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Concept in mathematics
In mathematics, the stability radius of an object (system, function, matrix, parameter) at a given nominal point is the radius of the largest ball, centered
Stability_radius
Topics referred to by the same term
algorithm Stability radius, a property of continuous polynomial functions Stable theory, concerned with the notion of stability in model theory Stability, a
Stability
Approach to optimizing robustness to failure
severe uncertainty, in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the parameter
Info-gap_decision_theory
Principle of automotive steering and handling
side, the resulting scrub radius difference is negligible. Negative scrub radius decreases torque steer and improves stability in the event of brake failure
Scrub_radius
Part of mathematics that addresses the stability of solutions
initial data Stability criterion Stability radius – Concept in mathematics Structural stability – Concept in mathematics von Neumann stability analysis –
Stability_theory
Property of a dynamical system where solutions near an equilibrium point remain so
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most
Lyapunov_stability
Rules to predict ionic compounds' crystal structures
ionic radii determines the cation-anion distance, while the cation-anion radius ratio r + / r − {\displaystyle r_{+}/r_{-}} (or r c / r a {\displaystyle
Pauling's_rules
Graphical method of determining the stability of a dynamical system
In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German
Nyquist_stability_criterion
Star in the constellation Perseus
The semimajor axis of their orbit is 1.27 AU, which means the inner stability radius for a hypothetical planet orbiting the pair would be at 4.35 AU. This
12_Persei
Characteristic polynomial whose associated linear system is stable
the open unit disk in the complex plane. Kharitonov region Stability criterion Stability radius Garloff, Jürgen; Wagner, David G. (1996). "Hadamard Products
Stable_polynomial
Region in which an astronomical body dominates the attraction of satellites
orbit. Therefore, for purposes of stability of test particles (for example, of small satellites), the Hill radius at the pericenter distance needs to
Hill_sphere
Subatomic particle with positive charge
energy of the gluon fields that bind the quarks together. The proton charge radius is around 0.841 fm but two different kinds of measurements give slightly
Proton
Science behind the motion of bicycles and motorcycles
crown radius and force generation. Increase the crown radius of the front tire has been shown to decrease the size or eliminate self stability. Increasing
Bicycle and motorcycle dynamics
Bicycle_and_motorcycle_dynamics
Ratio of cation radius to anion radius
repulsion; this occurs when the radius ratio drops below the critical radius ratio for that particular structure. At the stability limit the cation is touching
Cation-anion_radius_ratio
When a system's outputs are bounded for every bounded input
specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO
BIBO_stability
Approach to controller design that explicitly deals with uncertainty
Servomechanism Stable polynomial State space (controls) System identification Stability radius Iso-damping Active disturbance rejection control Quantitative feedback
Robust_control
Phenomenon affecting the orbit of a binary system
may push the satellite outside the Hill sphere. Recently, the Hill-stability radius has been found as a function of satellite inclination, also explains
Kozai_mechanism
Measurement of the initial static stability of a floating body
The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the centre of
Metacentric_height
Critical radius is the minimum particle size from which an aggregate is thermodynamically stable. In other words, it is the lowest radius formed by atoms
Critical_radius
Measure for the size of planets and other Solar System objects
The mean radius or volumetric radius in astronomy is a measure for the size of planets and small Solar System bodies. Alternatively, the closely related
Mean_radius_(astronomy)
Orbital radius at which a satellite might break up due to gravitational force
In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together
Roche_limit
Mathematical optimization theory
satisfy given stability/performance conditions associated with decision x {\displaystyle x} . In words, the robustness (radius of stability) of decision
Robust_optimization
Fracture of the radius bone near the wrist
A distal radius fracture, also known as wrist fracture, is a break of the part of the radius bone which is close to the wrist. Symptoms include pain,
Distal_radius_fracture
Star formation process
{\textstyle \rho (r)} is the density of the gas (at radius r), G is the gravitational constant, and r is the radius. The equilibrium is stable if small perturbations
Jeans_instability
Dynamical system which is neither asymptotically stable nor unstable
being bounded. A marginal system, sometimes referred to as having neutral stability, is between these two types: when displaced, it does not return to near
Marginal_stability
pairs of binary matrices. The joint spectral radius was introduced for its interpretation as a stability condition for discrete-time switching dynamical
Joint_spectral_radius
Type of fibrous joint
flexible enough to allow for rotation of the radius bone during forearm movements. Thus in contrast to the stability provided by the tibiofibular syndesmosis
Syndesmosis
Degree to which disturbing a plasma system at equilibrium will destabilize it
physics, plasma stability concerns the stability properties of a plasma in equilibrium and its behavior under small perturbations. The stability of the system
Plasma_stability
Characterized by some of the outputs or internal states growing without bounds
buckling or crippling. The general field of study is called structural stability. Atmospheric instability is a major component of all weather systems on
Instability
Fluid breakup of a falling stream
by two separate radius components. In this case one is the radius, already discussed, of the stream itself. The other is the radius of curvature of the
Plateau–Rayleigh_instability
When an ecosystem does not drastically change over time even after perturbation
Although the terms community stability and ecological stability are sometimes used interchangeably, community stability refers only to the characteristics
Ecological_stability
lists of smaller objects by observed mean radius. These lists can be sorted according to an object's radius and mass and, for the most massive objects
List of Solar System objects by size
List_of_Solar_System_objects_by_size
Natural satellite orbiting Earth
(Earth radius / Radius of Moon's orbit)2 ] relative to the direct solar illumination that occurs for a full moon. (Earth albedo = 0.367; Earth radius = (polar
Moon
Large self-illuminated object in space
approximately 1.9885×1030 kg. Although the exact values for the luminosity, radius, mass parameter, and mass may vary slightly in the future due to observational
Star
Special class of solitons
{\mathcal {L}}=|\partial _{\mu }\Phi |^{2}-U(|\Phi |)\,} the NTS is a ball with radius R filled with the field Φ = ( ϕ 0 / 2 ) e i ω t {\displaystyle \Phi =(\phi
Non-topological_soliton
{\displaystyle \theta } is the angle between the force applied and the radius The change in radius keeps the vehicle from veering outward and potentially leaving
Cornering_brake_control
Element on a suspension machine
moving back and forth; this motion is constrained by a separate link or radius rod. This is in contrast to the wishbone, which are triangular and have
Control_arm
Classifications systems of distal radius fractures aim to aggregate patterns of injury which behave in predictable ways, to distinguish between conditions
Classification of distal radius fractures
Classification_of_distal_radius_fractures
Region of a star
of radius r, and is approximately the whole star mass for large enough r. This gives the following form of the Schwarzschild criterion for stability against
Radiative_zone
eliminate scrub radius by moving the pivot point of the king pin outboard, in order to improve steering precision and straight line stability. It is typically
Dual_pivot_steering_geometry
Shape of a spinning body of self-gravitating fluid
mass of the spheroid and a ¯ {\displaystyle {\bar {a}}} is the mean radius, the radius of a sphere of the same volume as the spheroid. For a Maclaurin spheroid
Maclaurin_spheroid
Isotope of helium
nucleus size (as charge radius) has been estimated to be 1.67824(83) fm. The nucleus of the helium-4 atom has a type of stability called doubly magic. High-energy
Helium-4
Equilibrium points near two orbiting bodies
at approximately equal distances r from the smaller object, equal to the radius of the Hill sphere, given by: r ≈ R μ 3 3 {\displaystyle r\approx R{\sqrt[{3}]{\frac
Lagrange_point
Chemical element with atomic number 118 (Og)
and the location, the energy, and the time of the decay are measured. Stability of a nucleus is provided by the strong interaction. However, its range
Oganesson
Core of an atom composed of nucleons
of about 27,000 (uranium's atomic radius is about 156 pm (156×10−12 m)) to about 60,000 (hydrogen's atomic radius is about 52.92 pm). The branch of physics
Atomic_nucleus
Simple curve of Euclidean geometry
The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing
Circle
Disked object that eclipsed V1400 Centauri
the most likely hypothesis to date. J1407b's hypothetical disk spans a radius of about 90 million km (0.60 AU; 56 million mi) and consists of many rings
J1407b
Railway relying on adhesion to move trains
minimum radius of curvature is 360 m (1,180 ft). For a modern, exceptionally high-speed train at 80 m/s (290 km/h; 180 mph), the minimum radius would be
Adhesion_railway
Tabular arrangement of the chemical elements
increases in magnitude with the charge and radius of the ion. In Mg+, the outermost orbital (which determines ionic radius) is still 3s, so the hydration enthalpy
Periodic_table
Rotation of a vehicle about its vertical axis
speed around a constant radius, by the relationship tangential speed*yaw velocity = lateral acceleration = tangential speed^2/radius of turn, in appropriate
Yaw_(dynamics)
Theoretical chemical element with atomic number 119 (Uue)
atomic radius to around 240 pm, very close to that of rubidium (247 pm); the metallic radius is also correspondingly lowered to 260 pm. The ionic radius of
Ununennium
Arrangement of mirrors
this is the hemispherical cavity, with one plane mirror and one mirror of radius equal to the cavity length. A common and important design is the confocal
Optical_cavity
Ray tracing technique
resonator consists of two identical facing mirrors of 100% reflectivity and radius of curvature R, separated by some distance d. For the purposes of ray tracing
Ray_transfer_matrix_analysis
Minimised surface of liquid connecting two wetted objects
gravitational acceleration, γ is the surface tension and R is radius of the contact) the stability diagram can be represented by a single closed piecewise curve
Capillary_bridge
Series in chemistry
the relative stabilities of complexes formed by transition metals. In 1953 Harry Irving and Robert Williams observed that the stability of complexes formed
Irving–Williams_series
Periodic table of the elements with eight or more periods
hypothesized to be within an island of stability that is resistant to fission but not to alpha decay. Other islands of stability beyond the known elements may
Extended_periodic_table
Trajectory of Earth around the Sun
sphere of influence) of the Earth is about 1,500,000 kilometers (0.01 AU) in radius, or approximately four times the average distance to the Moon. This is the
Earth's_orbit
Values which describe behavior of a linear electric circuit
coordinates of the circle centre and the associated radius are given by the following equations: Radius r L = | S 12 S 21 | S 22 | 2 − | Δ | 2 | . {\displaystyle
Scattering_parameters
Decrease of ionic radii across the lanthanide series
in ionic radius is smooth and predictable allows for chromatographic separation of lanthanide ions exploiting the fact that complex stability with anionic
Lanthanide_contraction
Potential conditions for extraterrestrial life in binary star systems
found orbiting close to this radius. The planets have semi-major axes that lie between 1.09 and 1.46 times this critical radius. The reason could be that
Habitability of binary star systems
Habitability_of_binary_star_systems
Circular orbit above Earth's Equator and following the direction of Earth's rotation
(22,236 mi) in altitude above Earth's equator, 42,164 km (26,199 mi) in radius from Earth's center, and following the direction of Earth's rotation. An
Geostationary_orbit
Common type of fracture in children
PH; Sivertsen, EA (October 2009). "Distal radius fractures in children: substantial difference in stability between buckle and greenstick fractures".
Torus_fracture
Hypothetical vacuum, less stable than true vacuum
former tends as the cube of the bubble's radius while the latter is proportional to the square of its radius, so there is a critical size R c {\displaystyle
False_vacuum
Executive car produced by Ford (1985–1998)
two parallel cars – while Scorpio buyers valued high-speed stability, a tight turning radius, and a sizable rear seat, American buyers had other requirements
Ford_Scorpio
Meeting point of three tectonic plates
rigid assumption holds very well in the case of oceanic crust, and the radius of the Earth at the equator and poles only varies by a factor of roughly
Triple_junction
Smallest stable circular orbit of a particle
exist. Its radius is r p h = 3 G M c 2 = 1.5 R S . {\displaystyle r_{\mathrm {ph} }=3{\frac {GM}{c^{2}}}={1.5R_{S}}.} The lack of stability inside the
Innermost stable circular orbit
Innermost_stable_circular_orbit
Constants that describe stability of coordination complexes
results in a complex having extra stability. Another example of the effect of ionic radius the steady increase in stability of complexes with a given ligand
Stability constants of complexes
Stability_constants_of_complexes
Chemical element with atomic number 115 (Mc)
and the location, the energy, and the time of the decay are measured. Stability of a nucleus is provided by the strong interaction. However, its range
Moscovium
Type of rechargeable battery
ionic radius of Na+ (116 pm) is substantially larger than that of Fe2+ and Fe3+ (69–92 pm depending on the spin state), whereas the ionic radius of Li+
Sodium-ion_battery
Mathematical expression for the stability of rocks in water currents
used to calculate the stability of armourstone in flowing water environments. For the assessment of granular material stability in a current, the Shields
Izbash_formula
Set of adjacent groups
elements by abundance (in human body) by atomic properties by isotope stability by symbol Properties of elements Relative atomic mass Crystal structure
Block_(periodic_table)
List of largest planets by size
largest exoplanets so far discovered, in terms of physical size, ordered by radius. This list of extrasolar objects may and will change over time due to diverging
List_of_largest_exoplanets
Concept in differential equation mathematics
here ρ ( A ( Δ t ) ) {\displaystyle \rho (A(\Delta t))} is the spectral radius of the update matrix A ( Δ t ) {\displaystyle A(\Delta t)} . For the linear
Newmark-beta_method
Type of particle accelerator
accurately described as a series of arcs of constant radius. The particles' speed, and therefore orbital radius, only increases at the accelerating gaps. Away
Cyclotron
Four wheel steering system
wheels to a maximum of 15°, or 12° in trailer mode, decreasing the turning radius as much as 21%. At higher speeds the system will turn the rear wheels slightly
Quadrasteer
Particle with size less than 100 nm
Nucleation, for example, is vital to the size of the nanoparticle. A critical radius must be met in the initial stages of solid formation, or the particles will
Nanoparticle
area of a fluid thread undergoing breakup, the first radius of curvature is smaller than the radius of curvature in the thickened area, leading to a pressure
Fluid_thread_breakup
Eight bones that make up the wrist
tetrapods, the carpus is the sole cluster of bones in the wrist between the radius and ulna and the metacarpus. The bones of the carpus do not belong to individual
Carpal_bones
Chemical element with atomic number 117 (Ts)
"island of stability", a concept that explains why some superheavy elements are more stable despite an overall trend of decreasing stability for elements
Tennessine
US - UK thermonuclear warhead of the 1970s
it detonates the warhead before it can leave the kill radius of the target. The kill radius is a sphere, not a circle. In comparison, a warhead without
W76
Type of map used in mathematics, particularly dynamical systems
{\displaystyle \theta } increases monotonically and at constant rate. The radius r {\displaystyle r} tends to the equilibrium r ¯ = 1 {\displaystyle {\bar
Poincaré_map
Innermost part of Earth, a solid ball of iron-nickel alloy
primarily a solid ball with a radius of about 1,230 km (760 mi), which is about 20% of Earth's radius or 70% of the Moon's radius. As recently as February
Earth's_inner_core
Technique in digital signal processing
_{0}}} and e − j ω 0 {\displaystyle e^{-j\omega _{0}}} , on a circle of unit radius centered on the origin of the complex Z-transform plane. This property indicates
Goertzel_algorithm
Theorem in general relativity
and radius that must be satisfied for static, spherically symmetric matter configurations under certain conditions. In particular, for an areal radius R
Buchdahl's_theorem
Maximum mass of a stable white dwarf star
done, the model radius still decreases with mass, but becomes zero at Mlimit. This is the Chandrasekhar limit. The curves of radius against mass for
Chandrasekhar_limit
Exoplanet orbiting Kepler-16
discovery team. Kepler-16b is also unusual in that it falls inside the radius that was thought to be the inner limit for planet formation in a binary
Kepler-16b
Light boat that is paddled
of trade-offs: directional stability ("tracking") vs maneuverability; stability vs speed; and primary vs secondary stability. Multihull kayaks face a different
Kayak
Knife used to remove body hair
larger radius of curvature, also called the "belly", and the area between the ridge and the cutting edge which is more hollow i.e. with a smaller radius of
Straight_razor
the conversion of the BL 15-pounder to BLC 15-pounder. Calibre radius head: the radius of a circle with the curve of the shell's nose on its circumference
Glossary of British ordnance terms
Glossary_of_British_ordnance_terms
Measurement of viscosity in fluid dynamics
investigated the stability of Couette flow in a ground-breaking paper. Taylor's paper became a cornerstone in the development of hydrodynamic stability theory and
Taylor–Couette_flow
Shape containing unit line segments in all directions
segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane, or a ball of radius 1/2 in three-dimensional space, forms a Besicovitch
Kakeya_set
Extrasolar planet orbiting Gliese 876
indirectly through its gravitational effects on the star, properties such as its radius, composition, and temperature are unknown. Assuming a composition similar
Gliese_876_b
Chemical element with atomic number 116 (Lv)
and the location, the energy, and the time of the decay are measured. Stability of a nucleus is provided by the strong interaction. However, its range
Livermorium
Condensed matter phenomenon; vortex-like magnetic quasiparticle
{\displaystyle \theta (r)} ) and the in-plane magnetic variable independent of the radius ( ϕ ( α ) {\displaystyle \phi (\alpha )} ). Then the topological skyrmion
Magnetic_skyrmion
Country in Southeastern Europe
battleground for ancient Thracians, Persians, Celts, and Macedonians; stability came when the Roman Empire conquered the region in AD 45. After the Roman
Bulgaria
Russian chemist (1834–1907)
elements by abundance (in human body) by atomic properties by isotope stability by symbol Properties of elements Relative atomic mass Crystal structure
Dmitri_Mendeleev
Chemical element with atomic number 110 (Ds)
and the location, the energy, and the time of the decay are measured. Stability of a nucleus is provided by the strong interaction. However, its range
Darmstadtium
Chemical element with atomic number 47 (Ag)
second and third ionisation energies than copper and gold (showing the stability of the 4d orbitals), so that the chemistry of silver is predominantly
Silver
Single yellow-hued star in the constellation Cetus
age, mass, radius and luminosity of Tau Ceti can be estimated. However, using an astronomical interferometer, measurements of the radius of the star
Tau_Ceti
Terrestrial planet orbiting the star Proxima Centauri
terrestrial planet with a minimum mass of 1.06 M🜨 and a slightly larger radius than that of Earth. The planet orbits within the habitable zone of its parent
Proxima_Centauri_b
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STABILITY RADIUS
STABILITY RADIUS
STABILITY RADIUS
STABILITY RADIUS
STABILITY RADIUS
STABILITY RADIUS
STABILITY RADIUS
STABILITY RADIUS
STABILITY RADIUS
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