Narrow Results

Nanotube structures are unprecedented in their stability and current-carrying capacity at intense driving fields. A comprehensive understanding of electron conduction from equilibrium through to the high-driving-field regime is needed. We present a microscopically conserving quantum-kinetic description of transport for ohmically contacted carbon nanotubes. The approach is computationally straightforward and can describe nonequilibrium response over a wide range of parameters. We have analyzed the interplay of degeneracy and scattering dynamics on gate-controlled conduction in the one-dimensional channel, and have determined transconductances.

In the last 10 years, we have observed an important increase of interest in the application of time-dependent energy density functional (TD-EDF) theory. This approach allows to treat nuclear structure and nuclear reaction from small to large amplitude dynamics in a unified framework. The possibility to perform unrestricted three-dimensional simulations using state-of-the-art effective interactions has opened new perspectives. In the present paper, an overview of applications where the predictive power of TD-EDF has been benchmarked is given. A special emphasize is made on processes that are of astrophysical interest. Illustrations discussed here include giant resonances, fission, binary and ternary collisions leading to fusion, transfer and deep inelastic processes.

We develop spectral approximation for solving the three-dimensional transport equation with isotropic scattering in a bounded domain. The method can be extended easily to general linear transport problem in a unbounded domain or semi infinite domain. The technique used involves the reduction of the three-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching solutions to the multi-dimensional transport problems, leads us to a solution for all values of the independent variables.

Given a square integrable m-dimensional random variable X on a probability space (Ω, ℱ, ℙ) and a sub sigma-algebra 𝒜, we show that there exists another m-dimensional random variable Y, independent of 𝒜 and minimizing the L² distance to X. Such results have an importance to fairness and bias reduction in artificial intelligence, machine learning and network theory.

Nanotube structures are unprecedented in their stability and current-carrying capacity at intense driving fields. A comprehensive understanding of electron conduction from equilibrium through to the high-driving-field regime is needed. We present a microscopically conserving quantum-kinetic description of transport for ohmically contacted carbon nanotubes. The approach is computationally straightforward and can describe nonequilibrium response over a wide range of parameters. We have analyzed the interplay of degeneracy and scattering dynamics on gate-controlled conduction in the one-dimensional channel, and have determined transconductances.

In this lecture we review the theoretical investigation of heavy ion collisions in order to obtain information on the nuclear equation-of-state (EOS). We discuss the present knowledge of the EOS, and stress, in particular, the large uncertainty about the density dependence of the symmetry energy. We develop the treatment of heavy ion collisions with transport theory and non-equilibrium effects. We then discuss investigations both of the high density EOS with intermediate energy collisions and of the low density EOS in the Fermi energy regime. At the high density we make connections with neutron stars. At low density we discuss the fragmentation process and, in particular, the role and treatment of fluctuations and the dynamical fragment formation.

According to the 2001 international technology roadmap for semiconductors, MOSFETs with physical channel length less than 10nm will be mass produced in 2016. Such devices would have approximately 10 silicon atoms along the effective channel length. This poses challenging problems in the mathematical modeling of charge transport e.g. one has a major relevance of the discrete nature of the dopant distribution for intrinsic stochastic parameter variations. These topics will be discussed in this article along with a critical review of the already existing models.