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In this chapter we introduce some of the basic models and concepts that will be discussed throughout the volume. In particular we describe systems of nonlinear oscillators arranged on low-dimensional lattices and summarize the phenomenology…
In view of its local character, the semiclassical or Boltzmann theory is intrinsically unable to describe transport phenomena on ultrashort space and time scales, and to this purpose genuine quantum-transport approaches are imperative. By…
The ferromagnetic transition in a diluted magnetic semiconductor with localized charge carriers is inevitably a percolation transition. In this work we theoretically study the correlation between this magnetic percolation and transport…
This paper is written to provide an insight into the physics and engineering that go into power delivery of the future. Topics covered are Fault Current Limiters (FCL) including Superconducting FCL and Emission Limited FCL; Lightning and…
Using the advection-diffusion equation, we analytically study contaminant transport in a sharply contrasting medium with a diffusion barrier due to localization of a contaminant source in a low-permeability medium. Anomalous diffusion…
A novel nanoelectronic device is constructed by graphyne that is robustly connected between graphene electrodes, where graphyne is composed of hexagonal carbon rings and carbon chains. Owing to similarities between the bond lengths and unit…
Recent experiments have shown that highly efficient energy transfer can take place in organic nanocrystals at extremely low acceptor densities. This striking phenomenon has been ascribed to the formation of exciton polaritons thanks to the…
We consider reaction-diffusion equations of KPP type in a presence of a line of fast diffusion with non-local exchange terms between the line and the framework. Our study deals with the infimum of the spreading speed depending on the…
Fascinating developments in optical pulse engineering over the last 20 years lead to the generation of laser pulses as short as few femtosecond, providing a unique tool for high resolution time domain spectroscopy. However, a number of the…
The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…
We consider the junction of multiple one-dimensional systems and study how conserved currents transport at the junction. To characterize the transport process, we introduce reflection/transmission coefficients by applying boundary conformal…
A semi-analytical model for studying thermal transport at the nanoscale, able to accurately describe both the effect of out of equilibrium transport and the thermal transfer at interfaces, is presented. Our approach is based on the…
Semiconducting single-walled carbon nanotubes are studied in the diffusive transport regime. The peak mobility is found to scale with the square of the nanotube diameter and inversely with temperature. The maximum conductance, corrected for…
Soliton transport in tube-like networks is studied by solving the nonlinear Schroedinger equation (NLSE) on finite thickness ("fat") graphs. The dependence of the solution and of the reflection at vertices on the graph thickness and on the…
In this paper heat transport in carbon nanotubes is investigated. When the dimension of the structure is of the order of the de Broglie wave length transport phenomena must be analysed by quantum mechanics. In this paper we derived the…
We develop a detailed analysis of electron transport in normal diffusive conductors in the presence of proximity induced superconducting correlation. We calculated the linear conductance of the system and the profile of the electric field.…
A quasi-two-dimensional system of hard spheres strongly confined between two parallel plates is considered. The attention is focussed on the macroscopic self-diffusion process observed when the system is looked from above or from below. The…
Thermoelectric films and periodic structures have particularly intriguing electrical and thermal transport features due to their low dimensionality. As a result, they have piqued the attention of researchers from across the spectrum of…
The statistics of charge transport across a tunnel junction with energy-dependent scattering is investigated. A model with quadratic dispersion relation is discussed in general and, independently, in the two limiting cases of a large…
Recent advances in the synthesis of inorganic and organic nanowires and nanotubes have provided both components for various functional devices and platforms for the study of low- dimensional transport phenomena. However, tremendous…