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We explore the gravitational-wave emission from head-on collisions of equal-mass solitonic boson-star binaries from simulations spanning a two-dimensional parameter space, consisting of the central scalar-field amplitude of the stars and the solitonic potential parameter. We report the gravitational-wave energies emitted by boson-star binaries which, due to their combination of moderately high compactness with significant deformability, we often find to be louder by up to an order of magnitude than analogous black-hole collisions. The dependence of the radiated energy on the boson-star parameters exhibits striking needle-sharp features and discontinuous jumps to the value emitted by black-hole binaries. We explain these features in terms of the solitonic potential and the stability properties of the respective individual stars., Comment: 17 pages, 10 figures

Critical phenomena in gravitational collapse are characterized by the emergence of surprising structure in solution space, namely the appearance of universal power-laws and periodicities near the threshold of collapse, and a universal discretely self-similar solution at the threshold itself. The seminal work of M. Choptuik spurred a comprehensive investigation of extreme spherical spacetimes in numerical relativity, with analogous results for numerous matter models. Recent research suggests that the generalization to less symmetric scenarios is subtle. In twist-free axisymmetric vacuum collapse for instance, numerical evidence suggests a breakdown of universality of solutions at the threshold of collapse. In this study, we explore gravitational collapse involving a massless complex scalar field minimally coupled to general relativity. We employ the pseudospectral code BAMPS to investigate a neighborhood of the spherically symmetric critical solution in phase space, focusing on aspherical departures from it. First, working in explicit spherical symmetry, we find strong evidence that the spacetime metric of the spherical critical solution of the complex scalar field agrees with that of the Choptuik solution. We then examine universality of the behavior of solutions near the threshold of collapse as the departure from spherical symmetry increases, comparing with recent investigations of the real scalar field. We present a series of well-tuned numerical results and document shifts of the power-law exponent and periods as a function of the degree of asphericity of the initial data. At sufficiently high asphericities we find that the center of collapse bifurcates, on the symmetry axis, but away from the origin. Finally we look for and evaluate evidence that in the highly aspherical setting the collapse is driven by gravitational waves., Comment: 22 pages, 10 figures

Simulations of binary collisions involving compact objects require initial data that satisfy the constraint equations of general relativity. For binary boson star simulations it is common practice to use a superposition of two isolated star solutions to construct an approximate solution to the constraint equations. Such superposed data is simple to set up compared to solving these equations explicitly, but also introduces extra constraint violations in the time evolution. In this work we investigate how physical observables depend on the quality of initial data in the case of head-on boson star collisions. In particular we compare results obtained from data prepared using four different methods: the standard method to superpose isolated stars, a heuristic improvement to this superposition technique and two versions of this data where excess constraint violations were removed through a conformal thin-sandwich solver. We find that differences in the time evolutions are dominated by differences in the way the two superposition methods differ, whereas additionally constraint solving the superposed data has smaller impact. The numerical experiments are conducted using the pseudo-spectral code bamps. Our work demonstrates that bamps is a code suited for generating high accuracy numerical waveforms for boson star collisions due to the exponential convergence in the polynomial resolution of the numerical approximation.

The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating the need for a better gauge choice. Second, the constraint violations to which simulations are susceptible may be too large and force searches to terminate prematurely. This is a particularly serious issue for first order formulations. We want our adaptive pseudospectral code bamps to be a robust tool for the study of critical phenomena so, having encountered both of these difficulties in work on the vacuum setting, we turn here to investigate these issues in the classic context of a spherically symmetric massless scalar field. We suggest two general improvements. We propose a necessary condition for a gauge choice to respect discrete self-similarity (DSS). The condition is not restricted to spherical symmetry and could be verified with any 3+1 formulation. After evaluating common gauge choices against this condition, we suggest a DSS-compatible gauge source function in generalized harmonic gauge (GHG). To control constraint violations, we modify the constraint damping parameters of GHG, adapting them to collapse spacetimes. This allows us to improve our tuning of the critical amplitude for several families of initial data, even going from 6 up to 11 digits. This is the most precise tuning achieved with the first order GHG formulation to date. Consequently, we are able to reproduce the well known critical phenomena as well as competing formulations and methods, clearly observing up to 3 echoes., Comment: 19 pages, 10 figures

Fine-tuning generic but smooth spherically-symmetric initial data for general relativity to the threshold of dynamical black hole formation creates arbitrarily large curvatures, mediated by a universal self-similar solution that acts as an intermediate attractor. For vacuum gravitational waves, however, these critical phenomena have been elusive. We present, for the first time, excellent agreement among three independent numerical simulations of this collapse. Surprisingly, we find no universality, and observe approximate self-similarity for some families of initial data but not for others., Comment: 6 pages, 3 figures

When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code bamps in the form of fully adaptive, physics-agnostic hp-refinement. We describe the foundations of mesh refinement in the context of spectral element methods, the precise algorithm used to perform refinement in bamps, as well as several indicator functions used to drive it. Finally, we test the performance, scaling, and the accuracy of the code in treating several 1d and 2d example problems, showing clear improvements over static mesh configurations. In particular, we consider a simple non-linear wave equation, the evolution of a real scalar field minimally coupled to gravity, as well as nonlinear gravitational waves., Comment: 19 pages, 17 figures

As a first application of the new adaptive mesh functionality of the the pseudospectral numerical relativity code bamps, we evolve twist-free, axisymmetric gravitational waves close to the threshold of collapse. We consider six different one-parameter families of Brill wave initial data; two centered and four off-centered families. Of these the latter have not been treated before. Within each family we tune the parameter towards the threshold of black hole formation. The results for centered data agree with earlier work. Our key results are first, that close to the threshold of collapse the global peak in the curvature appears on the symmetry axis but away from the origin, indicating that in the limit they will collapse around disjoint centers. This is confirmed in three of the six families by explicitly finding apparent horizons around these large curvature peaks. Second, we find evidence neither for strict discrete-self-similarity nor for universal power-law scaling of curvature quantities. Finally, as in Ledvinka & Khirnov's recent study, we find approximately universal strong curvature features. These features appear multiple times within individual spacetimes close to the threshold and are furthermore present within all six families., Comment: 11 pages, 7 figures

This document summarizes a review of research, evaluation, resources, and stakeholder knowledge related to the topic of "Remote Learning Support for Students with Disabilities." Databases used for conducting this review included: Google Scholar, EBSCO general Academic Search, EBSCO ERIC, and 'Disability in the Modern World.' Literature from peer-reviewed, scholarly journals were reviewed (noted with an asterisk), along with conference papers, reports, and resources from education research centers and institutions. The search was limited to studies and sources published from 2000-2020. Sources were also vetted for readability. Search terms used include but are not limited to: "Remote Learning Support for Students with Disabilities" or "Remote learning support." The search for resources about "Remote Learning Support for Students with Disabilities" turned up many research papers and also a handful of resources from research and education centers. The knowledge database describes these resources in two tables, one for research papers and one for technical assistance and education centers. Overall, findings indicate that challenges involved with remote learning for students with disabilities are not new and that over the last five years, many resources have been developed. A handful of themes, listed in this review, emerged from the knowledge base.

The peculiar linear temperature-dependent swelling of core-shell microgels has been conjectured to be linked to the core-shell architecture combining materials of different transition temperatures. Here the structure of pNIPMAM-core and pNNPAM-shell microgels in water is studied as a function of temperature using small-angle neutron scattering with selective deuteration. Photon correlation spectroscopy is used to scrutinize the swelling behaviour of the colloidal particles and reveals linear swelling. Moreover, these experiments are also employed to check the influence of deuteration on swelling. Using a form free multi-shell reverse Monte Carlo approach, the small-angle scattering data are converted into radial monomer density profiles. The comparison of 'core-only' particles consisting of identical cores to fully hydrogenated core-shell microgels, and finally to H core/D shell architectures unambiguously shows that core and shell monomers display gradient profiles with strong interpenetration, leading to cores embedded in shells which are bigger than their isolated 'core only' precursor particles. This surprising result is further generalized to different core cross linker contents, for temperature ranges encompassing both transitions. Our analysis demonstrates that the internal structure of pNIPMAM-core and pNNPAM-shell microgels is heterogeneous and strongly interpenetrated, presumably allowing only progressive core swelling at temperatures intermediate to both transition temperatures, thus promoting linear swelling behaviour.

We classify the full set of convex central configurations in the Newtonian four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain $D$ that is the union of elementary regions in $\mathbb{R}^{+^3}$., Comment: 28 pages, 14 figures

We study the swelling and shrinking behavior of core-shell microgels adsorbed on silicon wafers. In these systems, the core is made of cross-linked poly(N isopropylmethacrylamide) and the shell consists of cross linked poly(N-n propylacrylamide). In suspension, these particles exhibit an extended linear swelling behavior in the temperature interval between the lower critical solution temperatures of the two polymers. Using ellipsometry and AFM, we show that this linear response is also observed in the adsorbed state.

We classify all planar four-body central configurations where two pairs of the bodies are on parallel lines. Using Cartesian coordinates, we show that the set of four-body trapezoid central configurations with positive masses forms a two-dimensional surface where two symmetric families, the rhombus and isosceles trapezoid, are on its boundary. We also prove that, for a given position of the bodies, in some cases an specific order of the masses determine the geometry of the configuration, namely acute or obtuse trapezoid central configuration. We also prove the existence on non-symmetric trapezoid central configuration with two pairs of equal masses.

We consider the planar central configurations of the Newtonian $\kappa n$-body problem consisting in $\kappa$ groups of $n$-gons where all $n$ bodies in each group have the same mass, called $(\kappa, n)$-crown. We study the location and the number of central configurations when $\kappa=2$. For $n=3$ the number of central configurations varies depending on the mass ratio, whereas for $n\geq 4$ the number is at least three. We also prove that for $n\geq 3$ there always exist three disjoint regions where the configuration can be located. Finally, we study which $(\kappa, n)$-crowns are convex.

We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem., Comment: 8 pages, 3 figures

We present a new methodology for efficient and high-quality patterning of biological reagents for surface-based biological assays. The method relies on hydrodynamically confined nanoliter volumes of reagents to interact with the substrate at the micrometer-length scale. We study the interplay between diffusion, advection, and surface chemistry and present the design of a noncontact scanning microfluidic device to efficiently present reagents on surfaces. By leveraging convective flows, recirculation, and mixing of a processing liquid, this device overcomes limitations of existing biopatterning approaches, such as passive diffusion of analytes, uncontrolled wetting, and drying artifacts. We demonstrate the deposition of analytes, showing a 2- to 5-fold increase in deposition rate together with a 10-fold reduction in analyte consumption while ensuring less than 6% variation in pattern homogeneity on a standard biological substrate. In addition, we demonstrate the recirculation of a processing liquid using a microfluidic probe (MFP) in the context of a surface assay for (i) probing 12 independent areas with a single microliter of processing liquid and (ii) processing a 2 mm2 surface to create 170 antibody spots of 50 x 100 {\mu}m2 area using 1.6 {\mu}L of liquid. We observe high pattern quality, conservative usage of reagents, micrometer precision of localization and convection-enhanced fast deposition. Such a device and method may facilitate quantitative biological assays and spur the development of the next generation of protein microarrays.

The microfluidic probe (MFP) is a non-contact, scanning microfluidic technology for local (bio)chemical processing of surfaces based on hydrodynamically confining nanoliter volumes of liquids over tens of micrometers. We present here a compact MFP (cMFP) that can be used on a standard inverted microscope and assist in the local processing of tissue sections and biological specimens. The cMFP has a footprint of 175 X 100 X 140 mm^3 and can scan an area of 45 X 45 mm^2 on a surface with an accuracy of +-15 um. The cMFP is compatible with standard surfaces used in life science laboratories such as microscope slides and Petri dishes. For ease of use, we developed self-aligned mounted MFP heads with standardized chip-to-world and chip-to-platform interfaces. Switching the processing liquid in the flow confinement is performed within 90 seconds using a selector valve with a dead-volume of approximately 5 uL. We further implemented height-compensation that allows a cMFP head to follow non-planar surfaces common in tissue and cellular ensembles. This was shown by patterning different macroscopic copper-coated topographies with height differences up to 750 um. To illustrate the applicability to tissue processing, 5 um thick M000921 BRAF V600E+ melanoma cell blocks were stained with hematoxylin to create contours, lines, spots, gradients of the chemicals, and multiple spots over larger areas. The local staining was performed in an interactive manner using a joystick and a scripting module. The compactness, user-friendliness and functionality of the cMFP will enable it to be adapted as a standard tool in research, development and diagnostic laboratories, particularly for the interaction with tissues and cells.