Different hierarchy of avalanches observed in the Bak-Sneppen evolution model

We introduce a new quantity, average fitness, into the Bak-Sneppen evolution model. Through the new quantity, a different hierarchy of avalanches is observed. The gap equation, in terms of the average fitness, is presented to describe the self-organization of the model. It is found that the critical value of the average fitness can be exactly obtained. Based on the simulations, two critical exponents, avalanche distribution and avalanche dimension, of the new avalanches are given.Comment: 5 pages, 3 figure

Avalanche Dynamics in Evolution, Growth, and Depinning Models

The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and evolution is presented. Specifically, we include the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models into a unified treatment encompassing a large class of far from equilibrium processes. The formation of fractal structures, the appearance of $1/f$ noise, diffusion with anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be related to the same underlying avalanche dynamics. This dynamics can be represented as a fractal in $d$ spatial plus one temporal dimension. We develop a scaling theory that relates many of the critical exponents in this broad category of extremal models, representing different universality classes, to two basic exponents characterizing the fractal attractor. The exact equations and the derived set of scaling relations are consistent with numerical simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the manuscript supplied on reques

Laser Interactions for the Synthesis and In Situ Diagnostics of Nanomaterials

Laser interactions have traditionall been at thec center of nanomaterials science, providing highly nonequilibrium growth conditions to enable the syn- thesis of novel new nanoparticles, nanotubes, and nanowires with metastable phases. Simultaneously, lasers provide unique opportunities for the remote char- acterization of nanomaterial size, structure, and composition through tunable laser spectroscopy, scattering, and imaging. Pulsed lasers offer the opportunity, there- fore, to supply the required energy and excitation to both control and understand the growth processes of nanomaterials, providing valuable views of the typically nonequilibrium growth kinetics and intermediates involved. Here we illustrate the key challenges and progress in laser interactions for the synthesis and in situ diagnostics of nanomaterials through recent examples involving primarily carbon nanomaterials, including the pulsed growth of carbon nanotubes and graphene

Electron-phonon coupling origin of the graphene pi*-band kink via isotope effect

The pi*-band renormalization of Li-doped quasifreestanding graphene has been investigated by means of isotope (C-13) substitution and angle-resolved photoemission spectroscopy. The well documented sudden slope change (known as kink) located at 169 meV from the Fermi level in the graphene made of C-12 atoms shifts to 162 meV once the carbon monolayer is composed by C-13 isotope. Such an energy shift is in excellent agreement with the expected softening of the phonon energy distribution due to the isotope substitution and provides, therefore, an indisputable experimental proof of the electron-phonon coupling origin of this well known many-body feature in the electronic structure of graphene

Emergent Dirac carriers across a pressure-induced Lifshitz transition in black phosphorus

The phase diagram of correlated systems like cuprate or pnictide high-temperature superconductors is likely defined by a topological change of the Fermi surface under continuous variation of an external parameter, the so-called Lifshitz transition. However, a number of low-temperature instabilities and the interplay of multiple energy scales complicate the study of this phenomenon. Here we identify the optical signatures of a pressure-induced Lifshitz transition in a clean elemental system, black phosphorus. By applying external pressures above 1.5 GPa, we observe a change in the pressure-dependent Drude plasma frequency due to the appearance of massless Dirac fermions. At higher pressures, optical signatures of two structural phase transitions are also identified. Our findings suggest that a key fingerprint of the Lifshitz transition, in the absence of structural transitions, is a Drude plasma frequency discontinuity due to a change in the Fermi surface topology

Associative memory with spatiotemporal chaos control

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