Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

Plasticity in the neural coding of auditory space in the mammalian brain

Sound localization relies on the neural processing of monaural and binaural spatial cues that arise from the way sounds interact with the head and external ears. Neurophysiological studies of animals raised with abnormal sensory inputs show that the map of auditory space in the superior colliculus is shaped during development by both auditory and visual experience. An example of this plasticity is provided by monaural occlusion during infancy, which leads to compensatory changes in auditory spatial tuning that tend to preserve the alignment between the neural representations of visual and auditory space. Adaptive changes also take place in sound localization behavior, as demonstrated by the fact that ferrets raised and tested with one ear plugged learn to localize as accurately as control animals. In both cases, these adjustments may involve greater use of monaural spectral cues provided by the other ear. Although plasticity in the auditory space map seems to be restricted to development, adult ferrets show some recovery of sound localization behavior after long-term monaural occlusion. The capacity for behavioral adaptation is, however, task dependent, because auditory spatial acuity and binaural unmasking (a measure of the spatial contribution to the “cocktail party effect”) are permanently impaired by chronically plugging one ear, both in infancy but especially in adulthood. Experience-induced plasticity allows the neural circuitry underlying sound localization to be customized to individual characteristics, such as the size and shape of the head and ears, and to compensate for natural conductive hearing losses, including those associated with middle ear disease in infancy.