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CLASSICAL SOLUTIONS OF THE BOLTZMANN EQUATION WITH IRREGULAR INITIAL DATA
No full textThis article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our result requires no assumption of strict positivity for the initial data, except locally in some small ball in phase space. We also obtain existence results for weak solutions when our decay and positivity assumptions for the initial data are relaxed. Because the regularity of our solutions may degenerate as t tends to 0, uniqueness is a challenging issue. We establish weak-strong uniqueness under the additional assumption that the initial data possesses no vacuum regions and is Hölder continuous. As an application of our short-time existence theorem, we prove global existence near equilibrium for bounded, measurable initial data that decays at a finite polynomial rate in velocity
Finding Belonging: The Search for Comprehensive Measurements of Student Belonging in Math
Get PDFThis report provides the background, methods, and findings of Phase One of the development of a new instrument to assess belonging in math. It includes a review of existing instruments, their evaluation, and integration. It also includes findings from a panel about perceptions of belonging in school-aged students. Contents include: 1) a comprehensive definition of belonging, 2) a listing of existing belonging instruments, 3) a multidimensional breakdown of belonging that accounts for context and perspective, 4) a list of belonging items from existing scales that met coder face validity assessments, and 5) a definitionally grounded recommended set of belonging items for future piloting, testing, and validation
Performance of various kernel functions for mass prediction with support vector machine
No full textThis manuscript explores the potential of Support Vector Machines (SVM) in predicting nuclear binding energies, emphasizing the critical role of kernel functions in improving model accuracy. We systematically assess the performance of various SVM kernel functions-linear, polynomial, radial basis function, and sigmoid-through rigorous hyperparameter optimization and cross-validation. The study demonstrates that the radial basis function kernel outperforms other kernels, achieving the lowest root-mean-square deviation of 0.199 MeV, making it the most effective for nuclear mass predictions. By integrating key nuclear physics features, including mass model information, the SVM model is able to capture complex nuclear behaviors across different mass ranges. We present a comprehensive comparison of our SVM model against conventional mass models such as liquid drop model and WS4, where our SVM model shows improved predictive accuracy. This work underscores the significance of kernel selection in SVM and highlights the power of machine learning in advancing nuclear mass spectroscopy, providing a valuable framework for future computational modeling in nuclear physics
Nuclear matrix elements of neutrinoless double- β decay in the SD -pair shell model with expanded model space
No full textTo investigate the impact of the finite nucleon size effects (FNS) and the short-range correction (SRC) on the Fermi, Gamow-Teller, and tensor matrix elements of the neutrinoless double-beta (0νββ) decay, calculations are performed within the SD-pair shell model framework for Te128, Te130, and Xe134. The results reveal that both FNS and SRC effectively reduce the magnitude of each type of matrix element in the decay process. Furthermore, when the model space is expanded from the 50-82 shell to the 50-126 shell, the magnitudes of all matrix elements increase significantly, consistent with the findings of the shell model. Additionally, the suppressing effect of higher-order contributions appears to be independent of model space truncation
A 3D Superposition Approximation for Gamma Knife Dose Calculation
Get PDFEffective dose calculation is essential for optimizing Gamma Knife (GK) stereotactic radiosurgery (SRS) treatment plans. Modern GK systems allow independent sector activation, enabling complex dose distributions per shot. This study presents a dose approximation method designed to account for shot flexibility and generate 3D doses external to GammaPlan. A treatment plan was created with the TMR10 calculation for individual sector activations using a Radiosurgery Head Phantom. The resulting dose arrays established a basis set of sector-specific distributions, which were then referenced by shot parameters from the plan, allowing dose accumulation through superposition. This superposition approximation (SA) was compared to the original TMR10 using the Dice Similarity Coefficient (DSC), 95% Hausdorff Distance (HD95), and GK deliverability metrics: coverage, selectivity, and gradient index, across an isodose normalization range from 10% to 90%. In a cohort of 30 patients with 71 targets, strong agreement was observed between TMR10 and SA in the clinically used 50–60% isodose range, with DSC above 85% and HD95 under 2.18 mm. The average differences for the coverage, selectivity, and gradient index were 0.014, 0.008, and 0.118, respectively. This method accurately approximates TMR10 calculations within clinically relevant ranges, offering an external tool to assess 3D dose distributions for GK treatment plans
Resonant propagation of extreme-ultraviolet pulses through strongly driven high-density media
Get PDFWe show that by combining strong-field dressing and resonant propagation of XUV pulses, the transition of absorption lines from their natural Lorentzian profiles through Fano and complex multipeak shapes all the way back to broadened near-Lorentzian profiles can be achieved, in the limit of optically thick samples. The final stage of this spectral modification can be understood in terms of a significant temporal stretching and delay of the resonant XUV pulse as it propagates through the dense gas, which alters the ultrafast absorption that is modified by the time-synchronized few-femtosecond laser pulse. We first demonstrate this concept in numerical calculations, both using a model system and through a fully coupled solution of the time-dependent Schrödinger equation and the Maxwell wave equation. The applicability and generality of the underlying mechanism is then illustrated in proof-of-principle attosecond transient absorption measurements in a helium gas with a widely varying atomic density. These results provide insights into the interaction of ultrashort laser pulses with dense media and its coherent control
Rapid mid-infrared spectral timing with JWST: GRS 1915+105 during an MIR-bright and X-ray-obscured state
Get PDFWe present mid-infrared (MIR) spectral-timing measurements of the prototypical Galactic microquasar GRS 1915+105. The source was observed with the Mid-Infrared Instrument (MIRI) onboard JWST in June 2023 at an MIR luminosity LMIR ≈ 1036 erg s−1 exceeding past infrared levels by about a factor of 10. In contrast, the X-ray flux is much fainter than the historical average, in the source’s now-persistent ‘obscured’ state. The MIRI low-resolution spectrum shows a plethora of emission lines, the strongest of which are consistent with recombination in the hydrogen Pfund (Pf) series and higher. Low-amplitude (∼1 per cent) but highly significant peak-to-peak photometric variability is found on time-scales of ∼1000 s. The brightest Pf (6–5) emission line lags the continuum. Though difficult to constrain accurately, this lag is commensurate with light-travel time-scales across the outer accretion disc or with expected recombination time-scales inferred from emission-line diagnostics. Using the emission line as a bolometric indicator suggests a moderate (∼5–30 per cent Eddington) intrinsic accretion rate. Multiwavelength monitoring shows that JWST caught the source close in time to unprecedentedly bright MIR and radio long-term flaring. Assuming a thermal bremsstrahlung origin for the MIRI continuum suggests an unsustainably high mass-loss rate during this time unless the wind remains bound, though other possible origins cannot be ruled out. Polycyclic aromatic hydrocarbon features previously detected with Spitzer are now less clear in the MIRI data, arguing for possible destruction of dust in the interim. These results provide a preview of new parameter space for exploring MIR spectral timing in X-ray binaries and other variable cosmic sources on rapid time-scales
Ab initio informed 20Ne(p, pα)16O reaction elucidates the emergence of alpha clustering from chiral potentials
Get PDFWe report on the first ab initio informed α knock-out reaction in the intermediate-mass region, with the aim to probe the underlying chiral potential and its impact on the emergence of alpha clustering in this mass region. The theoretical predictions of the α+16O clustering in the 20Ne ground state, based on the ab initio symmetry-adapted no-core shell model with continuum, yield a triple differential cross section for 20Ne(p, pα)16O that is in a remarkable agreement with the data. This allows us to examine predictions of surface and in-medium α-cluster features that emerge from the underlying realistic nucleon-nucleon interaction with no parameters fitted to nuclear data beyond the two-body system, and to compare these to the successful antisymmetrized molecular dynamics approach
Chip-based quantum signature network reaches 200 km
Get PDFA pioneering chip-based quantum digital signature (QDS) network achieves secure document signing over 200 km of fiber, leveraging integrated photonics to miniaturize transmitters and centralize measurement systems. This breakthrough paves the way for future scalable, cost-effective, and robust quantum-secure communication networks
Phylogenetic relationships and the repeated loss of traits associated with sicklebill pollination in Centropogon subgenus Centropogon (Campanulaceae)
No full textPremise: Centropogon subgenus Centropogon comprises 55 species found primarily in midelevation Andean forests featuring some of the most curved flowers among angiosperms. Floral curvature is linked to coevolution with the sicklebill hummingbird, which pollinates most species. Despite charismatic flowers, there is limited knowledge about the phylogenetic relationships and floral evolution. Methods: We conducted the first densely sampled phylogenomic analysis of the clade using methods that account for incomplete lineage sorting on a sequence capture dataset generated with a lineage-specific probe set. Using phylogenetic comparative methods, we test for correlated evolution of two traits central to sicklebill pollination. Results: We improve understanding of species relationships by more than doubling past taxon sampling. We confirm the monophyly of the subgenus and two sections, and the non-monophyly of remaining sections. The subgenus is characterized by high gene tree discordance. Three widespread species display contrasting phylogenetic dynamics, with C. cornutus forming a clade and C. granulosus and C. solanifolius forming non-monophyletic, biogeographically clustered lineages. Correlated evolution of floral curvature and inflorescence structure has led to multiple putative losses of sicklebill pollination. Conclusions: Centropogon subgenus Centropogon adds to a growing body of literature of Andean plant clades with high gene tree discordance. This phylogeny serves as a foundational framework for further macroevolutionary investigations into the environmental and biogeographic factors shaping the evolution of pollination-related traits