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Some Considerations on Confined Water: The Thermal Behavior of Transport Properties in Water-Glycerol and Water-Methanol Mixtures
- Francesco Mallamace, Carmelo Corsaro, Domenico Mallamace, Cirino Vasi, Sebastiano Vasi, H. Eugene Stanley
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- MRS Advances / Volume 1 / Issue 26 / 2016
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- 26 January 2016, pp. 1891-1902
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- 2016
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We discuss recent literature data on the relaxation times (the primary tα), viscosity, and self-diffusion in water-glycerol and water-methanol mixtures across a wide temperature range from the stable water phase to the deep supercooled regime (373–147K). In particular, to clarify the role of hydrophilicity interactions (the hydrogen bonds) and hydrophobic interactions we study the mixture in terms of the water molar fraction (XW) with fixed temperatures at 5K steps across the entire composition range, and we find a marked deviation from the ideal thermodynamic behavior of the transport functions. This deviation is strongly T and XW dependent and spans values that range from two orders of magnitude at the highest temperature to more than five in the deeply supercooled regime (more precisely, at ≃200K). We analyze these deviations in terms of how the measured values differ from ideal values and find that the hydrogen-bonding water network dominates system properties up to XW = 0.3. We also examine an Arrhenius plot of the maximum excess value (Δtα(T) vs. 1/T) and find two significant changes due to water: one at the dynamical crossover temperature (TL ≃ 225K, i.e., the locus of the Widom line), and one at T ≃ 315K (the water isothermal compressibility χT minimum).
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. 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Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. 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Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- The Cambridge Dictionary of Philosophy
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- 05 August 2015
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- 27 April 2015, pp ix-xxx
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Prenatal stress and risk of behavioral morbidity from age 2 to 14 years: The influence of the number, type, and timing of stressful life events—ERRATUM
- Monique Robinson, Eugen Mattes, Wendy H. Oddy, Craig E. Pennell, Anke van Eekelen, Neil J. McLean, Peter Jacoby, Jianghong Li, Nicholas H. de Klerk, Stephen R. Zubrick, Fiona J. Stanley, John P. Newnham
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- Development and Psychopathology / Volume 24 / Issue 1 / February 2012
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- 31 January 2012, e1
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Contents
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 05 August 2012
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- 02 June 2011, pp vii-x
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9 - Optimizing encounter rates
- from Part III - Theory of foraging
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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Summary
The central idea underlying theoretical studies of the movement of organisms is that they need to encounter their targets. The targets can be other organisms of the same species (e.g., mates) or of a different species (e.g., prey) or, more generally, anything else sought (e.g., nesting sites). In the context of reactiondiffusion processes, the reactions (e.g., eating and mating) only take place when the relevant organisms successfully diffuse toward each other and meet. We next discuss a general theoretical approach to the study of encounter rates.
A general theory of searchers and targets
We classify the two interacting reactive-diffusive species (i.e., organisms) as either searcher (e.g., predator, forager, parasite, pollinator, male) or target (e.g., prey, food, female). Both searchers and targets move stochastically. We can now include most of the interactions in real ecosystems in this general framework [19], including the classical predator-prey interactions where an organism eats (usually smaller) organisms. It also includes diverse other interactions, such as osmotrophs looking for substrates and nutrients; parasites (including viruses) infecting organisms much larger than themselves (classical host-parasite interactions); organisms looking for aggregates (mixtures of amorphous organic matter, micro-organisms and/or inorganic particles), swarms, wakes, etc., also larger than themselves; and even mating encounters in which both male and female may have similar sizes (although sexual dimorphism is common) [19].
According to the theory of optimal foraging [128, 364], evolution through natural selection has led over time to highly efficient – even optimal – strategies.
13 - Adaptational versus emergent superdiffusion
- from Part IV - Finale: A broader context
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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Summary
From the previous chapters, we see that (1) superdiffusion optimizes search efficiencies under specific (but common) circumstances and that (2) many animals move superdiffusively. Assuming these two facts, does it follow that there is a causal relation between them? Lévy strategies indeed optimize random searches, but does it necessarily follow that selective pressures systematically forced organism adaptation toward this optimal solution?
This is an important question because an adaptive pathway toward an optimal solution can prematurely stop at some suboptimal point that decreases the selection pressure on this particular feature to a level below the selective pressures on other issues [397]. Biology and physiology are replete with suboptimal solutions. The classic example is the structure of the human retina, which has blood vessels on the wrong side of the photosensitive layer [96]. Compromise solutions arise because adaptation (1) includes a stochastic component, (2) has to build on preexisting designs, and (3) occurs in a complex field where other pressures may be present and may possibly be stronger.
Dolphins, in the context of (mammalian) swimming adaptations, perform well, but how can we know whether or not their shape represents an optimal design? Some species of shark may have an even better hydrodynamic shape. Also, why did dolphins return to the ocean when selective pressures were pushing for improved terrestrial adaptation? The complex evolutionary history of real organisms contains many such contingent situations, such as changing selective pressures, genetic drift, low-number bottlenecks, and rare catastrophic events.
Part I - Introduction: Movement
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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4 - The wandering albatross
- from Part I - Introduction: Movement
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 02 June 2011, pp 42-50
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Summary
Do good theories always come from good data?
According to conventional wisdom concerning the scientific method, good theories come from good experimental data, and bad theories from bad experimental data. Yet the history of the physics of foraging is a remarkable counterexample. To illustrate this, we briefly recount one of the important scientific investigations in the field, published in Nature in 1996. The original study of wandering albatrosses [390] inspired dozens of other studies, yet later required correction due to its spurious data.
Lévy flights of the wandering albatross
The albatross can fly great distances, at exceptional speeds. There are significant differences among species of albatross [402]. Wandering albatrosses in southern Georgia can sustain a speed in excess of 100 km/h by taking advantage of the local wind field [284]. They frequently fly 500 km per day, with an upper limit in the range 750–950 km per day. Phillips et al. [284] report that one gray-headed albatross circumnavigated the Southern Ocean in only 46 days. Because of their great mobility and large size, we decided to focus on the albatross (instead of, e.g., the sparrow) in our original study. The foraging strategy of the wandering albatross [403] stands apart from that of other seabirds [401]. Weimerskirch et al. [404] studied the distribution of prey encounters for wandering albatrosses and reported results that strongly suggest a foraging strategy that differs from those of most seabirds.
Part II - Experimental findings
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 02 June 2011, pp 51-52
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5 - Early studies
- from Part II - Experimental findings
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 02 June 2011, pp 53-57
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Summary
Fickian transport
The classic paradigm of simple diffusion is used to describe a wide range of phenomena, ranging from how the original humans migrated and dispersed out of Africa to the spread of pollen. Until the twentieth century, Fick's laws were thought to be universally valid for describing diffusion. The physiologist Adolf Fick introduced the idea that diffusion is proportional to the gradient of concentration. For practical as well as for historical reasons, normal diffusion is commonly assumed for transport processes. For example, Fourier's law for heat flow is analogous to Fick's laws of diffusion, with temperature gradients playing the role of concentration gradients.
Like Gaussian statistics, normal diffusion is ubiquitous because of the wide applicability of the central limit theorem. Standard methods in spatial ecology traditionally have tended to assume Brownian motion and Fickian diffusion as two basic properties of animal movement in the long time limit, i.e., at large spatial scales and long temporal scales. We refer the reader to the seminal book by Berg [35] on random walks in biology.
Fickian or normal diffusion assumes that animal movements can be modeled, in the long-term limit, as uncorrelated random walks [21, 35, 265]. In many cases, normal diffusion describes experimentally observed phenomena. The classic study by Skellam [349] of the colonization of Europe by muskrats assumed normal diffusion, for example (Figure 5.1).
10 - Lévy flight foraging
- from Part III - Theory of foraging
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- 02 June 2011, pp 85-99
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The Physics of Foraging
- An Introduction to Random Searches and Biological Encounters
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Ernesto P. Raposo, H. Eugene Stanley
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- 05 August 2012
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- 02 June 2011
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Do the movements of animals, including humans, follow patterns that can be described quantitatively by simple laws of motion? If so, then why? These questions have attracted the attention of scientists in many disciplines, and stimulated debates ranging from ecological matters to queries such as 'how can there be free will if one follows a law of motion?' This is the first book on this rapidly evolving subject, introducing random searches and foraging in a way that can be understood by readers without a previous background on the subject. It reviews theory as well as experiment, addresses open problems and perspectives, and discusses applications ranging from the colonization of Madagascar by Austronesians to the diffusion of genetically modified crops. The book will interest physicists working in the field of anomalous diffusion and movement ecology as well as ecologists already familiar with the concepts and methods of statistical physics.
11 - Other search models
- from Part III - Theory of foraging
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- 02 June 2011, pp 100-108
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Summary
The results discussed in Chapter 10 have inspired a renewed interest in fundamental questions relating to random searches. We have seen that Lévy flights have scalefree properties such that there is no unique characteristic scale in the random walk flight length (or step length) distribution p(ℓ). In contrast, Wiener noise, unlike Lévy processes, has a well-defined characteristic scale because all moments are finite. Are the high search efficiencies of Lévy flight foraging due to the multiple scales or, equivalently, to the scale-free properties? How many scales would be sufficient to guarantee high encounter rates and search efficiencies? Perhaps scalefree properties are not needed after all, and a few scales would be sufficient. In this chapter, we review search models that contain free parameters embedding characteristic scales.
Correlated random walks with a single scale
The most natural and obvious choice for the fewest number of characteristic scales is one. Correlated random walks (CRWs) appeared the study of ecology when short- and medium-scaled animal movement data were analyzed. CRWs have a single characteristic scale – a correlation length or time that can be quantified via sinuosity. Experiments with ants, beetles, and butterflies were performed in 15 to 20 square meter arenas as well as in their natural environments (and usually lasted fewer than 45 minutes). From these studies, ecologists promptly became aware of the necessity of adding directional persistence to pure random walks to reproduce realistic animal movements [21, 42, 173].
References
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- 02 June 2011, pp 140-160
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6 - Evidence of anomalous diffusion
- from Part II - Experimental findings
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 02 June 2011, pp 58-63
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Summary
In addition to the early studies we discussed in Chapter 5, here we review other experimental studies. We focus on animal movement because of the relative abundance of data and larger velocities relative to plant seeds, pollen, etc. We note, however, that seed shadows are often fat tailed [408] (i.e., leptokurtic), so many plants may also disperse superdiffusively.
Arthropods and mollusks
Honey bees, fruit flies, and desert ants
Reynolds et al. [306, 307] studied bees using a variety of techniques. In one study, they [306] used harmonic radar to record the flight paths of honey bees that were searching for their hives. Harmonic radar can differentiate between the harmonic signal returned from a specific target and signals returned from all other passive reflectors. Analysis of the trajectories indicated scale-invariant walks with a power law exponent µ ≈ 2 (see also [300]), corresponding to a Lévy index α = 1. They argued that these results, combined with the no preferred direction characteristic of the segments, demonstrate that the bees were flying an optimal search pattern. An inverse square power law distribution (µ = 2) is exactly what the theory of Lévy flight foraging predicts (see Chapter 10).
In another study, Reynolds et al. [307] trained foraging honey bees to seek out an artificial feeder, which was subsequently removed. The resulting bee flight patterns were recorded using harmonic radar and showed that the flight patterns have the scale-free characteristic of Lévy walks.
14 - Perspectives and open problems
- from Part IV - Finale: A broader context
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 02 June 2011, pp 123-130
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The flavor of foraging research
The physics of foraging is exciting because so little is known and so many questions remain. Biological foraging and random searching are relatively new fields, and considerable effort is still being made to establish theoretical foundations and reliable and general methods of data collection and analysis. Many challenges are still to be overcome, most of them related to technical issues and interpretation of findings.
In this final chapter, we put the major open problems into perspective. One reason for the skepticism about anomalous diffusion and Lévy flights is the lack of obvious biological mechanisms for generating superdiffusive random walks. We will also discuss the issue of free will and the existence and uniqueness of globally optimum strategies. We begin with two problems currently being studied by researchers.
Foraging on the edge of extinction
In mass extinctions and smaller-scale extinctions, the density of organisms becomes zero (if extinction is total) or very low (if recovery eventually takes place). We saw in Chapter 13 that as the density of targets lowers, the importance of superdiffusion increases. How does organism movement change during extinction events? Is there any change in the selection pressure on how organisms move? Such questions remain relatively unexplored at the present time.
Lévy searches on small-world networks
We saw in Chapter 10 that Lévy motion can confer advantages to search processes not only in Euclidean spaces but also in discrete analogues (large-world networks), but what happens in the environment of small-world networks?
Preface
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 02 June 2011, pp xi-xiv
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As the FBI helps a 14-year-old victim who escaped from a dangerous polygamist self-proclaimed prophet, it is faced with the question of how to search 2200 square miles of mountain desert.
“How rough is the terrain? Because the rougher the terrain, the more likely she was forced into a Lévy flight type movement. I can create a viable search pattern,” says Charlie Eppes, the mathematical genius.
“It's like when you lose your keys,” explains Amita Ramanujan, his girlfriend and former doctoral student. “You don't methodically search every inch of your house from front to back. You look like crazy in one area, and then jump to the next most likely area and look there.”
The preceding dialogue, from the American television series Numb3rs, shows how far the theory of Lévy flight foraging has penetrated mainstream science. Although the term foraging has a biological connotation, in fact, biological foraging is a special case of random searches. Michael Shlesinger, for instance, has pointed out the relevance of random searches to operations research in World War II, involving the hunt for enemy submarines.
There are intriguing aspects of the random search problem that are peculiar to biological foraging. Why should the movements of freely moving animals follow any natural law at all? This is a fascinating question, and we find it remarkable that animals – and even humans – that possess a degree of “free will” actually move in a manner that can be described quantitatively by physical principles.
Index
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 05 August 2012
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- 02 June 2011, pp 161-164
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7 - Human dispersal
- from Part II - Experimental findings
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- The Physics of Foraging
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- 05 August 2012
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- 02 June 2011, pp 64-70
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Summary
This chapter reviews the evidence in favor of anomalous diffusion in the movement of human beings. Human diffusion constitutes a driving force for various spatiotemporal phenomena that occur on large geographical scales [52], and can synchronize and stabilize populations as well as diversify gene pools.
The spread of infectious disease, for example, depends on human diffusion. Consider, for example, the spread of swine flu (H1N1 influenza A [56]), resulting in the World Health Organization raising the pandemic alert to phase 6 – the highest level – in June 2009, only a few months after the virus's first appearance in Mexico. It is difficult to model or understand the pandemic in terms of normal diffusion or the kinds of wave fronts seen in solutions of the standard (i.e., nonfractional) Fisher-Kolmogorov equation. The virus appears to jump across continents and oceans in a very short time, in a manner more commensurate with superdiffusion than with normal diffusion. Similarly, the 1918 flu pandemic (Spanish flu) lasted only a couple years but reached nearly all corners of the planet with a rapidity consistent with a superdiffusive process mediated by human mobility.
Given the role of human diffusion – or superdiffusion – in pandemics and other reaction-diffusion processes, we now examine how humans diffuse. Because we assume that air, sea, and highway transportation increase mobility and diffusivity, we begin by looking at human societies that predate those modern modes of travel.
Part IV - Finale: A broader context
- Gandhimohan. M. Viswanathan, Marcos G. E. da Luz, Universidade Federal do Paraná, Brazil, Ernesto P. Raposo, Universidade Federal de Pernambuco, Brazil, H. Eugene Stanley, Boston University
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- Book:
- The Physics of Foraging
- Published online:
- 05 August 2012
- Print publication:
- 02 June 2011, pp 109-110
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