Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulent shear flow.

The small viscosity asymptotics of the inertial range of local structure and of the wall region in wallbounded turbulent shear flow are compared. The comparison leads to a sharpening of the dichotomy between Reynolds number dependent scaling (power-type) laws and the universal Reynolds number independent logarithmic law in wall turbulence. It further leads to a quantitative prediction of an essential difference between them, which is confirmed by the results of a recent experimental investigation. These results lend support to recent work on the zero viscosity limit of the inertial range in turbulence.

Substratal idiothetic navigation of rats is impaired by removal or devaluation of extramaze and intramaze cues

The spatial orientation of vertebrates is implemented by two complementary mechanisms: allothesis, processing the information about spatial relationships between the animal and perceptible landmarks, and idiothesis, processing the substratal and inertial information produced by the animal's active or passive movement through the environment. Both systems allow the animal to compute its position with respect to perceptible landmarks and to the already traversed portion of the path. In the present study, we examined the properties of substratal idiothesis deprived of relevant exteroceptive information. Rats searching for food pellets in an arena formed by a movable inner disk and a peripheral immobile belt were trained in darkness to avoid a 60° sector; rats that entered this sector received a mild foot shock. The punished sector was defined in the substratal idiothetic frame, and the rats had to determine the location of the shock sector with the use of substratal idiothesis only, because all putative intramaze cues were made irrelevant by angular displacements of the disk relative to the belt. Striking impairment of place avoidance by this “shuffling procedure” indicates that effective substratal idiothesis must be updated by exteroceptive intramaze cues.

Resonant tectorial membrane motion in the inner ear: its crucial role in frequency tuning.

The tectorial membrane has long been postulated as playing a role in the exquisite sensitivity of the cochlea. In particular, it has been proposed that the tectorial membrane provides a second resonant system, in addition to that of the basilar membrane, which contributes to the amplification of the motion of the cochlear partition. Until now, technical difficulties had prevented vibration measurements of the tectorial membrane and, therefore, precluded direct evidence of a mechanical resonance. In the study reported here, the vibration of the tectorial membrane was measured in two orthogonal directions by using a novel method of combining laser interferometry with a photodiode technique. It is shown experimentally that the motion of the tectorial membrane is resonant at a frequency of 0.5 octave (oct) below the resonant frequency of the basilar membrane and polarized parallel to the reticular lamina. It is concluded that the resonant motion of the tectorial membrane is due to a parallel resonance between the mass of the tectorial membrane and the compliance of the stereocilia of the outer hair cells. Moreover, in combination with the contractile force of outer hair cells, it is proposed that inertial motion of the tectorial membrane provides the necessary conditions to allow positive feedback of mechanical energy into the cochlear partition, thereby amplifying and tuning the cochlear response.

Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Turbulent diffusion phase transition is due to singular energy spectrum.

The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion.