Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem

Numerical simulations of the incompressible Euler equations are performed using the Taylor-Green vortex initial conditions and resolutions up to $4096^3$. The results are analyzed in terms of the classical analyticity strip method and Beale, Kato and Majda (BKM) theorem. A well-resolved acceleration of the time-decay of the width of the analyticity strip $\delta(t)$ is observed at the highest resolution for $3.7<t<3.85$ while preliminary 3D visualizations show the collision of vortex sheets. The BKM criterium on the power-law growth of supremum of the vorticity, applied on the same time-interval, is not inconsistent with the occurrence of a singularity around $t \simeq 4$. These new findings lead us to investigate how fast the analyticity strip width needs to decrease to zero in order to sustain a finite-time singularity consistent with the BKM theorem. A new simple bound of the supremum norm of vorticity in terms of the energy spectrum is introduced and used to combine the BKM theorem with the analyticity-strip method. It is shown that a finite-time blowup can exist only if $\delta(t)$ vanishes sufficiently fast at the singularity time. In particular, if a power law is assumed for $\delta(t)$ then its exponent must be greater than some critical value, thus providing a new test that is applied to our $4096^3$ Taylor-Green numerical simulation. Our main conclusion is that the numerical results are not inconsistent with a singularity but that higher-resolution studies are needed to extend the time-interval on which a well-resolved power-law behavior of $\delta(t)$ takes place, and check whether the new regime is genuine and not simply a crossover to a faster exponential decay

Statistics of Dissipation and Enstrophy Induced by a Set of Burgers Vortices

Dissipation and enstropy statistics are calculated for an ensemble of modified Burgers vortices in equilibrium under uniform straining. Different best-fit, finite-range scaling exponents are found for locally-averaged dissipation and enstrophy, in agreement with existing numerical simulations and experiments. However, the ratios of dissipation and enstropy moments supported by axisymmetric vortices of any profile are finite. Therefore the asymptotic scaling exponents for dissipation and enstrophy induced by such vortices are equal in the limit of infinite Reynolds number.Comment: Revtex (4 pages) with 4 postscript figures included via psfi

Finite time singularities in a class of hydrodynamic models

Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form ${\cal L}\sim\int k^\alpha|{\bf v_k}|^2d^3{\bf k}$ in 3D Fourier representation, where $\alpha$ is a constant, $0<\alpha< 1$. Unlike the case $\alpha=0$ (the usual Eulerian hydrodynamics), a finite value of $\alpha$ results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of anti-parallel vortex filaments and an analog of the Crow instability is found at small wave-numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically. They describe the formation of a finite time singularity, with all length scales decreasing like $(t^*-t)^{1/(2-\alpha)}$, where $t^*$ is the singularity time.Comment: LaTeX, 17 pages, 3 eps figures. This version is close to the journal pape

Design of Dressed Crab Cavities for the HL-LHC Upgrade

The HL-LHC upgrade relies on a set of RF crab cavities for reaching its goals. Two parallel concepts, the Double Quarter Wave (DQW) and the RF Dipole (RFD), are going through a comprehensive design process along with preparation of fabrication in view of extensive tests with beam in SPS. High Order Modes (HOM) couplers are critical in providing damping in RF cavities for operation in accelerators. HOM prototyping and fabrication have recently started at CERN. In this paper, an overview of the final geometry is provided along with an insight in the mechanical and thermal analyses performed to validate the design of this critical component. Emphasis is also given to material selection, prototyping, initial fabrication and test campaigns that are aimed at fulfilling the highly demanding tolerances of the couplers

On formation of a locally self-similar collapse in the incompressible Euler equations

The paper addresses the question of existence of a locally self-similar blow-up for the incompressible Euler equations. Several exclusion results are proved based on the $L^p$-condition for velocity or vorticity and for a range of scaling exponents. In particular, in $N$ dimensions if in self-similar variables $u \in L^p$ and u \sim \frac{1}{t^{\a/(1+\a)}}, then the blow-up does not occur provided \a >N/2 or -1<\a\leq N/p. This includes the $L^3$ case natural for the Navier-Stokes equations. For \a = N/2 we exclude profiles with an asymptotic power bounds of the form |y|^{-N-1+\d} \lesssim |u(y)| \lesssim |y|^{1-\d}. Homogeneous near infinity solutions are eliminated as well except when homogeneity is scaling invariant.Comment: A revised version with improved notation, proofs, etc. 19 page

Isolated and Syndromic Retinal Dystrophy Caused by Biallelic Mutations in RCBTB1, a Gene Implicated in Ubiquitination.

Inherited retinal dystrophies (iRDs) are a group of genetically and clinically heterogeneous conditions resulting from mutations in over 250 genes. Here, homozygosity mapping and whole-exome sequencing (WES) in a consanguineous family revealed a homozygous missense mutation, c.973C&gt;T (p.His325Tyr), in RCBTB1. In affected individuals, it was found to segregate with retinitis pigmentosa (RP), goiter, primary ovarian insufficiency, and mild intellectual disability. Subsequent analysis of WES data in different cohorts uncovered four additional homozygous missense mutations in five unrelated families in whom iRD segregates with or without syndromic features. Ocular phenotypes ranged from typical RP starting in the second decade to chorioretinal dystrophy with a later age of onset. The five missense mutations affect highly conserved residues either in the sixth repeat of the RCC1 domain or in the BTB1 domain. A founder haplotype was identified for mutation c.919G&gt;A (p.Val307Met), occurring in two families of Mediterranean origin. We showed ubiquitous mRNA expression of RCBTB1 and demonstrated predominant RCBTB1 localization in human inner retina. RCBTB1 was very recently shown to be involved in ubiquitination, more specifically as a CUL3 substrate adaptor. Therefore, the effect on different components of the CUL3 and NFE2L2 (NRF2) pathway was assessed in affected individuals' lymphocytes, revealing decreased mRNA expression of NFE2L2 and several NFE2L2 target genes. In conclusion, our study puts forward mutations in RCBTB1 as a cause of autosomal-recessive non-syndromic and syndromic iRD. Finally, our data support a role for impaired ubiquitination in the pathogenetic mechanism of RCBTB1 mutations

High Throughput, Multiplexed Pathogen Detection Authenticates Plague Waves in Medieval Venice, Italy

Background: Historical records suggest that multiple burial sites from the 14th-16(th) centuries in Venice, Italy, were used during the Black Death and subsequent plague epidemics.Methodology/Principal Findings: High throughput, multiplexed real-time PCR detected DNA of seven highly transmissible pathogens in 173 dental pulp specimens collected from 46 graves. Bartonella quintana DNA was identified in five (2.9%) samples, including three from the 16th century and two from the 15th century, and Yersinia pestis DNA was detected in three (1.7%) samples, including two from the 14th century and one from the 16th century. Partial glpD gene sequencing indicated that the detected Y. pestis was the Orientalis biotype.Conclusions: These data document for the first time successive plague epidemics in the medieval European city where quarantine was first instituted in the 14th century

Metagenomic Analysis of Human Diarrhea: Viral Detection and Discovery

Worldwide, approximately 1.8 million children die from diarrhea annually, and millions more suffer multiple episodes of nonfatal diarrhea. On average, in up to 40% of cases, no etiologic agent can be identified. The advent of metagenomic sequencing has enabled systematic and unbiased characterization of microbial populations; thus, metagenomic approaches have the potential to define the spectrum of viruses, including novel viruses, present in stool during episodes of acute diarrhea. The detection of novel or unexpected viruses would then enable investigations to assess whether these agents play a causal role in human diarrhea. In this study, we characterized the eukaryotic viral communities present in diarrhea specimens from 12 children by employing a strategy of “micro-mass sequencing” that entails minimal starting sample quantity (<100 mg stool), minimal sample purification, and limited sequencing (384 reads per sample). Using this methodology we detected known enteric viruses as well as multiple sequences from putatively novel viruses with only limited sequence similarity to viruses in GenBank

Predictors of early recurrence after resection of colorectal liver metastases

BACKGROUND: Early recurrence after resection of colorectal liver metastases (CLM) is common. Patients at risk of early recurrence may be candidates for enhanced preoperative staging and/or earlier postoperative imaging. The aim of this study was to determine if there are any risk factors that specifically predict early liver-only and systemic recurrence. METHODS: Retrospective analysis of prospective database of patients undergoing liver resection (LR) for CLM from 2004 to 2006 was undertaken. Early recurrence was defined as occurring within 18 months of LR. Patients were classified into three groups: early liver-only recurrence, early systemic recurrence and recurrence-free. Preoperative factors were compared between patients with and without early recurrence. RESULTS: Two hundred and forty-three consecutive patients underwent LR for CLM. Twenty-seven patients (11%) developed early liver-only recurrence. Dukes C stage and male sex were significantly associated with early liver-only recurrence (P < 0.05). Sixty-six patients (27%) developed early systemic recurrence. Tumour size ≥3.6 cm and tumour number (>2) were significantly associated with early systemic recurrence (P < 0.001). CONCLUSIONS: It is possible to stratify patients according to the risk of early liver-only or systemic recurrence after resection of CLM. High-risk patients may be candidates for preoperative MRI and/or computed tomography-positron emission tomography (CT-PET) scan and should receive intensive postoperative surveillance