scholarly journals Dynamics of a long chain in turbulent flows: impact of vortices

2020 ◽  
Vol 378 (2175) ◽  
pp. 20190405
Author(s):  
Jason R. Picardo ◽  
Rahul Singh ◽  
Samriddhi Sankar Ray ◽  
Dario Vincenzi
Keyword(s):  
Turbulent Flows ◽  
Soft Matter ◽  
Three Dimensional ◽  
Bending Stiffness ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Vortical Flow ◽  
2D Turbulence ◽  
Preferential Sampling ◽  
The Individual

We show and explain how a long bead–spring chain, immersed in a homogeneous isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of three-dimensional (3D) turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In the 3D case on the contrary, the chain is extended even in vortical regions, which suggests that the chain follows axially stretched tubular vortices by aligning with their axes. This physical picture is confirmed by examining the relative sampling behaviour of the individual beads, and by additional studies on an inextensible chain with adjustable bending-stiffness. A highly flexible, inextensible chain also shows preferential sampling in three dimensions, provided it is longer than the dissipation scale, but not much longer than the vortex tubes. This is true also for 2D turbulence, where a long inextensible chain can occupy vortices by coiling into them. When the chain is made inflexible, however, coiling is prevented and the extent of preferential sampling in two dimensions is considerably reduced. In three dimensions, on the contrary, bending stiffness has no effect, because the chain does not need to coil in order to thread a vortex tube and align with its axis. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

Micro- and noncrystalline materials

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Repeat Unit ◽  
Three Dimensional ◽  
Potassium Dihydrogen Phosphate ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Dihydrogen Phosphate ◽  
Chemical Ordering ◽  
The Individual ◽  
Inorganic Molecules ◽  
High Degree

The crystalline state is characterized by a high degree of internal order. There are two types of order that we will discuss here. One is chemical order, which consists of the connectivity (bond lengths and bond angles) and stoichiometry in organic and many inorganic molecules, or just stoichiometry in minerals, metals, and other such materials. Some degree of chemical ordering exists for any molecule consisting of more than one atom, and the molecular structure of chemically simple gas molecules can be determined by gaseous electron diffraction or by high-resolution infrared spectroscopy. The second type of order to be discussed is geometrical order, which is the regular arrangement of entities in space such as in cubes, cylinders, coiled coils, and many other arrangements. For a compound to be crystalline it is necessary for the geometrical order of the individual entities (which must each have the same overall conformation) to extend indefinitely (that is, apparently infinitely) in three dimensions such that a three-dimensional repeat unit can be defined from diffraction data. Single crystals of quartz, diamond, silicon, or potassium dihydrogen phosphate can be grown to be as large as six or more inches across. Imagine how many atoms or ions must be identically arranged to create such macroscopic perfection! Sometimes, however, this geometrical order does not extend very far, and microarrays of molecules or ions, while themselves ordered, are disordered with respect to each other on a macroscopic scale. In such a case the three-dimensional order does not extend far enough to give a sharp diffraction pattern. The crystal quality is then described as “poor” or the crystal is considered to be microcrystalline, as in the naturally occurring clay minerals. On the other hand, in certain solid materials the spatial extent of geometrical order may be less than three-dimensional, and this reduced order gives rise to interesting properties. For example, the geometrical order may exist only in two dimensions; this is the case for mica and graphite, which consist of planar structures with much weaker forces between the layers so that cleavage and slippage are readily observed.

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 On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

scholarly journals The House of Marie Shannon

2021 ◽  
Author(s):  
◽  
Sally Margaret Apthorp
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Domestic Architecture ◽  
Three Dimensions ◽  
Camera Obscura ◽  
Architectural Space ◽  
Domestic Lives ◽  
Architectural Tradition ◽  
Light And Shadow ◽  
Insight Into

<p>This thesis creatively explores the architectural implications present in the photographs by New Zealand photographer Marie Shannon. The result of this exploration is a house for Shannon. The focus is seven of Shannon's interior panoramas from 1985-1987 in which architectural space is presented as a domestic stage. In these photograph's furniture and objects are the props and Shannon is an actress. This performance, with Shannon both behind and in front of her camera, creates a double insight into her world; architecture as a stage to domestic life, and a photographers view of domestic architecture. Shannon's view on the world enables a greater understanding to our ordinary, domestic lives. Photography is a revealing process that teaches us to see more richly in terms of detail, shading, texture, light and shadow. Through an engagement with photographs and understanding architectural space through a photographer's eye, the hidden, secret or unnoticed aspects to Shannon's reality will be revealed. This insight into another's reality may in turn enable a deeper understanding of our own. The methodology was a revealing process that involved experimenting with Shannon's panoramic photographs. Models and drawing, through photographic techniques, lead to insights both formally in three dimensions and at surface level in two dimensions. These techniques and insights were applied to the site through the framework of a camera obscura. Shannon's new home is created by looking at her photographs with an architect's 'eye'. Externally the home acts as a closed vessel, a camera obscura. But internally rich and intriguing forms, surfaces, textures and shadings are created. Just as the camera obscura projects an exterior scene onto the interior, so does the home. Shannon will inhabit this projection of the shadows which oppose 30 O'Neill Street, Ponsonby, Auckland; her past home and site of her photographs. Photographers, and in particular Shannon, look at the architectural world with fresh eyes, free from an architectural tradition. Photography and the camera enable an improved power of sight. More is revealed to the camera. Beauty is seen in the ordinary, with detail, tone, texture, light and dark fully revealed. As a suspended moment, a deeper understanding and opportunity is created to observe and appreciate this beauty. Through designing with a photographer's eye greater insight is gained into Shannon's 'reality'. This 'revealing' process acts as a means of teaching us how to see pictorial beauty that is inherent in our ordinary lives. This is the beauty that is often hidden in secret, due to our unseeing eyes. This project converts the photographs beauty back into three dimensional architecture.</p>

Diffraction by crystals

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Fourier Transform ◽  
Three Dimensional ◽  
Incident Beam ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Dimensional Structure ◽  
Angle Of Incidence ◽  
X Ray ◽  
Max Von Laue ◽  
The Fourier Transform

In Chapter 4 many two-dimensional examples were shown, in which a diffraction pattern represents the Fourier transform of the scattering object. When a diffracting object is three-dimensional, a new effect arises. In diffraction by a repetitive object, rays are scattered in many directions. Each unit of the lattice scatters, but a diffracted beam arises only if the scattered rays from each unit are all in phase. Otherwise the scattering from one unit is cancelled out by another. In two dimensions, there is always a direction where the scattered rays are in phase for any order of diffraction (just as shown for a one-dimensional scatterer in Fig. 4.1). In three dimensions, it is only possible for all the points of a lattice to scatter in phase if the crystal is correctly oriented in the incident beam. The amplitudes and phases of all the scattered beams from a three-dimensional crystal still provide the Fourier transform of the three-dimensional structure. But when a crystal is at a particular angular orientation to the X-ray beam, the scattering of a monochromatic beam provides only a tiny sample of the total Fourier transform of its structure. In the next section, we are going to find what is needed to allow a diffracted beam to be generated. We shall follow a treatment invented by Lawrence Bragg in 1913. Max von Laue, who discovered X-ray diffraction in 1912, used a different scheme of analysis; and Paul Ewald introduced a new way of looking at it in 1921. These three methods are referred to as the Laue equations, Bragg’s law and the Ewald construction, and they give identical results. All three are described in many crystallographic text books. Bragg’s method is straightforward, understandable, and suffices for present needs. I had heard J.J. Thomson lecture about…X-rays as very short pulses of radiation. I worked out that such pulses…should be reflected at any angle of incidence by the sheets of atoms in the crystal as if these sheets were mirrors.…It remained to explain why certain of the atomic mirrors in the zinc blende [ZnS] crystal reflected more powerfully than others.

Radiolaria: validating the Turing theory

2017 ◽  
Author(s):  
Bernard Richards
Keyword(s):  
Diffusion Mechanism ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Black And White ◽  
Alan Turing ◽  
School Sports ◽  
The University ◽  
University Of Manchester

In his 1952 paper ‘The chemical basis of morphogenesis’ Turing postulated his now famous Morphogenesis Equation. He claimed that his theory would explain why plants and animals took the shapes they did. When I joined him, Turing suggested that I might solve his equation in three dimensions, a new problem. After many manipulations using rather sophisticated mathematics and one of the first factory-produced computers in the UK, I derived a series of solutions to Turing’s equation. I showed that these solutions explained the shapes of specimens of the marine creatures known as Radiolaria, and that they corresponded very closely to the actual spiny shapes of real radiolarians. My work provided further evidence for Turing’s theory of morphogenesis, and in particular for his belief that the external shapes exhibited by Radiolaria can be explained by his reaction–diffusion mechanism. While working in the Computing Machine Laboratory at the University of Manchester in the early 1950s, Alan Turing reignited the interests he had had in both botany and biology from his early youth. During his school-days he was more interested in the structure of the flowers on the school sports field than in the games played there (see Fig. 1.3). It is known that during the Second World War he discussed the problem of phyllotaxis (the arrangement of leaves and florets in plants), and then at Manchester he had some conversations with Claude Wardlaw, the Professor of Botany in the University. Turing was keen to take forward the work that D’Arcy Thompson had published in On Growth and Form in 1917. In his now-famous paper of 1952 Turing solved his own ‘Equation of Morphogenesis’ in two dimensions, and demonstrated a solution that could explain the ‘dappling’—the black-and-white patterns—on cows. The next step was for me to solve Turing’s equation in three dimensions. The two-dimensional case concerns only surface features of organisms, such as dappling, spots, and stripes, whereas the three-dimensional version concerns the overall shape of an organism. In 1953 I joined Turing as a research student in the University of Manchester, and he set me the task of solving his equation in three dimensions. A remarkable journey of collaboration began. Turing chatted to me in a very friendly fashion.

High-Resolution Thunderstorm Modeling

2020 ◽  
Author(s):  
Leigh Orf
Keyword(s):  
Three Dimensional ◽  
Simulated Data ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Computing Power ◽  
Steady Growth ◽  
Microphysical Processes ◽  
Computational Resources ◽  
Advanced Computing ◽  
Atmospheric Phenomena

Since the dawn of the digital computing age in the mid-20th century, computers have been used as virtual laboratories for the study of atmospheric phenomena. The first simulations of thunderstorms captured only their gross features, yet required the most advanced computing hardware of the time. The following decades saw exponential growth in computational power that was, and continues to be, exploited by scientists seeking to answer fundamental questions about the internal workings of thunderstorms, the most devastating of which cause substantial loss of life and property throughout the world every year. By the mid-1970s, the most powerful computers available to scientists contained, for the first time, enough memory and computing power to represent the atmosphere containing a thunderstorm in three dimensions. Prior to this time, thunderstorms were represented primarily in two dimensions, which implicitly assumed an infinitely long cloud in the missing dimension. These earliest state-of-the-art, fully three-dimensional simulations revealed fundamental properties of thunderstorms, such as the structure of updrafts and downdrafts and the evolution of precipitation, while still only roughly approximating the flow of an actual storm due computing limitations. In the decades that followed these pioneering three-dimensional thunderstorm simulations, new modeling approaches were developed that included more accurate ways of representing winds, temperature, pressure, friction, and the complex microphysical processes involving solid, liquid, and gaseous forms of water within the storm. Further, these models also were able to be run at a resolution higher than that of previous studies due to the steady growth of available computational resources described by Moore’s law, which observed that computing power doubled roughly every two years. The resolution of thunderstorm models was able to be increased to the point where features on the order of a couple hundred meters could be resolved, allowing small but intense features such as downbursts and tornadoes to be simulated within the parent thunderstorm. As model resolution increased further, so did the amount of data produced by the models, which presented a significant challenge to scientists trying to compare their simulated thunderstorms to observed thunderstorms. Visualization and analysis software was developed and refined in tandem with improved modeling and computing hardware, allowing the simulated data to be brought to life and allowing direct comparison to observed storms. In 2019, the highest resolution simulations of violent thunderstorms are able to capture processes such as tornado formation and evolution which are found to include the aggregation of many small, weak vortices with diameters of dozens of meters, features which simply cannot not be simulated at lower resolution.

Dimensional Quantification of Embedded Voids or Objects in Three Dimensions Using X-Ray Tomography

2012 ◽  
Vol 18 (2) ◽  
pp. 390-398 ◽  
Author(s):  
Brian M. Patterson ◽  
Juan P. Escobedo-Diaz ◽  
Darcie Dennis-Koller ◽  
Ellen Cerreta
Keyword(s):  
Digital Imaging ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Post Processing ◽  
X Ray ◽  
Individual Object ◽  
Starting Point ◽  
X Ray Computed ◽  
The Individual ◽  
Processing Steps

AbstractScientific digital imaging in three dimensions such as when using X-ray computed tomography offers a variety of ways to obtain, filter, and quantify data that can produce vastly different results. These opportunities, performed during image acquisition or during the data processing, can include filtering, cropping, and setting thresholds. Quantifying features in these images can be greatly affected by how the above operations are performed. For example, during binarization, setting the threshold too low or too high can change the number of objects as well as their measured diameter. Here, two facets of three-dimensional quantification are explored. The first will focus on investigating the question of how many voxels are needed within an object to have accurate geometric statistics that are due to the properties of the object and not an artifact of too few voxels. These statistics include but are not limited to percent of total volume, volume of the individual object, Feret shape, and surface area. Using simple cylinders as a starting point, various techniques for smoothing, filtering, and other processing steps can be investigated to aid in determining if they are appropriate for a specific desired statistic for a real dataset. The second area of investigation is the influence of post-processing, particularly segmentation, on measuring the damage statistics in high purity Cu. The most important parts of the pathways of processing are highlighted.

scholarly journals Improved Bounds for Incidences Between Points and Circles

2014 ◽  
Vol 24 (3) ◽  
pp. 490-520 ◽  
Author(s):  
MICHA SHARIR ◽  
ADAM SHEFFER ◽  
JOSHUA ZAHL
Keyword(s):  
Three Dimensional ◽  
Combinatorial Geometry ◽  
Two Dimensions ◽  
Three Dimensions ◽  
List Type ◽  
Planar Case ◽  
Constant Degree ◽  
Common Plane ◽  
Formula Group ◽  
Image Position

We establish an improved upper bound for the number of incidences betweenmpoints andncircles in three dimensions. The previous best known bound, originally established for the planar case and later extended to any dimension ≥ 2, isO*(m2/3n2/3+m6/11n9/11+m+n), where theO*(⋅) notation hides polylogarithmic factors. Since all the points and circles may lie on a common plane (or sphere), it is impossible to improve the bound in ℝ3without first improving it in the plane.Nevertheless, we show that if the set of circles is required to be ‘truly three-dimensional’ in the sense that no sphere or plane contains more thanqof the circles, for someq≪n, then for any ϵ > 0 the bound can be improved to\[ O\bigl(m^{3/7+\eps}n^{6/7} + m^{2/3+\eps}n^{1/2}q^{1/6} + m^{6/11+\eps}n^{15/22}q^{3/22} + m + n\bigr). \]For various ranges of parameters (e.g., whenm= Θ(n) andq=o(n7/9)), this bound is smaller than the lower bound Ω*(m2/3n2/3+m+n), which holds in two dimensions.We present several extensions and applications of the new bound.(i)For the special case where all the circles have the same radius, we obtain the improved boundO(m5/11+ϵn9/11+m2/3+ϵn1/2q1/6+m+n).(ii)We present an improved analysis that removes the subpolynomial factors from the bound whenm=O(n3/2−ϵ) for any fixed ϵ < 0.(iii)We use our results to obtain the improved boundO(m15/7) for the number of mutually similar triangles determined by any set ofmpoints in ℝ3.Our result is obtained by applying the polynomial partitioning technique of Guth and Katz using a constant-degree partitioning polynomial (as was also recently used by Solymosi and Tao). We also rely on various additional tools from analytic, algebraic, and combinatorial geometry.

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