5632 research outputs found
Sort by
Non-Semisimple TQFT's and BPS q-Series
No full textWe propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic q. Both types of invariants are labeled by extra data which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows to study (and perhaps even to formulate) q-series invariants labeled by spinᶜ structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory
Common Misconceptions about Text Recycling in Scientific Writing
No full textAmong the fundamental principles of scientific publishing, originality is one of the most important. Every manuscript is expected to offer a unique contribution, something clearly different from what has already been published. We typically think about originality in terms of a paper's content: What does this manuscript add to the knowledge of the field? An article may offer some fundamentally new idea or evidence that substantially alters the field, but more often, advances are incremental.
An example of such incremental advances is a series of articles investigating a new vaccine. Many papers are published before a promising vaccine gets to the stage of clinical trials. Then there will be many more studies: safety studies; pilot studies; studies on different populations, such as adults and children; studies about the efficacy of varying dosages; and so on. If done well, each new paper will offer important insights and inform future research. But from one study to the next, some things will stay the same: the essential problem being studied, the relevant prior research, the biochemistry of the vaccine, the method of vaccine delivery, and so on
Investigation of norms of overpartitions
No full textFor a partition, the norm is defined as the product of its parts. This paper aims to explore norms of overpartitions and develop their interpretations. The analysis begins by providing a two-variable generating function of the overline norm counting function r̅(i,n), which refers to the number of times i appears as a norm in the overpartitions of n. Thereafter, a wealth of intriguing relations like infinite series, integral representation, and recurrences are proved. Subsequently, an analogue of the multiplicative partition emerges, which is named the multiplicative overpartition function. Several curious results are unraveled on studying this function, which resemble the expressions involving the ordinary multiplicative partition function. The presented work opens a new avenue for research in norms and overpartitions
A new bound for the Brown-Erdős-Sós problem
No full textLet f(n, v, e) denote the maximum number of edges in a 3-uniform hypergraph not containing e edges spanned by at most v vertices. One of the most influential open problems in extremal combinatorics then asks, for a given number of edges e ≥ 3, what is the smallest integer d = d(e) such that f(n, e+d, e) = o(n²)? This question has its origins in work of Brown, Erdős and Sós from the early 70's and the standard conjecture is that d(e) = 3 for every e ≥ 3. The state of the art result regarding this problem was obtained in 2004 by Sárközy and Selkow, who showed that f(n, e+2+[log₂e], e) = o(n²). The only improvement over this result was a recent breakthrough of Solymosi and Solymosi, who improved the bound for d(10) from 5 to 4. We obtain the first asymptotic improvement over the Sárközy–Selkow bound, showing that f(n, e+O(log e / log log e), e) = o(n²)
Model-free Data-Driven viscoelasticity in the frequency domain
No full textWe develop a Data-Driven framework for the simulation of wave propagation in viscoelastic solids directly from dynamic testing material data, including data from Dynamic Mechanical Analysis (DMA), nano-indentation, Dynamic Shear Testing (DST) and Magnetic Resonance Elastography (MRE), without the need for regression or material modeling. The problem is formulated in the frequency domain and the method of solution seeks to minimize a distance between physically admissible histories of stress and strain, in the sense of compatibility and equilibrium, and the material data. We metrize the space of histories by means of the flat-norm of their Fourier transform, which allows consideration of infinite wave trains such as harmonic functions. Another significant advantage of the flat norm is that it allows the response of the system at one frequency to be inferred from data at nearby frequencies. We demonstrate and verify the approach by means of two test cases, a polymeric truss structure characterized by DMA data and a 3D soft gel sample characterized by MRE data. The examples demonstrate the ease of implementation of the Data-Driven scheme within conventional commercial codes and its robust convergence properties, both with respect to the solver and the data
Formation of Rocky Super-Earths From A Narrow Ring of Planetesimals
No full textThe formation of super-Earths, the most abundant planets in the Galaxy, remains elusive. These planets have masses that typically exceed that of the Earth by a factor of a few; appear to be predominantly rocky, although often surrounded by H/He atmospheres; and frequently occur in multiples. Moreover, planets that encircle the same star tend to have similar masses and radii, whereas those belonging to different systems exhibit remarkable overall diversity. Here, we advance a theoretical picture for rocky planet formation that satisfies the aforementioned constraints: building upon recent work - which demonstrates that planetesimals can form rapidly at discrete locations in the disk - we propose that super-Earths originate inside rings of silicate-rich planetesimals at approximately ~1 AU. Within the context of this picture, we show that planets grow primarily through pairwise collisions among rocky planetesimals, until they achieve terminal masses that are regulated by isolation and orbital migration. We quantify our model with numerical simulations and demonstrate that our synthetic planetary systems bear a close resemblance to compact, multi-resonant progenitors of the observed population of short-period extrasolar planets. Our results thus indicate that the absence of short-period super-Earths within the solar system can simply be attributed to the comparatively low mass of the primordial planetesimal ring within the protosolar nebula
Occurrence Rate of Hot Jupiters Around Early-type M Dwarfs Based on Transiting Exoplanet Survey Satellite Data
No full textWe present an estimate of the occurrence rate of hot Jupiters (7 R_⊕ ≤ R_p ≤ 2 R_J, 0.8 ≤ P_b ≤ 10 days) around early-type M dwarfs based on stars observed by the Transiting Exoplanet Survey Satellite (TESS) during its primary mission. We adopt stellar parameters from the TESS Input Catalog and construct a sample of 60,819 M dwarfs with 10.5 ≤ T_mag ≤ 13.5, effective temperatures 2900 ≤ T_eff ≤ 4000 K, and stellar masses 0.45 ≤ M_* ≤ 0.65 M_⊙. We conduct a uninformed transit search using a detection pipeline based on the box least square search and characterize the searching completeness through an injection and recovery experiment. We combine a series of vetting steps including light centroid measurement, odd/even and secondary eclipse analysis, rotation and transit period synchronization tests as well as inspecting the ground-based photometric, spectroscopic, and imaging observations. Finally, we find a total of nine planet candidates, all of which are known TESS objects of interest. We obtain an occurrence rate of 0.27% ± 0.09% for hot Jupiters around early-type M dwarfs that satisfy our selection criteria. Compared with previous studies, the occurrence rate of hot Jupiters around early-type M dwarfs is smaller than all measurements for FGK stars, although they are consistent within 1σ–2σ. There is a trend that the occurrence rate of hot Jupiters has a peak at G dwarfs and falls toward both hotter and cooler stars. Combining results from transit, radial velocity, and microlensing surveys, we find that hot Jupiters around early-type M dwarfs possibly show a steeper decrease in the occurrence rate per logarithmic semimajor axis bin (dN/d log_(10)a) when compared with FGK stars
The Final Season Reimagined: 30 Tidal Disruption Events from the ZTF-I Survey
No full textTidal disruption events (TDEs) offer a unique way to study dormant black holes. While the number of observed TDEs has grown thanks to the emergence of wide-field surveys in the past few decades, questions regarding the nature of the observed optical, UV, and X-ray emission remain. We present a uniformly selected sample of 30 spectroscopically classified TDEs from the Zwicky Transient Facility Phase I survey operations with follow-up Swift UV and X-ray observations. Through our investigation into correlations between light-curve properties, we recover a shallow positive correlation between the peak bolometric luminosity and decay timescales. We introduce a new spectroscopic class of TDE, TDE-featureless, which are characterized by featureless optical spectra. The new TDE-featureless class shows larger peak bolometric luminosities, peak blackbody temperatures, and peak blackbody radii. We examine the differences between the X-ray bright and X-ray faint populations of TDEs in this sample, finding that X-ray bright TDEs show higher peak blackbody luminosities than the X-ray faint subsample. This sample of optically selected TDEs is the largest sample of TDEs from a single survey yet, and the systematic discovery, classification, and follow-up of this sample allows for robust characterization of TDE properties, an important stepping stone looking forward toward the Rubin era
Self-Assembly in "Matrix-Free" Functionalized Boron Nitride Sheets as Free-Standing Thin Film Sieves for Stable Forward Osmosis and Robust Dye Removal Applications
No full textHerein, a facile "matrix-free" thin film membrane strategy is reported that exploits polymer brushes grafted hydroxyl-functionalized hexagonal boron nitride nanosheets (h-BNOH) toward forward osmosis desalination and dye rejection application. The functionalized nanosheets are characterized using Fourier transform infrared spectroscopy (FTIR), high-resolution transmission electron microscopy (HRTEM), X-ray diffraction (XRD), Nuclear magnetic resonance (NMR), UV–visible spectrophotometry, and thermogravimetric analysis (TGA). Covalently functionalized nanosheets of poly methyl methacrylate (PMMA) termed as boron nitride grafted PMMA (BN-g-PMMA) obtained via RAFT polymerization are deployed toward “matrix-free” nanocomposite membranes. The membranes exhibit ≈ 5260 L/m⁻² h⁻¹ at a moderate pressure of 0.21 MPa in cross-flow mode and a 70% of flux retention ratio against bovine serum albumin as protein foulant. The matrix-free membranes exhibit ≈ 93% salt rejection for NaCl and > 99% rejection for MgCl₂ and Ca(NO₃)₂·4H₂O for 2000 ppm draw solution (water TDS benchmark for domestic purifiers) while 90% NaCl, and > 96% rejection for MgCl₂ and Ca(NO₃)₂·4H₂O for 5000 ppm draw. In simulated domestic water salinity, 97.8% rejection is observed for 2000 ppm and 94.5% for 5000 ppm draw solution, respectively. The matrix-free membranes also achieve almost 100% dye rejection for eight model dye pollutants at 1 ppm and > 96.6% for 10 ppm concentrations, respectively
Vapors Are Lost to Walls, Not to Particles on the Wall: Artifact-Corrected Parameters from Chamber Experiments and Implications for Global Secondary Organic Aerosol
No full textAtmospheric models of secondary organic aerosol (OA) (SOA) typically rely on parameters derived from environmental chambers. Chambers are subject to experimental artifacts, including losses of (1) particles to the walls (PWL), (2) vapors to the particles on the wall (V2PWL), and (3) vapors to the wall directly (VWL). We present a method for deriving artifact-corrected SOA parameters and translating these to volatility basis set (VBS) parameters for use in chemical transport models (CTMs). Our process involves combining a box model that accounts for chamber artifacts (Statistical Oxidation Model with a TwO-Moment Aerosol Sectional model (SOM-TOMAS)) with a pseudo-atmospheric simulation to develop VBS parameters that are fit across a range of OA mass concentrations. We found that VWL led to the highest percentage change in chamber SOA mass yields (high NOₓ: 36–680%; low NOₓ: 55–250%), followed by PWL (high NOₓ: 8–39%; low NOₓ: 10–37%), while the effects of V2PWL are negligible. In contrast to earlier work that assumed that V2PWL was a meaningful loss pathway, we show that V2PWL is an unimportant SOA loss pathway and can be ignored when analyzing chamber data. Using our updated VBS parameters, we found that not accounting for VWL may lead surface-level OA to be underestimated by 24% (0.25 μg m⁻³) as a global average or up to 130% (9.0 μg m⁻³) in regions of high biogenic or anthropogenic activity. Finally, we found that accurately accounting for PWL and VWL improves model-measurement agreement for fine mode aerosol mass concentrations (PM₂.₅) in the GEOS-Chem model