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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. Toroidal coordinates Torus Zonal and poloidal Poloidal–toroidal decomposition Zonal
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
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
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
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)
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
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
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
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
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
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)
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
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
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
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 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
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
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)
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
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 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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
System consisting of two black holes in close orbit around each other
Simulations as of 2011[update] had not produced any event horizons with toroidal topology (ring-shaped). Some researchers suggested that it would be possible
Binary_black_hole
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
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
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
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
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
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
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
Quantity in electromagnetism
loop of B {\displaystyle \mathbf {B} } flux (as would be produced in a toroidal inductor) is qualitatively the same as the B {\displaystyle \mathbf {B}
Magnetic_vector_potential
Symmetric bipartite cubic graph with 16 vertices and 24 edges
subgraphs' crossing numbers differ from it by two or more. However, it is a toroidal graph: it has an embedding in the torus in which all faces are hexagons
Möbius–Kantor_graph
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
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
Simulation of a dynamical system of particles
conditions of these cosmological simulations are usually periodic (or toroidal), so that one edge of the simulation volume matches up with the opposite
N-body_simulation
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
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
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
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
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
Hospital in Los Angeles, California
NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive Hammer Museum Large Plasma Device
Ronald Reagan UCLA Medical Center
Ronald_Reagan_UCLA_Medical_Center
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
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
Measure of positive and negative charges
electric dipole moment Nuclear electric dipole moment Toroidal dipole moment Dynamic toroidal dipole Multipole expansion Multipole moments Solid harmonics
Electric_dipole_moment
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
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
Home stadium of the UCLA Bruins and site of the Rose Bowl Game. Pasadena, California
NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive Hammer Museum Large Plasma Device
Rose_Bowl_(stadium)
Certain vector fields are the sum of an irrotational and a solenoidal vector field
condition and the Coulomb gauge. An alternative is to use the poloidal–toroidal decomposition. The Helmholtz theorem is of particular interest in electrodynamics
Helmholtz_decomposition
Curve that winds around a central point
two-dimensional, or plane, spiral may be easily described using polar coordinates, where the radius r {\displaystyle r} is a monotonic continuous function
Spiral
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
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
Fusion research facility in Oxford, United Kingdom
is to generate a poloidal field that mixes with the one supplied by the toroidal magnets to produce the twisted field inside the plasma. The current also
Joint_European_Torus
Space of complex matrices with positive definite imaginary part
arithmetic subgroup, one can choose smooth toroidal compactifications with boundary a divisor. Among the best-known toroidal compactifications for the full Siegel
Siegel_upper_half-space
UK experimental fusion power reactor
shaped more like a cored apple than the conventional, doughnut-shaped toroidal design used by experiments such as ITER. Spherical tokamaks are more efficient
Mega_Ampere_Spherical_Tokamak
Archimedean solid with 14 faces
squares and eight hexagons, leaving out six square pyramids. The Cartesian coordinates of the vertices of a truncated octahedron with edge length 1 are all
Truncated_octahedron
Hospital 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
UCLA Santa Monica Medical Center
UCLA_Santa_Monica_Medical_Center
Graduate professional school of the University of California, Los Angeles
NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive Hammer Museum Large Plasma Device
UCLA School of Education and Information Studies
UCLA_School_of_Education_and_Information_Studies
Convex polyhedron with 14 triangle faces
has media related to Triaugmented triangular prism. Császár polyhedron – Toroidal polyhedron with 14 triangle faces Steffen's polyhedron – Flexible polyhedron
Triaugmented_triangular_prism
Class of data processing algorithms
by a vector addition modulo the simulation space's dimension to realize toroidal topologies: I c = { j ∣ ∃ x ∈ s : j = ( ( c + x ) mod ( n 1 , … , n k )
Iterative_Stencil_Loops
Garden in Los Angeles, 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
Hannah_Carter_Japanese_Garden
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
City_of_Manchester_Stadium
American public research university
NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive Hammer Museum Large Plasma Device
University of California, Los Angeles
University_of_California,_Los_Angeles
Archive for film and television production
NanoSystems Embedded Network Sensing Study of Women Chicano Studies Enormous Toroidal Plasma Device Film and Television Archive Hammer Museum Large Plasma Device
UCLA Film & Television Archive
UCLA_Film_&_Television_Archive
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
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
Boy/Male
Tamil
Hardik | ஹாரà¯à®¤à®¿à®•Â
Heartfelt, Affectionate, Cordial, Heart full
Boy/Male
Norse Scandinavian
A mythical monster wolf.
Boy/Male
American, British, English
Reddish Brown Hair
Surname or Lastname
English
English : nickname from Old French maquerel ‘bawd’.English : from Middle English makerel ‘mackerel’ (the fish), hence a metonymic occupational name for a fisherman or a seller of these fish.English : Possibly also from Middle English mackerel ‘red scorch marks (on the skin)’, perhaps a descriptive nickname for someone with a noticeable birthmark.
Girl/Female
German
Spear Ruler
Boy/Male
Indian
Unclothed
Boy/Male
Muslim/Islamic
Shorter Smaller, Junior
Girl/Female
Hindu, Indian, Marathi
Goddess of Birth and Death
Girl/Female
Tamil
Thanishka | தாநீஷà¯à®•à®¾
Goddess of gold and Angel
Girl/Female
Tamil
Tamalika | தமாலிகா
Belonging to a place full of Tamal
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
TOROIDAL COORDINATES
n.
The mensuration of such phenomena of earthquakes as can be expressed in numbers, or by their relation to the coordinates of space.
a.
Nearly, but not exactly, conical.
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, pertaining to, or included by, two lines; as, bilinear coordinates.
a.
Turning the plane of polarization circularly or spirally to the right or left.
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.
Shaped like an egg.
a.
Of, pertaining to, or included by, three lines; as, trilinear coordinates.
a.
Pertaining to, reckoned from, or having a common radiating point; as, polar coordinates.
a.
Spiral in arrangement or action.
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 /.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.
a.
Of or pertaining to a zooid; as, a zooidal form.
a.
Pertaining to the choroid coat.
a.
Same as Conoidal.
a.
Resembling a cone; conoidal.
a.
Resembling an egg in shape; egg-shaped; ovate; as, an ovoidal apple.
a.
Alt. of Ovoidal
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.