5,795 research outputs found
Power laws statistics of cliff failures, scaling and percolation
The size of large cliff failures may be described in several ways, for
instance considering the horizontal eroded area at the cliff top and the
maximum local retreat of the coastline. Field studies suggest that, for large
failures, the frequencies of these two quantities decrease as power laws of the
respective magnitudes, defining two different decay exponents. Moreover, the
horizontal area increases as a power law of the maximum local retreat,
identifying a third exponent. Such observation suggests that the geometry of
cliff failures are statistically similar for different magnitudes. Power laws
are familiar in the physics of critical systems. The corresponding exponents
satisfy precise relations and are proven to be universal features, common to
very different systems. Following the approach typical of statistical physics,
we propose a "scaling hypothesis" resulting in a relation between the three
above exponents: there is a precise, mathematical relation between the
distributions of magnitudes of erosion events and their geometry. Beyond its
theoretical value, such relation could be useful for the validation of field
catalogs analysis. Pushing the statistical physics approach further, we develop
a numerical model of marine erosion that reproduces the observed failure
statistics. Despite the minimality of the model, the exponents resulting from
extensive numerical simulations fairly agree with those measured on the field.
These results suggest that the mathematical theory of percolation, which lies
behind our simple model, can possibly be used as a guide to decipher the
physics of rocky coast erosion and could provide precise predictions to the
statistics of cliff collapses.Comment: 20 pages, 13 figures, 1 table. To appear in Earth Surface Processes
and Lanforms (Rocky Coast special issue
A-D-E Classification of Conformal Field Theories
The ADE classification scheme is encountered in many areas of mathematics,
most notably in the study of Lie algebras. Here such a scheme is shown to
describe families of two-dimensional conformal field theories.Comment: 19 pages, 4 figures, 4 tables; review article to appear in
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Field theory of self-organized fractal etching
We propose a phenomenological field theoretical approach to the chemical
etching of a disordered-solid. The theory is based on a recently proposed
dynamical etching model. Through the introduction of a set of Langevin
equations for the model evolution, we are able to map the problem into a field
theory related to isotropic percolation. To the best of the authors knowledge,
it constitutes the first application of field theory to a problem of chemical
dynamics. By using this mapping, many of the etching process critical
properties are seen to be describable in terms of the percolation
renormalization group fixed point. The emerging field theory has the
peculiarity of being ``{\it self-organized}'', in the sense that without any
parameter fine-tuning, the system develops fractal properties up to certain
scale controlled solely by the volume, , of the etching solution.
In the limit the upper cut-off goes to infinity and the system
becomes scale invariant. We present also a finite size scaling analysis and
discuss the relation of this particular etching mechanism with Gradient
Percolation.
Finally, the possibility of considering this mechanism as a new generic path
to self-organized criticality is analyzed, with the characteristics of being
closely related to a real physical system and therefore more directly
accessible to experiments.Comment: 9 pages, 3 figures. Submitted to Phys. Rev.
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Chemical etching of a disordered solid: from experiments to field theory
We present a two-dimensional theoretical model for the slow chemical
corrosion of a thin film of a disordered solid by suitable etching solutions.
This model explain different experimental results showing that the corrosion
stops spontaneously in a situation in which the concentration of the etchant is
still finite while the corrosion surface develops clear fractal features. We
show that these properties are strictly related to the percolation theory, and
in particular to its behavior around the critical point. This task is
accomplished both by a direct analysis in terms of a self-organized version of
the Gradient Percolation model and by field theoretical arguments.Comment: 7 pages, 3 figure
Closed-form expressions for the total power radiated by an electrically long multiconductor line
International audienceTwo analytical solutions based on transmission-line theory for the total power radiated by a multiconductor line above a ground-plane are proposed. The line is not assumed to be electrically short or close to the ground-plane, thus making the proposed model suitable for assessing the emission/immunity of actual transmission-lines employed in industrial contexts such as in the automotive domain, in railway lines and power-distribution lines. The model allows an imperfect ground plane to be considered through the complex-image approximation, together with propagation losses. Numerical and experimental results are provided as a validation, while an empirical rule to assess the accuracy of the results is proposed. The two expressions aim at allowing fast parametric analysis of radiation during the design phase of the electrical and geometrical configuration of an unshielded MTL
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