scholarly journals The area rule for circulation in three-dimensional turbulence

2021 ◽  
Vol 118 (43) ◽  
pp. e2114679118
Author(s):  
Kartik P. Iyer ◽  
Sachin S. Bharadwaj ◽  
Katepalli R. Sreenivasan
Keyword(s):  
Aspect Ratio ◽  
Gaussian Random Field ◽  
Three Dimensional ◽  
Internal Variable ◽  
Three Dimensions ◽  
Order Moment ◽  
High Resolution Data ◽  
Ratio Dependence ◽  
Area Rule ◽  
Minimal Area

An important idea underlying a plausible dynamical theory of circulation in three-dimensional turbulence is the so-called area rule, according to which the probability density function (PDF) of the circulation around closed loops depends only on the minimal area of the loop, not its shape. We assess the robustness of the area rule, for both planar and nonplanar loops, using high-resolution data from direct numerical simulations. For planar loops, the circulation moments for rectangular shapes match those for the square with only small differences, these differences being larger when the aspect ratio is farther from unity and when the moment order increases. The differences do not exceed about 5% for any condition examined here. The aspect ratio dependence observed for the second-order moment is indistinguishable from results for the Gaussian random field (GRF) with the same two-point correlation function (for which the results are order-independent by construction). When normalized by the SD of the PDF, the aspect ratio dependence is even smaller ( < 2%) but does not vanish unlike for the GRF. We obtain circulation statistics around minimal area loops in three dimensions and compare them to those of a planar loop circumscribing equivalent areas, and we find that circulation statistics match in the two cases only when normalized by an internal variable such as the SD. This work highlights the hitherto unknown connection between minimal surfaces and turbulence.

Primary and secondary instabilities in the wake of a cylinder with free ends

1997 ◽  
Vol 332 ◽  
pp. 295-339 ◽  
Author(s):  
Christophe Dauchy ◽  
Jan Dušek ◽  
Philippe Fraunié
Keyword(s):  
Aspect Ratio ◽  
Limit Cycle ◽  
Three Dimensional ◽  
Secondary Instability ◽  
Instability Threshold ◽  
Three Dimensions ◽  
Finite Cylinder ◽  
Minor Role ◽  
A Minor ◽  
Primary Instability

The wake of a finite cylinder with free ends and an aspect ratio of 21.4 is simulated in three-dimensions and analysed theoretically. Close to the primary-instability threshold, the flow is shown to settle on a limit cycle with a uniform frequency throughout the flow-field. About 20% above the primary-instability threshold, a secondary instability sets in and the limit cycle becomes unstable. The new attractor of the flow can be identified as a limit T2-torus characterized by two incommensurate frequencies. One of them is shown to evolve continuously from the primary-instability frequency, the other one, about 17 times smaller near the secondary-instability threshold, generates a slow modulation of the oscillations in the wake. The limit cycle and the limit torus are described in terms of their Fourier expansion and the spatial distribution of the most relevant Fourier components is investigated. The theoretical analysis and numerical results given shed some light on the mechanisms underlying a number of known but not satisfactorily explained three-dimensional effects in wakes of finite cylinders such as the ambiguity in the dominant Strouhal frequency, the existence of zones with different frequencies spanwise in the wake, the discreteness of coexisting frequencies observed in the wake as well as the spatial uniformity of the beating period. They moreover explain the Reynolds number variation of these effects and identify the recirculation around the cylinder ends as basically responsible for the onset of the secondary instability. The results are compared to the case of a cylinder with aspect ratio of 10.7 to determine the basic trends in aspect ratio dependence. It is shown that qualitatively the same behaviour is obtained, but that the secondary-instability threshold is shifted significantly upward to about twice the primary-instability threshold. Simulations of the wake of a finite NACA wing with incidence show that the form of the cross-section plays a minor role.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals The Everyday Life of Security: Capturing Space, Practice, and Affect

2021 ◽  
Author(s):  
Jonna Nyman
Keyword(s):  
Everyday Life ◽  
Research Methods ◽  
Lived Experiences ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Conceptual Clarity ◽  
The Everyday ◽  
Participatory Photography ◽  
High Politics ◽  
Ordinary Citizens

Abstract Security shapes everyday life, but despite a growing literature on everyday security there is no consensus on the meaning of the “everyday.” At the same time, the research methods that dominate the field are designed to study elites and high politics. This paper does two things. First, it brings together and synthesizes the existing literature on everyday security to argue that we should think about the everyday life of security as constituted across three dimensions: space, practice, and affect. Thus, the paper adds conceptual clarity, demonstrating that the everyday life of security is multifaceted and exists in mundane spaces, routine practices, and affective/lived experiences. Second, it works through the methodological implications of a three-dimensional understanding of everyday security. In order to capture all three dimensions and the ways in which they interact, we need to explore different methods. The paper offers one such method, exploring the everyday life of security in contemporary China through a participatory photography project with six ordinary citizens in Beijing. The central contribution of the paper is capturing—conceptually and methodologically—all three dimensions, in order to develop our understanding of the everyday life of security.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

scholarly journals Rethinking student-teacher relationships in higher education: a multidimensional approach

2021 ◽  
Author(s):  
Roland Tormey
Keyword(s):  
Higher Education ◽  
Classroom Management ◽  
Student Teacher ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Theoretical Development ◽  
Multidimensional Model ◽  
Three Dimensional Model ◽  
Teacher Relationships ◽  
Student Teacher Relationships

AbstractStudent-teacher relationships play an important role in both teacher and student experiences in higher education and have been found to be linked to learning, classroom management, and to student absenteeism. Although historically conceptualised in terms of immediacy or distance and measured with reference to behaviours, the growing recognition of the role of emotions and of power—as well as the development of a range of multidimensional models of social relationships—all suggest it is time to re-evaluate how student-teacher relationships are understood. This paper develops a theoretical model of student-teacher affective relationships in higher education based on three dimensions: affection/warmth, attachment/safety, and assertion/power. The three-dimensional model was tested using the Classroom Affective Relationships Inventory (CARI) with data from 851 students. The data supported the use of this multidimensional model for student-teacher relationships with both two- and three-dimensional models of relationships being identified as appropriate. The theoretical development of a multidimensional model and the empirical development of an instrument with which to explore these dimensions has important implications for higher education teachers, administrators and researchers.

scholarly journals Principal Component Analysis of Munich Functional Developmental Diagnosis

2021 ◽  
Vol 13 (2) ◽  
pp. 227-233
Author(s):  
Grażyna Pazera ◽  
Marta Młodawska ◽  
Jakub Młodawski ◽  
Kamila Klimowska
Keyword(s):  
Principal Component Analysis ◽  
Social Skills ◽  
Motor Development ◽  
Three Dimensional ◽  
Principal Component ◽  
Component Analysis ◽  
Three Dimensions ◽  
Matrix Analysis ◽  
Psychomotor Development ◽  
First Year Of Life

Objectives: Munich Functional Developmental Diagnosis (MFDD) is a scale for assessing the psychomotor development of children in the first months or years of life. The tool is based on standardized tables of physical development and is used to detect developmental deficits. It consists of eight axes on which the following skills are assessed: crawling, sitting, walking, grasping, perception, speaking, speech understanding, social skills. Methods: The study included 110 children in the first year of life examined with the MFDD by the same physician. The score obtained on a given axis was coded as a negative value (defined in months) below the child’s age-specific developmental level. Next, we examined the dimensionality of the scale and the intercorrelation of its axes using polychoric correlation and principal component analysis. Results: Correlation matrix analysis showed high correlation of MFDD axes 1–4, and MFDD 6–8. The PCA identified three principal components consisting of children’s development in the areas of large and small motor skills (axis 1–4), perception (axis 5), active speech, passive speech and social skills (axis 6–8). The three dimensions obtained together account for 80.27% of the total variance. Conclusions: MFDD is a three-dimensional scale that includes motor development, perception, and social skills and speech. There is potential space for reduction in the number of variables in the scale.

scholarly journals Structural analysis of mutations in the Drosophila beta 2-tubulin isoform reveals regions in the beta-tubulin molecular required for general and for tissue-specific microtubule functions.

Genetics ◽  
1995 ◽  
Vol 139 (1) ◽  
pp. 267-286 ◽  
Author(s):  
J D Fackenthal ◽  
J A Hutchens ◽  
F R Turner ◽  
E C Raff
Keyword(s):  
Amino Acid ◽  
Three Dimensional ◽  
Variable Region ◽  
Internal Variable ◽  
Microtubule Assembly ◽  
Dimensional Structure ◽  
Wild Type ◽  
Beta Tubulin ◽  
Assembly Kinetics ◽  
Beta 2

Abstract We have determined the lesions in a number of mutant alleles of beta Tub85D, the gene that encodes the testis-specific beta 2-tubulin isoform in Drosophila melanogaster. Mutations responsible for different classes of functional phenotypes are distributed throughout the beta 2-tubulin molecule. There is a telling correlation between the degree of phylogenetic conservation of the altered residues and the number of different microtubule categories disrupted by the lesions. The majority of lesions occur at positions that are evolutionarily highly conserved in all beta-tubulins; these lesions disrupt general functions common to multiple classes of microtubules. However, a single allele B2t6 contains an amino acid substitution within an internal cluster of variable amino acids that has been identified as an isotype-defining domain in vertebrate beta-tubulins. Correspondingly, B2t6 disrupts only a subset of microtubule functions, resulting in misspecification of the morphology of the doublet microtubules of the sperm tail axoneme. We previously demonstrated that beta 3, a developmentally regulated Drosophila beta-tubulin isoform, confers the same restricted morphological phenotype in a dominant way when it is coexpressed in the testis with wild-type beta 2-tubulin. We show here by complementation analysis that beta 3 and the B2t6 product disrupt a common aspect of microtubule assembly. We therefore conclude that the amino acid sequence of the beta 2-tubulin internal variable region is required for generation of correct axoneme morphology but not for general microtubule functions. As we have previously reported, the beta 2-tubulin carboxy terminal isotype-defining domain is required for suprastructural organization of the axoneme. We demonstrate here that the beta 2 variant lacking the carboxy terminus and the B2t6 variant complement each other for mild-to-moderate meiotic defects but do not complement for proper axonemal morphology. Our results are consistent with the hypothesis drawn from comparisons of vertebrate beta-tubulins that the two isotype-defining domains interact in a three-dimensional structure in wild-type beta-tubulins. We propose that the integrity of this structure in the Drosophila testis beta 2-tubulin isoform is required for proper axoneme assembly but not necessarily for general microtubule functions. On the basis of our observations we present a model for regulation of axoneme microtubule morphology as a function of tubulin assembly kinetics.

Sign in / Sign up

Export Citation Format

Share Document