrier production for important applications, such as photodetection and photochemistry.

While the photonic community is being occupied with exotic concepts portending a grand future and fame if not a fortune, I respectfully entertain the possibility that a humble concept of simply increasing refractive index by a modest factor may have a far greater payoff in many walks of life. With that in mind, I explore why higher index materials have not yet materialized, and point out a few tentative directions for the search of these elusive materials, be they natural or artificial.

"Reskilling for the Pandemic Recession and Recovery" focuses on the U.S. economic downturn since the beginning of the COVID-19 pandemic, which has had a disproportionate impact on Black and Hispanic individuals, women, and people without a postsecondary degree. Considering these challenges, the brief details policy proposals for large-scale workforce development initiatives and strategies that community colleges can implement to support unemployed and adult learners. The report also highlights examples of community colleges' responses to the pandemic, including the Michigan Futures for Frontliners scholarship program for essential workers, and healthcare training at Kirkwood Community College in Iowa to meet increased demand in this sector.

Community college students face a number of financial decisions and obligations along the path to degree completion. Students must secure resources to pay for college expenses, including their tuition, fees, and basic living necessities. Central to this is students' abilities to access financial aid resources including federal, state, and institutional aid. Colleges also play a role in providing clear and timely financial education to ensure students are aware of available resources and have a strong foundation in personal financial management. Existing research on students' financial wellness typically separates financial aid and financial education approaches. For this report, the aim is to address both categories to offer community colleges strategies for holistic supports. Key takeaways from the report include: (1) Community college students' expenses often exceed available grant aid; (2) Financial literacy can be a critical topic for students seeking to navigate the complex nature of college financing and personal expenses; but is not a replacement for financial aid resources; and (3) This report highlights the Guardian Money Management for Life (MMFL) Program as an example of a personal finance course that has expanded to a financial empowerment model to provide students with holistic support services.

Community college students often hold knowledge from various professional and academic experiences. A challenge for these students, and for their institutions and employers, is how to formally bridge these competencies to support students' efforts to reach their academic and career goals. This issue brief looks at the practice of awarding credit for prior learning, known as prior learning assessments (PLA), as part of community colleges' workforce development strategies. It is part of a series of Association of Community College Trustees (ACCT) reports focusing on best practices and innovative strategies for workforce development. This brief builds on the previously published reports "Partnerships for a Future-Ready Workforce" (2018) (ED605153) and "The College-Work Balancing Act" (2019) (ED605123). This issue brief serves as a primer on past and current developments in PLA, including how the strategy can help students bridge workforce and academic competencies, and how it can be incorporated into strategies for workforce development. In the first section of this brief, the authors introduce past and current developments in PLAs. In the second section, they describe the various cohorts of students who benefit most from PLA, including veterans and non-traditional students. In addition, this paper includes two examples of institutions that implement PLA in interesting and valuable ways. First, Eastern West Virginia Community and Technical College created a degree specific to students who enter with PLA credits and streamlined statewide policy to increase efficiency. Second, the Dallas County Community College District partnered with StraighterLine, a non-traditional education provider, to create pathways with guaranteed transfer in business and criminal justice.

The high demand for machine intelligence of doubling every three months is driving novel hardware solutions beyond charging of electrical wires given a resurrection to application specific integrated circuit (ASIC)-based accelerators. These innovations include photonic ASICs (P-ASIC) due to prospects of performing optical linear (and also nonlinear) operations, such as multiply-accumulate for vector matrix multiplications or convolutions, without iterative architectures. Such photonic linear algebra enables picosecond delay when photonic integrated circuits are utilized, via on-the-fly mathematics. However, the neurons full function includes providing a nonlinear activation function, knowns as thresholding, to enable decision making on inferred data. Many P-ASIC solutions performing this nonlinearity in the electronic domain, which brings challenges in terms of data throughput and delay, thus breaking the optical link and introducing increased system complexity via domain crossings. This work follows the notion of utilizing enhanced light-matter-interactions to provide efficient, compact, and engineerable electro-optic neuron nonlinearity. Here, we introduce and demonstrate a novel electro-optic device to engineer the shape of this optical nonlinearity to resemble a rectifying linear unit (ReLU) - the most-commonly used nonlinear activation function in neural networks. We combine the counter-directional transfer functions from heterostructures made out of two electro-optic materials to design a diode-like nonlinear response of the device. Integrating this nonlinearity into a photonic neural network, we show how the electrostatics of this thresholders gating junction improves machine learning inference accuracy and the energy efficiency of the neural network.

The discovery that axisymmetric dust rings are ubiquitous in protoplanetary disks has provoked a flurry of research on the role of pressure bumps in planet formation. High-resolution simulations by our group have shown that even a modest bump can collect enough dust to trigger planetesimal formation by the streaming instability. In this work, we probe the limits of planetesimal formation when the external source of pressure bump reinforcement is extremely weak. We conduct simulations of radially elongated shearing boxes to capture the entire bump, which is generated and maintained over some timescale $t_{\rm reinf}$ by a Newtonian relaxation scheme. We find that planetesimal formation is extremely resilient for cm-sized grains. We reduced the strength of reinforcement by up to a factor of 100 and the location and initial masses of planetesimals were essentially unaffected. However, we do find that strong reinforcement causes much faster pebble drift compared to the the standard pebble drift rates. The resulting larger pebble flux enhances the planetesimal growth rate by pebble accretion. We hypothesize that to sustain the bump, our code has to extract angular momentum (the strength of this negative torque depends on $t_{\rm reinf}$), and some of this torque is transferred to the particles, causing them to drift faster for a stronger torque (i.e., smaller $t_{\rm reinf}$). Since any physical process that sustains a pressure bump must do so by torquing the gas, we conjecture that the effect on pebble drift is a real phenomenon, motivating further work with physically realistic sources to generate the bump., Comment: 12 pages, 8 figures, accepted to ApJ