scholarly journals From 2D to 3D in fluid turbulence: unexpected critical transitions

2017 ◽  
Vol 828 ◽  
pp. 1-4 ◽  
Author(s):  
R. E. Ecke
Keyword(s):  
Degrees Of Freedom ◽  
Spatial Scales ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Fluid Turbulence ◽  
Critical Transitions ◽  
Energy Flows ◽  
The 1960S ◽  
Short Time

How do the laws of physics change with changes in spatial dimension? Maybe not at all in some cases, but in important cases, the changes are dramatic. Fluid turbulence – the fluctuating, intermittent and many-degree-of-freedom state of a highly forced fluid – determines the transport of heat, mass and momentum and is ubiquitous in nature, where turbulence is found on spatial scales from microns to millions of kilometres (turbulence in stars) and beyond (galactic events such as supernovae). When the turbulent degrees of freedom are suppressed in one spatial dimension, the resulting turbulent state in two dimensions (2D) is remarkably changed compared with the turbulence in three dimensions (3D) – energy flows to small scales in 3D but towards large scales in 2D. Although this result has been known since the 1960s due to the pioneering work of Kraichnan, Batchelor and Leith, how one transitions between 3D and 2D turbulence has remained remarkably unexplored. For real physical systems, this is a highly significant question with important implications about transport in geophysical systems that determine weather on short time scales and climate on longer scales. Is the transition from 3D to 2D smooth or are there sharp transitions that signal a threshold of the dominance of one type of turbulence over another? Recent results by Benavides & Alexakis (J. Fluid Mech., vol. 822 (2017), pp. 364–385) suggest that the latter may be the case – a surprising and provocative discovery.

scholarly journals THE “DUAL” VARIABLES OF YANG-MILLS THEORY AND LOCAL GAUGE-INVARIANT VARIABLES

1996 ◽  
Vol 11 (32) ◽  
pp. 5701-5728 ◽  
Author(s):  
ORI GANOR ◽  
J. SONNENSCHEIN
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Six Degrees Of Freedom ◽  
Local Gauge ◽  
Dual Variables ◽  
Topological Part

After adding auxiliary fields and integrating out the original variables, the Yang-Mills action can be expressed in terms of local gauge-invariant variables. This method reproduces the known solution of the two-dimensional SU (N) theory. In more than two dimensions the action splits into a topological part and a part proportional to αs. We demonstrate the procedure for SU (2) in three dimensions where we reproduce a gravitylike theory. We discuss the four-dimensional case as well. We use a cubic expression in the fields as a space-time metric to obtain a covariant Lagrangian. We also show how the four-dimensional SU (2) theory can be expressed in terms of a local action with six degrees of freedom only.

NUCLEON STRUCTURE AT JEFFERSON LAB: FROM TWO DIMENSIONS TO THREE DIMENSIONS

2009 ◽  
Vol 18 (10) ◽  
pp. 2181-2186
Author(s):  
MICHEL GUIDAL
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Form Factors ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nucleon Structure ◽  
Parton Distributions ◽  
Jefferson Lab ◽  
Generalized Parton Distributions ◽  
Nucleon Form Factors

We review very briefly a few recent highlight results from Jefferson Lab concerning nucleon Form Factors and Generalized Parton Distributions for which data with unprecedented precision and phase space coverage have be obtained these past few years. Along with new theoretical developements, these data allow to make some nucleon imaging in terms of partonic degrees of freedom in both momentum and space dimensions.

Kinematic strategies and sensorimotor transformations in the wiping movements of frogs

1989 ◽  
Vol 62 (3) ◽  
pp. 750-767 ◽  
Author(s):  
S. F. Giszter ◽  
J. McIntyre ◽  
E. Bizzi
Keyword(s):  
Degrees Of Freedom ◽  
Joint Angle ◽  
Video Recording ◽  
Two Dimensions ◽  
The Body ◽  
Three Dimensions ◽  
Postural Adjustment ◽  
Leopard Frogs ◽  
Motor Commands ◽  
Sensorimotor Transformations

1. Spinal frogs are known to make coordinated and successful wiping movements to almost all places on the body and legs. Such wiping movements involve a sensorimotor transformation. Information from both the spatial locations of stimuli on the skin and the body configuration of the frog is transformed into a set of motor commands that generate body movements adequate to successfully remove the irritant. The spinal cord itself therefore has a limited capacity for sensorimotor transformations. 2. We examined the kinematics of wiping motions in both spinal and intact leopard frogs and bullfrogs. This data was used to assess the flexibility, precision, and strategy of the kinematic sensorimotor transformations used during wiping. The movements involved the use of redundant degrees of freedom in the limbs. Thus many possible movements or solutions could generate successful wiping. This redundancy allows motor-equivalent movements to be used by the frog. 3. Movements were examined in two dimensions by the use of VHS shuttered-video recording and in three dimensions with the use of a WATSMART system of infrared diodes and cameras. The kinematic analysis was applied to those motions in which the limbs did not interact with kinematic constraints, such as the surface of the substrate or body. These unconstrained motions are directly related to motor commands and thus more easily interpreted. 4. Wiping movements to the back were retained in essentially the same form in both spinal and intact frogs. In both cases wiping had four phases with a fifth occasionally present. The phases included flexion, placing, aiming, and whisking, with occasional extension and multiply repeated wipes. However, the aiming phase was often very brief or absent in this data, and flexion was sometimes omitted in multiple wipes. We found that the placing posture was adjusted in a simple way in response to variations in the location of the target stimulus. The rostrocaudal position of the foot tip was strongly and linearly related to the rostrocaudal stimulus location. 5. During the placing posture, joint angles as well as the limb tip in back wipes had linear relationships to the stimulus' rostrocaudal coordinate. The limb configuration used by the frog allowed a strategy of linear (and potentially independent) postural adjustment of joint angle to stimulus position to generate almost linear endpoint adjustments in the placing phase of wiping. This solution to the ill-posed problem of choosing a joint angle for the placing posture in back-wiping may be computationally simple.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Driving Two Numerical Methods to Evaluate the Triple Integrals R(MSM),R(SMM) and Compare Between Them

2018 ◽  
Vol 7 (3.27) ◽  
pp. 303
Author(s):  
Safaa M. Aljassas ◽  
Fouad H.A. Alsharify ◽  
Nada A.M. Al–Karamy
Keyword(s):  
Numerical Methods ◽  
High Accuracy ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partial Derivatives ◽  
Simpson’S Rule ◽  
Short Time ◽  
Correction Terms ◽  
Simpson's Rule

The main objective of present work is the conclusion of two new numerical methods to evaluate the triple integrals with continuous integrands and their partial derivatives are continuous too, the first method   through using Mid-point rule on the interior dimension X, Simpson's rule on the middle dimension Y and Mid-point rule on the exterior dimension Z, which denoted by the symbol MSM. The second method by using Mid-point rule on  both two dimensions of interior X and middle dimension Y and Simpson's rule on the exterior dimension Z which denoted  by SMM, where the number of divisions on the three dimensions are equals. We have concluded two theorems with their proves to find their rules and the correction terms that we found it and to improve the results we used Romberg acceleration which denoted by R(MSM),R(SMM) where we got high accuracy in the results by little sub-intervals relatively and short time. 

TOPOLOGICAL MASS GENERATION IN 3+1 DIMENSIONS

1991 ◽  
Vol 06 (07) ◽  
pp. 559-571 ◽  
Author(s):  
THEODORE J. ALLEN ◽  
MARK J. BOWICK ◽  
AMITABHA LAHIRI
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Simons Theory ◽  
Mass Generation ◽  
Abelian Gauge ◽  
Four Dimensions ◽  
Schwinger Model ◽  
Massive Spin ◽  
Renormalizable Theory

The 4-dimensional theory of a 1-form Abelian gauge field A coupled to a 2-form (antisymmetric tensor) potential B is studied. The two gauge invariances of the theory admit a coupling mB ∧ F where F is the field strength (F=dA) of A. It is shown that this theory is a unitary, renormalizable theory of a massive spin-one field with no additional degrees of freedom. In this sense, it is a generalization to four dimensions of topological mechanisms in two dimensions (the Schwinger model) and three dimensions (Chern-Simons theory). The issue of spontaneous symmetry breaking is also examined.

scholarly journals On the collapse of locally isostatic networks

2009 ◽  
Vol 465 (2111) ◽  
pp. 3517-3530 ◽  
Author(s):  
V. Kapko ◽  
M. M. J. Treacy ◽  
M. F. Thorpe ◽  
S. D. Guest
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Unit Cell ◽  
Three Dimensions ◽  
Collapse Mechanism ◽  
Two Dimensional ◽  
Higher Symmetry ◽  
Collapse Mechanisms ◽  
Equilateral Triangles ◽  
As If

We examine the flexibility of periodic planar networks built from rigid corner-connected equilateral triangles. Such systems are locally isostatic, since for each triangle the total number of degrees of freedom equals the total number of constraints. These nets are two-dimensional analogues of zeolite frameworks, which are periodic assemblies of corner-sharing tetrahedra. If the corner connections are permitted to rotate, as if pin-jointed, there is always at least one collapse mechanism in two dimensions (and at least three mechanisms in three dimensions). We present a number of examples of such collapse modes for different topologies of triangular net. We show that the number of collapse mechanisms grows with the size of unit cell. The collapsible mechanisms that preserve higher symmetry of the network tend to exhibit the widest range of densities without sterical overlap.

scholarly journals Data on Orientation to Happiness in Higher Education Institutions from Mexico and El Salvador

Data ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 27
Author(s):  
Domingo Villavicencio-Aguilar ◽  
Edgardo René Chacón-Andrade ◽  
Maria Fernanda Durón-Ramos
Keyword(s):  
Higher Education ◽  
El Salvador ◽  
Latin American ◽  
Higher Education Institutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Stepwise Multiple Regression ◽  
Teacher Student ◽  
And Gender ◽  
Student’S T

Happiness-oriented people are vital in every society; this is a construct formed by three different types of happiness: pleasure, meaning, and engagement, and it is considered as an indicator of mental health. This study aims to provide data on the levels of orientation to happiness in higher-education teachers and students. The present paper contains data about the perception of this positive aspect in two Latin American countries, Mexico and El Salvador. Structure instruments to measure the orientation to happiness were administrated to 397 teachers and 260 students. This data descriptor presents descriptive statistics (mean, standard deviation), internal consistency (Cronbach’s alpha), and differences (Student’s t-test) presented by country, population (teacher/student), and gender of their orientation to happiness and its three dimensions: meaning, pleasure, and engagement. Stepwise-multiple-regression-analysis results are also presented. Results indicated that participants from both countries reported medium–high levels of meaning and engagement happiness; teachers reported higher levels than those of students in these two dimensions. Happiness resulting from pleasure activities was the least reported in general. Males and females presented very similar levels of orientation to happiness. Only the population (teacher/student) showed a predictive relationship with orientation to happiness; however, the model explained a small portion of variance in this variable, which indicated that other factors are more critical when promoting orientation to happiness in higher-education institutions.

scholarly journals Lost in Migration – Mirandese at a Crossroads

2019 ◽  
Vol 5 (1) ◽  
pp. 488-495
Author(s):  
Cláudia Martins ◽  
Sérgio Ferreira
Keyword(s):  
Minority Language ◽  
Three Dimensions ◽  
Highly Qualified ◽  
Linguistic Rights ◽  
The Bible ◽  
Literary Forms ◽  
Before And After ◽  
The 1960S ◽  
The One ◽  
The 19Th Century

AbstractThe linguistic rights of Mirandese were enshrined in Portugal in 1999, though its “discovery” dates back to the very end of the 19th century at the hands of Leite de Vasconcellos. For centuries, it was the first or only language spoken by people living in the northeast of Portugal, particularly the district of Miranda do Douro. As a minority language, it has always moved among three dimensions. On the one hand, the need to assert and defend this language and have it acknowledged by the country, which proudly believe(d) in their monolingual history. Unavoidably, this has ensued the action of translation, especially active from the mid of the 20th century onwards, with an emphasis on the translation of the Bible and Portuguese canonical literature, as well as other renowned literary forms (e.g. The Adventures of Asterix). Finally, the third axis lies in migration, either within Portugal or abroad. Between the 1950s and the 1960s, Mirandese people were forced to leave Miranda do Douro and villages in the outskirts in the thousands. They fled not only due to the deeply entrenched poverty, but also the almost complete absence of future prospects, enhanced by the fact that they were regarded as not speaking “good” Portuguese, but rather a “charra” language, and as ignorant backward people. This period coincided with the building of dams on the river Douro and the cultural and linguistic shock that stemmed from this forceful contact, which exacerbated their sense of not belonging and of social shame. Bearing all this in mind, we seek to approach the role that migration played not only in the assertion of Mirandese as a language in its own right, but also in the empowerment of new generations of Mirandese people, highly qualified and politically engaged in the defence of this minority language, some of whom were former migrants. Thus, we aim to depict Mirandese’s political situation before and after the endorsement of the Portuguese Law no. 7/99.

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.

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