Percolation threshold

Résumé

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability p, or more generally a critical surface for a group of parameters p1, p2, ..., such that infinite connectivity (percolation) first occurs. Percolation models The most common percolation model is to take a regular lattice, like a square lattice, and make it into a random network by randomly "occupying" sites (vertices) or bonds (edges) with a stat

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In this thesis, we study the quantum phase transition triggered by an external random po- tential in ultra-cold low-dimensional weakly-interacting Bose gases at zero temperature. In one-dimensional systems, the quantum phases are characterized by the decay at long-range of the one-body density matrix. This decay exhibits an algebraic behaviour in the superfluid quasi-condensed phase while in the insulating Bose glass phase this it becomes exponen- tial, signaling the complete loss of coherence in the system. In two-dimensional systems, a characterization based on the long-range behaviour of the one-body density matrix appears to be highly demanding from a computational point of view. We therefore characterized the superfluid-insulator transition in two-dimensional systems by the low-energy behaviour of the cumulative density of states of the Bogoliubov excitations. While in the superfluid condensed phase this quantity grows as the square of the excitation energy in agreement with the existence of a finite velocity of sound, in the insulating Bose glass phase this power law is less than quadratic. This study is performed in the framework of an extended Bogoliubov approach properly adapted to treat low-dimensional Bose gases. Using a systematic numerical study, we draw the interaction-disorder phase diagrams of the superfluid-insulator transition in 1D and 2D. The phase boundary follows two different power- laws depending on the length scales characterizing the spatial correlations of the disorder and the strength of interactions. The power-law exponents were found to be in agreement with the ones predicted by scaling arguments, both in the white noise and the Thomas-Fermi regimes. In the two-dimensional system, the classical percolation threshold in the Thomas-Fermi limit was found to overestimate the critical disorder below which the onset of superfluidity should be observed for a given interaction strength.

EPFL2016

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Large arrays of chemo-mechanical nanoswitches for ultralow-power hydrogen sensing

Jürgen Brugger, Thomas Kiefer, Arnaud Salette, Luis Guillermo Villanueva Torrijo

A hydrogen sensor based on large arrays of nanoswitches in palladium (Pd) is presented. An individual nanoswitch is realized by a suspended Pd/Ti/poly-Si trimorph electrode and a fixed Pd/Ti bottom electrode, which are separated by a vertical nanoscopic gap of approximately 10 nm in size. In hydrogen exposure, the volume expansion of Pd results in mechanical bending of the suspended electrode and the formation of an electric contact. A multitude of nanoswitches is arranged in interconnected arrays. These enable a dependence of the sensor signal on the H2 concentration by the occurrence of percolation effects. The combined use of thin film, etching and evaporation techniques allows for the large-scale fabrication of nanoswitch arrays in arbitrary topologies by design, such as parallel linear chains or square lattices. The results of hydrogen and temperature measurements are presented and discussed. In hydrogen exposure, reversible changes in the electrical resistance of up to three orders of magnitude are obtained for H2 concentrations below 4% and a power consumption down to a few picowatts.

Institute of Physics2010

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Synthesis of bone-like structured foams

Françoise Borcard, Sandrine Gerber

Here we present a processing route to produce multi-structured ceramic foams based on the combination of particle-stabilized foams with polymeric sponges to produce positive and negative templating structures. Polyester sponges are infiltrated with freshly produced calcium aluminate–alumina foams and upon sintering either positive templating structures are produced when wetting the sponges, or negative templating foams with a percolating pore network are obtained when completely filling the sponges. Additionally, by combining different layers of these particle-stabilized foam infiltrated sponges, various different structures can be produced, including sandwich structures, pore size gradients, and ceramic bone-like structures applying to different types of bone. The particle-stabilized foams used were in situ self-hardening calcium aluminate cement enriched alumina foams to obtain crack-free samples with pore interconnections and tailorable pore sizes.

Elsevier Sci Ltd2013

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