Failure of single-parameter scaling of wave functions in Anderson localization

We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $L \leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published

Anderson transition in the three dimensional symplectic universality class

We study the Anderson transition in the SU(2) model and the Ando model. We report a new precise estimate of the critical exponent for the symplectic universality class of the Anderson transition. We also report numerical estimation of the $\beta$ function.Comment: 4 pages, 5 figure

Symmetry, dimension and the distribution of the conductance at the mobility edge

The probability distribution of the conductance at the mobility edge, $p_c(g)$, in different universality classes and dimensions is investigated numerically for a variety of random systems. It is shown that $p_c(g)$ is universal for systems of given symmetry, dimensionality, and boundary conditions. An analytical form of $p_c(g)$ for small values of $g$ is discussed and agreement with numerical data is observed. For $g > 1$, $\ln p_c(g)$ is proportional to $(g-1)$ rather than $(g-1)^2$.Comment: 4 pages REVTeX, 5 figures and 2 tables include

Probability distribution of the conductance at the mobility edge

Distribution of the conductance P(g) at the critical point of the metal-insulator transition is presented for three and four dimensional orthogonal systems. The form of the distribution is discussed. Dimension dependence of P(g) is proven. The limiting cases $g\to\infty$ and $g\to 0$ are discussed in detail and relation $P(g)\to 0$ in the limit $g\to 0$ is proven.Comment: 4 pages, 3 .eps figure

Controlling the angiogenic switch in developing atherosclerotic plaques: possible targets for therapeutic intervention.

Plaque angiogenesis may have an important role in the development of atherosclerosis. Vasa vasorum angiogenesis and medial infiltration provides nutrients to the developing and expanding intima and therefore, may prevent cellular death and contribute to plaque growth and stabilization in early lesions. However in more advanced plaques, inflammatory cell infiltration, and concomitant production of numerous pro-angiogenic cytokines may be responsible for induction of uncontrolled neointimal microvessel proliferation resulting in production of immature and fragile neovessels similar to that seen in tumour development. These could contribute to development of an unstable haemorrhagic rupture-prone environment. Increasing evidence has suggested that the expression of intimal neovessels is directly related to the stage of plaque development, the risk of plaque rupture, and subsequently, the presence of symptomatic disease, the timing of ischemic neurological events and myocardial/cerebral infarction. Despite this, there is conflicting evidence regarding the causal relationship between neovessel expression and plaque thrombosis with some in vivo experimental models suggesting the contrary and as yet, few direct mediators of angiogenesis have been identified and associated with plaque instability in vivo.In recent years, an increasing number of angiogenic therapeutic targets have been proposed in order to facilitate modulation of neovascularization and its consequences in diseases such as cancer and macular degeneration. A complete knowledge of the mechanisms responsible for initiation of adventitial vessel proliferation, their extension into the intimal regions and possible de-novo synthesis of neovessels following differentiation of bone-marrow-derived stem cells is required in order to contemplate potential single or combinational anti-angiogenic therapies. In this review, we will examine the importance of angiogenesis in complicated plaque development, describe the current knowledge of molecular mechanisms of its initiation and maintenance, and discuss possible future anti-angiogenic therapies to control plaque stability

The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling

We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent $\nu$ for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyse the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent $\nu=2.73 \pm 0.02$