Fractal contours: Order, chaos, and art.

Over the recent decades, a variety of indices, such as the fractal dimension, Hurst exponent, or Betti numbers, have been used to characterize structural or topological properties of art via a singular parameter, which could then help to classify artworks. A single fractal dimension, in particular, has been commonly interpreted as characteristic of the entire image, such as an abstract painting, whether binary, gray-scale, or in color, and whether self-similar or not. There is now ample evidence, however, that fractal exponents obtained using the standard box-counting are strongly dependent on the details of the method adopted, and on fitting straight lines to the entire scaling plots, which are typically nonlinear.

Towards spectrally selective catastrophic response.

We study the large-amplitude response of classical molecules to electromagnetic radiation, showing the universality of the transition from linear to nonlinear response and breakup at sufficiently large amplitudes. We demonstrate that a range of models, from the simple harmonic oscillator to the successful Peyrard-Bishop-Dauxois type models of DNA, which include realistic effects of the environment (including damping and dephasing due to thermal fluctuations), lead to characteristic universal behavior: formation of domains of dissociation in driving force amplitude-frequency space, characterized by the presence of local boundary minima. We demonstrate that by simply following the progression of the resonance maxima in this space, while gradually increasing intensity of the radiation, one must necessarily arrive at one of these minima, i.

A bio-inspired 3D quasi-fractal nanostructure for an improved oxygen evolution reaction.

We demonstrate a bio-inspired three-dimensional (3D) hierarchical catalyst, based on the Fe-doped nanoarrays of dendritic nickel trees, which provides large surface area, close to optimal electron transport, and large inter-branch open-channels for improving gas-bubble release, outperforming the benchmark catalyst of noble RuO2.

Optimization of hierarchical structure and nanoscale-enabled plasmonic refraction for window electrodes in photovoltaics.

An ideal network window electrode for photovoltaic applications should provide an optimal surface coverage, a uniform current density into and/or from a substrate, and a minimum of the overall resistance for a given shading ratio. Here we show that metallic networks with quasi-fractal structure provides a near-perfect practical realization of such an ideal electrode. We find that a leaf venation network, which possesses key characteristics of the optimal structure, indeed outperforms other networks.

Bio-inspired networks for optoelectronic applications.

Modern optoelectronics needs development of new materials characterized not only by high optical transparency and electrical conductivity, but also by mechanical strength, and flexibility. Recent advances employ grids of metallic micro- and nanowires, but the overall performance of the resulting material composites remains unsatisfactory. In this work, we propose a new strategy: application of natural scaffoldings perfected by evolution.