Second-order Structure Research Articles

Toward mapping turbulence in the intra-cluster medium

Context. Future X-ray observatories with high spectral resolution and imaging capabilities will enable measurements and mappings of emission line shifts in the intracluster medium (ICM). Such direct measurements can serve as unique probes of turbulent motions in the ICM. Determining the level and scales of turbulence will improve our understanding of the galaxy cluster dynamical evolution and assembly, together with a more precise evaluation of the non thermal support pressure budget. This will allow for more accurate constraints to be placed on the masses of galaxy clusters, among other potential benefits. Aims. In this view, we implemented the methods presented in the previous instalments of our work to characterising the turbulence in the intra-cluster medium in a feasibility study with the X-ray Integral Field Unit (X-IFU) on board the future European X-ray observatory, Athena. Methods. From idealized mock observations of a toy model cluster, we reconstructed the second-order structure function built with the observed velocity field to constrain the turbulence. We carefully accounted for the various sources of errors to derive the most realistic and comprehensive error budget within the limits of our approach. With prior assumptions on the dissipation scale and power spectrum slope, we constrained the parameters of the turbulent power spectrum model through the use of Markov chain Monte Carlo (MCMC) sampling. Results. With a very long exposure time, a favourable configuration, and a prior assumption of the dissipation scale, we were able to retrieve the injection scale, velocity dispersion, and power spectrum slope, with 1σ uncertainties for better than ∼15% of the input values. We demonstrated the efficiency of our carefully set framework to constrain the turbulence in the ICM from high-resolution X-ray spectroscopic observations, paving the way for more in-depth investigation of the optimal required observing strategy within a more restrictive observational setup with the future Athena/X-IFU instrument.

Bi-level distributionally robust optimization model for low-carbon planning of integrated electricity and heat systems

Interdependence among diverse energy forms within integrated electricity and heat systems (IEHSs) holds the potential to harness cooperation effects. This paper proposes a bi-level optimization model for the low-carbon planning of IEHSs, which realizes the coordination between IEHSs and their upstream networks. The precise carbon emissions of IEHSs are traced through carbon emission flows of components, power distribution networks, and district heating networks. Moreover, the distributionally robust optimization approach is employed to account for the inherent uncertainty in renewable power outputs faced by IEHS planning, by incorporating the moment information into an ambiguity set. The bi-level distributionally robust planning model of IEHSs is initially reconfigured into a second-order cone structure, employing the strong duality theory, second-order cone duality theory, and linear decision rules. Subsequently, an iterative approach is introduced to attain convergence of the reformulated bi-level model. Numerical results demonstrate the effectiveness and superiority of the proposed approach for reducing carbon emissions and economic costs of IEHSs.

Measuring Shame Related to Sexual Orientation: Validation of Sexual Minority—External and Internal Shame Scale (SM-EISS)

Abstract Introduction Shame is a self-conscious emotion involving negative self-evaluations, being a transdiagnostic factor for psychopathology. Due to stigma and discrimination experiences related to having a minority sexual orientation, LGB+ (lesbian, gay, bisexual, and other minority sexual orientations) people report higher levels of general shame than heterosexual people. To our knowledge, there is no specific measure of shame related to sexual orientation. This study aimed to develop and explore the psychometric properties of the Sexual Minority—External and Internal Shame Scale (SM-EISS) in a sample of Portuguese LGB+ people. Method The sample was recruited online between December 2021 and January 2022 and comprised 200 Portuguese LGB+ people (Mage = 27.8 ± 8.9) who completed measures about shame, proximal minority stressors, and mental health. Results Good psychometric characteristics were found for a second-order two-factor structure (general, external, and internal shame related to sexual orientation), with the SM-EISS demonstrating good reliability and validity values. Conclusion The SM-EISS seems to be a valid and reliable instrument to assess shame related to sexual orientation among LGB+ people and may be beneficial in clinical and research contexts. Policy Implications Measuring shame related to sexual orientation experienced by LGB+ people could enhance the clinical understanding of this population. It can help researchers and clinicians to better understand this emotion and how it affects LGB+ people’s mental health and well-being. The research has important implications for clinical practice, social interventions, and public policies to protect LGB+ people’s rights. This is especially relevant in Portugal, where, despite positive legal developments, LGB+ people continue to experience harmful situations that negatively impact their mental health.

Implicit visuospatial sequence representations are accessible in both the practice and the transfer hand

A serial reaction time task was used to test whether the representations of a probabilistic second-order sequence structure are (i) stored in an effector-dependent, effector-independent intrinsic or effector-independent visuospatial code and (ii) are inter-manually accessible. Participants were trained either with the dominant or non-dominant hand. Tests were performed with both hands in the practice sequence, a random sequence, and a mirror sequence. Learning did not differ significantly between left and right-hand practice, suggesting symmetric intermanual transfer from the dominant to the non-dominant hand and vice versa. In the posttest, RTs were shorter for the practice sequence than for the random sequence, and longest for the mirror sequence. Participants were unable to freely generate or recognize the practice sequence, indicating implicit knowledge of the probabilistic sequence structure. Because sequence-specific learning did not differ significantly between hands, we conclude that representations of the probabilistic sequence structure are stored in an effector-independent visuospatial code.

Temperature statistics of settling particles in homogeneous isotropic turbulence

Heat transfer of settling particles in homogeneous isotropic turbulence is investigated in one-way coupled Eulerian–Lagrangian direct numerical simulations. In the absence of gravity, our observations highlight that there was a correlation between particles concentration and temperature fronts, which are characterized by high-temperature gradients. The particle clustering is mainly influenced by the preferential concentration and the non-local effect, the latter being the memory of their interaction with the flow along their trajectories. Nevertheless, gravity significantly affects the clustering of particles, which further influence the heat transfer of particles with the fluid. We find that the heat transfer of particles is intricately related to particle dynamic inertia and thermal inertia, which can be quantified by the particle Stokes number St and particle thermal Stokes number Stθ, respectively. In this study, we observe that the variance of particle temperature rate of change is independent of Stθ at small thermal inertia but inversely proportional to Stθ2 for large thermal inertia. In the presence of gravity, the variance converges to Stθ−1 for particles with negligible thermal inertia. Our findings reveal that the second-order structure function of the particle temperature, indicating the enhancement of Lagrangian scalar intermittency, adheres to a power-law behavior with limited thermal inertial particles in the dissipation region, denoted as r2. However, as Stθ increases, the power law of the structure function of the particle temperature is disrupted leading to ‘thermal caustics’. The present findings of the heat transfer behavior of settling particles advance the understanding of gravity effect, and are valuable for the modeling of heat transfer in particle-laden turbulent flows.

Finite Reynolds Number Effect on Small-Scale Statistics in Decaying Grid Turbulence

Since about 1997, the realisation that the finite Reynolds number (FRN) effect needs to be carefully taken into account when assessing the behaviour of small-scale statistics came to the fore. The FRN effect can be analysed either in the real domain or in the spectral domain via the scale-by-scale energy budget equation or the transport equation for the energy spectrum. This analysis indicates that the inertial range (IR) is established only when the Taylor microscale Reynolds number Reλ is infinitely large, thus raising doubts about published power-law exponents at finite values of Reλ, for either the second-order velocity structure function (δu)2¯ or the energy spectrum. Here, we focus on the transport equation of (δu)2¯ in decaying grid turbulence, which represents a close approximation to homogeneous isotropic turbulence. The effect on the small-scales of the large-scale forcing term associated with the streamwise advection decreases as Reλ increases and finally disappears when Reλ is sufficiently large. An approach based on the dual scaling of (δu)2¯, i.e., a scaling based on the Kolmogorov scales (when the separation r is small) and another based on the integral scales (when r is large), yields (δu)2¯∼r2/3 when Reλ is infinitely large. This approach also yields (δu)n¯∼rn/3 when Reλ is infinitely large. These results seem to be supported by the trend, as Reλ increases, of available experimental data. Overall, the results for decaying grid turbulence strongly suggest that a tendency towards the predictions of K41 cannot be dismissed at least at Reynolds numbers which are currently beyond the reach of experiments and direct numerical simulations.

Adopting molecular tagging velocimetry for high-resolution measurements of oscillating grid turbulence

AbstractSingle-component molecular tagging velocimetry (1c-MTV) experiments are conducted in an oscillating grid turbulence facility to systematically clarify the trade-offs between maximizing measurement dynamic range and minimizing measurement uncertainty. The primary aim is to obtain reliable turbulence data with the maximum possible vector resolution ($$\varDelta {x}_{1}$$ Δ x 1 ). Four optical magnifications ($$M{_{0}}$$ M 0 =0.11, 0.22, 0.45, 1.11) with four interframe time delay ($$\varDelta {t}$$ Δ t ) values, for each optical magnification case, ranging from 3 to 10 ms, are investigated. The grid oscillates with a frequency (f) of 3.2 and 4.1 Hz, and a single fixed stroke length (S) of 55 mm. The measurement quality is quantified using three important turbulence descriptors — the second-order transverse velocity correlation function $$(\langle {g(r)}\rangle )$$ ( ⟨ g ( r ) ⟩ ) , the second-order transverse velocity structure function $$([\Delta {_{g}u}]^2)$$ ( [ Δ g u ] 2 ) , and the turbulence energy dissipation rate ($$\langle \epsilon \rangle$$ ⟨ ϵ ⟩ ). Other descriptors such as the longitudinal integral length scale (l) and the longitudinal Taylor microscale ($${\lambda }$$ λ ) are also used to compare with reference values reported in literature. The degree of agreement with the reference values from literature, and insensitivity of the descriptor estimates to different MTV design parameters are used to determine the most robust means of obtaining high-resolution turbulence data from 1c-MTV. The experimental design parameters are contextualized using the Kolmogorov length ($${\eta }$$ η ), time ($${\tau _{\eta }}$$ τ η ), and velocity ($${u_{\eta }}$$ u η ) scales that are based on the most reliable $$\langle {\epsilon }\rangle$$ ⟨ ϵ ⟩ estimates from the current experiments. The pixel-displacement corresponding to $${u_{\eta }}$$ u η $$({\varDelta {x}{_{2}}{_{\eta }}})$$ ( Δ x 2 η ) describes the interdependencies between $${M_{0}}$$ M 0 and $$\varDelta {t}$$ Δ t . The data set with $${M_{0}}=0.45$$ M 0 = 0.45 ($${\eta =}18{\varDelta {x}_{1}}$$ η = 18 Δ x 1 for f=3.2 Hz, and $${\eta =}13{\varDelta {x}_{1}}$$ η = 13 Δ x 1 for f=4.1 Hz) represents the most reliable and the highest resolution case. This conclusion was deduced by taking the performance of all the turbulence descriptors into account. As far as the interframe time delay is concerned, $$\varDelta {t} \ge$$ Δ t ≥ 4 ms ($${\varDelta {x}{_{2}}{_{\eta }}}\ge 0.5 \text {pixels}$$ Δ x 2 η ≥ 0.5 pixels ) works well for all $${{M}_{0}}$$ M 0 . To the authors’ knowledge, the present study documents the first instance of a series of 1c-MTV experiments conducted for a systematic clarification of the nature of balancing the available dynamic range and the measurement uncertainty. Additionally, since the study involves turbulent flow with negligible mean-flow, it serves as an adequate representation of 1c-MTV performance in a three-dimensional flow.

Vibration control of giant electrorheological damper combining nonlinear fractional-order controller and extended state observer

As a typical smart material, giant electrorheological fluid (GERF) has a greater yield stress than electrorheological fluid for vibration isolation. However, as rheological material, the modeling precision is severely degraded by its innate rate-dependent hysteretic nonlinearity and uncertainty. In this paper, a novel control method is proposed, which requires little information about the damper based on GERF. The proposed method combines nonlinear fractional-order control (FC) and extended state observer (ESO) by constructing damper as a second-order disturbance-based structure to handle hysteretic nonlinearities, dynamic uncertainties and unknown disturbances. In contrast to the prevalent model-free control (MFC) that neglects hysteresis nonlinearity, the proposed control algorithm considers it as a general disturbance and eliminates it. In addition, compared with linear FC with complex fractional-order ESO, where the order needs to be known in advance, nonlinear FC has improved robustness for uncertain fractional-order systems only via pure ESO. Simulations and experimental results demonstrate that the nonlinear controller outperforms the linear counterpart and the proposed method exhibits superior control performance compared to the existing MFC, with an improvement of 26.9%.

Measurement Invariance of a Quality-of-life Measure, CASP-12, within the English Longitudinal Study of Ageing (ELSA)

CASP-12 is a frequently used quality of life scale for older people, but limited efforts have been made to test the factor structure or to explore the measurement consistency of the scale across key characteristics. The aim of this study is to examine if the CASP-12 questionnaire has a well-defined factor structure with a second-order structure factor nested within four first-order domains: control, autonomy, pleasure, and self-realization. The study also aims to investigates if this factor structure is interpreted similarly by respondents of different genders, ages, educational levels, net wealth, and at two time periods, using a multi-group confirmatory factor analysis (MG-CFA). The results show that CASP-12 with lower four first-order domains (CASP-12-4D) is consistent across genders and two time periods and satisfies the second-order strong-invariance criteria. Furthermore, the instrument demonstrates consistency in weak levels across three age groups (50–59, 60–69, and 70–90), educational levels and net wealth, but not strong invariance. The sample was divided into three subsamples based on age groups to address this issue. The consistency of CASP-12-4D has met the second-order strong invariance level requirement across gender, age, education level and two-time periods. Net wealth however still fails to meet the strong invariance levels. The CASP-12-4D version will suit social and public health research which controls for age and wealth status.

Robust relation of streamwise velocity autocorrelation in atmospheric surface layers based on an autoregressive moving average model

We construct an autoregressive moving average (ARMA) model consisting of the history and random effects for the streamwise velocity fluctuation in boundary-layer turbulence. The distance to the wall and the boundary-layer thickness determine the time step and the order of the ARMA model, respectively. Based on the autocorrelation's analytical expression of the ARMA model, we obtain a global analytical expression for the second-order structure function, which asymptotically captures the inertial, dynamic and large-scale ranges. Specifically, the exponential autocorrelation of the ARMA model arises from the autoregressive coefficients and is modified to logarithmic behaviour by the moving-average coefficients. The asymptotic expressions enable us to determine model coefficients by existing parameters, such as the Kolmogorov and the Townsend–Perry constants. A consequent double-log expression for the characteristic length scale is derived and is justified by direct numerical simulation data with $Re_\tau \approx 5200$ and field-measured neutral atmospheric surface layer data with $Re_\tau \sim O(10^6)$ from the Qingtu Lake Observation Array site. This relation is robust because it applies to $Re_\tau$ from $O(10^4)$ to $O(10^6)$ , and even when the statistics of natural ASL deviate from those of canonical boundary-layer turbulence, e.g. in the case of imbalance in energy production and dissipation, and when the Townsend–Perry constant deviates from traditional values.

Development and validation of Questionnaire for Self-regulated Learning Writing Strategies (QSRLWS) for EFL learners

Abstract Drawing on a proposed theoretical framework that integrates a social cognitive perspective of self-regulation and a process genre approach to L2 writing, this research describes the development and validation process of a new instrument, Questionnaire for Self-regulated Learning Writing Strategies (QSRLWS). QSRLWS was validated with satisfactory psychometric qualities. Nine hundred eighty Chinese university EFL learners participated in the study (N = 960 after data screening). The study first described the questionnaire development process and adopted exploratory factor analysis to validate the factorial structure with half of the sample (n = 480). It further confirmed the structure with confirmatory factor analysis with another half of the sample (n = 480). Model comparisons confirmed a four-factor second-order structure in which QSRLWS comprised 12 SRL writing strategy types into four dimensions of strategy groups, i.e., metacognitive, cognitive, social, and motivational/affective regulation. Predictive validity of these strategies on students’ English writing performance was also reported. Theoretical and pedagogical implications are discussed.

Effects of streamwise rotation on helicity and vortex in channel turbulence

Helicity plays a key role in the evolution of vortex structures and turbulent dynamics. The helicity dynamics and vortex structures in streamwise-rotating channel turbulence are discussed in this paper using the helicity budget equation and the differentiated second-order structure function equation of helicity. Generally, rotation and Reynolds numbers exhibit opposing effects on the interscale helicity dynamics and the vortices. Under the buffer layer, the positions of the helicity peaks are proportional to the ratio between the Reynolds and rotation numbers. The mechanism is related to the opposing effects of convection and rotation. Rotation directly affects the helicity balance through the Coriolis term and corresponding pressure term. In the buffer layer, the scale helicity is negative at small scales but positive at large scales, which is mainly induced by the spatial effects (the production and the spatial turbulent convection) but reduced by interscale cascades. Examination of structures reveals the close association between scale helicity and streaks, with streak lift angles exhibiting an increase with rotation and a decrease with Reynolds numbers. In the log-law layer, the Coriolis terms and corresponding pressure terms are proportional to the rotation numbers but remain independent of the Reynolds numbers. The negative scale helicity is forward cascaded towards small scales. Generally, spanwise vortices in the log-law layer are related to sweep events and forward cascades. Our findings indicate that these spanwise vortices are suppressed by rotation but recover with increasing Reynolds numbers, aligning with the effects observed in the scale helicity balance.

Improving Volume and Biomass Equations for Pinus oocarpa in Nicaragua

We present a new set of equations for tree level volume and aboveground biomass estimation for ocote pine (Pinus oocarpa Schiede ex Schltdl). These equation systems are the first developed for this species in Nicaragua. The first system includes a taper function, a merchantable volume equation, and volume equations for stem, coarse branches, and whole trees. The second system estimates whole tree and individual tree component biomass (stem wood, bark, branches, and needles). Data from 112 sampled trees were used for models’ development. Seemingly Unrelated Iterative Regression and the Generalized Method of Moments were used to simultaneously fit the volume and biomass equations systems, respectively; both methods ensure additivity and compatibility between equations. Weighted regression and a second-order continuous autoregressive error structure were used to correct heteroscedasticity and autocorrelation within the hierarchical dataset. The predictive power of the new proposed equations is higher than the currently used models for P. oocarpa in the country. These equation systems represent a scientific advancement that will enhance forest inventories, optimize timber management of the species, and facilitate accurate monitoring of forest carbon dynamics. Additionally, the new equations will contribute to a more precise accounting of CO2 emissions from the country’s forestry sector.

Measurement Invariance of FFWEL Scores of Helping Professionals by Sex and Race Across U.S. and Filipino Samples

Objective This study explored the structure validity and sex and country measurement invariance for Filipino and U.S. adults using the Five Factor Wellness Inventory (FFWEL-A2). Method Confirmatory factor analysis and measurement invariance were conducted to determine consistency of responses across sex and country categories. Factorial ANOVAs were used to determine differences by sex, race, and country. Results The hypothesized 5-factor and second-order factor structure of the FFWEL provided equivalent but poor to adequate fit to the data in a large sample (N = 2,071) of U.S. and a smaller sample (N = 269) of Filipino counselors and counselors-in-training. Coefficients α were >0.80 for almost all domain scores, but only five of the 17 facet scores met the 0.80 criterion. Weak measurement invariance was evident for men (n = 502) and women (N = 1838) across both the U.S. White and Filipino group comparisons. Conclusions Counselors should take care to explore the way they and clients understand wellness and consider that not everyone will have the same understanding of the individual factors as outlined in the FFWEL-A2, especially among male, female, and diverse people from different countries. Significance statement Wellness is an ethical and professional imperative for counselors to avoid professional impairment and burn out. In this study, scores on the FFWEL-A2, a prominent measure of wellness, displayed partially biased measures of male and female scores across U.S. and Filipino samples and across diverse racial groups, probably due to complexity of the wellness model.

Characterization of physical properties of a coastal upwelling filament with evidence of enhanced submesoscale activity and transition from balanced to unbalanced motions in the Benguela upwelling region

Abstract. We combine high-resolution in situ data (acoustic Doppler current profiler (ADCP), Scanfish, and surface drifters) and remote sensing to investigate the physical characteristics of a major filament observed in the Benguela upwelling region. The 30–50 km wide and about 400 km long filament persisted for at least 40 d. Mixed-layer depths were less than 40 m in the filament and over 60 m outside of it. Observations of the Rossby number Ro from the various platforms provide the spatial distribution of Ro for different resolutions. Remote sensing focuses on geostrophic motions of the region related to the mesoscale eddies that drive the filament formation and thereby reveals |Ro|<0.1. Ship-based measurements in the surface mixed layer reveal 0.5<|Ro|<1, indicating the presence of unbalanced, ageostrophic motions. Time series of Ro from triplets of surface drifters trapped within the filament confirm these relatively large Ro values and show a high variability along the filament. A scale-dependent analysis of Ro, which relies on the second-order velocity structure function, was applied to the latter drifter group and to another drifter group released in the upwelling zone. The two releases explored the area nearly distinctly and simultaneously and reveal that at small scales (<15 km) Ro values are twice as large in the filament in comparison to its environment with Ro>1 for scales smaller than ∼500 m. This suggests that filaments are hotspots of ageostrophic dynamics, pointing to the presence of a forward energy cascade. The different dynamics indicated by our Ro analysis are confirmed by horizontal kinetic energy wavenumber spectra, which exhibit a power law k−α with α∼5/3 for wavelengths 2π/k smaller than a transition scale of 15 km, supporting significant submesoscale energy at scales smaller than the first baroclinic Rossby radius (Ro1∼30 km). The detected transition scale is smaller than those found in regions with less mesoscale eddy energy, consistent with previous studies. We found evidence for the processes which drive the energy transfer to turbulent scales. Positive Rossby numbers 𝒪(1) associated with cyclonic motion inhibit the occurrence of positive Ertel potential vorticity (EPV) and stabilize the water column. However, where the baroclinic component of EPV dominates, submesoscale instability analysis suggests that mostly gravitational instabilities occur and that symmetric instabilities may be important at the filament edges.

A novel complex-high-order graph convolutional network paradigm: ChyGCN

Abstract In recent years, there has been a growing interest in Graph Convolutional Networks (GCN). However, existing GCN and variants are predominantly based on simple graph or hypergraph structures, which restricts their ability to handle complex data correlations in practical applications. These limitations stem from the difficulty in establishing multiple hierarchies and acquiring adaptive weights for each of them. To address this issue, this paper introduces the latest concept of complex hypergraphs and constructs a versatile high-order multi-level data correlation model. This model is realized by establishing a three-tier structure of complexes-hypergraphs-vertices. Specifically, we start by establishing hyperedge clusters on the foundational network, utilizing a second-order hypergraph structure to depict potential correlations. For this second-order structure, truncation methods are applied to assess and generate a three-layer composite structure. During the construction of the composite structure, an adaptive learning strategy is implemented to merge correlations across different levels. We evaluate this model on several popular datasets and compare it with recent state-of-the-art methods. The comprehensive assessment results demonstrate that the proposed model surpasses existing methods, particularly in modeling implicit data correlations (the classification accuracy of nodes on five public datasets Cora, Citeseer, Pubmed, Github Web ML, and Facebook is 86.1±0.33, 79.2±0.35, 83.1±0.46, 83.8±0.23, and 80.1±0.37, respectively). This indicates that our approach holds advantages when handling datasets with implicit multi-level structures.

LRD spectral analysis of multifractional functional time series on manifolds

This paper addresses the estimation of the second-order structure of a manifold cross-time random field (RF) displaying spatially varying Long Range Dependence (LRD), adopting the functional time series framework introduced in Ruiz-Medina (Fract Calc Appl Anal 25:1426–1458, 2022). Conditions for the asymptotic unbiasedness of the integrated periodogram operator in the Hilbert–Schmidt operator norm are derived beyond structural assumptions. Weak-consistent estimation of the long-memory operator is achieved under a semiparametric functional spectral framework in the Gaussian context. The case where the projected manifold process can display Short Range Dependence (SRD) and LRD at different manifold scales is also analyzed. The performance of both estimation procedures is illustrated in the simulation study, in the context of multifractionally integrated spherical functional autoregressive–moving average (SPHARMA(p,q)) processes.

Unraveling corporate brand equity: a measurement model based on consumer perception of corporate brands

PurposeConsumer perception of corporate brand equity has primarily focused on product brand dimensions, neglecting considerations at the firm analysis level. Assessing corporate brands requires different criteria relevant to the competitiveness of companies, such as their prominence, management and meeting society’s demands. In this sense, this study aims to develop and validate a scale of corporate brand equity founded on consumer perceptions, transcending industry boundaries and comparing its relationship with companies' market share.Design/methodology/approachThe authors used an integrative approach to clarify the construct’s domain, building on previous measures. They took several steps to select appropriate items, refine the measure, validate it through reliability tests and convergent and discriminant analyses, test the validity of the second-order formative structure of corporate brand equity and assess associations between first-order factors, the second-order factor and market share.FindingsThe model identifies three first-order dimensions of corporate brands (presence, outstanding management and responsible) that shape the second-order factor (corporate brand equity). They are directly related, but not proportionally, to market share, contributing to the general and joint assessment of the company’s competitive performance considering the consumer.Originality/valueTo the best of the authors’ knowledge, this study is the first attempt to develop a comprehensive measurement model of corporate brand equity that considers the firm level of analysis, combines metrics from previous research on corporate brand evaluation criteria and includes consumer perceptions of the company’s competitiveness, unifying branding theory with the theory of the marketing firm.

Scaling law of the second-order structure function over the entire sandstorm process

This study reveals the competitive evolutionary process of the main driving factors in the early, middle and late stages of sandstorms, as shear turbulence becomes dominant and is then suppressed by enhanced thermal stability, based on quadrant analysis of the sand-laden turbulent wind field acquired from field observations over the entire sandstorm process. Moreover, the self-organized state of multiscale structures in the energy-containing region of the sand-laden turbulence is found to change significantly as the sandstorm develops. The logarithmic scaling law that governs the cumulative turbulent kinetic energy for the non-stationary flow in the early and late stages of the sandstorm is different from the existing theoretical formula. The corresponding rate of increase in the cumulative kinetic energy with increasing scale is much higher in these stages than in the middle stage of the sandstorm with steady flow. The change in self-organized state of turbulence is responsible for the flow acceleration and the thermal superimposed effect, rather than the addition of sand particles.

Construction of Nonlinear Interpolants With Second-Order Equation Structure in the Loewner Framework

This paper studies the construction of nonlinear interpolants consisting of second-order equations in the Loewner framework. First, conditions are given for which a system of second-order equations interpolates sets of right and left tangential data mappings, which results in second-order tangential generalized controllability and observability mappings allowing for the direct treatment of systems in second-order form. Following this, a family of interpolants with second-order equation structure is given. The results are demonstrated by constructing a reduced order model of a two link robotic manipulator in second-order equation form.