Relevant bibliographies by topics / Scalar-On-Function

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Scalar-On-Function'

Author: Grafiati
Published: 18 May 2024

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Journal articles on the topic "Scalar-On-Function"

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Reiss, Philip T., Jeff Goldsmith, Han Lin Shang, and R. Todd Ogden. "Methods for Scalar-on-Function Regression." International Statistical Review 85, no. 2 (February 23, 2016): 228–49. http://dx.doi.org/10.1111/insr.12163.

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Fan, Zhaohu, and Matthew Reimherr. "High-dimensional adaptive function-on-scalar regression." Econometrics and Statistics 1 (January 2017): 167–83. http://dx.doi.org/10.1016/j.ecosta.2016.08.001.

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Chen, Yakuan, Jeff Goldsmith, and R. Todd Ogden. "Variable selection in function-on-scalar regression." Stat 5, no. 1 (2016): 88–101. http://dx.doi.org/10.1002/sta4.106.

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Guo, X., J. Hua, and H. Qin. "Scalar-function-driven editing on point set surfaces." IEEE Computer Graphics and Applications 24, no. 4 (July 2004): 43–52. http://dx.doi.org/10.1109/mcg.2004.16.

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Bauer, Alexander, Fabian Scheipl, Helmut Küchenhoff, and Alice-Agnes Gabriel. "An introduction to semiparametric function-on-scalar regression." Statistical Modelling 18, no. 3-4 (January 18, 2018): 346–64. http://dx.doi.org/10.1177/1471082x17748034.

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Abstract: Function-on-scalar regression models feature a function over some domain as the response while the regressors are scalars. Collections of time series as well as 2D or 3D images can be considered as functional responses. We provide a hands-on introduction for a flexible semiparametric approach for function-on-scalar regression, using spatially referenced time series of ground velocity measurements from large-scale simulated earthquake data as a running example. We discuss important practical considerations and challenges in the modelling process and outline best practices. The outline of our approach is complemented by comprehensive R code, freely available in the online appendix. This text is aimed at analysts with a working knowledge of generalized regression models and penalized splines.
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Wang, Xu, Jiaqing Kou, and Weiwei Zhang. "Unsteady aerodynamic modeling based on fuzzy scalar radial basis function neural networks." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 14 (March 19, 2019): 5107–21. http://dx.doi.org/10.1177/0954410019836906.

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In this paper, a fuzzy scalar radial basis function neural network is proposed, in order to overcome the limitation of traditional aerodynamic reduced-order models having difficulty in adapting to input variables with different orders of magnitude. This network is a combination of fuzzy rules and standard radial basis function neural network, and all the basis functions are defined as scalar basis functions. The use of scalar basis function will increase the flexibility of the model, thus enhancing the generalization capability on complex dynamic behaviors. Particle swarm optimization algorithm is used to find the optimal width of the scalar basis function. The constructed reduced-order models are used to model the unsteady aerodynamics of an airfoil in transonic flow. Results indicate that the proposed reduced-order models can capture the dynamic characteristics of lift coefficients at different reduced frequencies and amplitudes very accurately. Compared with the conventional reduced-order model based on recursive radial basis function neural network, the fuzzy scalar radial basis function neural network shows better generalization capability for different test cases with multiple normalization methods.
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Reiss, Philip T., David L. Miller, Pei-Shien Wu, and Wen-Yu Hua. "Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates." Journal of Computational and Graphical Statistics 26, no. 3 (April 11, 2017): 569–78. http://dx.doi.org/10.1080/10618600.2016.1217227.

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Goldsmith, Jeff, and Fabian Scheipl. "Estimator selection and combination in scalar-on-function regression." Computational Statistics & Data Analysis 70 (February 2014): 362–72. http://dx.doi.org/10.1016/j.csda.2013.10.009.

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Ciarleglio, Adam, and R. Todd Ogden. "Wavelet-based scalar-on-function finite mixture regression models." Computational Statistics & Data Analysis 93 (January 2016): 86–96. http://dx.doi.org/10.1016/j.csda.2014.11.017.

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Yang, Hojin, Veerabhadran Baladandayuthapani, Arvind U. K. Rao, and Jeffrey S. Morris. "Quantile Function on Scalar Regression Analysis for Distributional Data." Journal of the American Statistical Association 115, no. 529 (June 21, 2019): 90–106. http://dx.doi.org/10.1080/01621459.2019.1609969.

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Dissertations / Theses on the topic "Scalar-On-Function"

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Gnanguenon, guesse Girault. "Modélisation et visualisation des liens entre cinétiques de variables agro-environnementales et qualité des produits dans une approche parcimonieuse et structurée." Electronic Thesis or Diss., Montpellier, 2021. http://www.theses.fr/2021MONTS139.

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L'essor de l'agriculture numérique permet de plus en plus d'observer de manière automatisée et parfois à haute fréquence des dynamiques d'élaboration de la production et de sa qualité en fonction du climat. Les données issues de ces observations dynamiques peuvent être considérées comme des données fonctionnelles. Analyser ce nouveau type de données nécessite d'étendre les outils statistiques usuels au cas fonctionnel ou d'en proposer de nouveaux.Nous avons proposé dans cette thèse une nouvelle approche (SpiceFP: Sparse and Structured Procedure to Identify Combined Effects of Functional Predictors) permettant d'expliquer les variations d'une variable réponse scalaire par deux ou trois prédicteurs fonctionnels dans un contexte d'influence conjointe de ces derniers. Une attention particulière a été apportée à l'interprétabilité des résultats via l'utilisation de classes d'intervalles combinées définissant une partition du domaine d'observation des facteurs explicatifs. Les développements récents autour des modèles LASSO (Least Absolute Shrinkage and Selection Operator) ont été adaptés pour estimer les régions d'influence dans la partition via une régression pénalisée généralisée. L'approche intègre aussi une double sélection, de modèles (parmi les partitions possibles) et de variables (pour une partition donnée) à partir des critères d'information AIC et BIC. La présentation méthodologique de l'approche, son étude grâce à des simulations ainsi qu'une étude de cas basée sur des données réelles ont été présentés dans le chapitre 2.Les données réelles utilisées au cours de cette thèse proviennent d'une expérimentation viticole visant à mieux comprendre l'impact du changement climatique sur l'accumulation d'anthocyanes dans les baies. L'analyse de ces données dans le chapitre 3 à l'aide de l'approche SpiceFP que nous avons étendue a permis d'identifier un impact négatif des combinaisons matinales de faible irradiance (inférieure à environ 100 µmol/s/m2 ou 45 µmol/s/m2 selon l'état avancé-retardé des baies) et température élevée (supérieure à environ 25°C). Une légère différence induite par la température de la nuit a été observée entre ces effets identifiés en matinée.Dans le chapitre 4 de cette thèse, nous proposons une implémentation de l'approche proposée sous la forme d'un package R. Cette implémentation fournit un ensemble de fonctions permettant de construire les intervalles de classes suivant des échelles linéaire ou logarithmique, de transformer les prédicteurs fonctionnels grâces aux classes d'intervalles combinées puis de mettre en oeuvre l'approche en deux ou trois dimensions. D'autres fonctions facilitent la réalisation de post-traitements ou permettent à l'utilisateur de s'intéresser à d'autres modèles que ceux retenus par l'approche comme par exemple une moyenne de différents modèles.Mots clés: Régressions pénalisées, Interaction, critères d'information, scalar-on-function, coefficients interprétables, microclimat de la vigne
The development of digital agriculture allows to observe at high frequency the dynamics of production according to the climate. Data from these dynamic observations can be considered as functional data. To analyze this new type of data, it is necessary to extend the usual statistical tools to the functional case or develop new ones.In this thesis, we have proposed a new approach (SpiceFP: Sparse and Structured Procedure to Identify Combined Effects of Functional Predictors) to explain the variations of a scalar response variable by two or three functional predictors in a context of joint influence of these predictors. Particular attention was paid to the interpretability of the results through the use of combined interval classes defining a partition of the observation domain of the explanatory factors. Recent developments around LASSO (Least Absolute Shrinkage and Selection Operator) models have been adapted to estimate the areas of influence in the partition via a generalized penalized regression. The approach also integrates a double selection, of models (among the possible partitions) and of variables (areas inside a given partition) based on AIC and BIC information criteria. The methodological description of the approach, its study through simulations as well as a case study based on real data have been presented in chapter 2 of this thesis.The real data used in this thesis were obtained from a vineyard experiment aimed at understanding the impact of climate change on anthcyanins accumulation in berries. Analysis of these data in chapter 3 using SpiceFP and one extension identified a negative impact of morning combinations of low irradiance (lower than about 100 µmol/s/m2 or 45 µmol/s/m2 depending on the advanced-delayed state of the berries) and high temperature (higher than about 25°C). A slight difference associated with overnight temperature occurred between these effects identified in the morning.In chapter 4 of this thesis, we propose an implementation of the proposed approach as an R package. This implementation provides a set of functions allowing to build the class intervals according to linear or logarithmic scales, to transform the functional predictors using the joint class intervals and finally to execute the approach in two or three dimensions. Other functions help to perform post-processing or allow the user to explore other models than those selected by the approach, such as an average of different models.Keywords: Penalized regressions, Interaction, information criteria, scalar-on-function, interpretable coefficients,grapevine microclimate
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Ciarleglio, Adam J. "On Wavelet-Based Methods for Scalar-on-Function Regression." Thesis, 2013. https://doi.org/10.7916/D8PN951Q.

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This thesis consists of work done on three projects which extend and employ wavelet-based functional linear regression. In the first project, we propose a wavelet-based approach to functional mixture regression. In our approach, the functional predictor and the unknown component-specific coefficient functions are projected onto an appropriate wavelet basis and simultaneous regularization and estimation are achieved via an l1-penalized fitting procedure that is carried out using an expectation-maximization algorithm. We provide an efficient fitting algorithm, propose a technique for constructing non-parametric confidence bands, demonstrate the performance of our methods through extensive simulations, and apply them to real data in order to investigate the relationship between fractional anisotropy profiles and cognitive function in subjects with multiple sclerosis. In the second project, we propose a new wavelet-based estimator for estimating the coefficient function in a functional linear model. Our estimator attempts to take account of the structured sparsity of the wavelet coefficients used to represent the coefficient function in the fitting procedure. We propose a characterization of the neighborhood structure of wavelet coefficients and exploit this structure in our estimation procedure. We discuss the motivation for our penalized estimator, describe the fitting procedure which can be carried out with existing software, and examine properties of the estimator through simulation. The third and final project explores three novel approaches to using functional data derived from optical coherence tomography devices for diagnosing glaucoma. The first approach uses wavelet-based functional logistic regression to develop predictive models based on measures of retinal nerve fiber layer (RNFL) thickness. The estimates are obtained via an elastic net penalized fitting procedure. The second and third approaches consist of using novel measures of RNFL characteristics to discriminate between healthy and glaucomatous eyes. The three new approaches are compared with commonly used predictive models using data from a case-control study of African American subjects recruited by ophthalmologists at the Harkness Eye Center of Columbia University.
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Chou, Chia-Chun, and 周佳俊. "3D Movies Office Box Analysis via Function-On-Scalar Regression." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/11594350718416740604.

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碩士
國立中興大學
統計學研究所
104
This paper forecasting method is divided into two parts. Start by using of the film’s box office revenue departments into low, medium, and high class. Each film has their own cast feature: directors, writers, composers, actors to classify into their catogory. Second, we are able to model into function-on-scalar regression. Responses are functional type of movies office box. Construction of the base functions use principal component analysis to establish release dates associated with characteristic function. Explanatory variables which we used are the budgets, a number of cinemas screening, the directors, actors, writers, composers and Metacritic Scores. Finally, we employ the model which we fit to predicted 2016 new film. Fisrt, we need to decide the new film revenue fell low, medium and high class. Second, we able to predict the future box office within 42 days after the new movie release trend to address the problems of investors concern.
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Books on the topic "Scalar-On-Function"

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Plümmer, Franziska. Rethinking Authority in China’s Border Regime. NL Amsterdam: Amsterdam University Press, 2022. http://dx.doi.org/10.5117/9789463726351.

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In the 21st century, governments around the globe are faced with the question on how to tackle new migratory mobilities. Governments increasingly become aware of irregular immigration and are forced to re-negotiate the dilemma of open but secure borders. Rethinking Authority in China’s Border Regime: Regulating the Irregular investigates the Chinese government’s response to this phenomenon. Hence, this book presents a comprehensive analysis of the Chinese border regime. It explores the regulatory framework of border mobility in China by analysing laws, institutions, and discourses as part of an ethnographic border regime analysis. It argues that the Chinese state deliberately creates ‘zones of exception’ along its border. In these zones, local governments function as ‘scalar managers’ that establish cross-border relations to facilitate cross-border mobility and create local migration systems that build on their own notion of legality by issuing locally valid border documents. The book presents an empirically rich story of how border politics are implemented and theoretically contributes to debates on territoriality and sovereignty as well as to the question of how authority is exerted through border management. Empirically, the analysis builds on two case studies at the Sino-Myanmar and Sino-North Korean borders to illustrate how local practices are embedded in multiscalar mobility regulation including regional organizations such as the Greater Mekong Subregion and the Greater Tumen Initiative.
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Ganguly, Debjani, ed. The Cambridge History of World Literature. Cambridge University Press, 2021. http://dx.doi.org/10.1017/9781009064446.

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World Literature is a vital part of twentieth-first century critical and comparative literary studies. As a field that engages seriously with function of literary studies in our global era, the study of World literature requires new approaches. The Cambridge History of World Literature is founded on the assumption that World Literature is not all literatures of the world nor a canonical set of globally successful literary works. It highlights scholarship on literary works that focus on the logics of circulation drawn from multiple literary cultures and technologies of the textual. While not rejecting the nation as a site of analysis, these volumes will offer insights into new cartographies – the hemispheric, the oceanic, the transregional, the archipelagic, the multilingual local – that better reflect the multi-scalar and spatially dispersed nature of literary production. It will interrogate existing historical, methodological and cartographic boundaries, and showcase humanistic and literary endeavors in the face of world scale environmental and humanitarian catastrophes.
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Haspelmath, Martin. Negative Indefinite Pronouns. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198235606.003.0008.

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This chapter examines the typology of negative indefinite pronouns, with particular emphasis on their relation with other indefinites. It first considers the received taxonomy of negated indefinites, showing that it is inadequate and that the implicational map for representing the functions of indefinite pronouns offers a better classification. Four main syntactic ways of expressing negative indefinites, or the direct-negation function of indefinite pronouns, are described: verbal negation plus (ordinary) indefinite, verbal negation plus ‘special indefinite’, verbal negation plus ‘negative indefinite’, and ‘negative indefinite’ without verbal negation. The chapter proceeds by analysing one important aspect of the syntax of negative indefinites: the co-occurrence with a negative element associated with the verb. It also formulates a number of cross-linguistic generalizations and proposes functional explanations for them before concluding with an assessment of various diachronic sources of negative indefinites, including negative scalar focus particles and minimal-unit expressions.
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Book chapters on the topic "Scalar-On-Function"

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Crainiceanu, Ciprian M., Jeff Goldsmith, Andrew Leroux, and Erjia Cui. "Function-on-Scalar Regression." In Functional Data Analysis with R, 143–74. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003278726-5.

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Crainiceanu, Ciprian M., Jeff Goldsmith, Andrew Leroux, and Erjia Cui. "Scalar-on-Function Regression." In Functional Data Analysis with R, 101–42. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003278726-4.

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Pumir, A. "On the Three-Point Correlation Function of a Passive Scalar Mixed by a Turbulent Flow." In Fluid Mechanics and Its Applications, 577–80. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5118-4_144.

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Kondratyev, Kirill Y., Vladimir V. Kozoderov, and Oleg I. Smokty. "The Effect of Horizontal Inhomogeneities of the Underlying Surface on the Scalar Transfer Function of the Atmospheric." In Remote Sensing of the Earth from Space: Atmospheric Correction, 187–228. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-76747-0_6.

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Tucker, Bram. "Mikea, Malagasy, or hunter-gatherers?" In Scale Matters, 179–206. Bielefeld, Germany: transcript Verlag, 2022. http://dx.doi.org/10.14361/9783839460993-009.

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Are ethnic units also cultural and sociopolitical units? Barth (1969a) argued that they are not. However, some recent cultural evolutionary studies argue that ethnicity may function to facilitate within-group cooperation and between-group competition, referred to as parochial altruism (Choi and Bowles 2007; García and van den Bergh 2011; Handley and Mathew 2020; Jones 2018). Ethnographers have historically treated ethnicity and culture as equivalent with assertions that X people have particular beliefs, habits, customs, etc. In this paper I explore the ramifications of scale in ethnographic description and generalization, with a focus on my research participants in southwestern Madagascar, whom I usually label with the ethnonyms Mikea, Masikoro, and Vezo, or with the anthropological categories of hunter-gatherers, farmers, and fishermen. These are people who refer to themselves by these same ethnonyms or hyphenated combinations of terms (Masikoro-Mikea, Vezo-Mikea), or as Malagasy, a term referring to all peoples of Madagascar, or by village or clan affiliations. By contrasting evidence from my research (Tucker et al. 2021) with a study by Handley and Mathew (2020) about East African herders, I argue that the appropriate scale for ethnographic description may depend on patterns of similarity and difference in shared cultural traits and social networks, and these may be related to, or independent of, historically constituted ethnonyms. Careful thought is required to avoid scalar errors of over-particularization and exoticism (which I call Type 1 scalar errors) and over-generalization and stereotyping (Type 2 scalar errors). Because "ethnicity" is not just one "thing," ethnicity is not always the proper scale for ethnographic description.
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Miessein, Désiré, Norman J. M. Horing, Godfrey Gumbs, and Harry Lenzing. "Numerical Analysis of the Helmholtz Green’s Function for Scalar Wave Propagation Through a Nano-hole on a Plasmonic Layer." In Topics in Applied Physics, 515–32. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93460-6_17.

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Balogh, Kata, and Rainer Osswald. "A Frame-Based Analysis of Verbal Particles in Hungarian." In Language, Cognition, and Mind, 219–37. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-50200-3_11.

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AbstractThe verbal particle in Hungarian raises a number of intriguing issues for any theory of the syntax-semantics interface. In this article, we aim at a formal account of the semantic contribution of various verbal particles in Hungarian and we show how the semantic representation of the clause can be compositionally derived. We will concentrate on the four frequent particles meg-, le-, el- and fel-. Our approach makes use of a formalized version of Role and Reference Grammar and the framework of decompositional frame semantics. In particular, we give a formal representation of the boundary-setting function of the verbal particle in terms of decompositional frames which builds on a scalar change analysis. We furthermore analyze the interaction of the particle with resultative adjectives and provide a formal model of how their syntactic representations drive their frame-semantic composition.
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Iavarone, S., H. Yang, Z. Li, Z. X. Chen, and N. Swaminathan. "On the Use of Machine Learning for Subgrid Scale Filtered Density Function Modelling in Large Eddy Simulations of Combustion Systems." In Lecture Notes in Energy, 209–43. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-16248-0_8.

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AbstractThe application of machine learning algorithms to model subgrid-scale filtered density functions (FDFs), required to estimate filtered reaction rates for Large Eddy Simulation (LES) of chemically reacting flows, is discussed in this chapter. Three test cases, i.e., a low-swirl premixed methane-air flame, a MILD combustion of methane-air mixtures, and a kerosene spray turbulent flame, are presented. The scalar statistics in these test cases may not be easily represented using the commonly used presumed shapes for modeling FDFs of mixture fraction and progress variable. Hence, the use of ML methods is explored. Particularly, deep neural network (DNN) to infer joint FDFs of mixture fraction and progress variable is reviewed here. The Direct Numerical Simulation (DNS) datasets employed to train the DNNs in each test case are described. The DNN performances are shown and compared to typical presumed probability density function (PDF) models. Finally, this chapter examines the advantages and caveats of the DNN-based approach.
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Kokoszka, Piotr. "Scalar-on-function regression." In Introduction to Functional Data Analysis, 45–65. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315117416-4.

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Lukas, Andre. "Scalar products." In The Oxford Linear Algebra for Scientists, 287–301. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780198844914.003.0022.

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Abstract Symmetric and Hermitian scalar product on real and complex vector spaces are introduced. Examples include the standard scalar products on real and complex coordinate vector space, as well as scalar products on matrix and function vector spaces. The notion of an ortho-normal basis is defined and such bases are shown to exist from the Gram-Schmidt procedure.
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Conference papers on the topic "Scalar-On-Function"

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Deb, P., and Pradip Majumdar. "Direct Numerical Simulation of Mixing of a Passive in Decaying Turbulence." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-1086.

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Abstract Research on turbulent mixing processes is of great interest to those working on turbulent-reactive flows. In this paper, a detailed study has been performed for the evolution of scalar fields of different initial integral scales in decaying, homogeneous and isotropic turbulence using DNS technique. Passive scalar mixing in a cubical decaying, homogeneous, isotropic turbulence field is considered. The three-dimensional incompressible Navier-Stokes equations together with scalar equation are solved using Fractional Step Method. The convective and diffusive terms in governing equations are discretised by Compact Finite Difference Scheme. The 32 × 32 × 32 uniform staggered grids are used. The present simulation is performed at Taylor Reynolds number of 28.83. In this paper, the evolution of scalar RMS and scalar dissipation rate for different integral length scales has been presented. The initial velocity vector and Probability Density Function (PDF) of scalar at different eddy turn over time have also been presented.
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Suzuki, Hiroki, Kouji Nagata, Yasuhiko Sakai, and Ryota Ukai. "An Experimental Study on Turbulent Mixing of High-Schmidt-Number Scalar in Grid Turbulence by Means of PIV and PLIF." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-21013.

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Turbulent mixing of high-Schmidt-number passive scalar in shear-free grid turbulence is experimentally investigated using a water channel. The Reynolds number based on the mesh size of the grid and cross-sectionally averaged mean velocity is 2,500. Rhodamine B (fluorescent dye) was used as a high-Schmidt-number passive scalar. The Schmidt number is about 2,100. The time-resolved particle image velocimetry (PIV) and the planar laser induced fluorescence (PLIF) technique were used to measure instantaneous two-component velocities and nondimensional concentration. Our PLIF algorithm corrects the following errors: spatiotemporal variation of local excitation intensity due to an inhomogeneous concentration field along the light path, time variation of fluorescence quantum yield, and spatiotemporal variation of incident laser intensity. The results show that the vertical profile of mean scalar can be well approximated by the error function. In contrast, the profile of scalar variance in outer region of the mixing layer cannot be approximated by the Gaussian profile. In addition, the half width of mean scalar is larger than that of the scalar variance profile.
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Clarke, Philip L., Reza Abedi, Bahador Bahmani, Katherine A. Acton, and Sarah C. Baxter. "Effect of the Spatial Inhomogeneity of Fracture Strength on Fracture Pattern for Quasi-Brittle Materials." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71515.

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The response of quasi-brittle materials is greatly influenced by their microstructural architecture and variations. To model such statistical variability, Statistical Volume Elements (SVEs) are used to derive a scalar fracture strength for domains populated with microcracks. By employing the moving window approach the probability density function and covariance function of the scalar fracture strength field are obtained. The Karhunen-Loève method is used to generate realizations of fracture strength that are consistent with the SVE-derived statistics. The effect of homogenization scheme, through the size of SVE, on fracture pattern is studied by using an asynchronous spacetime discontinuous Galerkin (aSDG) finite element method, where cracks are exactly tracked by the method’s adaptive operations.
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Piatrovich, Siarhei, and Haris J. Catrakis. "Multiscale Aspects and Resolution Robustness of Turbulent Scalar Fields and Interfaces." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37093.

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This study focuses on fundamental issues regarding multiscale and multiresolution geometrical properties of turbulent scalar fields and interfaces. The probability density function of the scalar field is examined in terms of geometrical properties of the turbulent interfaces using a high-resolution experimental database of fully-developed turbulent scalar fields in jets at a Reynolds number of Re = 20,000. The pdf is found to exhibit significant robustness to resolution scale. The multiscale properties of the volume of fluid regions enclosed by outer turbulent interfaces are also investigated. The enclosed interfacial volume appears to be significantly robust to the resolution scale as well. An explanation for this behavior is proposed in terms of the opposite effects of protrusions of the scalar interface compared to indentations, which provide positive and negative contributions to the volume respectively. This is in contrast to the interfacial surface area for which protrusions and indentations both have additive contributions.
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Moharam, M. G. "Validity of the scalar theory in the design of diffractive optical elements." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.tho3.

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Scalar diffraction theory based on Fourier optics is widely used for the analysis and the design of diffractive optical elements. The approach, which involves Fourier expansion of the transmittance function of the grating structure, is believed to be valid for the analysis of gratings with large grating spacing and small depth at near normal incidence. Recent uses for diffractive optical elements such as fast lenses require grating periods comparable to the light wavelength. In this work, the range of validity of the approximate scalar Fourier optics approach in the analysis of these structures is investigated. Exact diffraction characteristics of several multilevel binary dielectric gratings are calculated using the rigorous vector electromagnetic-based coupled wave approach as a function of the grating period to light wavelength ratio and of the grating refractive index for both TE and TM polarizations. Comparisons with those characteristics obtained by the approximate scalar diffraction theory (corrected to account for specular reflection) are made. It is shown that the error in the diffraction efficiency calculated by the approximate scalar analysis relative to that obtained by the rigorous vector analysis is >15% for a grating period light wavelength ratio of more than 10. It is also shown that the error increases as the number of binary levels or the grating substrate index increases. As the ratio between the grating period and the light wavelength decreases (<5) strong polarization dependence is observed.
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Fontaine, Marie, Velko P. Tzolov, Nicolas Godbout, and Suzanne Lacroix. "Limits of the Perturbative Scalar Calculation of Self-Phase Modulation Effects." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/nlgw.1995.nsab7.

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Kerr-type nonlinear optical devices working in a self-phase modulation (SPM) regime, such as tapered nonlinear fibers, appear to be very promising for the design of all-fiber optical switches [1]. Crucially important for devices based on nonlinear tapered fibers is the waist diameter to maximize the magnitude of the nonlinear Kerr effect. To determine the optimal diameter, we computed the nonlinear propagation constant β NL as a function of the guided power P. In the range of diameters of interest for nonlinear applications, the field is guided by the air-cladding interface. Due to the strongly guiding conditions, the scalar theory is expected not to provide the exact modal characteristics. In this paper, four different numerical methods are used to investigate the nonlinear modal properties of tapered fibers: (1) a first-order scalar perturbation method; (2) a first-order vectorial perturbation method; (3) an exact numerical solution of the scalar (Helmholtz) equation; (4) an exact numerical solution of the Maxwell's equations. A comparison of the results obtained by the scalar approaches and by their vectorial counterparts is presented.
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Hasan, Md Kamrul, Md Azazul Haque, and Rajib Mahamud. "Modeling and Implementation of a Flamelet Based Model With Presumed Shaped Probability Distribution Function Integration in Fortran for Non-Premixed Flame Dynamics." In ASME 2023 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/imece2023-113566.

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Abstract Numerical modeling of combustion dynamics for various applications is a complex problem that involves flow-chemistry interaction and requires the implementation of efficient numerical schemes. Computational modeling of turbulent combustion is essential in predicting different combustion attributes like flame stability and heat release. Despite being a reasonable alternative to the experimental data, the modeling approach also requires tremendous computational resources. Various strategies have been introduced over the year to minimize computational time. This study reports on a Fortran-based Computational Fluid Dynamics (CFD) code to investigate non-premixed flame applications, utilizing a fourth-order accurate compact finite difference scheme. The CFD code incorporates the flamelet model combined with the Navier-Stokes (NS) equations to solve for various variables, including velocity, pressure, temperature, mixture fraction, mixture fraction variance, and scalar dissipation rate. Flamelet model uses laminar flame components in turbulent flame, where the laminar flamelet characterizes the local structure at each point on the flame front. The reactant fluxes depend on the gradients of flow velocity and are controlled by the scalar dissipation rate. The flamelet model and the β(beta)-pdf integration for species transport and temperature distribution are incorporated into the code. The laminar diffusion flame provides unique relationships for all thermochemical variables (such as temperature, species concentrations, and heat release rate) in terms of the mixture fraction. These relationships can be averaged for the non-premixed flame using an assumed probability distribution function of the conserved scalar. The steady-state flamelet libraries are generated from a zero-dimensional chemical kinetics solver with dependencies on mixture fraction and scalar dissipation rate.
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Shaw, Kenneth D. "Vector Versus Scalar Theory of the Double Phase Conjugate Mirror." In Nonlinear Optics. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.pd14.

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The operation of the double phase conjugate mirror (DPCM) has in the past been described theoretically [1] through the use of one-dimensional scalar coupled wave theory [2], This 1-d scalar theory predicts that the DPCM works as an oscillator, with the phase conjugate beams building up from zero at the crystal boundaries (as a function the longitudinal spatial coordinate) when the coupling strength is above some threshold value. In the laboratory, the DPCM does indeed appear to have this property, since its operation is observed to depend critically on the angles of the pump beams inside the crystal with respect to each other and to the crystal’s optic axis, parameters upon which the coupling strength depends. The phase conjugate beams appear to “turn on” suddenly to full intensity as the orientation of the pump beams within the crystal is changed slightly.
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Isoz, Martin, and Marie Plachá. "A Parallel Algorithm for Flux-Based Bounded Scalar Re-distribution." In Topical Problems of Fluid Mechanics 2022. Institute of Thermomechanics of the Czech Academy of Sciences, 2022. http://dx.doi.org/10.14311/tpfm.2022.013.

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Let us assume a bounded scalar function ? : Q = I × ? ? ?0, 1?, I ? R, ? ? R3, where Q is an open bounded domain and its discrete counterpart ?h defined on a computational mesh Qh = Ih × ?h. The problem of redistribution of ?h over ?h ensuring the scalar boundedness while maintaining the invariance of R ?h ?h dV is surprisingly frequent within the field of computational fluid dynamics (CFD). The present contribution is motivated by the case arising from coupling Lagrangian particle tracking and particle deposition within ?h with Eulerian CFD computation. We propose an algorithm for ?h redistribution that is (i) based on fluxes over the computational cells faces, i.e. suitable for finite volume (FV) computations, (ii) localized, meaning that a cell ?h P with ?hP > 1 affects only its closest neighbors with ?h < 1, and (iii) designed for parallel computations leveraging the standard domain decomposition methods.
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Michopoulos, John G., and Athanasios Iliopoulos. "High Dimensional Full Inverse Characterization of Fractal Volumes." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71050.

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The present paper describes a methodology for the inverse identification of the complete set of parameters associated with the Weirstrass-Mandelbrot (W-M) function that can describe any fractal scalar field distribution of measured data defined within a volume. Our effort is motivated by the need to be able to describe a scalar field quantity distribution in a volume in order to be able to represent analytically various non-homogeneous material properties distributions for engineering and science applications. Our method involves utilizing a refactoring of the W-M function that permits defining the characterization problem as a high dimensional singular value decomposition problem for the determination of the so-called phases of the function. Coupled with this process is a second level exhaustive search that enables the determination of the density of the frequencies involved in defining the trigonometric functions involved in the definition of the W-M function. Numerical applications of the proposed method on both synthetic and actual volume data, validate the efficiency and the accuracy of the proposed approach. This approach constitutes a radical departure from the traditional fractal dimension characterization studies and opens the road for a very large number of applications and generalizes the approach developed by the authors for fractal surfaces to that of fractal volumes.
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Reports on the topic "Scalar-On-Function"

1

Tanny, Josef, Gabriel Katul, Shabtai Cohen, and Meir Teitel. Micrometeorological methods for inferring whole canopy evapotranspiration in large agricultural structures: measurements and modeling. United States Department of Agriculture, October 2015. http://dx.doi.org/10.32747/2015.7594402.bard.

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Original objectives and revisions The original objectives as stated in the approved proposal were: (1) To establish guidelines for the use of micrometeorological techniques as accurate, reliable and low-cost tools for continuous monitoring of whole canopy ET of common crops grown in large agricultural structures. (2) To adapt existing methods for protected cultivation environments. (3) To combine previously derived theoretical models of air flow and scalar fluxes in large agricultural structures (an outcome of our previous BARD project) with ET data derived from application of turbulent transport techniques for different crops and structure types. All the objectives have been successfully addressed. The study was focused on both screenhouses and naturally ventilated greenhouses, and all proposed methods were examined. Background to the topic Our previous BARD project established that the eddy covariance (EC) technique is suitable for whole canopy evapotranspiration measurements in large agricultural screenhouses. Nevertheless, the eddy covariance technique remains difficult to apply in the farm due to costs, operational complexity, and post-processing of data – thereby inviting alternative techniques to be developed. The subject of this project was: 1) the evaluation of four turbulent transport (TT) techniques, namely, Surface Renewal (SR), Flux-Variance (FV), Half-order Time Derivative (HTD) and Bowen Ratio (BR), whose instrumentation needs and operational demands are not as elaborate as the EC, to estimate evapotranspiration within large agricultural structures; and 2) the development of mathematical models able to predict water savings and account for the external environmental conditions, physiological properties of the plant, and structure properties as well as to evaluate the necessary micrometeorological conditions for utilizing the above turbulent transfer methods in such protected environments. Major conclusions and achievements The major conclusions are: (i) the SR and FV techniques were suitable for reliable estimates of ET in shading and insect-proof screenhouses; (ii) The BR technique was reliable in shading screenhouses; (iii) HTD provided reasonable results in the shading and insect proof screenhouses; (iv) Quality control analysis of the EC method showed that conditions in the shading and insect proof screenhouses were reasonable for flux measurements. However, in the plastic covered greenhouse energy balance closure was poor. Therefore, the alternative methods could not be analyzed in the greenhouse; (v) A multi-layered flux footprint model was developed for a ‘generic’ crop canopy situated within a protected environment such as a large screenhouse. The new model accounts for the vertically distributed sources and sinks within the canopy volume as well as for modifications introduced by the screen on the flow field and microenvironment. The effect of the screen on fetch as a function of its relative height above the canopy is then studied for the first time and compared to the case where the screen is absent. The model calculations agreed with field experiments based on EC measurements from two screenhouse experiments. Implications, both scientific and agricultural The study established for the first time, both experimentally and theoretically, the use of four simple TT techniques for ET estimates within large agricultural screenhouses. Such measurements, along with reliable theoretical models, will enable the future development of lowcost ET monitoring system which will be attainable for day-to-day use by growers in improving irrigation management.
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