A mathematical and physical Study of multiscale deconvolution models of turbulence

This work presents a rigorous analysis of mathematical and physical properties for solutions of multiscale deconvolution turbulence models. We show that solutions of these models exactly conserve model quantities for the integral invariants of fundamental physical importance: kinetic energy, helicity, and (in two dimensions) enstrophy. The kinetic energy conservation is the key that allows us to next apply the phenomenology of homogeneous, isotropic turbulence to establish the existence of a model energy cascade and, in particular, that the cascade exhibits enhanced energy dissipation in a secondary accelerated cascade, which ends at the model's microscale (which we establish is larger than the Kolmogorov microscale). We also prove that the model dissipates energy at the same rate as true turbulent flow, ～ O(U³ ∕ L), independent of Reynolds number. Lastly, we prove the existence of global attractors for the model solutions; the proof of which also shows that solutions are actually one degree of regularity higher than previously known. Copyright © 2012 John Wiley & Sons, Ltd.     

Effects of multi-Schell beams on orbital angular momentum of entangled signal photons in low-order turbulence aberration channels

We model the detection and crosstalk probability of orbital angular momentum (OAM) states of the entangled signal photon in the Kolmogorov channels of the low-order turbulence aberrations and by the Rytov approximation. The results show that lower OAM mode number of signal photons and larger sub-beam number of multi-Gaussian Schell-model pump beam, the less susceptible of the detection probability of the signal photon to spatial coherence of source and turbulence aberrations is achieved. The maximum crosstalk probability is decrease as the decreasing of the sub-beam number of multi-Gaussian Schell-model. Enlarging OAM difference value or decreasing sub-beam number of multi-Gaussian Schell-model pump beam results in a lower crosstalk probability of the OAM of entangled signal photons.     

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

In this work, various turbulent solutions of the two‐dimensional (2D) and three‐dimensional compressible Reynolds averaged Navier–Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications. The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data. In the transonic buffet case, the baseflow is computed using the Spalart–Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear‐layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three‐dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected. Copyright © 2014 John Wiley & Sons, Ltd.     

Eulerian spatial and temporal autocorrelations: assessment of Taylor's hypothesis and a model

We present measurements of Eulerian longitudinal velocity autocorrelations in homogeneous, isotropic, high-intensity (～9%) free-stream turbulence behind an active grid. Spatial correlations are measured using particle image velocimetry as well as with two-point hot-wire anemometry (HWA), while temporal correlations are measured using HWA. The temporal correlations are transformed into spatial correlations by using Taylor's ‘frozen’ hypothesis with both the mean as well as instantaneous velocities. A model relating Eulerian spatial and temporal autocorrelations is also used for this purpose. The differences from the measured spatial correlation resulting from the use of Taylor's hypothesis on the temporal correlation is quantified; even at this moderately high level of turbulent intensity, the result from the use of the instantaneous velocity as convection velocity is practically indistinguishable from that obtained using the mean velocity. Use of the model produces a good agreement between the estimates of the spatial correlation function. A relation between Eulerian spatial and temporal integral scales is also derived.     

Design of a reaction field using a linear‐combination‐based isotropic periodic sum method

In our previous study (Takahashi et al., J. Chem. Theory Comput. 2012, 8, 4503), we developed the linear‐combination‐based isotropic periodic sum (LIPS) method. The LIPS method is based on the extended isotropic periodic sum theory that produces a ubiquitous interaction potential function to estimate homogeneous and heterogeneous systems. The LIPS theory also provides the procedure to design a periodic reaction field. To demonstrate this, in the present work, a novel reaction field of the LIPS method was developed. The novel reaction field was labeled LIPS‐SW, because it provides an interaction potential function with a shape that resembles that of the switch function method. To evaluate the ability of the LIPS‐SW method to describe in homogeneous and heterogeneous systems, we carried out molecular dynamics (MD) simulations of bulk water and water–vapor interfacial systems using the LIPS‐SW method. The results of these simulations show that the LIPS‐SW method gives higher accuracy than the conventional interaction potential function of the LIPS method. The accuracy of simulating water–vapor interfacial systems was greatly improved, while that of bulk water systems was maintained using the LIPS‐SW method. We conclude that the LIPS‐SW method shows great potential for high‐accuracy, high‐performance computing to allow large scale MD simulations. © 2014 Wiley Periodicals, Inc.     

Bonding,Aromaticity and Isomerization of Furfuraldehyde through Off-Nucleus Isotropic Magnetic Shielding

Off-nucleus isotropic magnetic shielding (σ_iso(r)) and multi-points nucleus independent chemical shift (NICS(0-2 Å)) index were utilized to find the impacts of the isomerization of gas-phase furfuraldehyde (FD) on bonding and aromaticity of FD. Multidimensional (1D to 3D) grids of ghost atoms (bqs) were used as local magnetic probes to evaluate σ_iso(r) through gauge-including atomic orbitals (GIAO) at density functional theory (DFT) and B3LYP functional/6-311+G(d,p) basis set level of theory. 1D σ_iso(r) responses along each bond of FD were examined. Also, a σ_iso(r) 2D-scan was performed to obtain σ_iso(r) behavior at vertical heights of 0–1 Å above the FD plane in its cis, transition state (TS) and trans forms. New techniques for evaluating 2D σ_iso(r) cross-sections are also included. Our findings showed that bonds in cyclic and acyclic parts of FD are dissimilar. Unlike the C−O bond of furanyl, the C=O bond of the formyl group is magnetically different. C−C and C−H bonds in furanyl are found similar to those in aromatic rings. A unique σ_iso(r) trend was observed for the C₂−C₆ bond during FD isomerization. Based on NICS(0-2 Å) values, the degree of aromaticity follows the order of cis FD<trans FD<furan<TS FD.     

Analysis of marine atmospheric turbulence effects on infrared imaging system by angle of arrival fluctuations

For the long-range infrared imaging system, the marine atmospheric turbulence degrades seriously the probability of object recognition and tracking. In this study, the angle of arrival fluctuations of an optical wave, which describes the distortion effects of marine atmospheric turbulence on an infrared optical imaging system, is investigated in detail both analytically and numerically. Analytic expressions of the angle of arrival fluctuations are derived for optical plane and spherical waves propagating through weak marine atmospheric turbulence with horizontal path, and they consider simultaneously finite turbulence inner scale, turbulence outer scale, wavelength, and aperture diameters. Numerical calculations are conducted to analyze the influence of marine weak turbulence on the infrared imaging. The results are useful for understanding the potential impact of deviations from the terrestrial turbulence.     

Gold‐Catalyzed Cycloisomerization of 1,6,8‐Dienyne Carbonates and Esters to cis‐Cyclohepta‐4,8‐diene‐Fused Pyrrolidines

A synthetic approach that provides access to cis‐cyclohepta‐4,8‐diene‐fused pyrrolidines efficiently through Au^I‐catalyzed cycloisomerization of 1,6,8‐dienyne carbonates and esters at a low catalyst loading of 2 mol % is reported. Starting carbonates and esters with a pendant alkyl group on the terminal alkenyl carbon center were found to favor tandem 1,2‐acyloxy migration/cyclopropanation followed by Cope rearrangement of the resulting cis‐3‐azabicyclo[3.1.0]hexane intermediate. On the other hand, substrates containing a terminal diene or starting materials in which the distal alkene moiety bears a phenyl substituent were observed to undergo competitive but reversible 1,3‐acyloxy migration prior to the nitrogen‐containing bicyclic ring formation. The delineated reaction mechanism also provides experimental evidence for the reversible interconversion between the oft‐proposed organogold intermediates obtained in this step of the tandem process.     

超声心动图联合动态心电图检查对急性心肌梗死诊断和预后评估的价值

为探讨超声心动图联合动态心电图检查在急性心肌梗死(AMI)患者诊断和预后评估中的应用价值,本研究选取2016年6月~2018年6月我院收治并确诊的100例AMI患者作为观察组,另选取同期100例非冠心病患者作为对照组。以AMI患者心源性死亡为终点事件,将观察组分为死亡组(n=15)和存活组(n=85)。所有患者均采用飞利浦IU-Elite及EPIQ5彩色多普勒超声诊断仪进行超声心动图检查,采用DMS-3004A进行标准的12导联动态心电图检查。比较各组患者心率震荡指标[震荡起始(TO)、震荡斜率(TS)]、心率变异性指标[NN间期标准差(SDNN)、QT离散度(QTd)、经心率校正的QT离散度(QTcd)]及心功能指标[左心室舒张末期内径(LVEDD)、左心室射血分数(LVEF)]水平的变化。结果显示,观察组TO、QTd、QTcd、LVEDD均明显高于对照组,TS、SDNN、LVEF均明显低于对照组,差异有统计学意义(P<0.05)。死亡组TS、SDNN均明显低于存活组,差异有统计学意义(P<0.05);死亡组TO高于存活组,QTd、QTcd、LVEF、LVEDD均低于存活组,但差异无统计学意义(P>0.05)。本研究结果表明,AMI患者心率震荡(HRT)明显减弱甚至消失,HRV、LVEF明显降低,LVEDD、QTd明显增大,QT间期明显延长。超声心动图和动态心电图联合检查对AMI患者诊断及预后评估均有重要的临床应用价值。