In physics , there are several distinct notions of mixing, all of which try to capture the common-sense notion of mixing, but using rather disparate formal methods, techniques and definitions. One approach is to focus on mixtures of fluids, in three-dimensional space, described by differential equations suitable for fluids, such as the Navier–Stokes equations . The route to the final mixed state typically proceeds through turbulence created during mixing. A second approach considers the mixing of aggregates, such as rocks and sand, which are lumpy on the small scale; this is commonly seen in mixing in process engineering . A third approach uses the mathematical formalisms of measure theory and measure-preserving dynamical systems , to define mixing abstractly for generic dynamical systems in arbitrary dimensions. For example, by assigning a position and a velocity to each atom in a fluid, the mixing takes place in a 6 N {\displaystyle 6^{N}} -dimensional space, where N {\displaystyle N} is approximately the Avogadro number and 6 = 3 + 3 {\displaystyle 6=3+3} is the dimension of the phase space (position plus velocity) of a single atom.
22-498: (Redirected from MIX ) [REDACTED] Look up Mix or mix in Wiktionary, the free dictionary. Mix , MIX , mixes , or mixing may refer to: Audio and music [ edit ] Audio mixing (recorded music) , the process of combining and balancing multiple sound sources DJ mix , a sequence of musical tracks mixed to appear as one continuous track Mixtape ,
44-471: A 1998 remix album by Australian singer-songwriter Kylie Minogue Mix (Stellar album) , a 1999 studio album by New Zealand pop rock band Stellar Mixes , a 2008 self-released album by C418 Computing [ edit ] Mix (build tool) , a build tool for working with the Elixir programming language MIX (email) , a high performance email storage system for use with IMAP MIX (abstract machine) ,
66-472: A 1999 studio album by New Zealand pop rock band Stellar Mixes , a 2008 self-released album by C418 Computing [ edit ] Mix (build tool) , a build tool for working with the Elixir programming language MIX (email) , a high performance email storage system for use with IMAP MIX (abstract machine) , the computer and the instruction set architecture used in the textbook The Art of Computer Programming by Donald Knuth MIX (Microsoft) ,
88-455: A Filipino cable TV channel Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Mix . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Mix&oldid=1251035539 " Category : Disambiguation pages Hidden categories: Short description
110-455: A Filipino cable TV channel Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Mix . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Mix&oldid=1251035539 " Category : Disambiguation pages Hidden categories: Short description
132-768: A commercial-free channel on XM Satellite Radio Mix (Malaysian radio station) , a radio station in Malaysia MixRadio , an online music streaming service Mix TV , a Brazilian television music channel aimed at young people Sky Sports Mix, a TV channel Sony Mix , an Indian television music channel People [ edit ] Mix Diskerud (born 1990), Norwegian-American soccer player Mix (surname) Places [ edit ] Mix camp , an informal settlement in Namibia Mix, Louisiana , an unincorporated community Mix Run, Pennsylvania , village Science [ edit ] Mixing (mathematics) ,
154-483: A compilation of songs or tracks Remix , a variation of a song Mix, short way to refer to the Mixolydian mode . Mix (magazine) , a periodical for the professional recording and sound production technology industry Albums [ edit ] Mixes (Transvision Vamp album) , 1992 Mixes (Kylie Minogue album) , a 1998 remix album by Australian singer-songwriter Kylie Minogue Mix (Stellar album) ,
176-471: A concept in ergodic theory Mixing (physics) , a descriptive condition of a dynamical system Mixing (process engineering) , a unit operation for manipulating physical systems Crossbreeding , also called mixing, a genetic concept Other [ edit ] MIX, the Roman numeral for the number 1009 or year 1009 Microfinance Information Exchange (MIX), a non-profit business information provider in
198-423: A concept in ergodic theory Mixing (physics) , a descriptive condition of a dynamical system Mixing (process engineering) , a unit operation for manipulating physical systems Crossbreeding , also called mixing, a genetic concept Other [ edit ] MIX, the Roman numeral for the number 1009 or year 1009 Microfinance Information Exchange (MIX), a non-profit business information provider in
220-595: A discontinued annual Microsoft conference Mix network , an anonymous email system proposed by David Chaum in 1981 Malta Internet Exchange , an Internet backbone for the country of Malta Milan Internet eXchange , in Milan, Italy MIX (Z39.87): NISO Metadata for Images in XML Radio and television [ edit ] Mix FM (disambiguation) Mix (radio station) , a radio station in New Zealand MIX (XM) ,
242-700: A radio station in New Zealand MIX (XM) , a commercial-free channel on XM Satellite Radio Mix (Malaysian radio station) , a radio station in Malaysia MixRadio , an online music streaming service Mix TV , a Brazilian television music channel aimed at young people Sky Sports Mix, a TV channel Sony Mix , an Indian television music channel People [ edit ] Mix Diskerud (born 1990), Norwegian-American soccer player Mix (surname) Places [ edit ] Mix camp , an informal settlement in Namibia Mix, Louisiana , an unincorporated community Mix Run, Pennsylvania , village Science [ edit ] Mixing (mathematics) ,
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#1732851184766264-424: A sequence of musical tracks mixed to appear as one continuous track Mixtape , a compilation of songs or tracks Remix , a variation of a song Mix, short way to refer to the Mixolydian mode . Mix (magazine) , a periodical for the professional recording and sound production technology industry Albums [ edit ] Mixes (Transvision Vamp album) , 1992 Mixes (Kylie Minogue album) ,
286-446: Is different from Wikidata All article disambiguation pages All disambiguation pages Mix [REDACTED] Look up Mix or mix in Wiktionary, the free dictionary. Mix , MIX , mixes , or mixing may refer to: Audio and music [ edit ] Audio mixing (recorded music) , the process of combining and balancing multiple sound sources DJ mix ,
308-405: Is different from Wikidata All article disambiguation pages All disambiguation pages Mixing (physics) The mixing of gases or liquids is a complex physical process, governed by a convective diffusion equation that may involve non-Fickian diffusion as in spinodal decomposition . The convective portion of the governing equation contains fluid motion terms that are governed by
330-559: Is the associated measure . Other definitions are possible, including weak mixing and topological mixing . The above definition of mixing is meant to capture the intuitive notion of physical mixing. A canonical example is the Cuba libre : suppose one is adding rum (the set A {\displaystyle A} ) to a glass of cola. After stirring the glass (the transformation T k {\displaystyle T^{k}} for large k {\displaystyle k} ),
352-458: The Navier–Stokes equations . When fluid properties such as viscosity depend on composition, the governing equations may be coupled. There may also be temperature effects. Small rigid objects (such as rocks) are sometimes mixed in a rotating drum or tumbler. The 1969 Selective Service draft lottery was carried out by mixing plastic capsules which contained a slip of paper (marked with a day of
374-445: The bottom half of the glass (the set B {\displaystyle B} ) will contain rum, and it will be in equal proportion as it is elsewhere in the glass. The mixing is uniform: no matter which region B {\displaystyle B} one looks at, some of A {\displaystyle A} will be in that region. The use of T − k {\displaystyle T^{-k}} in
396-534: The computer and the instruction set architecture used in the textbook The Art of Computer Programming by Donald Knuth MIX (Microsoft) , a discontinued annual Microsoft conference Mix network , an anonymous email system proposed by David Chaum in 1981 Malta Internet Exchange , an Internet backbone for the country of Malta Milan Internet eXchange , in Milan, Italy MIX (Z39.87): NISO Metadata for Images in XML Radio and television [ edit ] Mix FM (disambiguation) Mix (radio station) ,
418-430: The definition, instead of T k {\displaystyle T^{k}} , is required because the time evolution transformation T {\displaystyle T} is typically not an injective function (one-to-one). That is, if T {\displaystyle T} maps two points into one, the measure is preserved only by counting the two points in the pre-image , instead of one point in
440-690: The microfinance sector MIX NYC , a nonprofit organization dedicated to queer experimental film Mix (manga) , a 2012 baseball shōnen manga series by Mitsuru Adachi The Mix (charity) , in the U.K. Mixed Doubles , also known as Mix , a 2017 Japanese film Zeekr Mix , a battery electric minivan "Mixy" or "myxy", slang for the rabbit disease myxomatosis See also [ edit ] All pages with titles beginning with Mix All pages with titles containing Mix The Mix (disambiguation) Mixe (disambiguation) Mixed (disambiguation) Mixer (disambiguation) Mixture (disambiguation) Mixx (disambiguation) Myx ,
462-690: The microfinance sector MIX NYC , a nonprofit organization dedicated to queer experimental film Mix (manga) , a 2012 baseball shōnen manga series by Mitsuru Adachi The Mix (charity) , in the U.K. Mixed Doubles , also known as Mix , a 2017 Japanese film Zeekr Mix , a battery electric minivan "Mixy" or "myxy", slang for the rabbit disease myxomatosis See also [ edit ] All pages with titles beginning with Mix All pages with titles containing Mix The Mix (disambiguation) Mixe (disambiguation) Mixed (disambiguation) Mixer (disambiguation) Mixture (disambiguation) Mixx (disambiguation) Myx ,
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#1732851184766484-479: The year). A dynamical system is said to be mixing if the phase space of the system becomes strongly intertwined over time, according to at least one of several formal mathematical definitions . For example, a measure-preserving transformation T is said to be strong mixing if whenever A {\displaystyle A} and B {\displaystyle B} are any measurable sets and μ {\displaystyle \mu }
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