Heller EJ, Fleischmann R and Kramer T (2019), "Branched Flow", arXiv:1910.07086 [physics]., October, 2019. |
Abstract: In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual sub-wavelength features) is absent. Eventually the weak refraction leads to imperfect focal "cusps". Much later, a statistical regime characterized by momentum diffusion is manifested. An important intermediate regime is often overlooked, one that is diffusive only in an ensemble sense. Each realization of the ensemble possesses dramatic ray limit structure that guides the waves (in the same sense that ray optics is used to design lens systems). This structure is a universal phenomenon called branched flow. Many important phenomena develop in this intermediate regime. Here we give examples and some of the physics of this emerging field. |
BibTeX:
@article{heller_branched_2019, author = {Heller, Eric J. and Fleischmann, Ragnar and Kramer, Tobias}, title = {Branched Flow}, journal = {arXiv:1910.07086 [physics]}, year = {2019}, note = {arXiv: 1910.07086}, url = {http://arxiv.org/abs/1910.07086} } |
Degueldre H, Metzger JJ, Schultheis E and Fleischmann R (2017), "Channeling of Branched Flow in Weakly Scattering Anisotropic Media", Physical Review Letters., January, 2017. Vol. 118(2), pp. 024301. |
Abstract: When waves propagate through weakly scattering but correlated, disordered environments they are randomly focused into pronounced branchlike structures, a phenomenon referred to as branched flow, which has been studied in a wide range of isotropic random media. In many natural environments, however, the fluctuations of the random medium typically show pronounced anisotropies. A prominent example is the focusing of tsunami waves by the anisotropic structure of the ocean floor topography. We study the influence of anisotropy on such natural focusing events and find a strong and nonintuitive dependence on the propagation angle which we explain by semiclassical theory. |
BibTeX:
@article{degueldre_channeling_2017, author = {Degueldre, Henri and Metzger, Jakob J. and Schultheis, Erik and Fleischmann, Ragnar}, title = {Channeling of Branched Flow in Weakly Scattering Anisotropic Media}, journal = {Physical Review Letters}, year = {2017}, volume = {118}, number = {2}, pages = {024301}, doi = {10.1103/PhysRevLett.118.024301} } |
Metzger JJ, Fleischmann R and Geisel T (2014), "Statistics of Extreme Waves in Random Media", Physical Review Letters., May, 2014. Vol. 112(20), pp. 203903. |
Abstract: Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the statistics of the highest waves is important for their analysis and forecast, it remains poorly understood, in particular, in the regime where the waves are highest. We suggest a new approach that greatly simplifies the mathematical analysis and calculate the scaling and the distribution of the highest waves valid for a wide range of parameters. |
BibTeX:
@article{metzger_statistics_2014, author = {Metzger, Jakob J. and Fleischmann, Ragnar and Geisel, Theo}, title = {Statistics of Extreme Waves in Random Media}, journal = {Physical Review Letters}, year = {2014}, volume = {112}, number = {20}, pages = {203903}, note = {00000}, doi = {10.1103/PhysRevLett.112.203903} } |
Metzger JJ, Fleischmann R and Geisel T (2013), "Intensity Fluctuations of Waves in Random Media: What Is the Semiclassical Limit?", Physical Review Letters., July, 2013. Vol. 111(1), pp. 013901. |
Abstract: Waves traveling through weakly random media are known to be strongly affected by their corresponding ray dynamics, in particular in forming linear freak waves. The ray intensity distribution, which, e.g., quantifies the probability of freak waves is unknown, however, and a theory of how it is approached in an appropriate semiclassical limit of wave mechanics is lacking. We show that this limit is not the usual limit of small wavelengths, but that of decoherence. Our theory, which can describe the intensity distribution for an arbitrary degree of coherence is relevant to a wide range of physical systems, as decoherence is omnipresent in real systems. |
BibTeX:
@article{metzger_intensity_2013, author = {Metzger, Jakob J. and Fleischmann, Ragnar and Geisel, Theo}, title = {Intensity Fluctuations of Waves in Random Media: What Is the Semiclassical Limit?}, journal = {Physical Review Letters}, year = {2013}, volume = {111}, number = {1}, pages = {013901}, doi = {10.1103/PhysRevLett.111.013901} } |
Metzger J, Fleischmann R and Geisel T (2010), "Universal Statistics of Branched Flows", Physical Review Letters., July, 2010. Vol. 105(2), pp. 020601. |
BibTeX:
@article{metzger_universal_2010, author = {Metzger, Jakob and Fleischmann, Ragnar and Geisel, Theo}, title = {Universal Statistics of Branched Flows}, journal = {Physical Review Letters}, year = {2010}, volume = {105}, number = {2}, pages = {020601}, doi = {10.1103/PhysRevLett.105.020601} } |
Wilkinson M and Mehlig B (2005), "Caustics in turbulent aerosols", Europhysics Letters. Vol. 71(2), pp. 186-192.
[BibTeX] |
BibTeX:
@article{Wilkinson2005, author = {Wilkinson, M. and Mehlig, B.}, title = {Caustics in turbulent aerosols}, journal = {Europhysics Letters}, year = {2005}, volume = {71}, number = {2}, pages = {186--192} } |
Kaplan L (2002), "Statistics of Branched Flow in a Weak Correlated Random Potential", Physical Review Letters., October, 2002. Vol. 89(18), pp. 184103. |
BibTeX:
@article{Kaplan2002, author = {Kaplan, Lev}, title = {Statistics of Branched Flow in a Weak Correlated Random Potential}, journal = {Physical Review Letters}, year = {2002}, volume = {89}, number = {18}, pages = {184103}, doi = {10.1103/PhysRevLett.89.184103} } |
Klyatskin VI (1993), "Caustics in random media", Waves in Random and Complex Media. Vol. 3(2), pp. 93-100.
[BibTeX] |
BibTeX:
@article{Klyatskin1993, author = {Klyatskin, V. I.}, title = {Caustics in random media}, journal = {Waves in Random and Complex Media}, year = {1993}, volume = {3}, number = {2}, pages = {93--100} } |
Kravtsov YA and Orlov YI (1993), "Caustics, Catastrophes and Wave Fields" Berlin, Heidelberg Vol. 15 Springer Berlin Heidelberg. |
BibTeX:
@book{Kravtsov1993, author = {Kravtsov, Yu. A. and Orlov, Yu. I.}, editor = {Brekhovskikh, Leonid M. and Felsen, Leopold B. and Haus, Hermann A.}, title = {Caustics, Catastrophes and Wave Fields}, publisher = {Springer Berlin Heidelberg}, year = {1993}, volume = {15}, doi = {10.1007/978-3-642-97491-5} } |
White BS (1984), "The Stochastic Caustic" Vol. 44(1), pp. 127-149. |
BibTeX:
@article{White1984, author = {White, B. S}, title = {The Stochastic Caustic}, year = {1984}, volume = {44}, number = {1}, pages = {127--149}, url = {http://www.jstor.org/stable/2101309} } |
Kulkarny VA and White B (1982), "Focusing of waves in turbulent inhomogeneous media", Physics of Fluids. Vol. 25(10), pp. 1770. |
BibTeX:
@article{Kulkarny1982, author = {Kulkarny, V. A. and White, B.S.}, title = {Focusing of waves in turbulent inhomogeneous media}, journal = {Physics of Fluids}, year = {1982}, volume = {25}, number = {10}, pages = {1770}, doi = {10.1063/1.863654} } |