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Topic: Selfsimilar

	MIND Exchange
		The most fundamental selfsimilar structure is the forking (bifurcating) structure (Jean, 1994) of tree branches, tree roots, river tributaries, branched lightning, etc. The complex branching architecture is a selfsimilar fractal since branching occurs on all scales (sizes) and forms the geometrical shape of the whole object.
		Selfsimilar spiral structures such as on the shell of the very old mollusk called Nautilus pompilius (Jean, 1994) incorporate the golden mean in their radial growth.
		In summary, selfsimilar space-time structures or self-organized criticality is ubiquitous to dynamical systems in nature and also to mathematical models of dynamical systems which incorporate finite precision iterative computations with resultant feedback and magnification of round-off error primarily, in addition to initial errors.
	www.kurzweilai.net /mindx/show_thread.php?rootID=47830 (9092 words)

	2.2 Golden Mean and Selfsimilar, Fractal Geometrical Structures in Nature (Site not responding. Last check: 2007-10-29)
		The most fundamental selfsimilar structure is the forking (bifurcating) structure (Jean, 1994Reference) of tree branches, tree roots, river tributaries, branched lightning, etc.The complex branching architecture is a selfsimilar fractal since branching occurs on all scales (sizes) and forms the geometrical shape of the whole object.Selfsimilar structures incorporate in their geometrical design the noble numbers, i.e.
		Selfsimilar spiral structures such as on the shell of the very old mollusk called Nautilus pompilius (Jean, 1994Reference) incorporate the golden mean in their radial growth.
		Thompson described that the nautilus followed a pattern originally described by Rene Descartes in 1683 as the equiangular spiral and subsequently by Jacob Bernoulli as the logarithmic spiral(West 1990Reference).The commonly found shapes in nature are the helix and the dodecahedron (Stoddart, 1988;Muller and Beugholt,1996Reference) which are signatures of selfsimilarity underlying Fibonacci numbers.
	www.geocities.com /amselvam/chaos22.html (500 words)

	Embrechts, P.: Selfsimilar Processes.
		Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful.
		Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications.
		Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes.
	www.pupress.princeton.edu /titles/7319.html (395 words)

	chaos22d
		The most fundamental selfsimilar structure is the forking (bifurcating) structure (Jean, 1994 Reference) of tree branches, tree roots, river tributaries, branched lightning, etc. The complex branching architecture is a selfsimilar fractal since branching occurs on all scales (sizes) and forms the geometrical shape of the whole object.
		Selfsimilar structures incorporate in their geometrical design the noble numbers, i.e.
		Selfsimilar spiral structures such as on the shell of the very old mollusk called Nautilus pompilius (Jean, 1994 Reference) incorporate the golden mean in their radial growth.
	members.tripod.com /amselvam/tnk/chaos22.html (506 words)

	gorilla: Product: 'SELFSIMILAR PROCESSES' (Site not responding. Last check: 2007-10-29)
		Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behaviour, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful.
		Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a rich theory with far-flung applications.;After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications.
		Concepts, definitions and basic properties are emphasized, giving the reader a map of the realm of selfsimilarity that allows for further exploration.
	www.gorilla.it /gorilla/product.4print.asp?sku=0691096279 (222 words)

	2.3 Turbulent (chaotic) Fluctuations and Selfsimilar Structure Formation (Site not responding. Last check: 2007-10-29)
		Recent studies show that clouds of all sizes (Tessier et al, 1993Reference) are selfsimilar in shape which is consistent with commonly visualized shape of clouds as billows upon billows.
		The selfsimilar architecture for fractal objects serve for collection and distribution of information/energy between the largest and smallest scales.
		Jean (1994Reference) has emphasized the functional importance of ramified structures underlying selfsimilar fractals and gives reference to earlier studies which show that such branching structures can be organized into hierarchies which incorporate the Fibonacci mathematical sequence.
	www.geocities.com /CapeCanaveral/Lab/5833/chaos23.html (475 words)

	EPrint Series of Department of Mathematics, Hokkaido University - SELFSIMILAR EXPANDING SOLUTIONS IN A SECTOR FOR A ...
		For a given sector a selfsimilar expanding solution to a crystalline flow is constructed.
		Because of selfsimilarity the problem is reduced to solve a system of algebraic equations of degree two.
		The selfsimilar expanding solution is useful to construct a crystalline flow from an arbitrary polygon not necessarily admissible.
	eprints.math.sci.hokudai.ac.jp /archive/00000198 (141 words)

	Selfsimilar Processes - Paul Embrechts
		Everybody is talking about scaling, and selfsimilar stochastic processes are the basic and the clearest examples of models with scaling.
		In applications from finance to communication networks, selfsimilar processes are believed to be important.
		Selfsimilar processes crop up in a wide range of subjects from finance to physics, so this book will have a correspondingly wide readership."--Chris Rogers, Bath University
	www.englishbooks.it /BUS/0691096279/Selfsimilar_Processes.htm (206 words)

	projects
		The particular aim of this joint project in the intersection of Ricci flow and complex geometry is to use the now rich class of available techniques from the theory of geometric evolution equations, in particular in the Kähler-Ricci flow combined with the global methods from complex geometry to obtain classifications of Sasaki manifolds.
		In the project on selfsimilar solutions of the mean curvature flow we want to derive classification results for selfsimilar submanifolds under mild geometric conditions and to get a better understanding of what kind of constraints and obstructions for the existence of such submanifolds are necessary.
		While minimal submanifolds - as a subcase of the selfsimilar solutions - are analogue to Ricci flat metrics, the contracting selfsimilar solutions correspond to Einstein metrics with positive scalar curvature.
	www-ifm.math.uni-hannover.de /~smoczyk/projects.html (345 words)

	MaPhySto Publication: MPS-RR 1998-1 (Site not responding. Last check: 2007-10-29)
		Using bivariate Lévy processes, stationary and selfsimilar processes, with prescribed one-dimensional marginal laws of type G, are constructed.
		In the case of square integrability, the arbitrary spectral distribution of the stationary process can be chosen so that the corresponding selfsimilar process has second order stationary increments.
		The spectral distribution in question, which yields fractional Brownian motion when the driving Lévy process is the bivariate Brownian motion, is shown to possess a density, and an explicit expression for the density is derived.
	www.maphysto.dk /cgi-bin/w3-msql/publications/genericpublication.html?publ=3 (98 words)

	Semi-Selfsimilar Processes - Maejima, Sato (ResearchIndex)
		Abstract: A notion of semi-selfsimilarity of R d -valued stochastic processes is introduced as a natural extension of the selfsimilarity.
		De nition 6.2 A stochastic process fX(t) t 0g is said to be semi selfsimilar if there exist a 2 (0; 1) 1; 1) and b 0 such that...
		An Introduction to the Theory of Selfsimilar Stochastic..
	citeseer.ist.psu.edu /maejima99semiselfsimilar.html (443 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		We present here theoretical reasons to use selfsimilar additive processes to model asset prices and a program for calibrations and implementations.
		L\'evy processes are stationary additive processes and are selfsimilar only in the stable case.
		Selfsimilar additive processes due to nonstationarity need not adhere to a Central Limit Theorem.
	www.math.fsu.edu /~aluffi/archive/paper208.abs.html (82 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		We have further obtained that the dynamics is selfsimilar, i.e., that there is dynamical scaling.
		In spite of the nonrelaxational dynamics we have found a regime of selfsimilar evolution with a growth law characteristic of curvature driven motion.
		In other regimes, obtained just by changing the pump amplitude, domain growth is contaminated by the emergence of LS or suppressed by an instability of the domain wall that leads to a nearly frozen labyrinthine pattern.
	www.imedea.uib.es /physdept/publications/downfile.php?fid=2349 (2521 words)

	UK Nonlinear News 32 (May 2003): Report
		The precise mathematical definition of a selfsimilar process is given in the first chapter, where relations are made to Fractional Brownian Motion (FBM) and Stable Lvy Processes.
		Sample path properties for general selfsimilar stable processes with stationary increments are discussed in chapter six.
		The final chapter discusses how the concept of selfsimilarity in d-dimensional real space, R, can be extended to allow for scaling of linear operators on R. Further, selfsimilarity is generalised to the concept semi-selfsimilarity which is relevant to diffusion on fractals such as the Sierpinski gasket.
	amsta.leeds.ac.uk /Applied/news.dir/issue32.dir/art/selfsimilar.html (680 words)

	Session M7 - Other Topics and Applications.
		Small non-radial blast wave perturbations are expanded to spherical harmonics components of expansion being represented in a selfsimilar form (The perturbation front amplitudes are supposed to be power functions of time with power exponent being complex number).
		The adiabatic exponent of the non-ideal gas is supposed to be a function of the gas density.
		So the selfsimilar approach to the blast wave stability problem is used that was previously used in the case of blast wave in ideal gas (Ref.1-3).
	flux.aps.org /meetings/YR99/SHOCK99/abs/S5300.html (2105 words)

	Citebase - Selfsimilar random fractal measure using contraction method in probabilistic metric spaces (Site not responding. Last check: 2007-10-29)
		Selfsimilar random fractal measure using contraction method in probabilistic metric spaces
		Authors: Kolumban, J. Soos, A. We use contraction method in probabilistic metric spaces to prove existence and uniqueness of selfsimilar random fractal measures.
		Use the Correlation Generator to explore the correlation between download impact ("hits") and citation impact.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0202100 (462 words)

	Climate Dynamics, Chaos and Quantum Mechanics
		A hierarchy of selfsimilar structures: The large scale is a magnified version of the small scale.
		Selfsimilar spatial structures imply long-range spatial correlations or non-local connections.
		Global cloud cover pattern exhibits fractal geometry.The existence of long-range spatial correlations such as the El-Nino impact on global climate is now accepted.The global atmosphere acts as a unified whole, where,local perturbations produce a global response.
	amselvam.tripod.com (1615 words)

	UIUC Dept. of Mathematics Seminar Calendar
		In the critical case, Witelski, Bertozzi, and Bernoff propose a critical mass, $M_c$, and demonstrate that if the mass of the initial data is less than $M_c$ then finite-time blow-up is impossible.
		Their computations and asymptotics case suggest that (generically) if the initial mass is larger than $M_c$ the resulting solution demonstrates selfsimilar blowup focussed at points.
		Their mass can be arbitrarily close to the critical mass proposed by Witelski et al., proving the sharpness of the critical mass.
	torus.math.uiuc.edu /cal/math/cal?year=2005&month=04&day=18&interval=day (287 words)

	Amazon.ca: Selfsimilar Processes: Books (Site not responding. Last check: 2007-10-29)
		Authoritative and written by leading experts, this book is a significant contribution to a growing field.
		Selfsimilar processes crop up in a wide range of subjects from finance to physics, so this book will have a correspondingly wide readership.
		Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of
	www.amazon.ca /exec/obidos/ASIN/0691096279/papiermacouk-20 (438 words)

	Selfsimilar Processes (Princeton Series in Applied Mathematics) \| Evie's Eden (Site not responding. Last check: 2007-10-29)
		The Selfsimilar Processes (Princeton Series in Applied Mathematics) is part of our discount Book catalog.
		Used Selfsimilar Processes (Princeton Series in Applied Mathematics) are in stock for only $24.95.
		Discount pricing is subject to change, in order to get the Book Selfsimilar Processes Princeton Series in Applied Mathematics at this reduced price, you must buy now!
	evieseden.com /amazon/asin.0691096279.Book_Selfsimilar_Processes_Princeton_Series_in_Applied_Mathematics_.html (338 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		In this talk, we will discuss the multi-dimensional (M-D) conservation laws whose Riemann data just contain two different constant states which are separated by a smooth curve or surface.
		Non-selfsimilar M-D elementary waves, their new structures and properties are disclosed, for example the contour surface of M-D rarefaction wave is a family of cylindrical surface etc., which are essentially different from that in M-D selfsimilar case.
		Furthermore, global solutions of a class of 2-D systems of conservation laws will be also presented and are formulated by implicit function, their structure combining 2-D non-selfsimilar elementary waves and non-constant intermediate states will be shown.
	www.math.wisc.edu /~bolotin/AMPDE/abstracts/Feb_4.html (112 words)

	MIT PDE/Analysis Seminar, Fall 2004 (Site not responding. Last check: 2007-10-29)
		The gradient-flow structure of these equations suggests a framework in which to study stability of selfsimilar solutions.
		In the case of porus-medium and fast-diffusion equations it provides a way to show the asymptotic stability of the selfsimilar solutions, with optimal rates of convergence.
		Of particular interest to us will be the blow-up behaviour of long-wave unstable thin-film equations and the stability of blow-up profiles.
	www-math.mit.edu /~andras/PDE.html (345 words)

	Simulations of Gas-dynamic Flows ... (Site not responding. Last check: 2007-10-29)
		For the case of selfsimilar solution for the problem of streamer channel expansion at the electric breakdown in liquid, computations using the lattice gas (LG) and lattice Boltzmann equation (LBE) methods were carried out.
		For the one-dimensional problem of the conductive channel expansion a selfsimilar solution exists when three conditions are satisfied:
		Under these conditions, the mass velocity of "plasma" inside the channel is zero, and the temperarure, density and pressure are constant both across the channel section and in time.
	itp.nat.uni-magdeburg.de /~dmedv/nist3/nist3d.htm (2099 words)

	Selfsimilar Processes; Embrechts, Paul; Hardcover; World Retail Store - English Books
		Selfsimilar Processes; Embrechts, Paul; Hardcover; World Retail Store - English Books
		This item ships direct to you within 72 hours.
		Prices subject to change to be advised on confirmation of order.
	www.worldretailstore.com /item/BE-0691096279.html (213 words)

	Nonlinear Dynamics and Chaos: Applications for Prediction of Weather and Climate
		to describe the selfsimilar fluctuations that are generic to dynamical evolution of systems in nature.
		Recent studies (since 1988) in all branches of science reveal that selfsimilar multifractal spatial pattern formation by selfsimilar fluctuations on all space-time scales is generic to dynamical systems in nature and is identified as signature of self-organized criticality
		Such multifractal temporal fluctuations in atmospheric flows are associated with selfsimilar multifractal spatial patterns for cloud and rain areas documented and discussed in great detail by Lovejoy and his group
	amselvam.tripod.com /jsp/physcad.html (1299 words)

	Volker Elling, Tai-Ping Liu: The ellipticity principle for selfsimilar polytropic potential flow (Site not responding. Last check: 2007-10-29)
		Volker Elling, Tai-Ping Liu: The ellipticity principle for selfsimilar polytropic potential flow
		We consider self-similar potential flow for compressible gas with polytropic pressure law.
		We also discuss the case of slip boundary conditions at straight solid walls.
	sccm.stanford.edu /%7Eelling/ellipticity-abstract.html (151 words)

	Citations: Accurate Approximation of Cell Loss Probability for SelfSimilar Traffic in ATM Networks - Fan, Mars ... (Site not responding. Last check: 2007-10-29)
		The remainder of this paper is organized as follows.
		First the formula depends on the traffic being sufficiently Gaussian, which is more likely to be the case when traffic is aggregated from a large number of independent sources.
		Fan and P. Mars, "Accurate Approximation of Cell Loss Probability for SelfSimilar Traffic in ATM Networks", Electronics Letters, Vol.
	citeseer.ifi.unizh.ch /context/849940/0 (694 words)

	Selfsimilar Processes (Princeton Series in Applied Mathematics) (Site not responding. Last check: 2007-10-29)
		Home > Shop > Selfsimilar Processes (Princeton Series in Applied Mathematics)
		Selfsimilar processes are stochastic processes that are invariant in distribution under suitable scaling of time and/or space.
		Fractional Brownican motion is perhaps the best known of these, and it is used in telecommunication and in stochastic integration.
	www.hilaryking.net /shop/us/0691096279.html (282 words)

	Untitled Document (Site not responding. Last check: 2007-10-29)
		We discuss issues of existence, uniqueness and stability of selfsimilar solutions for variable hard sphere models.
		We show selfsimilar solutions deviate from statistical equilibrium solutions (Maxwellian distributions) in steady and transient regimes.
		In addition, we point out the differences in terms of high energy tail behavior between Maxwell molecules and variable hard spheres models for self-similar energy dissipative collisional flows.
	math.stanford.edu /~applmath/fall04/gamba.htm (135 words)

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