Finite speed axially symmetric Navier-Stokes flows passing a cone

Let $D$ be the exterior of a cone inside a ball, with its altitude angle at most $\pi/6$ in $\mathbb{R}^3$, which touches the $x_3$ axis at the origin. For any initial value $v_0 = v_{0,r}e_{r} + v_{0,\theta} e_{\theta} + v_{0,3} e_{3}$ in a $C^2(\overline{D})$ class, which has the usual even-odd-odd symmetry in the $x_3$ variable and has the partial smallness only in the swirl direction: $| r v_{0, \theta} | \leq \frac{1}{100}$, the axially symmetric Navier-Stokes equations (ASNS) with Navier-Hodge-Lions slip boundary condition has a finite-energy solution that stays bounded for all time. In particular, no finite-time blowup of the fluid velocity occurs. Compared with standard smallness assumptions on the initial velocity, no size restriction is made on the components $v_{0,r}$ and $v_{0,3}$. In a broad sense, this result appears to solve $2/3$ of the regularity problem of ASNS in such domains in the class of solutions with the above symmetry. Equivalently, this result is connected to the general open question which asks that if an absolute smallness of one component of the initial velocity implies the global smoothness, see e.g. page 873 in \cite{CZZ17}. Our result seems to give a positive answer in a special setting. As a byproduct, we also construct an unbounded solution of the forced Navier Stokes equation in a special cusp domain that has finite energy. The forcing term, with the scaling factor of $-1$, is in the standard regularity class. This result confirms the intuition that if the channel of a fluid is very thin, arbitrarily high speed in the classical sense can be attained under a mildly singular force which is physically reasonable in view that Newtonian gravity and Coulomb force have scaling factor $-2$.Comment: 85 pages. A blow up solution in a special cusp domain, two references and a few sentences adde

Case report and literature review: Orally ingested toothpick perforating the lower rectum

IntroductionMost foreign bodies (FBs) can spontaneously pass through the gastrointestinal tract. Sharp FBs are believed to be able to puncture any part of the gastrointestinal tract, causing perforation and potentially secondary damage to adjacent organs.Case descriptionA 44-year-old man complained of having persistent dull pain in the perianal region. He was diagnosed with a toothpick impacted into the wall of the lower rectum after accepting a digital rectal examination of the lower rectum and a pelvic computed tomography (CT). The surgeon extracted the FB using vascular forceps guided by the operator’s index finger. The patient was discharged after intravenous ceftriaxone was given for 6 days. A follow-up pelvic CT performed 2 weeks after surgery revealed that the perirectal fat and muscles had already normalized.ConclusionA systematic review of relevant literature from the past decade was performed to summarize the imaging features of an orally ingested toothpick perforating the gastrointestinal tract. The location of abdominal pain is an important clue for the diagnosis of toothpick perforation, and a CT examination is recommended as the first option for the detection of an ingested toothpick. Determining the location of the toothpick perforation and assessing the severity of local inflammation are important bases for the selection of treatment

Decreased Pituitary Height and Stunted Linear Growth After Radiotherapy in Survivors of Childhood Nasopharyngeal Carcinoma Cases

To examine the morphological changes of the pituitary glands and linear growth of childhood nasopharyngeal carcinoma (NPC) cases who accepted radiotherapy. A total of 90 children (i.e., age less than 18 years) who were diagnosed as NPC at Sun Yat-sen University Cancer Center from January 2009 to January 2016 were identified by reviewing medical records. Two radiologists reviewed and measured the pre-radiation, post-radiation, and the latest available pituitary gland heights independently. Patients' current height information was collected by telephone interviews. We compared the pituitary height differences using paired t-tests and estimated the pituitary height trajectories within each sex by mixed regression models. Height-for-age Z-score was calculated for each patient using the WHO growth reference data for 5–19 years as reference. Most of the included participants were of male sex (75.6%) and over half were diagnosed at stage IV (58.4%). Among the 90 included participants, 89 had one repeated measurement of the pituitary height and 79 had two repeated measurements of the pituitary height. Seventy six of the 89 childhood NPC participants had reduced pituitary heights after radiation and accounted for 85.4% of the whole population. The means of the pituitary heights before and after radiotherapy were 6.4 ± 1.3 mm and 5.6 ± 1.2 mm (P < 0.001), respectively. The mean of height-for-age Z-score for childhood NPC cases was significantly below zero (−0.54, 95% CI = −0.74, −0.34). We concluded that childhood NPC cases had decreased pituitary heights and stunted linear growth after radiotherapy

Discovery of charge order and corresponding edge state in kagome magnet FeGe

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge order, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to non-kagome surface layers. Here we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifes a 2x2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin-mapping across steps of unit-cell-height demonstrates that this charge order emerges from spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including orbital magnetism and bulk-boundary correspondence

A Search for Technosignatures Around 11,680 Stars with the Green Bank Telescope at 1.15-1.73 GHz

We conducted a search for narrowband radio signals over four observing sessions in 2020-2023 with the L-band receiver (1.15-1.73 GHz) of the 100 m diameter Green Bank Telescope. We pointed the telescope in the directions of 62 TESS Objects of Interest, capturing radio emissions from a total of ~11,680 stars and planetary systems in the ~9 arcminute beam of the telescope. All detections were either automatically rejected or visually inspected and confirmed to be of anthropogenic nature. In this work, we also quantified the end-to-end efficiency of radio SETI pipelines with a signal injection and recovery analysis. The UCLA SETI pipeline recovers 94.0% of the injected signals over the usable frequency range of the receiver and 98.7% of the injections when regions of dense RFI are excluded. In another pipeline that uses incoherent sums of 51 consecutive spectra, the recovery rate is ~15 times smaller at ~6%. The pipeline efficiency affects calculations of transmitter prevalence and SETI search volume. Accordingly, we developed an improved Drake Figure of Merit and a formalism to place upper limits on transmitter prevalence that take the pipeline efficiency and transmitter duty cycle into account. Based on our observations, we can state at the 95% confidence level that fewer than 6.6% of stars within 100 pc host a transmitter that is detectable in our search (EIRP > 1e13 W). For stars within 20,000 ly, the fraction of stars with detectable transmitters (EIRP > 5e16 W) is at most 3e-4. Finally, we showed that the UCLA SETI pipeline natively detects the signals detected with AI techniques by Ma et al. (2023).Comment: 22 pages, 9 figures, submitted to AJ, revise