Transport in rough self-affine fractures

Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium approximation predicts the right scaling behavior of the permeability and of the velocity fluctuations, in terms of the aperture of the fracture, the roughness exponent and the characteristic length of the fracture surfaces, in the limit of small separation between surfaces. The permeability of the fractures is also investigated as a function of the normal and lateral relative displacements between surfaces, and is shown that it can be bounded by the permeability of two-dimensional fractures. The development of channel-like structures in the velocity field is also numerically investigated for different relative displacements between surfaces. Finally, the dispersion of tracer particles in the velocity field of the fractures is investigated by analytic and numerical methods. The asymptotic dominant role of the geometric dispersion, due to velocity fluctuations and their spatial correlations, is shown in the limit of very small separation between fracture surfaces.Comment: submitted to PR

The Non-Ideal Organic Electrochemical Transistors Impedance

Organic electrochemical transistors offer powerful functionalities for biosensors and neuroinspired electronics, with still much to understand on the time dependent behavior of this electrochemical device. Here, we report on distributed element modeling of the impedance of such microfabricated device, systematically performed under a large concentration variation for KCl(aq) and CaCl2(aq). We propose a new model which takes into account three main deviations to ideality, that were systematically observed, caused by both the materials and the device complexity, over large frequency range (1 Hz to 1 MHz). More than introducing more freedom degree, the introduction of these non redundant parameters and the study of their behaviors as function of the electrolyte concentration and applied voltage give a more detailed picture of the OECT working principles. This optimized model can be further useful for improving OECT performances in many applications (e.g. biosensors, neuroinspired devices) and circuit simulations.Comment: Full paper with supporting informatio

First order devices, hybrid memristors, and the frontiers of nonlinear circuit theory

Several devices exhibiting memory effects have shown up in nonlinear circuit theory in recent years. Among others, these circuit elements include Chua's memristors, as well as memcapacitors and meminductors. These and other related devices seem to be beyond the, say, classical scope of circuit theory, which is formulated in terms of resistors, capacitors, inductors, and voltage and current sources. We explore in this paper the potential extent of nonlinear circuit theory by classifying such mem-devices in terms of the variables involved in their constitutive relations and the notions of the differential- and the state-order of a device. Within this framework, the frontier of first order circuit theory is defined by so-called hybrid memristors, which are proposed here to accommodate a characteristic relating all four fundamental circuit variables. Devices with differential order two and mem-systems are discussed in less detail. We allow for fully nonlinear characteristics in all circuit elements, arriving at a rather exhaustive taxonomy of C^1-devices. Additionally, we extend the notion of a topologically degenerate configuration to circuits with memcapacitors, meminductors and all types of memristors, and characterize the differential-algebraic index of nodal models of such circuits.Comment: Published in 2013. Journal reference included as a footnote in the first pag

Fractal and Multifractal Scaling of Electrical Conduction in Random Resistor Networks

This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic results related to percolation: namely, the conduction properties of a large random resistor network as the fraction of resistors is varied. We focus on how the conductance of such a network vanishes as the percolation threshold is approached from above. We also discuss the more microscopic current distribution within each resistor of a large network. At the percolation threshold, this distribution is multifractal in that all moments of this distribution have independent scaling properties. We will discuss the meaning of multifractal scaling and its implications for current flows in networks, especially the largest current in the network. Finally, we discuss the relation between resistor networks and random walks and show how the classic phenomena of recurrence and transience of random walks are simply related to the conductance of a corresponding electrical network.Comment: 27 pages & 10 figures; review article for the Encyclopedia of Complexity and System Science (Springer Science

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges

A new traceability chain for the derivation of the farad from dc quantum Hall effect has been implemented at INRIM. Main components of the chain are two new coaxial transformer bridges: a resistance ratio bridge, and a quadrature bridge, both operating at 1541 Hz. The bridges are energized and controlled with a polyphase direct-digital-synthesizer, which permits to achieve both main and auxiliary equilibria in an automated way; the bridges and do not include any variable inductive divider or variable impedance box. The relative uncertainty in the realization of the farad, at the level of 1000 pF, is estimated to be 64E-9. A first verification of the realization is given by a comparison with the maintained national capacitance standard, where an agreement between measurements within their relative combined uncertainty of 420E-9 is obtained.Comment: 15 pages, 11 figures, 3 table

Ultra Structurally Based Impedance Model for Oral Cancer Detection

abstract: This research investigated using impedance as a minimally invasive oral cancer-screening tool by modeling healthy and diseased tissue. This research developed an ultra-structurally based tissue model for oral mucosa that is versatile enough to be easily modified to mimic the passive electrical impedance responses of multiple benign and cancerous tissue types. This new model provides answers to biologically meaningful questions related to the impedance response of healthy and diseased tissues. This model breaks away from the old empirical top down "black box" Thèvinin equivalent model. The new tissue model developed here was created from a bottom up perspective resulting in a model that is analogous to having a "Transparent Box" where each network element relating to a specific structural component is known. This new model was developed starting with sub cellular ultra-structural components such as membranes, proteins and electrolytes. These components formed the basic network elements and topology of the organelles. The organelle networks combine to form the cell networks. The cell networks combine to make networks of cell layers and the cell layers were combined into tissue networks. This produced the complete "Transparent Box" model for normal tissue. This normal tissue model was modified for disease based on the ultra-structural pathology of each disease. The diseased tissues evaluated include cancers type one through type three; necrotic-inflammation, hyperkeratosis and the compound condition of hyperkeratosis over cancer type two. The impedance responses for each of the disease were compared side by side with the response of normal healthy tissue. Comparative evidence from the models showed the structural changes in cancer produce a unique identifiable impedance "finger print." The evaluation of the "Transparent Box" model for normal tissues and diseased tissues show clear support for using comparative impedance measurements as a clinical tool for oral cancer screening.Dissertation/Thesisnormal oral mucosal tissue modelcancer type 1 oral mucosal tissue modelcancer type 2 oral mucosal tissue modelcancer type 3 oral mucosal tissue modelhyperkeratosis oral mucosal tissue modelhyperkeratosis over cancer type 2 oral mucosal tissuenecrotic inflammation oral tissue modelPh.D. Electrical Engineering 201

Dimers and cluster integrable systems

We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph. The sum of Hamiltonians is essentially the partition function of the dimer model. Any graph on a torus gives rise to a bipartite graph on the torus. We show that the phase space of the latter has a Lagrangian subvariety. We identify it with the space parametrizing resistor networks on the original graph.We construct several discrete quantum integrable systems.Comment: This is an updated version, 75 pages, which will appear in Ann. Sci. EN