Discrete Fourier transformIn mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.
Molecular cloudA molecular cloud, sometimes called a stellar nursery (if star formation is occurring within), is a type of interstellar cloud, the density and size of which permit absorption nebulae, the formation of molecules (most commonly molecular hydrogen, H2), and the formation of H II regions. This is in contrast to other areas of the interstellar medium that contain predominantly ionized gas. Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H2 is carbon monoxide (CO).
Interplanetary dust cloudThe interplanetary dust cloud, or zodiacal cloud (as the source of the zodiacal light), consists of cosmic dust (small particles floating in outer space) that pervades the space between planets within planetary systems, such as the Solar System. This system of particles has been studied for many years in order to understand its nature, origin, and relationship to larger bodies. There are several methods to obtain space dust measurement.
Orion molecular cloud complexThe Orion molecular cloud complex (or, simply, the Orion complex) is a star-forming region with stellar ages ranging up to 12 Myr. Two giant molecular clouds are a part of it, Orion A and Orion B. The stars currently forming within the complex are located within these clouds. A number of other somewhat older stars no longer associated with the molecular gas are also part of the complex, most notably the Orion's Belt (Orion OB1b), as well as the dispersed population north of it (Orion OB1a).
Interstellar cloudAn interstellar cloud is generally an accumulation of gas, plasma, and dust in our and other galaxies. Put differently, an interstellar cloud is a denser-than-average region of the interstellar medium, the matter and radiation that exists in the space between the star systems in a galaxy. Depending on the density, size, and temperature of a given cloud, its hydrogen can be neutral, making an H I region; ionized, or plasma making it an H II region; or molecular, which are referred to simply as molecular clouds, or sometime dense clouds.
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
WellA well is an excavation or structure created in the ground by digging, driving, or drilling to access liquid resources, usually water. The oldest and most common kind of well is a water well, to access groundwater in underground aquifers. The well water is drawn up by a pump, or using containers, such as buckets or large water bags that are raised mechanically or by hand. Water can also be injected back into the aquifer through the well.
Accretion (astrophysics)In astrophysics, accretion is the accumulation of particles into a massive object by gravitationally attracting more matter, typically gaseous matter, in an accretion disk. Most astronomical objects, such as galaxies, stars, and planets, are formed by accretion processes. The accretion model that Earth and the other terrestrial planets formed from meteoric material was proposed in 1944 by Otto Schmidt, followed by the protoplanet theory of William McCrea (1960) and finally the capture theory of Michael Woolfson.
Circumstellar discA circumstellar disc (or circumstellar disk) is a torus, pancake or ring-shaped accretion disk of matter composed of gas, dust, planetesimals, asteroids, or collision fragments in orbit around a star. Around the youngest stars, they are the reservoirs of material out of which planets may form. Around mature stars, they indicate that planetesimal formation has taken place, and around white dwarfs, they indicate that planetary material survived the whole of stellar evolution. Such a disc can manifest itself in various ways.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Nebular hypothesisThe nebular hypothesis is the most widely accepted model in the field of cosmogony to explain the formation and evolution of the Solar System (as well as other planetary systems). It suggests the Solar System is formed from gas and dust orbiting the Sun which clumped up together to form the planets. The theory was developed by Immanuel Kant and published in his Universal Natural History and Theory of the Heavens (1755) and then modified in 1796 by Pierre Laplace.
Discrete-time Fourier transformIn mathematics, the discrete-time Fourier transform (DTFT), also called the finite Fourier transform, is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Finite difference methodIn numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
DustDust is made of fine particles of solid matter. On Earth, it generally consists of atmospheric particulates (particles in the atmosphere) that come from various sources such as soil lifted by wind (an aeolian process), volcanic eruptions, and pollution. Dust in homes is composed of about 20–50% dead skin cells. The rest, and in offices, and other human environments is composed of small amounts of plant pollen, human hairs, animal fur, textile fibers, paper fibers, minerals from outdoor soil, burnt meteorite particles, and many other materials which may be found in the local environment.
NumPyNumPy (pronounced ˈnʌmpaɪ () or sometimes ˈnʌmpi ()) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with contributions from several other developers. In 2005, Travis Oliphant created NumPy by incorporating features of the competing Numarray into Numeric, with extensive modifications.
Cosmic dustCosmic dust - also called extraterrestrial dust, space dust, or star dust - is dust that occurs in outer space or has fallen onto Earth. Most cosmic dust particles measure between a few molecules and , such as micrometeoroids. Larger particles are called meteoroids. Cosmic dust can be further distinguished by its astronomical location: intergalactic dust, interstellar dust, interplanetary dust (as in the zodiacal cloud), and circumplanetary dust (as in a planetary ring). There are several methods to obtain space dust measurement.
Continuous or discrete variableIn mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively. If it can take on two particular real values such that it can also take on all real values between them (even values that are arbitrarily close together), the variable is continuous in that interval. If it can take on a value such that there is a non-infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value.
Method of characteristicsIn mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partial differential equation. The method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data given on a suitable hypersurface.
Discrete sine transformIn mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample. A family of transforms composed of sine and sine hyperbolic functions exists.
