Stellar Pulsation

picture info	Stellar Pulsation Stellar pulsations are caused by expansions and contractions in the outer layers as a star seeks to maintain equilibrium. These fluctuations in stellar radius cause corresponding changes in the luminosity of the star. Astronomers are able to deduce this mechanism by measuring the spectrum and observing the Doppler effect. Many intrinsic variable stars that pulsate with large amplitudes, such as the classical Cepheids, RR Lyrae stars and large-amplitude Delta Scuti stars show regular light curves. This regular behavior is in contrast with the variability of stars that lie parallel to and to the high-luminosity/low-temperature side of the classical variable stars in the Hertzsprung–Russell diagram. These giant stars are observed to undergo pulsations ranging from weak irregularity, when one can still define an average cycling time or period, (as in most RV Tauri and semiregular variables) to the near absence of repetitiveness in the irregular variables. The W Virginis variab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Delta Cephei Lightcurve Delta commonly refers to: * Delta (letter) (Δ or δ), a letter of the Greek alphabet * River delta, at a river mouth * D ( NATO phonetic alphabet: "Delta") * Delta Air Lines, US * Delta variant of SARS-CoV-2 that causes COVID-19 Delta may also refer to: Places Canada * Delta, British Columbia Delta (electoral district), a federal electoral district Delta (provincial electoral district) * Delta, Ontario United States * Mississippi Delta * Delta, Alabama * Delta Junction, Alaska * Delta, Colorado * Delta, Illinois * Delta, Iowa * Delta, Kentucky * Delta, Louisiana * Delta, Missouri * Delta, North Carolina * Delta, Ohio * Delta, Pennsylvania * Sacramento–San Joaquin River Delta, California * Delta, Utah * Delta, Wisconsin, a town * Delta (community), Wisconsin * Delta County (other) Elsewhere * Delta Island, Antarctica * Delta Stream, Antarctica * Delta, Minas Gerais, Brazil * Nile Delta, Egypt * Delta, Thessaloniki, Greece * Delta State, Nigeria * Delta, A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Irregular Variable An irregular variable is a type of variable star in which variations in brightness show no regular periodicity. There are two main sub-types of irregular variable: eruptive and pulsating. Eruptive irregular variables are divided into three categories: * Group I variables are split into subgroups IA (spectral types O to A) and IB (spectral types F through M). * Orion variables, GCVS type IN (irregular and nebulous), indigenous to star-forming regions, may vary by several magnitudes with rapid changes of up to 1 magnitude in 1 to 10 days, are similarly divided by spectral type into subgroups INA and INB, but with the addition of another subgroup, INT, for T Tauri stars, or INT(YY) for YY Orionis stars. * The third category of eruptive irregulars are the IS stars, which show rapid variations of 0.5 to 1 magnitude in a few hours or days; again, these come in subgroups ISA and ISB. Pulsating irregular giants or supergiants, called slow irregular variable A slow irregular variable ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Nuclear Burning Time Scale Nuclear may refer to: Physics Relating to the nucleus of the atom: Nuclear engineering Nuclear physics Nuclear power Nuclear reactor Nuclear weapon Nuclear medicine Radiation therapy Nuclear warfare Mathematics Nuclear space Nuclear operator Nuclear congruence Nuclear C-algebra Biology Relating to the nucleus of the cell: Nuclear DNA Society Nuclear family, a family consisting of a pair of adults and their children Music "Nuclear" (band), group music. * "Nuclear" (Ryan Adams song), 2002 "Nuclear", a song by Mike Oldfield from his ''Man on the Rocks'' album ''Nu.Clear'' (EP) by South Korean girl group CLC See also Nucleus (other) Nucleolus Nucleation Nucleic acid Nucular ''Nucular'' is a common, proscribed pronunciation of the word " nuclear". It is a rough phonetic spelling of . The ''Oxford English Dictionary''s entry dates the word's first published appearance to 1943. Dictionary notes This is one of two co ... * {{Disamb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Ordinary Differential Equations In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Normal Modes A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. The most general motion of a system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. General definitions Mode In the wave theory of physics and engineering, a mode in a dynamical system is a standing wave state of ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Poincaré–Lindstedt Method In perturbation theory, the Poincaré–Lindstedt method or Lindstedt–Poincaré method is a technique for uniformly approximating periodic solutions to ordinary differential equations, when regular perturbation approaches fail. The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear problems with finite oscillatory solutions. The method is named after Henri Poincaré, and Anders Lindstedt. Example: the Duffing equation The undamped, unforced Duffing equation is given by :\ddot + x + \varepsilon\, x^3 = 0\, for ''t'' > 0, with 0 < ''ε'' ≪ 1.J. David Logan. ''Applied Mathematics'', Second Edition, John Wiley & Sons, 1997. . Consider initial conditions : $x(0) = 1,\,$ $\dot x(0) = 0.\,$ A perturbation-serie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Plasma Physics Plasma ()πλάσμα , Henry George Liddell, Robert Scott, ''A Greek English Lexicon'', on Perseus is one of the four fundamental states of matter. It contains a significant portion of charged particles – ions and/or electron s. The presence of these charged particles is what primarily sets plasma apart from the other fundamental states of matter. It is the most abundant form of ordi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Oceanography Oceanography (), also known as oceanology and ocean science, is the scientific study of the oceans. It is an Earth science, which covers a wide range of topics, including ecosystem dynamics; ocean currents, waves, and geophysical fluid dynamics; plate tectonics and the geology of the sea floor; and fluxes of various chemical substances and physical properties within the ocean and across its boundaries. These diverse topics reflect multiple disciplines that oceanographers utilize to glean further knowledge of the world ocean, including astronomy, biology, chemistry, climatology, geography, geology, hydrology, meteorology and physics. Paleoceanography studies the history of the oceans in the geologic past. An oceanographer is a person who studies many matters concerned with oceans, including marine geology, physics, chemistry and biology. History Early history Humans first acquired knowledge of the waves and currents of the seas and oceans in pre-historic times. Observation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Population Dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years,Malthus, Thomas Robert. An Essay on the Principle of Population: Library of Economics although over the last century the scope of mathematical biology has greatly expanded. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model. According to Malthus, assuming that the conditions (the environment) remain constant (''ceteris paribus''), a population will grow (or decline) exponentially. This principle provided the basis for the subsequent predictive theories, such as the demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic mode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Oscillatory System Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term ''vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Center Manifold In the mathematics of evolving systems, the concept of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised to be fundamental to mathematical modelling. Center manifolds play an important role in bifurcation theory because interesting behavior takes place on the center manifold and in multiscale mathematics because the long time dynamics of the micro-scale often are attracted to a relatively simple center manifold involving the coarse scale variables. Informal example Saturn's rings provide a rough example of the center manifold of the tidal forces acting on particles within the rings. Tidal forces have a characteristic "compress and stretch" action on bodies, with the compressing direction defining the stable manifold, the stretching direction defining the unstable manifold, and the neutral direction being the center manifold. In the case of Saturn, a particle in orbit above or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Stability Analysis Stability may refer to: Mathematics * Stability theory, the study of the stability of solutions to differential equations and dynamical systems Asymptotic stability Linear stability Lyapunov 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 (algebraic geometry) Engineering In atmospheric fl ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]