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Perturbation Methods In Fluid Mechanics
Perturbation or perturb may refer to: * Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial deposits over time * Perturbation (astronomy), alterations to an object's orbit (e.g., caused by gravitational interactions with other bodies) * Perturbation theory (quantum mechanics), a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one * Perturbation (biology), an alteration of the function of a biological system, induced by external or internal mechanisms * Perturbation function, mathematical function which relates the primal and dual problems See also * Annoy, annoyance * Disturbance (other) * Non-perturbative In mathematics and physics, a non-perturbative function or process is one that cannot be described by perturbation theory. An example is the function : f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation (geology)
Perturbation (from Latin: ''perturbare'' "to confuse, disorder, disturb", from ''per''- "through" + ''turbare'' "disturb, confuse," from ''turba'' "turmoil, crowd") is a set of pedology (soil study) and sedimentary geology processes relating to changes in the nature of water-borne alluvial sediments and ''in situ'' soil deposits over time. * Pedoturbation (from Greek: πέδον (''pédon''), "soil") involves mixing between soil horizons, and is an important factor in soil formation. Pedoturbation includes churning clays, cryoturbation, and bioturbation. Types of bioturbation include faunal pedoturbation (animal burrowing), and floral pedoturbation (root growth, tree-uprootings). Pedoturbation transforms soils through destratification, mixing, and sorting, as well as creating preferential flow paths for soil gas and infiltrating water. The zone of active bioturbation is termed the soil biomantle. * Soil perturbation that is not pedoturbation. Precipitation of surface salts al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation (astronomy)
In astronomy, perturbation is the complex motion of a massive body subjected to forces other than the gravitational attraction of a single other massive body. The other forces can include a third (fourth, fifth, etc.) body, resistance, as from an atmosphere, and the off-center attraction of an oblate or otherwise misshapen body. Introduction The study of perturbations began with the first attempts to predict planetary motions in the sky. In ancient times the causes were unknown. Isaac Newton, at the time he formulated his laws of motion and of gravitation, applied them to the first analysis of perturbations, recognizing the complex difficulties of their calculation. Many of the great mathematicians since then have given attention to the various problems involved; throughout the 18th and 19th centuries there was demand for accurate tables of the position of the Moon and planets for marine navigation. The complex motions of gravitational perturbations can be broken down. The hy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory (quantum Mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system. Approximate Hamiltonians Perturbation theory is an important tool for de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation (biology)
In ecology, a disturbance is a temporary change in environmental conditions that causes a pronounced change in an ecosystem. Disturbances often act quickly and with great effect, to alter the physical structure or arrangement of biotic and abiotic elements. A disturbance can also occur over a long period of time and can impact the biodiversity within an ecosystem. Major ecological disturbances may include fires, flooding, storms, insect outbreaks and trampling. Earthquakes, various types of volcanic eruptions, tsunami, firestorms, impact events, climate change, and the devastating effects of human impact on the environment ( anthropogenic disturbances) such as clearcutting, forest clearing and the introduction of invasive species can be considered major disturbances. Not only invasive species can have a profound effect on an ecosystem, but also naturally occurring species can cause disturbance by their behavior. Disturbance forces can have profound immediate effects on ecosy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Function
In mathematical optimization, the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any such function defines a perturbation of the initial problem. In many cases this takes the form of shifting the constraints. In some texts the value function is called the perturbation function, and the perturbation function is called the bifunction. Definition Given two dual pairs of separated locally convex spaces \left(X,X^*\right) and \left(Y,Y^*\right). Then given the function f: X \to \mathbb \cup \, we can define the primal problem by :\inf_ f(x). \, If there are constraint conditions, these can be built into the function f by letting f \leftarrow f + I_\mathrm where I is the characteristic function. Then F: X \times Y \to \mathbb \cup \ is a ''perturbation function'' if and only if F(x,0) = f(x). Use in duality The duality gap is the difference of the right and left hand side of the inequality :\sup_ -F^*(0,y^*) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annoy
Annoyance is an unpleasant mental state that is characterized by irritation and distraction from one's conscious thinking. It can lead to emotions such as frustration and anger. The property of being easily annoyed is called irritability. Psychology Various reasons exist for why one finds particular stimuli annoying. Measurement of annoyance is highly subjective. As an attempt at measurement, psychological studies on annoyance often rely on their subjects' own ratings of levels of annoyance on a scale. Any kind of stimuli can cause annoyance, such as getting poked in the side or listening to a song repeatedly. Many stimuli that one is at first neutral to, or even finds pleasant, can turn into annoyances from repeated continued exposure. One can often encounter annoyance factors in media, including popular music, memes, commercials, and advertising jingles, which by their nature are continually repeated over a period of weeks or months. A study published in the ''Internat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annoyance
Annoyance is an unpleasant mental state that is characterized by irritation and distraction from one's conscious thinking. It can lead to emotions such as frustration and anger. The property of being easily annoyed is called irritability. Psychology Various reasons exist for why one finds particular stimuli annoying. Measurement of annoyance is highly subjective. As an attempt at measurement, psychological studies on annoyance often rely on their subjects' own ratings of levels of annoyance on a scale. Any kind of stimuli can cause annoyance, such as getting poked in the side or listening to a song repeatedly. Many stimuli that one is at first neutral to, or even finds pleasant, can turn into annoyances from repeated continued exposure. One can often encounter annoyance factors in media, including popular music, memes, commercials, and advertising jingles, which by their nature are continually repeated over a period of weeks or months. A study published in the ''Internatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disturbance (other)
Disturbance and its variants may refer to: Math and science * Disturbance (ecology), a temporary change in average environmental conditions that causes a pronounced change in an ecosystem * Disturbance (geology), linear zone of faults and folds * Sudden ionospheric disturbance, an abnormally high plasma density in the D region of the ionosphere caused by a solar flare * Disturbance (statistics), the deviation of the observed value from the (unobservable) true function value * Serious emotional disturbance, a mental illness Arts and media Film * Disturbance (2014 film), a section, and former title, of the film ''Tales of the Supernatural'' * ''Disturbance'' (1942 film), an Italian drama film * ''Domestic Disturbance'', a 2001 American psychological thriller film Music * ''Disturbance'' (Concord Dawn album), 2001 * ''Disturbance'' (Test Dept. album), 2019 * "Disturbance" (BoA song) , a 2013 digital single by South Korean singer BoA * "Disturbance," a song by Eyehategod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
