The behavior of a single impurity in a one-dimensional Luttinger liquid is numerically investigated by means of the density matrix renormalization group. By analyzing the finite size scaling behavior of the low energy spectrum, we confirm the theoretical prediction of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)] both for attractive and repulsive interactions. Moreover, we calculate the ex...

The class of nilpotent groups of class c and prime exponent p> c with additional predicates Pc ⊆Pc−1 ⊆ . . . ⊆P1 for suitable subgroups has the amalgamation property. Hence the Fräıssé limit D of the finite groups of this class exists. 〈1〉⊆Pc(D)⊆ . . . ⊆P2(D)⊆P1(D)=D is the lower and the upper central series of D. In this extended language, D is ultrahomogeneous. The elementary theory of D allo...

It is known in thin-film deposition that the density of nucleated clusters N varies with the deposition rate F as a power law, N ∼ Fα. The exponent α is a function of the critical nucleus size i in a way that changes with the aggregation limiting process. We extend here the derivation of the analytical capture-zone distribution function Pβ(s) = aß ·sβ ·exp(-bβs2) of Pimpinelli and Einstein to g...

The out-degree distribution is one of the most reported topological properties to characterize real complex networks. This property describes the probability that a node in the network has a particular number of outgoing links. It has been found that in many real complex networks the out-degree has a behavior similar to a power-law distribution, therefore some network growth models have been pr...

the simultaneous flow of oil and water in porous media is described by relative permeability curves, mainly derived from laboratory experiments. relative permeability is of paramount importance in predicting reservoir production performance and drive mechanisms and its value depends largely on the volume fraction of fluids present in the test samples. nowadays x-ray scanners are one of the most...

The results from measuring the capacity of thin-film solid-state lithium-ion batteries (SSLIBs) Ti|Si@O@Al|LiPON|LiCoO2|Ti, Ti|Si@O@Al|LiPON|LixV2O5|Ti, and Ti|LiPON|LiCoO2|Ti at different charge currents are reported. It is shown that dependence on current density Q(j) follows Peukert’s law, which characterized by a low value exponents in region high currents. exponent for anode-free cell rema...