Scale-free random branching tree in supercritical phase

We study the size and the lifetime distributions of scale-free random branching tree in which $k$ branches are generated from a node at each time step with probability $q_k\sim k^{-\gamma}$. In particular, we focus on finite-size trees in a supercritical phase, where the mean branching number $C=\sum_k k q_k$ is larger than 1. The tree-size distribution $p(s)$ exhibits a crossover behavior when $2 < \gamma < 3$; A characteristic tree size $s_c$ exists such that for $s \ll s_c$, $p(s)\sim s^{-\gamma/(\gamma-1)}$ and for $s \gg s_c$, $p(s)\sim s^{-3/2}\exp(-s/s_c)$, where $s_c$ scales as $\sim (C-1)^{-(\gamma-1)/(\gamma-2)}$. For $\gamma > 3$, it follows the conventional mean-field solution, $p(s)\sim s^{-3/2}\exp(-s/s_c)$ with $s_c\sim (C-1)^{-2}$. The lifetime distribution is also derived. It behaves as $\ell(t)\sim t^{-(\gamma-1)/(\gamma-2)}$ for $2 < \gamma < 3$, and $\sim t^{-2}$ for $\gamma > 3$ when branching step $t \ll t_c \sim (C-1)^{-1}$, and $\ell(t)\sim \exp(-t/t_c)$ for all $\gamma > 2$ when $t \gg t_c$. The analytic solutions are corroborated by numerical results.Comment: 6 pages, 6 figure

A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations

In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.Comment: 25 page

Quantum Smoluchowski equation: Escape from a metastable state

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.Comment: 10 pages, To appear in the Proceedings of Statphys - Kolkata I

Impact of COVID-19 pandemic on eye cancer care in United Kingdom

The COVID-19 pandemic has had an unprecedented impact on the National Health Service in United Kingdom. The UK Ocular Oncology Services evaluated the impact on the adult eye cancer care in the UK. All four adult Ocular Oncology centres participated in a multicentre retrospective review comparing uveal melanoma referral patterns and treatments in a 4-month period during the national lockdown and first wave of the COVID-19 pandemic in 2020 with corresponding periods in previous 2 years. During the national lockdown, referral numbers and confirmed uveal melanoma cases reduced considerably, equalling to ~120 fewer diagnosed uveal melanoma cases compared to previous 2 years. Contrary to the recent trend, increased caseloads of enucleation and stereotactic radiosurgery (p > 0.05), in comparison to fewer proton beam therapy (p < 0.05), were performed. In the 4-month period following lockdown, there was a surge in clinical activities with more advanced diseases (p < 0.05) presenting to the services. As the COVID-19 pandemic continues to mount pressure and reveal its hidden impact on the eye cancer care, it is imperative for the Ocular Oncology Services to plan recovery strategies and innovative ways of working

Coseismic deformation and source modeling of the May 2012 Emilia (Northern Italy) earthquakes

On May 20th, 2012, an ML 5.9 earthquake (Table 1) occurred near the town of Finale Emilia, in the Central Po Plain, Northern Italy (Figure 1). The mainshock caused 7 casualties and the collapse of several historical buildings and industrial sheds. The earthquake sequence continued with diminishing aftershock magnitudes until May 29th, when an ML 5.8 earthquake occurred near the town of Mirandola, ~12 km WSW of the mainshock (Scognamiglio et al., 2012). This second mainshock started a new aftershock sequence in this area, and increased structural damage and collapses, causing 19 more casualties and increasing to 15.000 the number of evacuees. Shortly after the first mainshock, the Department of Civil Protection (DPC) activated the Italian Space Agency (ASI), which provided post-seismic SAR Interferometry data coverage with all 4 COSMO-SkyMed SAR satellites. Within the next two weeks, several SAR Interferometry (InSAR) image pairs were processed by the INGV-SIGRIS system (Salvi et al., 2012), to generate displacement maps and preliminary source models for the emergency management. These results included continuous GPS site displacement data, from private and public sources, located in and around the epicentral area. In this paper we present the results of the geodetic data modeling, identifying two main fault planes for the Emilia seismic sequence and computing the corresponding slip distributions. We discuss the implication of this seismic sequence on the activity of the frontal part of the Northern Apennine accretionary wedge by comparing the co-seismic data with the long term (geological) and present day (GPS) velocity fields.Published645-6551.1. TTC - Monitoraggio sismico del territorio nazionale1.9. Rete GPS nazionale1.10. TTC - Telerilevamento3.2. Tettonica attivaJCR Journalrestricte

Early intervention in acute upper respiratory tract infections

Upper respiratory tract infections (URTIs) are one of the most common diagnoses in the primary care setting across the world,1 with more than 18.8 billion cases2 occurring worldwide every year. Most adults will have 2–4 episodes of acute URTI each year, while children have an average of 6–10 episodes.http://www.sapj.co.za/index.php/sapjam2023Pharmacolog