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Three-dimensional orthogonal coordinate system
Toroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about
Toroidal_coordinates
Coordinate system relative to a torus
}\end{aligned}}} Look up toroidal or poloidal in Wiktionary, the free dictionary. Poloidal–toroidal decomposition Toroidal coordinates Torus Zonal and poloidal
Toroidal and poloidal coordinates
Toroidal_and_poloidal_coordinates
Class of compact connected topological spaces
of the circle, together with an expanding self-immersion. In the toroidal coordinates with radius R {\displaystyle R} , the solenoid can be parametrized
Solenoid_(mathematics)
Topics referred to by the same term
up toroidal in Wiktionary, the free dictionary. Toroidal describes something which resembles or relates to a torus or toroid: Toroidal coordinates, a
Toroidal
Doughnut-shaped surface of revolution
of the polyhedron. The term "toroidal polyhedron" is also used for higher-genus polyhedra and for immersions of toroidal polyhedra, although some authors
Torus
Technique in mathematics for representing solenoidal vector fields
mathematics, a poloidal–toroidal decomposition is a restricted form of the Helmholtz decomposition. It is often used in the spherical coordinates analysis of solenoidal
Poloidal–toroidal decomposition
Poloidal–toroidal_decomposition
2-dimensional orthogonal coordinate system based on Apollonian circles
i.e., the axis connecting the foci. The toroidal coordinates are produced by rotating the bipolar coordinates about the y-axis, i.e., the axis separating
Bipolar_coordinates
Set of coordinates where the coordinate hypersurfaces all meet at right angles
with the exception of toroidal), and the Helmholtz equation is separable in 11 orthogonal coordinate systems. Orthogonal coordinates never have off-diagonal
Orthogonal_coordinates
Partial differential equations
cylindrical coordinates spherical coordinates Prolate spheroidal coordinates Oblate spheroidal coordinates Parabolic coordinates Toroidal coordinates Bispherical
Green's function for the three-variable Laplace equation
Green's_function_for_the_three-variable_Laplace_equation
Topics referred to by the same term
cylindrical coordinate system ρ, a term in toroidal coordinates ρ, magnetic coordinates in toroidal and poloidal coordinates ρ, spectral radius of a square matrix
Rho_(disambiguation)
Experimental fusion reactor in the United Kingdom
compact toroid class. Taylor went on to study the ballooning transformation, a problem that was occurring in the latest high-performance toroidal machines
ZETA_(fusion_reactor)
spherical harmonics, now that we view the equations in terms of toroidal coordinates, whole new symmetries of Legendre functions arise. For associated
Whipple_formulae
Torus-shaped vortex in a fluid
A vortex ring, also called a toroidal vortex, is a torus-shaped vortex in a fluid; that is, a region where the fluid mostly spins around an imaginary axis
Vortex_ring
Mathematical object
directions. This means that a 3-sphere is an example of a 3-manifold. In coordinates, a 3-sphere with center (C0, C1, C2, C3) and radius r is the set of all
3-sphere
CERN LHC experiment
The outer toroidal magnetic field is produced by eight very large air-core superconducting barrel loops and two smaller end-caps air toroidal magnets,
ATLAS_experiment
Equilibrium equation
case of toroidal axisymmetry (the case relevant in a tokamak). Taking ( r , θ , z ) {\displaystyle (r,\theta ,z)} as the cylindrical coordinates, the flux
Grad–Shafranov_equation
Experimental tokamak
the first tokamak to utilize superconducting coils to establish both the toroidal and poloidal magnetic fields[citation needed]. EAST followed China's first
Experimental Advanced Superconducting Tokamak
Experimental_Advanced_Superconducting_Tokamak
Directions in a toroidal magnetically confined plasma
magnetic coordinates. However, in the fusion context, usage is restricted to the context of zonal plasma flows and there will, in general, be a toroidal component
Zonal_and_poloidal
Study of geometry using a coordinate system
real number coordinates. Similarly, Euclidean space is given coordinates where every point has three coordinates. The value of the coordinates depends on
Analytic_geometry
Seventeenth letter of the Greek alphabet
coordinate in polar, cylindrical, spherical, and toroidal coordinate systems, and toroidal and poloidal coordinates of the Earth's magnetic field. The correlation
Rho
Geometric model of the planar projection of the physical universe
that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular
Euclidean_plane
Series of 1960s US high-altitude nuclear tests
Map all coordinates in "Operation Fishbowl" using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary
Operation_Fishbowl
Type of polyhedron
{2}}\right)\end{aligned}}} The excavated truncated rhombicuboctahedron is a toroidal polyhedron, constructed from a truncated rhombicuboctahedron with its 12
Truncated_rhombicuboctahedron
Mathematical space with two coordinates
degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional
Two-dimensional_space
Arrangement of plasma formed into a toroidal shape
followed. One magnetic probe measurement found the toroidal magnetic field profile of a spheromak; the toroidal field was zero on axis, rose to a maximum at
Spheromak
Any of the five regular polyhedra
polytopes Prince Rupert's cube Regular polytope Regular skew polyhedron Toroidal polyhedron Gardner (1987): Martin Gardner wrote a popular account of the
Platonic_solid
Mathematical graph relating to chess
listing of which ones do and which do not. When it is modified to have toroidal boundary conditions (meaning that a knight is not blocked by the edge of
Knight's_graph
French tokamak
tokamak of this size with superconducting toroidal magnets, allowing the creation of a strong permanent toroidal magnetic field. After a major upgrade to
WEST_(formerly_Tore_Supra)
Straight figure with zero width and depth
primitive and geometry is established analytically in terms of numerical coordinates. In an axiomatic formulation of Euclidean geometry, such as that of Hilbert
Line_(geometry)
Four-dimensional analog of the icosahedron
Discretising the fibration for the {3, 3, 5}; "Let us now proceed to a toroidal decomposition of the {3, 3, 5} polytope." Coxeter 1970, pp. 19–23, §9.
600-cell
Relation between sides of a right triangle
Cartesian coordinates are not used, for example, if polar coordinates are used in two dimensions or, in more general terms, if curvilinear coordinates are used
Pythagorean_theorem
International nuclear fusion research and engineering megaproject
magnet, poloidal magnets around the edges of the tokamak, 18 D-shaped toroidal-field coils, and correction coils. A solid confinement vessel is also needed
ITER
Surface created by rotating a curve about an axis
surface of revolution when revolved around the x-axis has Cartesian coordinates given by r ( t , θ ) = ⟨ y ( t ) cos ( θ ) , y ( t ) sin ( θ ) ,
Surface_of_revolution
Space with one dimension
is a model of the sphere, two-dimensional with respect to real-number coordinates). For every eigenvector of a linear transformation T on a vector space
One-dimensional_space
Experimental physics device
The Enormous Toroidal Plasma Device (ETPD) is an experimental physics device housed at the Basic Plasma Science Facility at University of California, Los
Enormous Toroidal Plasma Device
Enormous_Toroidal_Plasma_Device
Geometric algorithm
embeddings of a data set into Euclidean space (often low-dimensional) whose coordinates can be computed from the eigenvectors and eigenvalues of a diffusion
Diffusion_map
Flat-sided three-dimensional shape
Timaeus, later soon treatment studied in Euclid's Elements. In Renaissance, toroidal polyhedra were used for sketching on polyhedral's perspective views, skeletal
Polyhedron
Pattern of oscillating motion in a system
standing waves. For an elastic, isotropic, homogeneous sphere, spheroidal, toroidal and radial (or breathing) modes arise. Spheroidal modes only involve P
Normal_mode
Archimedean solid with 62 faces
rotundae between inner pentagons and outer decagons. The remaining part is a toroidal polyhedron. The truncated icosidodecahedron has seven special orthogonal
Truncated_icosidodecahedron
Type of plasma diffusion
neoclassical diffusion is a theoretical description of collisional transport in toroidal plasmas, usually found in tokamaks or stellarators. It is a modification
Neoclassical_transport
Geometric model of the physical space
three-dimensional (3D) space is a mathematical space in which three values (termed coordinates) are required to determine the position of a point. Alternatively, it
Three-dimensional_space
Geometry without using coordinates
axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few
Synthetic_geometry
Archimedean solid with 26 faces
similar name: the nonconvex great rhombicuboctahedron. The Cartesian coordinates for the vertices of a truncated cuboctahedron having edge length 2 and
Truncated_cuboctahedron
Mathematical series
magnets are used in particle accelerators Solid harmonics Toroidal moment Dynamic toroidal dipole Edmonds, A. R. (1960). Angular Momentum in Quantum Mechanics
Multipole_expansion
Equations of fluid dynamics
coordinates, in fact most of the common coordinates systems are orthogonal, including familiar ones like cylindrical and obscure ones like toroidal.
Derivation of the Navier–Stokes equations
Derivation_of_the_Navier–Stokes_equations
Field theory linked to string theory
strings on toroidal backgrounds translates to a generalized coordinate transformation on a doubled spacetime, where one set of its coordinates is dual to
Double_field_theory
Experimental fusion reactor
Massachusetts. In September 2021, the project successfully tested a prototype toroidal high-field coil, achieving a record for high-temperature superconducting
SPARC_(tokamak)
Region within a prokaryotic cell containing genetic material
respectively. The handedness of the toroidal supercoils is opposite to those of plectonemes. Both plectonemes and toroidal supercoils can be either in a free
Nucleoid
Property of a mathematical space
mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of
Dimension
Type of geometry
included the theory of complex projective space, the coordinates used (homogeneous coordinates) being complex numbers. Several major types of more abstract
Projective_geometry
Fundamental study of potential theory
(2000). "Developments in determining the grativational potential using toroidal functions". Astron. Nachr. 321 (5/6): 363–372. Bibcode:2000AN....321..363C
Gravitational_potential
Concept in geometry
In these coordinates, the geodesic distance from z to any other point x ∈ S 2 ( 1 ) {\displaystyle \mathbf {x} \in S^{2}(1)} having coordinates ( φ , θ
Area_of_a_circle
Second stage of the Saturn V, built by North American Aviation
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Besides
S-II
Type of non-Euclidean geometry
line (the x-axis) and after that many choices exist. The Lobachevsky coordinates x and y are found by dropping a perpendicular onto the x-axis. x will
Hyperbolic_geometry
Algebraic variety containing an algebraic torus
obtained by replacing the step of taking a GIT quotient by a quotient stack) Toroidal embedding Cox, David (2003), "What is a toric variety?" (PDF), Topics in
Toric_variety
Nuclear fusion experiment
for the toroidal field coils which was supplied through fifteen iron cores that were spirally wound from a .03 millimeter iron strip. The toroidal field
Small Tight Aspect Ratio Tokamak
Small_Tight_Aspect_Ratio_Tokamak
Dimensionless group in fluid mechanics
equations for the steady axially uniform flow of a Newtonian fluid in a toroidal pipe, obtained by retaining just the leading order curvature effects (i
Dean_number
Fusion power reactor design
ends of the linear tubes. Scyllac (Scylla-closed) was designed to test a toroidal version that would improve confinement a thousandfold. A design mistake
Theta_pinch
Structure formed by double-stranded molecules
will be appropriately altered, making the molecule undergo plectonemic or toroidal superhelical coiling. When the ends of a piece of double stranded helical
Nucleic_acid_double_helix
Archimedean solid with 14 faces
polygonal faces, thirty-six edges, and twenty-four vertices. Cartesian coordinates for the vertices of a truncated cube centered at the origin with edge
Truncated_cube
Limiting set in dynamical systems
systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they
Attractor
Russian nuclear energy research and development laboratory
Institute Tokamak Year Major torus radius (m) Minor plasma column radius (m) Toroidal magnetic field (T) Longitudinal plasma current (MA) Notes R a Bt I TMF
Kurchatov_Institute
Reversed-field pinch device
extremely high current is induced (up to 2 MA); combined with a voltage on the toroidal turn of 20 Volts, 40 MW are dissipated during the discharge, so that heating
Reversed-Field_eXperiment
Russian tokamak
right path. In the original (circular cross-section with limiter) shape, a toroidal chamber design, it had a major radius of 2.43 m and minor radius 0.7 m
T-15_(reactor)
Compact astronomical body
Eddington limit are often referred to as polish donuts due to their thick, toroidal shape that resembles that of a donut. Quasar accretion disks are expected
Black_hole
diffeomorphic to a toroidal cylinder T m − r × R r {\displaystyle T^{m-r}\times \mathbb {R} ^{r}} . Integrable system Action-angle coordinates Nambu mechanics
Superintegrable Hamiltonian system
Superintegrable_Hamiltonian_system
Church in Manhattan, New York
experience the interconnectedness of all beings and things in the form of a "toroidal fountain and drain of self-illuminating love energy, a cellular node or
Chapel_of_Sacred_Mirrors
Branch of mathematics
algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study
Algebraic_geometry
Mathematical object studied in the field of algebraic geometry
toric varieties (or torus embeddings) gives a way to compactify D / Γ, a toroidal compactification of it. But there are other ways to compactify D / Γ; for
Algebraic_variety
Compromise map projection
torus. Raisz singled it out and named it the "armadillo" projection. The toroidal shape and the angle it is viewed from tend to emphasize continental areas
Armadillo_projection
Algorithm for supervised learning of binary classifiers
occupied an entire room. It had 4 layers with 12,000 weights implemented by toroidal magnetic cores. By the time of its completion, simulation on digital computers
Perceptron
Geometric object with flat sides
others may be tilings of other elliptic, flat or toroidal (p−1)-surfaces – see elliptic tiling and toroidal polyhedron. A polyhedron is understood as a surface
Polytope
Electromagnetic phenomenon
In fact, the spherical harmonic function (sin θ) responsible for such toroidal angular distribution is precisely the l = 1 "p" wave. The total time-average
Dipole
Fusion energy facility in California, USA
economically attractive fusion power plant. The tokamak consists of a toroidal vacuum chamber surrounded by magnetic field coils which contain and shape
DIII-D
Particle accelerator at CERN, Switzerland
of the LHC experiments and the preaccelerators. LHC experiments ATLAS A Toroidal LHC Apparatus CMS Compact Muon Solenoid LHCb LHC-beauty ALICE A Large Ion
Large_Hadron_Collider
Graph-theoretic description of polyhedra
037, hdl:1773/2276, MR 2287486 Erickson, Jeff; Lin, Patrick (2020), "A toroidal Maxwell–Cremona-Delaunay correspondence", in Cabello, Sergio; Chen, Danny
Steinitz's_theorem
Neutrino detector at the South Pole
Symmetric Torus McArdle Laboratory Morgridge Institute for Research Pegasus Toroidal Experiment UW Hospital & Clinics Viaspan WIYN Consortium WiCell Wisconsin
IceCube_Neutrino_Observatory
Global radio telescope array
reveal a helically bent jet and the polarization of its emission suggest a toroidal magnetic field structure. The object is used as calibrator for Sagittarius
Event_Horizon_Telescope
Unbounded quadric surface
1968. Cathedral of Brasília, Brazil, 1970. Hyperboloid water tower with toroidal tank, Ciechanów, Poland, 1972. Roy Thomson Hall, Toronto, Canada, 1982
Hyperboloid
{\displaystyle c_{1},c_{3},c_{5}\neq 0,\ c_{2},c_{4}=0} represents a type of toroidal vortex etc. The homogeneous solution for C = 0 {\displaystyle C=0} as shown
Beltrami_flow
Generalization of the one-dimensional normal distribution to higher dimensions
the coordinates of x {\displaystyle \mathbf {x} } such that the covariance matrix for this subset is positive definite; then the other coordinates may
Multivariate normal distribution
Multivariate_normal_distribution
Relationship between two lines that meet at a right angle
of vectors can be also used to obtain the same result: First, shift coordinates so that the origin is situated where the lines cross. Then define two
Perpendicular
Branch of mathematics
At this time, the recent work of René Descartes introducing analytic coordinates to geometry allowed geometric shapes of increasing complexity to be described
Differential_geometry
Overview of and topical guide to geometry
transformation Möbius transformation Cross-ratio Duality Homogeneous coordinates Pappus's hexagon theorem Incidence Pascal's theorem Affine geometry Affine
Outline_of_geometry
Reflector that has the shape of a paraboloid
produced by rotation Parabolic antenna Parabolic trough Solar furnace Toroidal reflector Tschirnhausen cubic, the caustic of off-axis parallel light rays
Parabolic_reflector
Linear stacking of regular tetrahedra that form helices
Mito is based on a Boerdijk–Coxeter helix. Clifford parallel cell rings Toroidal polyhedron Line group#Helical symmetry Skew apeirogon#Helical apeirogons
Boerdijk–Coxeter_helix
Theoretical framework for strongly magnetized plasmas
Barnes, and A.G. Peeters. Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks. Phys. Plasmas, 18(6):062501, 2011. J.B. Taylor
Gyrokinetics
Mathematics of varieties with integer coordinates
Reuleaux cuboid Cube Octahedron Dodecahedron Icosahedron Pyramid Star Toroidal Ideal Solid of revolution Sphere Great circle Cylinder Cone Four - other-dimensional
Diophantine_geometry
trigonometric forms) Oblate spheroidal chart (rational and trigonometric forms) Toroidal chart Hyperbolic spaces n-dimensional hyperbolic space Hn Upper half-space
List_of_coordinate_charts
Public medical school in Los Angeles, California, US
NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive Hammer Museum Large Plasma Device
David Geffen School of Medicine at UCLA
David_Geffen_School_of_Medicine_at_UCLA
Axisymmetric eigenfunctions
z} direction to be toroidal and θ {\displaystyle \theta } direction to be poloidal, consistent with the convention. Poloidal–toroidal decomposition Woltjer's
Chandrasekhar–Kendall function
Chandrasekhar–Kendall_function
Concept in the physics of electromagnetism
of magnitude (magnetic moment) Moment (physics) Electric dipole moment Toroidal dipole moment Magnetic susceptibility Orbital magnetization Magnetic dipole–dipole
Magnetic_moment
Football stadium in Manchester, England
grass growth with similarities also made to high-tech architecture. The toroidal-shaped stadium roof is held together by a tensioned system, which has been
Etihad_Stadium
scalar function of spatial coordinates. The magnetic flux surfaces are toroidal, with the current being totally toroidal at the core of the torus and
Trisops
Neighborhood of Los Angeles in California, United States
NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive Hammer Museum Large Plasma Device
Westwood,_Los_Angeles
Entertainment and retail complex in Singapore
owned by Temasek Holdings, the state-owned investment company. Jewel's toroidal glass-and-steel façade was designed by a consortium of architects, led
Jewel_Changi_Airport
Detector experiment at CERN
heavy charm and bottom quarks can be identified by reconstructing the coordinates at which they decay. The ITS1 consisted of six layers, listed here outward
ALICE_experiment
of the LHC experiments and the preaccelerators. LHC experiments ATLAS A Toroidal LHC Apparatus CMS Compact Muon Solenoid LHCb LHC-beauty ALICE A Large Ion
MoEDAL_experiment
Branch of mathematics
geometry. The first was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes (1596–1650) and Pierre de Fermat (1601–1665)
Geometry
Graphing calculator software bundled with macOS
variety of samples ranging from differential equations to 3D-rendered Toroids and Lorenz attractors. It is also capable of dealing with functions and
Grapher
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
Girl/Female
Hindu
Male
Norwegian
 Danish and Norwegian form of Old Norse Ãki, Ã…GE means "father."
Boy/Male
Arabic, Muslim
Revelation of the Merciful
Boy/Male
Hindu, Indian, Marathi, Traditional
Salutation
Boy/Male
Hindu
Somebody who gives shelter, One who gives refuge to others, God of wealth, One who protects others, Rite of dependency, Trust on God, One who is dependent on God), Subramaniam Swami
Girl/Female
Biblical
Infirmity, a harp, pardon.
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Lady of the House
Girl/Female
Muslim
Kind affectionate
Girl/Female
American, Australian, British, Christian, Dutch, English, French, German, Hebrew, Japanese, Latin
A Combination of Mary and Ann; Bitter; Sea of Bitterness; Rebelliousness; Wished for Child; Of the Clan Marius
Girl/Female
English
The bird teal; also the blue-green color.
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
a.
Pertaining to the choroid coat.
a.
Spiral in arrangement or action.
a.
Nearly, but not exactly, conical.
a.
Resembling an egg in shape; egg-shaped; ovate; as, an ovoidal apple.
n.
In the theory of gravitation, or of other forces acting in space, a function of the rectangular coordinates which determine the position of a point, such that its differential coefficients with respect to the coordinates are equal to the components of the force at the point considered; -- also called potential function, or force function. It is called also Newtonian potential when the force is directed to a fixed center and is inversely as the square of the distance from the center.
a.
Of, pertaining to, or included by, three lines; as, trilinear coordinates.
n.
The mensuration of such phenomena of earthquakes as can be expressed in numbers, or by their relation to the coordinates of space.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.
a.
Pertaining to, reckoned from, or having a common radiating point; as, polar coordinates.
a.
Alt. of Ovoidal
a.
That can be passed over in a single course; -- said of a curve when the coordinates of the point on the curve can be expressed as rational algebraic functions of a single parameter /.
a.
Same as Conoidal.
a.
Shaped like an egg.
a.
Of, pertaining to, or included by, two lines; as, bilinear coordinates.
a.
Having the planes arranged spirally, so that they incline all to the right (or left) of a vertical line; -- said of certain hemihedral forms.
a.
Resembling a cone; conoidal.
a.
Turning the plane of polarization circularly or spirally to the right or left.
a.
Having the power to produce a purple color; as, the purpurogenous membrane, or choroidal epithelium, of the eye. See Visual purple, under Visual.
a.
Of or pertaining to a zooid; as, a zooidal form.