We construct an approximate renormalization transformation that combines Kolmogorov-Arnol'd-Moser and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of t...

We present asymptotic-preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime. A major challenge in this regime is that there may be no explicit expression of the local equilibrium which is the main component of classical asymptotic-preserving schemes. Inspired by [14] and [13], our idea is to penalize the stiff collision term by a ‘classical’ BG...

Due to the chemical stability and perfection of Carbon Nanotubes (CNTs) structure, carrier mobility is not affected by processing and roughness scattering as it is in the conventional semiconductor channel. Therefore, CNTs are being considered as viable candidates for high-speed applications. The mobility and saturation velocity are the two important parameters that control the charge transport...

This paper introduces and develops a general framework for studying triple factorisations of the form G = ABA of finite groups G, with A and B subgroups of G. We call such a factorisation nondegenerate if G 6= AB. Consideration of the action of G by right multiplication on the right cosets of B leads to a nontrivial upper bound for |G| by applying results about subsets of restricted movement. F...

Charge transport in doped quantum paraelectrics (QPs) presents a number of puzzles, including pronounced ${T}^{2}$ regime the resistivity. We analyze charge QP within model electrons coupled to soft transverse optical (TO) mode via two-phonon mechanism. For $T$ above soft-mode frequency but below some characteristic scale (${E}_{0}$), resistivity scales with occupation phonons squared, i.e., as...

Complex matrices that are structured with respect to a possibly degenerate indefinite inner product are studied. Based on the theory of linear relations, the notion of an adjoint is introduced: the adjoint of a matrix is defined as a linear relation which is a matrix if and only if the inner product is nondegenerate. This notion is then used to give alternative definitions of selfadjoint and un...

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar’s canonical reformulation of Einstein’s equations is studied. Several examples are given of such “phase boundaries” in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of flat space, Schwarzschild, and plane wave solutions joined to...

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such \phase boundaries" in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of at space, Schwarzschild, and plane wave solutions joined to d...