A sequential regularization method for time-dependent incompressible Navier--Stokes equations

The objective of the paper is to present a method, called sequential regularization method (SRM), for the nonstationary incompressible Navier-Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs) , and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is O(ffl m ), where m is the number of the SRM iterations and ffl is the regularization parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit difference scheme is analyzed and its stability is proved under the usual step size condition of explicit schemes. It appears that the SRM formulation is new in the Navier-Stokes context. Unlike other regularizations or pseudo-compressibility methods in the Navier-Stokes context, the regularization parameter ffl in the SRM need not be very small, and the regularized..

Patient safety culture among European cancer nurses - an exploratory, cross-sectional survey comparing data from Estonia, Germany, Netherlands and United Kingdom

Aim To explore the differences in perceived patient safety culture in cancer nurses working in Estonia, Germany, the Netherlands and the United Kingdom. Design An exploratory cross‐sectional survey. Methods In 2018, 393 cancer nurses completed the 12 dimensions of the Hospital Survey on Patient Safety Culture. Results The mean score for the overall patient safety grade was 61.3. The highest rated dimension was ‘teamwork within units' while ‘staffing' was the lowest in all four countries. Nurses in the Netherlands and in the United Kingdom, scored higher on ‘communication openness', the ‘frequency of events reported' and ‘nonpunitive response to errors', than nurses from Estonia or Germany. We found statistically significant differences between the countries for the association between five of the 12 dimensions with the overall patient safety grade: overall perception of patient safety, communication openness, staffing, handoffs and transitions and nonpunitive response to errors. Conclusion Patient safety culture, as reported by cancer nurses, varies between European countries and contextual factors, such as recognition of the nursing role and education have an impact on it. Cancer nurses' role in promoting patient safety is a key concern and requires better recognition on a European and global level

Nanoliter high throughput quantitative PCR

Understanding biological complexity arising from patterns of gene expression requires accurate and precise measurement of RNA levels across large numbers of genes simultaneously. Real time PCR (RT-PCR) in a microtiter plate is the preferred method for quantitative transcriptional analysis but scaling RT-PCR to higher throughputs in this fluidic format is intrinsically limited by cost and logistic considerations. Hybridization microarrays measure the transcription of many thousands of genes simultaneously yet are limited by low sensitivity, dynamic range, accuracy and sample throughput. The hybrid approach described here combines the superior accuracy, precision and dynamic range of RT-PCR with the parallelism of a microarray in an array of 3072 real time, 33 nl polymerase chain reactions (RT-PCRs) the size of a microscope slide. RT-PCR is demonstrated with an accuracy and precision equivalent to the same assay in a 384-well microplate but in a 64-fold smaller reaction volume, a 24-fold higher analytical throughput and a workflow compatible with standard microplate protocols

Perfectly Translating Lattices on a Cylinder

We perform molecular dynamics simulations on an interacting electron gas confined to a cylindrical surface and subject to a radial magnetic field and the field of the positive background. In order to study the system at lowest energy states that still carry a current, initial configurations are obtained by a special quenching procedure. We observe the formation of a steady state in which the entire electron-lattice cycles with a common uniform velocity. Certain runs show an intermediate instability leading to lattice rearrangements. A Hall resistance can be defined and depends linearly on the magnetic field with an anomalous coefficient reflecting the manybody contributions peculiar to two dimensions.Comment: 13 pages, 5 figure

Numerical Stability and Accuracy of Temporally Coupled Multi-Physics Modules in Wind Turbine CAE Tools

In this paper we examine the stability and accuracy of numerical algorithms for coupling time-dependent multi-physics modules relevant to computer-aided engineering (CAE) of wind turbines. This work is motivated by an in-progress major revision of FAST, the National Renewable Energy Laboratory's (NREL's) premier aero-elastic CAE simulation tool. We employ two simple examples as test systems, while algorithm descriptions are kept general. Coupled-system governing equations are framed in monolithic and partitioned representations as differential-algebraic equations. Explicit and implicit loose partition coupling is examined. In explicit coupling, partitions are advanced in time from known information. In implicit coupling, there is dependence on other-partition data at the next time step; coupling is accomplished through a predictor-corrector (PC) approach. Numerical time integration of coupled ordinary-differential equations (ODEs) is accomplished with one of three, fourth-order fixed-time-increment methods: Runge-Kutta (RK), Adams-Bashforth (AB), and Adams-Bashforth-Moulton (ABM). Through numerical experiments it is shown that explicit coupling can be dramatically less stable and less accurate than simulations performed with the monolithic system. However, PC implicit coupling restored stability and fourth-order accuracy for ABM; only second-order accuracy was achieved with RK integration. For systems without constraints, explicit time integration with AB and explicit loose coupling exhibited desired accuracy and stability

Long Range Magnetic Order and the Darwin Lagrangian

We simulate a finite system of $N$ confined electrons with inclusion of the Darwin magnetic interaction in two- and three-dimensions. The lowest energy states are located using the steepest descent quenching adapted for velocity dependent potentials. Below a critical density the ground state is a static Wigner lattice. For supercritical density the ground state has a non-zero kinetic energy. The critical density decreases with $N$ for exponential confinement but not for harmonic confinement. The lowest energy state also depends on the confinement and dimension: an antiferromagnetic cluster forms for harmonic confinement in two dimensions.Comment: 5 figure