منابع مشابه
Acoustic Waves in Long Range Random Media
We consider waves propagating through multiscale media. Much is known about waves propagating through a medium that satisfies a scale separation assumption with random fluctuations on a microscale. Here we go beyond this situation and consider waves propagating through a medium defined in terms of a long range process. Such a medium can for instance be modeled in terms of a one-dimensional frac...
متن کاملAcoustic Waves in Long Range
We consider waves propagating through multiscale media. Much is known about waves propagating through a medium that satisfies a scale separation assumption with random fluctuations on a microscale. Here we go beyond this situation and consider waves propagating through a medium defined in terms of a long range process. Such a medium can, for instance, be modeled in terms of a one-dimensional fr...
متن کاملA General Framework for Waves in Random Media with Long-range Correlations
We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in [19] and leads in particular to an asymptotic travel time described in terms of a fractional Brownian motion. Here we study the asymptotic transmitted pulse under very general assumptions on the long-range correlations. In the framework that we introduce in this pap...
متن کاملPulse Propagation in Random Media with Long-Range Correlation
Abstract. This paper analyses wave propagation in a one-dimensional random medium with long-range correlations. The asymptotic regime where the fluctuations of the medium parameters are small and the propagation distance is large is studied. In this regime pulse propagation is characterized by a random time shift described in terms of a fractional Brownian motion and a deterministic spreading d...
متن کاملWaves in Random Neural Media
Translationally invariant integro-differential equations are a common choice of model in neuroscience for describing the coarse-grained dynamics of cortical tissue. Here we analyse the propagation of travelling wavefronts in models of neural media that incorporate some form of modulation or randomness such that translational invariance is broken. We begin with a study of neural architectures in...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Mathematics
سال: 2009
ISSN: 0036-1399,1095-712X
DOI: 10.1137/07068610x