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Stability Pattern
Stability may refer to: Mathematics *Stability theory, the study of the stability of solutions to differential equations and dynamical systems ** Asymptotic stability **Exponential stability **Linear stability **Lyapunov stability **Marginal stability **Orbital stability **Structural stability *Stability (probability), a property of probability distributions * Stability (learning theory), a property of machine learning algorithms *Stability, a property of sorting algorithms *Numerical stability, a property of numerical algorithms which describes how errors in the input data propagate through the algorithm * Stability radius, a property of continuous polynomial functions *Stable theory, concerned with the notion of stability in model theory *Stability, a property of points in geometric invariant theory *K-Stability, a stability condition for algebraic varieties. * Bridgeland stability conditions, a class of stability conditions on elements of a triangulated category. * Stability (al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stability Theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp space, Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff convergence, Gromov–Hausdorff distance. In dynamical systems, an orbit (dynamics), orbit is called ''Lyapunov stability, Lyapunov stable'' if the forward orbit of any point is in a small enough neighborhood or it stays in a small (but perhaps, larger) neighborhood. Various criteria have been developed to prove stability or instability of an orbit. Under favorable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangulated Category
In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles generalize the short exact sequences in an abelian category, as well as fiber sequences and cofiber sequences in topology. Much of homological algebra is clarified and extended by the language of triangulated categories, an important example being the theory of sheaf cohomology. In the 1960s, a typical use of triangulated categories was to extend properties of sheaves on a space ''X'' to complexes of sheaves, viewed as objects of the derived category of sheaves on ''X''. More recently, triangulated categories have become objects of interest in their own right. Many equivalences between triangulated categories of different origins have been proved or conjectured. For example, the homological mirror symmetry c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stability Model
In software development, the stability model (SM) is a method for designing and modelling software. It is an extension of object-oriented software design (OOSD) methodology, such as Unified Modeling Language (UML), but adds its own set of rules, guidelines, procedures, and heuristics to achieve more advanced object-oriented (OO) software. The motivation is to achieve a higher level of OO features, such as * Stability: the objects will be stable over time and will not need changes * Reusability: the objects can be reused for various kind of applications * Maintainability: the objects will need the least amount of maintenance Principles The design tries to make use of common sense while guiding through the process of SM based design. It will need minimum amount of rampup time for people to understand new applications and objects once the process and methodology is kept in mind. The stability model is built using three main concepts - * Enduring business themes (EBT) * Business ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slope Stability
Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement; the opposite condition is called slope instability or slope failure. The stability condition of slopes is a subject of study and research in soil mechanics, geotechnical engineering, and engineering geology. Analyses are generally aimed at understanding the causes of an occurred slope failure, or the factors that can potentially trigger a slope movement, resulting in a landslide, as well as at preventing the initiation of such movement, slowing it down or arresting it through mitigation countermeasures. The stability of a slope is essentially controlled by the ratio between the available shear strength and the acting shear stress, which can be expressed in terms of a safety factor if these quantities are integrated over a potential (or actual) sliding surface. A slope can be globally stable if the safety factor, computed along any potential sliding surface running from the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stability Conditions (watercraft)
The stability conditions of watercraft are the various standard loading configurations to which a ship, boat, or offshore platform may be subjected. They are recognized by classification societies such as Det Norske Veritas, Lloyd's Register and American Bureau of Shipping (ABS). Classification societies follow rules and guidelines laid down by International Convention for the Safety of Life at Sea (SOLAS) conventions, the International Maritime Organization and laws of the country under which the vessel is flagged, such as the Code of Federal Regulations. Stability is normally broken into two distinct types: intact and damaged. Intact stability The vessel is in normal operational configuration. The hull is not breached in any compartment. The vessel will be expected to meet various stability criteria such as GMt (metacentric height), area under the GZ (righting lever) curve, range of stability, trim, etc. Intact conditions Lightship or Light Displacement The vessel is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit Of Positive Stability
In sailing, the limit of positive stability (LPS) or angle of vanishing stability (AVS) is the angle from the vertical at which a boat will no longer stay upright but will capsize, becoming inverted, or turtled. For example, if a boat with an LPS of 120 degrees rolls past this point, i.e. its mast is already at an angle of 30 degrees below the water, it will continue to roll and be completely upside down in the water. Except for dinghy sailboats and multihulls, most larger sailboats (monohull keelboats) have lead or other heavy materials in their keel at the bottom of their hulls to keep them from capsizing or turtling. The LPS was a part of the Offshore Racing Rules and is used to measure how stable or seaworthy a sailboat is. The modern offshore racing rules published by the International Sailing Federation may also use the measurement. See also * Angle of loll * Capsizing * Kayak roll * Metacentric height * Naval architecture * Initial stability – concerning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ship Stability
Ship stability is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves, whether intact or damaged. Stability calculations focus on center of mass#center of gravity, centers of gravity, buoyancy, centers of buoyancy, the metacenters of vessels, and on how these interact. History Ship stability, as it pertains to naval architecture, has been taken into account for hundreds of years. Historically, ship stability calculations relied on rule of thumb calculations, often tied to a specific system of measurement. Some of these very old equations continue to be used in naval architecture books today. However, the advent of calculus-based methods of determining stability, particularly Pierre Bouguer's introduction of the concept of the metacenter in the 1740s ship model basin, allow much more complex analysis. Master shipbuilders of the past used a system of adaptive and variant design. Ships were often copied from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relaxed Stability
In aviation, an aircraft is said to have relaxed stability if it has low or negative stability. An aircraft with negative stability will have a tendency to change its pitch and bank angles spontaneously. An aircraft with negative stability cannot be trimmed to maintain a certain attitude, and will, when disturbed in pitch or roll, continue to pitch or roll in the direction of the disturbance at an ever-increasing rate. This can be contrasted with the behaviour of an aircraft with positive stability, which can be trimmed to fly at a certain attitude, which it will continue to maintain in the absence of control input, and, if perturbed, will oscillate in simple harmonic motion on a decreasing scale around, and eventually return to, the trimmed attitude. A positively stable aircraft will also resist any bank movement. A Cessna 152 is an example of a stable aircraft. Similarly, an aircraft with neutral stability will not return to its original attitude without control input, but w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nyquist Stability Criterion
In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer at Siemens in 1930 and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, is a graphical technique for determining the stability criterion, stability of a linear dynamical system. Because it only looks at the Nyquist plot of the Open-loop controller, open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed-loop or open-loop system (although the number of each type of right-half-plane Singularity (mathematics), singularities must be known). As a result, it can be applied to systems defined by non-rational functions, such as systems with delays. In contrast to Bode plots, it can handle transfer functions with right half-plane singularities. In addition, there is a natural generalization to more complex systems with M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longitudinal Stability
In flight dynamics, longitudinal stability is the Flight dynamics (fixed-wing aircraft), stability of an aircraft in the longitudinal, or Aircraft principal axes, pitching, plane. This characteristic is important in determining whether an aircraft pilot will be able to control the aircraft in the pitching plane without requiring excessive attention or excessive strength. The longitudinal stability of an aircraft, also called pitch stability, refers to the aircraft's stability in its plane of symmetry about the lateral axis (the axis along the wingspan). It is an important aspect of the handling qualities of the aircraft, and one of the main factors determining the ease with which the pilot is able to maintain level flight. Longitudinal static stability refers to the aircraft's initial tendency on pitching. Dynamic stability refers to whether oscillations tend to increase, decrease or stay constant. Static stability If an aircraft is longitudinally statically stable, a small i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flight Dynamics
Flight dynamics in aviation and spacecraft, is the study of the performance, stability, and control of vehicles flight, flying through the air or in outer space. It is concerned with how forces acting on the vehicle determine its velocity and attitude with respect to time. For a fixed-wing aircraft, its changing Orientation (geometry), orientation with respect to the local air flow is represented by two critical angles, the angle of attack of the wing ("alpha") and the angle of attack of the vertical tail, known as the slip (aerodynamics), sideslip angle ("beta"). A sideslip angle will arise if an aircraft yaws about its centre of gravity and if the aircraft sideslips bodily, i.e. the centre of gravity moves sideways.Flightwise - Volume 2 - Aircraft Stability And Control, Chris Carpenter 1997, Airlife Publishing Ltd., , p.145 These angles are important because they are the principal source of changes in the aerodynamic forces and moments applied to the aircraft. Spacecraft fligh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buckling
In structural engineering, buckling is the sudden change in shape (Deformation (engineering), deformation) of a structural component under Structural load, load, such as the bowing of a column under Compression (physics), compression or the wrinkling of a plate under Shearing (physics), shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have ''buckled''. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column. Buckling may occur even though the Stress (mechanics), stresses that develop in the structure are well below those needed to cause Catastrophic failure, failure in the material of which the structure is composed. Further loading may cause significant and somewhat unpredictable deformations, possibly leading to complete loss of the member's load-carrying capacity. However, if the deformation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
