Scale Separation Research Articles

Data-driven modal decomposition methods as feature detection techniques for flow problems: A critical assessment

Modal decomposition techniques are showing a fast growth in popularity for their wide range of applications and their various properties, especially as data-driven tools. There are many modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are the most widespread methods, especially in the field of fluid dynamics. Following their highly competent performance on various applications in several fields, numerous extensions of these techniques have been developed. In this work, we present an ambitious review comparing eight different modal decomposition techniques, including most established methods, i.e., POD, DMD, and Fast Fourier Transform; extensions of these classical methods: based either on time embedding systems, Spectral POD and Higher Order DMD, or based on scales separation, multi-scale POD (mPOD) and multi-resolution DMD (mrDMD); and also a method based on the properties of the resolvent operator, the data-driven Resolvent Analysis. The performance of all these techniques will be evaluated on four different test cases: the laminar wake around cylinder, a turbulent jet flow, the three-dimensional wake around a cylinder in transient regime, and a transient and turbulent wake around a cylinder. All these mentioned datasets are publicly available. First, we show a comparison between the performance of the eight modal decomposition techniques when the datasets are shortened. Next, all the results obtained will be explained in detail, showing both the conveniences and inconveniences of all the methods under investigation depending on the type of application and the final goal (reconstruction or identification of the flow physics). In this contribution, we aim at giving a—as fair as possible—comparison of all the techniques investigated. To the authors' knowledge, this is the first time a review paper gathering all these techniques have been produced, clarifying to the community what is the best technique to use for each application.

Integrated digital image correlation for micro-mechanical parameter identification in multiscale experiments

Micromechanical constitutive parameters are important for many engineering materials, typically in microelectronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of the microstructure is observable only at small scales, requiring SEM or other microscopy techniques; (ii) external loadings are applied at a (larger) engineering or device scale; and (iii) material parameters typically depend on the applied manufacturing process, necessitating measurements on material produced with the same process. In this paper, micromechanical parameter identification in heterogeneous solids is addressed through multiscale experiments combined with Integrated Digital Image Correlation (IDIC) in conjunction with various possible computational homogenization schemes. To this end, some basic concepts underlying multiscale approaches available in the literature are first reviewed, discussing their respective advantages and disadvantages from the computational as well as experimental point of view. A link is made with recently introduced uncoupled methods, which allow for identification of material parameter ratios at the microscale, still lacking a proper normalization. Two multiscale methods are analysed, allowing to bridge the gap between microstructural kinematics and macroscopically measured forces, providing the required normalization. It is shown that an integrated experimental--computational scheme provides relaxed requirements on scale separation. The accuracy and performance of the discussed techniques are analysed by means of virtual experimentation under plane strain and large strain assumptions for unidirectional fibre-reinforced composites. The robustness against image noise is also assessed.

A Psychometric Validation of the Claremont Purpose Scale with an Emerging Adult University Student Population

Purpose is a key protective factor for well-being, resilience, and satisfaction with life. The Claremont Purpose Scale (CPS) was developed by Bronk and colleagues with adolescents and emerging adults to measure three dimensions of purpose: Meaning, Goal-Directedness, and Beyond-the-Self. The psychometric properties examined in the original scale development paper were replicated with our independent, emerging adult college student sample: confirmatory factor analysis (CFA) of a 3-factor model, good-to-excellent internal consistency, convergent validity with a measure of general perceived meaning in life (MLQ-P), and discriminant validity with a measure of self-reported depression (DASS-21-D). Additional psychometrics examined in this study were test–retest reliability, a 1-factor CFA model, correlations with stress and anxiety, and descriptive statistics that had not yet been reported in the literature. Beyond-the-self items did not load well onto the overall factor in the 1-factor model, and their correlations with other scales (MLQ-S, DASS-21 subscales) differed significantly from the correlations between these other scales and the CPS total, General Meaning, and Goal-Directedness scores. Implications of these data include strong support for the use of each subscale as a distinct, psychometric index, and we recommend the total scale score not be used as a measure of overall purpose. Clearly, there are separate, but related, facets to this measure that, while positive, undermine the utility of a global purpose score. A slightly changed naming of the CPS to the “Claremont Purpose Scales” could promote their use as three separate scales instead of a single, total scale score.

Solar Wind Magnetic Field Line Dispersal: Multispacecraft Analysis and Comparison with Theoretical Results

The dominance of the global over the relative, cross-field transport of magnetic field lines (MFLs), up to scales of a couple of hours in the solar wind (SW), has been predicted both theoretically and numerically, in the approximation of self-similar, single-level power spectra of magnetic fluctuations. Here the predictions for the MFL relative cross-field transport or dispersal are tested against the results of in situ data analysis, using 23 yr of field and flow measurements on board ACE and Wind. The theoretical results are confirmed/refined by nonlinear theoretical computations and corrected to include the effects of power-level variability or intermittency. Other than confirming earlier theoretical findings at the separation scales ρ between a few ×1010 cm and the large-separation limit, with a ballistic regime followed by decorrelation and transition to diffusion in the -space, the new study reveals two new supradiffusive regimes in and clock angle θ for the MFL dispersal, distinct from a drift-induced supradiffusion found earlier, and distinct from each other. The first supradiffusion, of the nonlinear computations, is a simple nonlinear effect, which cannot be recovered by data analysis at two spacecraft of fixed separation on the analysis timescale. The second supradiffusion, of the data analysis, is much stronger for ρ < few × 1010 cm than the two previous supradiffusions, and it becomes stronger at shorter separations. It follows the ballistic regime without transition through diffusion and is recovered by multiscale, theoretical estimates. It is a Lévy-type supradiffusion, due to the intermittency observed in the SW.

Towards the Upper-Ocean Unbalanced Submesoscale Motions in the Oleander Observations

Abstract Oceanic submesoscale dynamics with horizontal scales &lt; 20 km have similar temporal and spatial scales as internal gravity waves (IGWs), but they differ dynamically and have distinct impacts on the ocean. Separating unbalanced submesoscale motions (USMs), quasi-balanced submesoscale motions (QBMs), and IGWs in observations remains a great challenge. Based on the wave–vortex decomposition and the vertical scale separation approach for distinguishing IGWs and USMs, the long-term repeat Oleander observations in the Gulf Stream region provide an opportunity to quantify these processes separately. Here in this study, the role of USMs in the divergence is emphasized, which has confounded the wave–vortex decomposition of wintertime data in previous analyses. We also adopt the vertical filtering approach to identify the USMs by applying a high-pass filter to the vertical scales, as USMs are characterized by smaller vertical scales. This approach is tested with submesoscale-permitting model data to confirm its effectiveness in filtering the submesoscale velocity perturbations, before being applied to the compiled velocity data of the Oleander dataset (years 2005–18). The results show that the averaged submesoscale eddy kinetic energy by USMs can reach ∼1 × 10−3 m2 s−2 at z = −30 m in winter, much stronger than found in other seasons. Importantly, this study exemplifies the possibility of obtaining USMs from existing ADCP observations and reveals the seasonal dynamical regimes for the submesoscales.

The problem of capturing marginality in model reductions of turbulence

Reduced quasilinear and nonlinear (gradient-driven) models with scale separations, commonly used to interpret experiments and to forecast turbulent transport levels in magnetised plasmas, are tested against nonlinear models without scale separations (flux-driven). Two distinct regimes of turbulence—either above threshold or near marginal stability—are investigated with Boltzmann electrons. The success of reduced models hinges in particular on the reproduction of nonlinear fluxes. Good agreement between models is found above threshold, whilst reduced models significantly underpredict fluxes near marginality, overlooking mesoscale flow organisation and turbulence self-advection. Constructive prescriptions whereby to improve reduced models are discussed.

Методика изучения социально-психологического климата в коллективах обучающихся образовательных организаций МВД России

The aim of the research is to develop a methodology for studying the socio-psychological climate in teams of students of educational organisations of the Ministry of Internal Affairs of Russia.&#x0D; Theoretical grounds for the methodology were the ideas that the main structural elements that make up the socio-psychological climate in teams of students are: features of the organisation of educational and professional activities; features of the daily living, material and sanitary conditions in an educational organisation; nature of the relationship between students and teachers, students and officers, students’ relationships with each other; emotional and physical well-being of students; features of the organisation of extracurricular (scientific, sports and creative) activities; opportunities for meeting existential needs (in self-actualisation, self-development, etc.).&#x0D; These factors form the basis of the scales of the methodology being developed. The methodology also contains an overall scale that reflects the integral level of socio-psychological climate in a team.&#x0D; The points in the methodology are represented with statements and questions, asking respondents to answer them in a dichotomous way. Open-ended questions are also included to collect additional information. The processing of the results is limited to calculating the percentages of interviewees satisfied with the various aspects of the socio-psychological climate represented in separate scales of the methodology. On the basis of these data, a conclusion about the level of socio-psychological climate in the team is made. The climate can be satisfactory, unstable or unsatisfactory.&#x0D; The methodology is characterised by satisfactory values of discriminativeness, internal consistency reliability, construct validity and criterion validity. The procedure for collecting and processing the results is standardised.

Magnetohydrodynamic simulations of the Tayler instability in rotating stellar interiors

ABSTRACT The Tayler instability is an important but poorly studied magnetohydrodynamic (MHD) instability that likely operates in stellar interiors. The non-linear saturation of the Tayler instability is poorly understood and has crucial consequences for dynamo action and angular momentum transport in radiative regions of stars. We perform three-dimensional MHD simulations of the Tayler instability in a cylindrical geometry, including strong buoyancy and Coriolis forces as appropriate for its operation in realistic rotating stars. The linear growth of the instability is characterized by a pre-dominantly m = 1 oscillation with growth rates roughly following analytical expectations. The non-linear saturation of the instability appears to be caused by secondary shear instabilities and is also accompanied by a morphological change in the flow. We argue, however, that non-linear saturation likely occurs via other mechanisms in real stars where the separation of scales is larger than those reached by our simulations. We also observe dynamo action via the amplification of the axisymmetric poloidal magnetic field, suggesting that Tayler instability could be important for magnetic field generation and angular momentum transport in the radiative regions of evolving stars.

The Brief Emotion Dysregulation Scale: Development, Preliminary Validation, and Recommendations for Use.

Emotion dysregulation is a multi-faceted, transdiagnostic construct, and its assessment is crucial for characterizing its role in the development, maintenance, and treatment of psychiatric problems. We developed the Brief Emotion Dysregulation Scale (BEDS) to capture four components of emotion dysregulation: sensitivity, lability, reactivity, and consequences. We examined factor structure and construct validity in four independent samples of college students (N = 1,485). We elected to treat consequences as a separate index of problems associated with emotion dysregulation. Exploratory and confirmatory factor analyses did not support the reactivity subscale and instead supported a well-fitting two-factor solution for sensitivity and lability. Multi-group analyses demonstrated strong factorial invariance by gender. The resulting 12-item BEDS includes sensitivity and lability subscales and a separate consequences scale to indicate associated problems. Convergent correlations suggested good construct validity. This provides preliminary support for the BEDS as a brief transdiagnostic screening tool for emotion dysregulation and associated consequences.

Nonlinear Molecular Electronic Spectroscopy via MCTDH Quantum Dynamics: From Exact to Approximate Expressions.

We present an accurate and efficient approach to computing the linear and nonlinear optical spectroscopy of a closed quantum system subject to impulsive interactions with an incident electromagnetic field. It incorporates the effect of ultrafast nonadiabatic dynamics by means of explicit numerical propagation of the nuclear wave packet. The fundamental expressions for the evaluation of first- and higher-order response functions are recast in a general form that can be used with any quantum dynamics code capable of computing the overlap of nuclear wave packets evolving in different states. Here we present the evaluation of these expressions with the multiconfiguration time-dependent Hartree (MCTDH) method. Application is made to pyrene, excited to its lowest bright excited state S2 which exhibits a sub-100-fs nonadiabatic decay to a dark state S1. The system is described by a linear vibronic coupling Hamiltonian, parametrized with multiconfiguration electronic structure methods. We show that the ultrafast nonadiabatic dynamics can have a remarkable effect on the spectral line shapes that goes beyond simple lifetime broadening. Furthermore, a widely employed approximate expression based on the time scale separation of dephasing and population relaxation is recast in the same theoretical framework. Application to pyrene shows the range of validity of such approximations.

Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale Λ ~ 400 MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale Λ, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to γ∗γ∗ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level γ∗γ∗→ e+e− cross-section, we predict the expected lattice-QCD integrand resulting from the γ∗γ∗→ π0 process.

Using Gaussian Process Regression (GPR) models with the Matérn covariance function to predict the dynamic viscosity and torque of SiO[formula omitted]/Ethylene glycol nanofluid: A machine learning approach

Studying the dynamic viscosity (DV) is a key factor to determine the nanofluids’ hydrodynamic behavior (NFs). In this research, the effect of volume fraction (φ), shear rate (SR), and temperature (T) on the DV, and torque of SiO2 nanoparticles (NPs)/ Ethylene glycol (EG) nanofluid (NF) are studied with an artificial neural network (ANN). Different machine learning (ML) models are examined to predict the rheological properties, and then the best model is selected for prediction. The results show that the torque mostly increased linearly with the SR in all samples. The slope of this enhancing trend is higher for lower T. The Gaussian Process Regression (GPR) models with the Matérn covariance function provided the best results on both datasets to predict the DV. The correlation results provided by this method to predict the DV in terms of Pearson’s Linear Correlation Coefficient (PLCC), and Spearman’s Rank Order Correlation Coefficient (SROCC) were 0.999 and 1, respectively. R squared (R2) was 0.996 and, the Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) values of about 0.24 and 1.61 represented the accuracy and power of this method to predict the DV values unseen data by the model. The GPR torque predictor model performed very well by providing a correlation of about 0.98 and an RMSE of about 4. Matérn covariance functions that used separate length scales per predictor with ν=3/2 (ardmatern 32) and ν=5/2 (ardmatern52) were superior to other functions. All 100 models trained on each dataset were well-trained and quite reliable. The trained models were accurate enough to be used in related applications.

Moderate Averaged Deviations for a Multi-Scale System with Jumps and Memory

This work studies a two-time-scale functional system given by two jump diffusions under the scale separation by a small parameter ε→0. The coefficients of the equations that govern the dynamics of the system depend on the segment process of the slow variable (responsible for capturing delay effects on the slow component) and on the state of the fast variable. We derive a moderate deviation principle for the slow component of the system in the small noise limit using the weak convergence approach. The rate function is written in terms of the averaged dynamics associated with the multi-scale system. The core of the proof of the moderate deviation principle is the establishment of an averaging principle for the auxiliary controlled processes associated with the slow variable in the framework of the weak convergence approach. The controlled version of the averaging principle for the jump multi-scale diffusion relies on a discretization method inspired by the classical Khasminkii’s averaging principle.

Dual separation control and drag mitigation in high speed flows using viscoelastic materials

Boundary layer separation and friction drag form key delimiting phenomena that subvert the aerial platforms from achieving greater efficiency and accessing wider operation envelope. Both these phenomena are significantly aggravated in supersonic platforms due to the interactions between shock waves with the boundary layer that develops over the vehicle surface and within the engines. The present work demonstrates a new paradigm that leverages the native or programmable material properties of the aerostructures to engender simultaneous reduction in the separation scales and mitigation of skin friction drag. As a first step toward realizing this paradigm, the present work demonstrates, for the first time, the simultaneous skin friction drag mitigation in a Mach 2.5 boundary layer and control of shock induced boundary layer separation, both using viscoelastic implants placed under the flow. It is experimentally demonstrated that the appropriately chosen viscoelastic materials can simultaneously reduce the skin friction coefficient at the measurement location by 11% and mitigate the size of a large-scale separated flow by up to 28%. The reported performance matches the current generation flow effectors in both separation scale and skin friction mitigation. The present study opens a new application space for soft/programmable materials in high speed aerial vehicles.

Scalar interfaces in the near field of a unity velocity ratio coaxial jet

Planar laser-induced fluorescence is employed to investigate the concentration field in the developing region of a coaxial jet with an annular to inner jet velocity of one. Seeding the annular flow with a scalar shows that prior to the erosion of the inner scalar core, an inner interface exists, across which the scalar quantities exhibit sharp gradients akin to the traditional outer interface. Coarse grain filtering revealed that the outer interface establishes the universal fractal scaling before the onset of self-similarity, while the inner interface does not develop sufficient scale separation to do so due to the lack of shear.

파라과이 한인 현황과 문화적응 유형

This study utilized Declan Berry's acculturation type to analyze the cultural identity of Koreans in Paraguay, a major Korean residential area in Latin America. As a result of the survey, among the four scales of assimilation, separation, integration, and marginalization, Koreans showed strong tendencies toward integration and separation. The strong tendency of integration and separation can be attributed to the attitude of actively accepting the local culture while maintaining the culture of the home country. This seems to be related to the transitional situation in which the number of first-generation Koreans and second and third-generation Koreans are similar. In addition, the fact that Korean schools(Colegio Coreano del Paraguay) serve as a window for the next generation of Koreans to learn the Korean language and related culture can be seen as a factor in maintaining the culture of the homeland.

Quantification of multiscale links of key factors with watershed nitrogen and sediment exports based on a Bayesian modelling approach

The identification of key influencing factors of nonpoint source pollution is important to control such pollution in watersheds. The choice of spatial scale is vital in influencing factor analysis. However, many previous analyses were only carried out on a specific scale or evaluated different topics on different scales, which could not integrate various information of different scales. In this study, a multiscale approach based on Bayesian belief networks (BBNs), which can quantify the links between watershed nitrogen and sediment exports and their key factors, was developed. The main results indicated that influencing factors have relatively higher level of importance, i.e. higher degree of interpretation, at town scale or subcatchment scale compared with 1 km2 scale. Key factor set based on the nesting of town scale and subcatchment scale (i.e., town_sub scale) predict nitrogen and sediment exports better than those based on three separate scales (1 km2 scale, subcatchment scale and town scale), which implies that multiscale nesting reflects more comprehensive information about watershed processes. Moreover, different nitrogen and sediment reduction targets were achieved through land use changes and resulting economic benefits or losses were compared across three scales (subcatchment scale, town scale and town_sub scale). A relatively more appropriate scale with the lowest economic loss was determined. The decreased cultivated land and increased woodland and waterbody areas mostly contributed to the reductions in nitrogen and sediment exports and the economic loss of each reduction target. When achieving the same nitrogen and sediment reduction targets, the economic loss resulting from the land use changes at the subcatchment scale was lowest, followed by the town_sub and town scales. This multiscale approach attempted to determine how key factors with the highest level of importance at different scales and watershed nonpoint source pollution can be connected, which would better inform the management of watershed nonpoint source pollution.

ROBUST CONTROL OF LOW-COST DIRECT DRIVES BASED ON INTERIOR PERMANENT MAGNET SYNCHRONOUS MOTORS

Torque ripple compensation problem is considered for electrical drives, based on low-cost direct drive interior perma-nent magnet synchronous motors. Robustness properties of the speed and position control systems have been studied using time scale separation properties of the current, speed and position control loops. It is shown that system closed-loop dynamics according to new controller design has cascaded properties with speed and position control loops con-nected in series and therefore has potential of high frequency torque ripple compensation by increasing controllers gains. Experimental results are presented for two motors with similar rated data but significantly different level of the torque ripple. It is shown that despite of significand difference in parasitic torque amplitude, the similar position con-trol performance can be achieved. It makes proposed control algorithms suitable for both high dynamic performance and low-cost direct drive applications with medium performance requirements. References 13, figures 7.

Identifying impacts of global climate teleconnection patterns on land water storage using machine learning

Study RegionThe Zambezi River Basin in southern Africa Study focusModelling global freshwater systems is difficult because of the complexities of climate and anthropogenic influence on hydrological systems, especially at local scales. The rapid changes in hydrological systems caused by the influence of global climate trigger complex processes that make traditional machine learning algorithms limited in quantifying impacts of climate variability on freshwater. In this study, we developed a novel machine learning routine based on the Gaussian process regression (GPR) technique to improve understanding of the interaction of non-linear climatic variables with hydrological stores (includes surface water and terrestrial water storage-TWS). The GPR is built on the principle of the Gaussian process, which is a stochastic process that simplifies multivariate Gaussian distribution to infinite-dimensional space, such that the distributions over function values can be defined. The prediction of the GPR is tested using twenty-three independent climate variables against satellite observations of TWS between April 2002 and June 2017. We explored the use of a characteristic length scale for the kernels, which we tagged as ‘first order kernels’, and another set of kernels having a separate length scale for each discrete predictor. The latter was implemented using the automatic relevance determination (ARD), tagged as ‘higher order kernels’. The first and higher order kernels of the GPR technique were further examined using multivariate statistical indices to reveal the close relationship among hydro-climatic similarity and predictability. New hydrological insights for the regionOur results indicate that the large fluctuations of TWS in our tentative test-bed (the Zambezi Basin) for the GPR technique are largely caused by strong changes in sea surface temperature and global teleconnection patterns of the nearby oceans. The GPR introduced in this study provides an improved modelling framework to keep track on the influence of these global climate teleconnection patterns on major hydrological systems, like the Zambezi Basin, which contributes to global hydro-climatology but currently showing large amplitudes of land water storage loss.

Novel data dependent divider circuit block implementation for complex division and area critical applications

This article elaborates on the state-of-the-art novel Udayan S. Patankar (USP)-Awadhoot algorithm for distinctive implementation area improvement for area-critical electronic applications. The proposed USP-Awadhoot divider is a digit recurrence class, but it can be flexibly implemented as a restoring or nonrestoring algorithm. The implementation example indicates the use of the Baudhayan-Pythagoras triplet method in association with the proposed USP-Awadhoot divider. The triplet method provides an easy way to generate Mat_Term1, Mat_Term2, and T_Term, which are further utilized with the proposed USP-Awadhoot divider. The USP-Awadhoot divider is implemented in three parts. First is preprocessing circuit stage for executing a dynamic separate scaling operation on input operands, ensuring the inputs are in the correct form. Second is the processing circuit stage for implementing the conversion logic expressed by the Awadhoot matrix, and third is the postprocessing circuit stage for recombining the individual results into the final result. The proposed divider works upto 285 MHz frequency with a power estimation of 3.366 W, also significantly improves the chip area requirements over those of the commercially and noncommercially implemented solutions.