Hopping transport on a fractal: ac conductivity of porous silicon

We have measured the frequency dependence of the conductivity and the dielectric constant of various samples of porous Si in the regime 1 Hz-100 kHz at different temperatures. The conductivity data exhibit a strong frequency dependence. When normalized to the dc conductivity, our data obey a universal scaling law, with a well-defined crossover, in which the real part of the conductivity sigma' changes from an sqrt(omega) dependence to being proportional to omega. We explain this in terms of activated hopping in a fractal network. The low-frequency regime is governed by the fractal properties of porous Si, whereas the high-frequency dispersion comes from a broad distribution of activation energies. Calculations using the effective-medium approximation for activated hopping on a percolating lattice give fair agreement with the data.

Universality in the merging dynamics of parametric active contours:a study in MRI based lung segmentation

Measurement of lung ventilation is one of the most reliable techniques in diagnosing pulmonary diseases. The time-consuming and bias-prone traditional methods using hyperpolarized H 3He and 1H magnetic resonance imageries have recently been improved by an automated technique based on 'multiple active contour evolution'. This method involves a simultaneous evolution of multiple initial conditions, called 'snakes', eventually leading to their 'merging' and is entirely independent of the shapes and sizes of snakes or other parametric details. The objective of this paper is to show, through a theoretical analysis, that the functional dynamics of merging as depicted in the active contour method has a direct analogue in statistical physics and this explains its 'universality'. We show that the multiple active contour method has an universal scaling behaviour akin to that of classical nucleation in two spatial dimensions. We prove our point by comparing the numerically evaluated exponents with an equivalent thermodynamic model. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Universal duality in a Luttinger liquid coupled to a generic environment

We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.