Conformal invariance in two-dimensional turbulence

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2d) locality often promotes scale invariance to a wider class of conformal transformations which allow for nonuniform re-scaling. Conformal invariance allows a thorough classification of universality classes of critical phenomena in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example of strongly-interacting non-equilibrium system? Here, using numerical experiment, we show that some features of 2d inverse turbulent cascade display conformal invariance. We observe that the statistics of vorticity clusters is remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a new step in the unification of 2d physics within the framework of conformal symmetry.Comment: 10 pages, 5 figures, 1 tabl

Auditory temporal processing in healthy aging: a magnetoencephalographic study

<p>Abstract</p> <p>Background</p> <p>Impaired speech perception is one of the major sequelae of aging. In addition to peripheral hearing loss, central deficits of auditory processing are supposed to contribute to the deterioration of speech perception in older individuals. To test the hypothesis that auditory temporal processing is compromised in aging, auditory evoked magnetic fields were recorded during stimulation with sequences of 4 rapidly recurring speech sounds in 28 healthy individuals aged 20 – 78 years.</p> <p>Results</p> <p>The decrement of the N1m amplitude during rapid auditory stimulation was not significantly different between older and younger adults. The amplitudes of the middle-latency P1m wave and of the long-latency N1m, however, were significantly larger in older than in younger participants.</p> <p>Conclusion</p> <p>The results of the present study do not provide evidence for the hypothesis that auditory temporal processing, as measured by the decrement (short-term habituation) of the major auditory evoked component, the N1m wave, is impaired in aging. The differences between these magnetoencephalographic findings and previously published behavioral data might be explained by differences in the experimental setting between the present study and previous behavioral studies, in terms of speech rate, attention, and masking noise. Significantly larger amplitudes of the P1m and N1m waves suggest that the cortical processing of individual sounds differs between younger and older individuals. This result adds to the growing evidence that brain functions, such as sensory processing, motor control and cognitive processing, can change during healthy aging, presumably due to experience-dependent neuroplastic mechanisms.</p

Geometry and field theory in multi-fractional spacetime

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with fixed dimension, presented in a companion paper, we generalize to a multi-fractional scenario inspired by multi-fractal geometry, where the dimension changes with the scale. This is related to the renormalization group properties of fractional field theories, illustrated by the example of a scalar field. Depending on the symmetries of the Lagrangian, one can define two models. In one of them, the effective dimension flows from 2 in the ultraviolet (UV) and geometry constrains the infrared limit to be four-dimensional. At the UV critical value, the model is rendered power-counting renormalizable. However, this is not the most fundamental regime. Compelling arguments of fractal geometry require an extension of the fractional action measure to complex order. In doing so, we obtain a hierarchy of scales characterizing different geometric regimes. At very small scales, discrete symmetries emerge and the notion of a continuous spacetime begins to blur, until one reaches a fundamental scale and an ultra-microscopic fractal structure. This fine hierarchy of geometries has implications for non-commutative theories and discrete quantum gravity. In the latter case, the present model can be viewed as a top-down realization of a quantum-discrete to classical-continuum transition.Comment: 1+82 pages, 1 figure, 2 tables. v2-3: discussions clarified and improved (especially section 4.5), typos corrected, references added; v4: further typos correcte

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe