On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations

We investigate the large time behavior of an axisymmetric model for the 3D Euler equations. In \cite{HL09}, Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier-Stokes equations with swirl. This model shares many properties of the 3D incompressible Euler and Navier-Stokes equations. The main difference between the 3D model of Hou and Lei and the reformulated 3D Euler and Navier-Stokes equations is that the convection term is neglected in the 3D model. In \cite{HSW09}, the authors proved that the 3D inviscid model can develop a finite time singularity starting from smooth initial data on a rectangular domain. A global well-posedness result was also proved for a class of smooth initial data under some smallness condition. The analysis in \cite{HSW09} does not apply to the case when the domain is axisymmetric and unbounded in the radial direction. In this paper, we prove that the 3D inviscid model with an appropriate Neumann-Robin boundary condition will develop a finite time singularity starting from smooth initial data in an axisymmetric domain. Moreover, we prove that the 3D inviscid model has globally smooth solutions for a class of large smooth initial data with some appropriate boundary condition.Comment: Please read the published versio

Exact Solution of boundary-dissipated transverse field Ising model: structure of Liouvillian spectrum and dynamical duality

We study the boundary-dissipated transverse field Ising model described by a Lindblad Master equation and exactly solve its Liouvillian spectrum in the whole parameter space. By mapping the Liouvillian into a Su-Schrieffer-Heeger model with imaginary boundary potentials under a parity constraint, we solve the rapidity spectrum analytically and thus construct the Liouvillian spectrum strictly with a parity constraint condition. Our results demonstrate that the Liouvillian spectrum displays four different structures, which are characterized by different numbers of segments. By analyzing the properties of rapidity spectrum, we can determine the phase boundaries between different spectrum structures analytically and prove the Liouvillian gap fulfilling a duality relation in the weak and strong dissipation region. Furthermore, we unveil the existence of a dynamical duality, i.e., the long-time relaxation dynamics exhibits almost the same dynamical behavior in the weak and strong dissipation region as long as the duality relation holds true.Comment: 6 pages, 4 figure

Design method for stabilization of earth slopes with micropiles

AbstractAs one of the measures for slope fast reinforcement, micropiles are always designed as a group. In this paper, an analytic model for the ultimate resistance of micropile is proposed, based on a beam–column equation and an existing p–y curve method. As such, an iterative process to find the bending moment and shear capacity of the micropile section has been developed. The formulation for calculating the inner force and deflection of the micropile using the finite difference method is derived. Special attention is given to determine the spacing of micropiles with the aim of achieving the ultimate shear capacity of the micropile group. Thus, a new design method for micropiles for earth slope stabilization is proposed that includes details about choosing a location for the micropiles within the existing slope, selecting micropile cross section, estimating the length of the micropile, evaluating the shear capacity of the micropiles group, calculating the spacing required to provide force to stabilize the slope and the design of the concrete cap beam. The application of the method to an embankment landslide in Qinghai province, China, is described, and monitoring data indicated that slope movement had effectively ceased as a result of the slope stabilization measure, which verified the effectiveness of the design method

2-Eth­oxy-4-[2-(3-nitro­phen­yl)­hydrazono­meth­yl]phenol

The title Schiff base compound, C15H15N3O4, was prepared from a condensation reaction of 3-eth­oxy-4-hydroxy­benz­aldehyde and 3-nitro­phenyl­hydrazine. The mol­ecule is nearly planar; the dihedral angle between the hydroxy­benzene ring and the nitro­benzene ring is 6.57 (7)°. O—H⋯O, O—H⋯N and C—H⋯O hydrogen bonding helps to stabilize the crystal structure

Design And Fabrication of Condenser Microphone Using Wafer Transfer And Micro-electroplating Technique

A novel fabrication process, which uses wafer transfer and micro-electroplating technique, has been proposed and tested. In this paper, the effects of the diaphragm thickness and stress, the air-gap thickness, and the area ratio of acoustic holes to backplate on the sensitivity of the condenser microphone have been demonstrated since the performance of the microphone depends on these parameters. The microphone diaphragm has been designed with a diameter and thickness of 1.9 mm and 0.6 $\mu$m, respectively, an air-gap thickness of 10 $\mu$m, and a 24% area ratio of acoustic holes to backplate. To obtain a lower initial stress, the material used for the diaphragm is polyimide. The measured sensitivities of the microphone at the bias voltages of 24 V and 12 V are -45.3 and -50.2 dB/Pa (at 1 kHz), respectively. The fabricated microphone shows a flat frequency response extending to 20 kHz.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838

Extracellular RNA in a single droplet of human serum reflects physiologic and disease states.

Extracellular RNAs (exRNAs) are present in human serum. It remains unclear to what extent these circulating exRNAs may reflect human physiologic and disease states. Here, we developed SILVER-seq (Small Input Liquid Volume Extracellular RNA Sequencing) to efficiently sequence both integral and fragmented exRNAs from a small droplet (5 μL to 7 μL) of liquid biopsy. We calibrated SILVER-seq in reference to other RNA sequencing methods based on milliliters of input serum and quantified droplet-to-droplet and donor-to-donor variations. We carried out SILVER-seq on more than 150 serum droplets from male and female donors ranging from 18 y to 48 y of age. SILVER-seq detected exRNAs from more than a quarter of the human genes, including small RNAs and fragments of mRNAs and long noncoding RNAs (lncRNAs). The detected exRNAs included those derived from genes with tissue (e.g., brain)-specific expression. The exRNA expression levels separated the male and female samples and were correlated with chronological age. Noncancer and breast cancer donors exhibited pronounced differences, whereas donors with or without cancer recurrence exhibited moderate differences in exRNA expression patterns. Even without using differentially expressed exRNAs as features, nearly all cancer and noncancer samples and a large portion of the recurrence and nonrecurrence samples could be correctly classified by exRNA expression values. These data suggest the potential of using exRNAs in a single droplet of serum for liquid biopsy-based diagnostics