We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Direct numerical simulations of temporally developing compressible mixing layers have been performed to investigate the effects of large-scale structures (LSSs) on turbulent kinetic energy (TKE) budgets at convective Mach numbers ranging from 
$M_c=0.2$ to 
$1.8$ and at Taylor Reynolds numbers up to 290. In the core region of mixing layers, the volume fraction of low-speed LSSs decreases linearly with respect to the vertical distance at a Mach-number-independent rate. The contributions of low-speed LSSs to TKE, and its budget, including production, dissipation, pressure-strain and spatial diffusion terms, are primarily concentrated in the upper region of mixing layer. The streamwise and vertical mass flux coupling terms mainly transport TKE downwards in low-speed LSSs, and their magnitudes are comparable to the other dominant terms. Near the edges of LSSs, the sources and losses of all three components of TKE are completely different to each other, and dominated by turbulent diffusion, pressure diffusion, pressure-strain and dissipation terms. The TKE, their total variation and dissipation are significantly amplified at edges of low-speed LSSs, especially at the upper edge. This observation supports the existence of amplitude modulation exerted by the LSSs onto the near-edge small-scale structures in mixing layers. The level of amplitude modulation is strongest for the vertical velocity, followed by the streamwise velocity, and weakest for the spanwise velocity. Additionally, the amplitude modulation effect decreases significantly with increasing convective Mach number. The results on the amplitude modulation effect is helpful for developing predictive models of budget terms of TKE in mixing layers.
Establishing the invariance property of an instrument (e.g., a questionnaire or test) is a key step for establishing its measurement validity. Measurement invariance is typically assessed by differential item functioning (DIF) analysis, i.e., detecting DIF items whose response distribution depends not only on the latent trait measured by the instrument but also on the group membership. DIF analysis is confounded by the group difference in the latent trait distributions. Many DIF analyses require knowing several anchor items that are DIF-free in order to draw inferences on whether each of the rest is a DIF item, where the anchor items are used to identify the latent trait distributions. When no prior information on anchor items is available, or some anchor items are misspecified, item purification methods and regularized estimation methods can be used. The former iteratively purifies the anchor set by a stepwise model selection procedure, and the latter selects the DIF-free items by a LASSO-type regularization approach. Unfortunately, unlike the methods based on a correctly specified anchor set, these methods are not guaranteed to provide valid statistical inference (e.g., confidence intervals and p-values). In this paper, we propose a new method for DIF analysis under a multiple indicators and multiple causes (MIMIC) model for DIF. This method adopts a minimal \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L_1$$\end{document}
norm condition for identifying the latent trait distributions. Without requiring prior knowledge about an anchor set, it can accurately estimate the DIF effects of individual items and further draw valid statistical inferences for quantifying the uncertainty. Specifically, the inference results allow us to control the type-I error for DIF detection, which may not be possible with item purification and regularized estimation methods. We conduct simulation studies to evaluate the performance of the proposed method and compare it with the anchor-set-based likelihood ratio test approach and the LASSO approach. The proposed method is applied to analysing the three personality scales of the Eysenck personality questionnaire-revised (EPQ-R).
The breaking and energy distribution of mode-1 depression internal solitary wave interactions with Gaussian ridges are examined through laboratory experiments. A series of processes, such as shoaling, breaking, transmission and reflection, are captured completely by measuring the velocity field in a large region. It is found that the maximum interface descent (
$a_{max}$) during wave shoaling is an important parameter for diagnosing the type of wave–ridge interaction and energy distribution. The wave breaking on the ridge depends on the modified blockage parameter 
$\zeta _m$, the ratio of the sum of the upper layer depth and 
$a_{max}$ to the water depth at the top of the ridge. As 
$\zeta _m$ increases, the interaction type transitions from no breaking to plunging and mixed plunging–collapsing breaking. Within the scope of this experiment, the energy distribution can be characterized solely by 
$\zeta _m$. The transmission energy decreases monotonically with increasing 
$\zeta _m$, and there is a linear relationship between 
$\zeta _m^2$ and the reflection coefficient. The value of 
$a_{max}$ can be determined from the basic initial parameters of the experiment. Based on the incident wave parameters, the depth of the upper and lower layers, and the topographic parameters, two new simple methods for predicting 
$a_{max}$ on the ridge are proposed.
In the present paper, we consider the following fractional double phase problem with nonlocal reaction:
\begin{align*}\qquad \quad \left\{\begin{array}{lll}(- \Delta)_p^s u + (- \Delta)_q ^s u + V(\varepsilon x) (|u|^{p - 2} u + |u|^{q - 2} u) = \left(\frac{1}{|x|^\mu} * F(u)\right) f(u) & \ \text{in}\ \mathbb{R}^N, \\u \in W^{s,p}(\mathbb{R}^N) \cap W^{s,q}(\mathbb{R}^N) ,\ u \gt 0 & \ \text{in}\ \mathbb{R}^N,\end{array}\right\}\end{align*}
where ɛ is apositive parameter, 
$0 \lt s \lt 1$, 
$2 \leqslant p \lt q \lt \min\{2p, N / s\}$, 
$0 \lt \mu \lt sp$, 
$(- \Delta)_t^s$ 
$(t \in \left\{p,q\right\})$ is the fractional t-Laplace operator, the reaction term 
$f : \mathbb{R} \mapsto \mathbb{R}$ is continuous, and the potential 
$V \in C (\mathbb{R}^N , \mathbb{R})$ satisfying a local condition. Using a variational approach and topological tools (the non-standard C1-Nehari manifold analysis and the abstract category theory), multiplicity of positive solutions and concentration properties for the above problem are established. Our results extend and complement some previous contributions related to double phase variational integrals.
Direct numerical simulations of temporally developing mixing layers have been performed to investigate the effects of compressibility on statistics and structures near the interfaces of high- and low-speed large-scale structures (LSSs), covering a range of convective Mach numbers from 
$M_c=0.2$ to 
$1.8$ and Taylor Reynolds numbers up to 290. The interfaces of LSSs are directly defined by the isosurface of zero fluctuating streamwise velocity. The characteristic velocity jump at the interfaces grows rapidly in the transition stage and then decreases until reaching a gradual self-similar stage. The evolution of velocity jump is evidently delayed as the convective Mach number increases. The interface layer is formed by the shearing motion of neighbouring LSSs. A small vortical motion characterized by the Kolmogorov scale is induced in the interface layer by shear-dominated outer regions. The strengths of outer shearing motion and central vortical motion are greater at the leading edge, but smaller at the trailing edge, which is also reflected in a larger velocity jump at the leading edge. As the convective Mach number increases, the small-scale vortical structure is obviously suppressed by compressibility. At high convective Mach number 
$M_c=1.8$, the compressive shear-dominated outer regions are linked with a sheet-like structure passing through the centre of the expansion region corresponding to a small-scale vortical structure. The compressibility and shearing strength near the interface are highly dependent on the interface orientation.
