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Topic: Levy flights

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	Anomalous diffusion and Levy flights in two-dimensional rotating flows (Site not responding. Last check: 2007-10-23)
		The goal of this project was to propose a transport model for experiments on anomalous diffusion and Levy flights in a rotating fluid [Solomon, Weeks, and Swinney, Phys.
		In particular, evidence of anomalous diffusion and Levy flights was observed in the statistics of particles alternating between being trapped in the vortices and moving in the azimuthal direction.The proposed model is a Hamiltonian system consisting of the superposition of an azimuthal shear flow and two neutral modes of the quasigeostrophic equation.
		Quantitative agreement was observed between the model and the experiment for the value of the anomalous diffusion exponent, and the Levy flight exponent.
	www.ornl.gov /sci/fed/Theory/csd/research/projects/ad/adl.htm (180 words)

	Weeks et al 1995 (Site not responding. Last check: 2007-10-23)
		The flight PDFs are power laws, indicated in some cases that the particle motion can be characterized as Levy flights (with a divergent second moment for flight times).
		The dependence of the variance exponent d on the flight and sticking PDFs is studied and found to be consistent with calculations relating Levy flights and anomalous diffusion (d not equal 1).
		In a turbulent flow, Levy flights no longer are present and the mixing appears to be normally diffusive (d=1).
	www.physics.emory.edu /~weeks/abs/nice95.html (223 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		Conversely, we could show that Lévy flights in a superharmonic external potential exhibit a bifurcation to a multimodal state at some critical time, and that the variance for this process is finite.
		An important issue for both Lévy flights and Lévy walks is the correct formulation of boundary value problems.
		We have established a correct way to formulate such first passage problems for Lévy flights, finding that the method of images (known from normal and subdiffusion) becomes inconsistent for processes with long jump lengths, and that the first passage time density differs from the probability density of first arrival.
	www.nordita.dk /~metz/anom_diffusion.html (497 words)

	Relief group to start air-dropping food over Kosovo next week: 5/29/99
		The U.S. Agency for International Development is helping to pay for the costs of the flights, which are expected to begin early next week, said Barbara Smith, the International Rescue Committee's vice president for overseas operations.
		In Washington, U.S. State Department spokesman James Rubin said arrangements have been made to inform the Yugoslav authorities of the flight patterns and the timing of flights and no escorts flights are planned.
		Levy said the committee also recognizes that some food might not get to the needy.
	www.s-t.com /daily/05-99/05-29-99/c06wn122.htm (555 words)

	Wilmott Forums - stochastic integration on alpha-stable processes (Site not responding. Last check: 2007-10-23)
		One should think of Levy flights as the some of jump processes, with jumps of size q happening with frequency K(q); the reason that K is singular at q=0 is just that microscopic jumps happen inifinitely often.
		Yes, Levy flights are infinitely divisible, which is another way of saying they are a local martingale.
		Levy processes can be (local) martingales and BM is a special case of Levy processes, as well as stable processes, you can define stochastic integrals for Levy processes, since they are semimartingales.
	www.wilmott.com /messageview.cfm?catid=4&threadid=4841 (1781 words)

	Interstellar Levy Flights (Site not responding. Last check: 2007-10-23)
		Levy Flights and Random Walks: A random walk is a path composed of many independent random steps.
		For pulsars, Levy statistics can explain the multipath broadening of pulses, as a function of the integrated electron density along the line of sight (the "tau-DM plot" for pulsars, sometimes known as the "elbow diagram").
		Levy model for insterstellar scintillations: Boldyrev and Gwinn 2003, Phys Rev Lett, 91, 131101
	www.physics.ucsb.edu /~cgwinn/levy/levy.html (688 words)

	Anomalous Diffusion Annulus Experiments
		The slope of the flight plot is -2.3, indicating that long flights of duration T occur with a probability proportional to T^(-2.2).
		This is the first experiment where the Lévy flights of tracer particles can be seen directly with a camera, and their distributions measured from their actual motions.
		The slope of the sticking plot is -1.6, thus the probability of being stuck in a vortex for a duration T is proportional to T^(-1.6).
	chaos.ph.utexas.edu /research/annulus/anom.html (998 words)

	EU Air Tax Could Hurt Demand
		A mandatory European Union levy on airline tickets to boost aid to Africa could curb demand for air travel and significantly hit airline profitability, a study by the European Commission showed on Thursday.
		The European Commission study said a 1 euro levy on flights within the EU and a 2 euro tax to places outside could curb demand for air travel by 0.5 and 1 percent respectively.
		Since the introduction of the levy by all member states was unlikely, the Commission focused on two scenarios -- when countries voluntarily adopt a mandatory levy for all passengers flying from its airports and when countries, if they want to, give passengers a choice whether to pay such a fee or not.
	news.airwise.com /story/view/1125608294.html (533 words)

	Passengers on inland flights to pay $2.5 security levy
		The levy on inland flights will be significantly lower, at $2.5 per passenger, compared with the $10-15 fee for passengers on international flights.
		All the levies will apparently go into effect before October, and are intended to cover the new expenses incurred by the application of measures based on the lessons drawn from the terrorist attacks on the planes in the US.
		Although flight security regulations in Israel are better than in the rest of the world, some changes will have to be made in Israel as well.
	www.freerepublic.com /focus/f-news/532463/posts (337 words)

	Guardian \| Rival airlines rally to aid of stranded EUjet passengers
		Up to 5,000 passengers, mainly in Spain and Portugal, are reported to have been left without flights home after EUjet called a halt to its operations.
		The Civil Aviation Authority has submitted plans for a levy on flights from the UK to cover the costs of refunds and bringing stranded passengers back to the UK, but this is resisted by many of the airlines as an additional cost to customers.
		Yesterday, in the wake of EUjet's decision to halt flights, Monarch said it was offering flights home for £25 plus taxes, while easyJet is charging £25.
	www.guardian.co.uk /print/0,3858,5249588-103690,00.html (361 words)

	Physics News Update
		Models of random motion that include such leaps from one area to another, known to mathematicians as Levy flights, are often applied in studying the physics of chaotic systems involving fluid flow, chemical kinetics, and semiconductors.
		In addition to the new CVC transmission insights, Levy flights have recently proven valuable in understanding the foraging activity of animals from amoebas to deer, and for simulating human activities such as the childhood game of hide-and-seek.
		Plant stress and seasonal effects were among the factors that influenced the Lévy flights in the model which predicts CVC epidemic progression much more accurately than models relying on less sophisticated, random-walk simulations of insect behavior.
	www.aip.org /pnu/2000/split/510-3.html (204 words)

	Random Walks and Anomalous Diffusion
		In the Lévy flight case the probability of a long step is proportional to L^(-2.2), which is more probable than the normal case.
		For a Lévy flight, the overall position is nearly completely determined by the long, rare steps -- the "flights" -- and thus there is no averaging out of the individual steps.
		The exponent gamma is equal to one for the normal diffusion case.
	chaos.ph.utexas.edu /research/annulus/rwalk.html (1697 words)

	Fractal Geometry (Site not responding. Last check: 2007-10-23)
		Levy flights model acivities that involve a lot of small steps, interspersed with occasional very large excursions.
		In the case of foraging paths, this result is sensible because the stopping points of a Levy flight are fractal (scale invariant is the main point here), and in complex ecosystems the distribution of food is fractal.
		As to why hide-and-seek is well-described by a Levy flight, reccall how it is played.
	classes.yale.edu /Fractals/RandFrac/Levy/Levy5.html (177 words)

	Branching annihilating Lévy flights: Irreversible phase transitions with long-range exchanges (Site not responding. Last check: 2007-10-23)
		The branching annihilation walk (BAW) process is generalized allowing either the particles or the offsprings (or both) to undergo Lévy flights, where the flying length
		The proposed branching annihilating Lévy flights (BALF) process exhibits irreversible phase transitions between an active stationary state and a vacuum state.
		It is suggested that transitions of the BALF model may belong to a superuniversality class of DP where the exponents are tunable functions of
	www.edpsciences.org /articles/epl/abs/1996/11/34204/34204.html (224 words)

	Lévy flights and anomalous diffusion in the stratosphere
		The flight time probability density functions (PDFs) are described by power laws with a decay exponent of less than 3, which indicates that the trajectories can be characterized as Lévy flights (random walk processes with divergent second moment).
		The relationship between the power law decay exponents and the zonal mean and variance exponents is consistent with an analytical derivation.
		Citation: Seo, K., and K. Bowman (2000), Lévy flights and anomalous diffusion in the stratosphere, J.
	www.agu.org /pubs/crossref/2000/2000JD900078.shtml (265 words)

	BMI cheap flights to and from Heathrow, BMI flight tickets and fares at Euro 25
		BMI's research has found half the customers on its mainline flights were travelling on business but most were doing so in the rear of its aircraft.
		BMI would have gone low-cost for entire flights at Heathrow but for the high airport costs.
		Flights to Amsterdam, Prague and Paris from Basel by EasyJet
	www.dancewithshadows.com /pub/bmi-discount-heathrow.asp (498 words)

	Scotsman.com News - Politics - MPs want £1 levy to help passengers if an airline collapses
		MPS have urged the government to back a £1 levy on flights abroad to protect passengers from airline collapses like EUJet and Duo.
		The report says the proportion of international passengers covered by ATOL had fallen from 96 per cent in 1996 to 66 per cent in 2004, and was expected to reach just 20 per cent by 2010.
		A spokesman for the Department for Transport said: "The government thought long and hard about the recommendation for a £1 levy on air passengers departing the UK, but it was felt that consumers should be free to choose for themselves whether to insure against airline failure."
	news.scotsman.com /politics.cfm?id=179122006 (550 words)

	18.325 Spring 2001 Bazant, Lecture Notes
		Asymptotics of the position distribution of the "student-t walk", p(x) = A/(1+x^2)^2, with a dominant power-law tail from the end-point at the origin and a central Gaussian from a nonzero saddle point in the integrand of the inverse Fourier transform.
		Symmetric Levy distributions, "stability" of Levy flights, addivitity of power-law tail amplitudes for general random walks.
		Applications of Levy flights to financial time series (truncated Levy flights) and polymer surface adsorption.
	www-math.mit.edu /~bazant/teach/18.325/lectures (823 words)

	Chamber plays down flights levy » ABC Great Southern » Local News
		The airline has introduced a levy of $5 per sector on all bookings to cover the cost of higher fuel prices.
		Skywest says the levy is regrettable, but necessary to offset a 25 per cent rise in fuel costs during the past six months.
		Mr Juers says the $5 levy is justified in light of the rapid rise in fuel prices.
	www.abc.net.au /greatsouthern/news/200406/s1136395.htm (204 words)

	Treasury oppose £1 levy on flights : Gatwick Airport News Stories
		A plan to add a £1 levy on flights from the UK has caused a row within the Government.
		The levy, which would replace the ATOL bond to cover travellers if an airline goes bust, is opposed by Gordon Brown and the Treasury.
		The levy was proposed by the Civil Aviation Authority, the industry's regulator, and has attracted the backing of much of the travel industry and the House of Commons Transport Committee.
	www.uk-airport-news.info /gatwick-airport-news-260605.htm (300 words)

	Analysis of blackout in Power Transmission Systems (Site not responding. Last check: 2007-10-23)
		The use of reaction-diffusion models rests on the key assumption that the underlying diffusive process is Gaussian.
		However, a growing number of studies have pointed out the prevalence of anomalous diffusion, and there is a need to understand the dynamics of reactive systems in the presence of this type of non-Gaussian diffusion.
		Here we present a study of front dynamics in reaction-diffusion systems where anomalous diffusion is due to the presence of asymmetric Levy flights.
	www.ornl.gov /sci/fed/Theory/csd/research/projects/pf/frd.htm (157 words)

	Fractal Geometry (Site not responding. Last check: 2007-10-23)
		Some care is needed to simulate Levy flights.
		To build a random process with the desired properties, Levy added together many step functions, each multiplied by a factor to change the height of the step, and with the jumps happening at different times.
		To finish the construction, Levy specified the probability of including steps with times and amplitudes in a particular interval.
	classes.yale.edu /fractals/Randfrac/Levy/Levy4.html (92 words)

	Random walks and Lévy flights observed in fluid flows (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		The random walks in our experiment with coherent structures are L'evy flights: random walks with infinite mean square...
		4 Observation of anomalous diffusion and L'evy flights in a tw..
		3 Chaotic advection in a two-dimensional flow: L'evy flights a..
	citeseer.ist.psu.edu /432301.html (540 words)

	Fractal Geometry (Site not responding. Last check: 2007-10-23)
		First, we present the basic idea of Levy flights, and a visual example.
		The distribution of jumps of Levy flights is different from that of Brownain or fractional Brownian motion.
		Here are some examples of Levy flights in nature.
	classes.yale.edu /Fractals/RandFrac/Levy/Levy.html (47 words)

	Multi-scaling properties of truncated Lévy flights (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		Abstract: Multi-scaling properties of one-dimensional truncated Levy flights are studied.
		Due to the broken self-similarity of the distribution of jumps, they are expected to possess multi-scaling properties in contrast to the ordinary Levy flights.
		We argue this fact based on a smoothly truncated Levy distribution, and derive the functional form of the scaling exponents.
	citeseer.ist.psu.edu /379792.html (195 words)

	wojbor.html
		Probability theory, Levy stochastic processes, random fields and their statistics, nonlinear, stochastic and fractional evolution equations, harmonic and functional analysis, random graphs, statistical physics and hydrodynamics, chaotic dynamics, applications to chemistry, physics, operations research, financial mathematics, medicine, oceanography and atmospheric physics.
		Levy processes in the physical sciences, in Levy Processes - Theory and Applications, T. Mikosch, O. Barndorff-Nielsen, S. Resnick, Eds., (2001)Birkhauser-Boston, 241-266.
		Distributions of suprema of Levy processes via the heavy traffic invariance principle, (with W. czotka), Probability and Mathematical Statistics,23(2003), 251-272.
	stat.cwru.edu /~Wojbor (1575 words)

	Sunday afternoon, 19 November 1995, 14:00 (Site not responding. Last check: 2007-10-23)
		This anomalous (superdiffusive) transport arises because particles occasionally escape from a vortex and travel long distances before being captured by another vortex.
		The variance of the path length of the flights between vortices is in fact infinite -- such a divergent second moment is a defining property of L\'evy distributions.
		The anomalous diffusion appears with increasing Reynolds number as soon as the propagating chain of vortices (which forms from an instability of the initial axisymmetric flow) becomes time dependent.
	flux.aps.org /meetings/BAPSDFD95/abs/SS101.html (279 words)

	Publications (Site not responding. Last check: 2007-10-23)
		T. Garoni and N. Frankel, On the ubiquity of the Lévy integral - its relationship with the generalized Euler-Jacobi series and their asymptotics beyond all orders, Fractals 11, 93 (2003).
		T. Garoni and N. Frankel, d-dimensional Lévy flights: Exact and asymptotic, J.
		T. Garoni and N. Frankel, Lévy flights: Exact results and asymptotics beyond all orders, J.
	www.ima.umn.edu /~garoni/publications.html (186 words)

	Gregory Berkolaiko
		G. Berkolaiko, S. Havlin, Number of distinct sites visited by Lévy flights injected into a d-dimensional lattice, Phys.
		G. Berkolaiko, S. Havlin, Territory covered by N Lévy flights on d-dimensional lattices, Phys.
		G. Berkolaiko, S. Havlin, H. Larralde, G. Weiss Expected number of distinct sites visited by N Lévy flights on a one-dimensional lattice, Phys.
	www.math.tamu.edu /~berko/bib.html (528 words)

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