LEADER 04026nam 22006375 450 001 9910254326403321 005 20200703125558.0 010 $a3-319-56922-8 024 7 $a10.1007/978-3-319-56922-2 035 $a(CKB)3850000000027394 035 $a(DE-He213)978-3-319-56922-2 035 $a(MiAaPQ)EBC6298228 035 $a(MiAaPQ)EBC5595474 035 $a(Au-PeEL)EBL5595474 035 $a(OCoLC)985437072 035 $a(PPN)200513001 035 $a(EXLCZ)993850000000027394 100 $a20170428d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFundamentals of Stochastic Nature Sciences /$fby Valery I. Klyatskin 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XII, 190 p. 62 illus., 11 illus. in color.) 225 1 $aUnderstanding Complex Systems,$x1860-0832 311 $a3-319-56921-X 320 $aIncludes bibliographical references. 327 $aTwo-dimensional geophysical ?uid dynamics.- Parametrically excited dynamic systems.- Examples of stochastic dynamic systems.- Statistical characteristics of a random velocity ?eld u(r, t).- Lognormal processes, intermittency, and dynamic localization -- Stochastic parametric resonance -- Wave localization in randomly layered media -- Lognormal ?elds, statistical topography, and clustering -- Stochastic transport phenomena in a random velocity ?eld -- Parametrically excited dynamic systems with Gaussian pumping -- Conclusion. 330 $aThis book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens ? or doesn?t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under which such structure formation takes place. To make the content more accessible, these conditions are described at a comparatively elementary mathematical level by employing ideas from statistical topography. 410 0$aUnderstanding Complex Systems,$x1860-0832 606 $aComputational complexity 606 $aStatistical physics 606 $aDynamics 606 $aGeotechnical engineering 606 $aComplexity$3https://scigraph.springernature.com/ontologies/product-market-codes/T11022 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aGeotechnical Engineering & Applied Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/G37010 615 0$aComputational complexity. 615 0$aStatistical physics. 615 0$aDynamics. 615 0$aGeotechnical engineering. 615 14$aComplexity. 615 24$aComplex Systems. 615 24$aGeotechnical Engineering & Applied Earth Sciences. 676 $a003.76 700 $aKlyatskin$b Valery I$4aut$4http://id.loc.gov/vocabulary/relators/aut$0934990 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254326403321 996 $aFundamentals of Stochastic Nature Sciences$92105546 997 $aUNINA LEADER 01479oas 2200601 a 450 001 9910145750703321 005 20251106213014.0 011 $a1812-5697 035 $a(DE-599)ZDB2177257-5 035 $a(OCoLC)57666212 035 $a(CONSER) 2009253051 035 $a(CKB)1000000000018802 035 $a(EXLCZ)991000000000018802 100 $a20050215a20029999 sy 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aAsian journal of plant sciences 210 $aFaisala?ba?d $cANSInet 215 $a1 online resource 300 $aRefereed/Peer-reviewed 311 08$a1682-3974 517 1 $aAJPS 531 1 $aAsian j. plant sci. 606 $aCrop science$vPeriodicals 606 $aCrop science$zSouth Asia$vPeriodicals 606 $aCrop science$2fast$3(OCoLC)fst00883934 607 $aSouth Asia$2fast 608 $aPeriodicals.$2fast 615 0$aCrop science 615 0$aCrop science 615 7$aCrop science. 801 0$bSNM 801 1$bSNM 801 2$bAGL 801 2$bOCLCQ 801 2$bCUS 801 2$bWAU 801 2$bAGL 801 2$bOCLCQ 801 2$bOCLCF 801 2$bOCLCQ 801 2$bVT2 801 2$bOCLCQ 801 2$bOCLCO 801 2$bCUS 801 2$bOCLCQ 906 $aJOURNAL 912 $a9910145750703321 996 $aAsian journal of plant sciences$92272531 997 $aUNINA