Conformal Theory of the Dimensions of Diffusion Limited Aggregates

We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process which is complementary to the iterative cluster growth. We use this method to establish the existence of a series of random scaling functions that yield, via the thermodynamic formalism of multifractals, the generalized dimensions D(q) of DLA for q >= 1. The scaling function is determined just by the last stages of the iterative growth process which are relevant to the complementary dynamics. Using the scaling relation D(3) = D(0)/2 we estimate the fractal dimension of DLA to be D(0) = 1.69 +- 0.03.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let

Magnetic Impurity in a Metal with Correlated Conduction Electrons: An Infinite Dimensions Approach

We consider the Hubbard model with a magnetic Anderson impurity coupled to a lattice site. In the case of infinite dimensions, one-particle correlations of the impurity electron are described by the effective Hamiltonian of the two-impurity system. One of the impurities interacts with a bath of free electrons and represents the Hubbard lattice, and the other is coupled to the first impurity by the bare hybridization interaction. A study of the effective two-impurity Hamiltonian in the frame of the 1/N expansion and for the case of a weak conduction-electron interaction (small U) reveals an enhancement of the usual exponential Kondo scale. However, an intermediate interaction (U/D = 1 - 3), treated by the variational principle, leads to the loss of the exponential scale. The Kondo temperature T_K of the effective two-impurity system is calculated as a function of the hybridization parameter and it is shown that T_K decreases with an increase of U. The non-Fermi-liquid character of the Kondo effect in the intermediate regime at the half filling is discussed.Comment: 12 pages with 8 PS figures, RevTe

Amyotrophic Lateral Sclerosis: New Perpectives and Update

Amyotrophic lateral sclerosis (ALS), Charcot’s disease or Lou Gehrig’s disease, is a term used to cover the spetrum of syndromes caracterized by progressive degeneration of motor neurons, a paralytic disorder caused by motor neuron degeneration. Currently, there are approximately 25,000 patients with ALS in the USA, with an average age of onset of 55 years. The incidence and prevalence of ALS are 1-2 and 4-6 per 100,000 each year, respectively, with a lifetime ALS risk of 1/600 to 1/1000. It causes progressive and cumulative physical disabilities, and leads to eventual death due to respiratory muscle failure. ALS is diverse in its presentation, course, and progression. We do not yet fully understand the causes of the disease, nor the mechanisms for its progression; thus, we lack effective means for treating this disease. In this chapter, we will discuss the diagnosis, treatment, and how to cope with impaired function and end of life based on of our experience, guidelines, and clinical trials. Nowadays ALS seems to be a more complex disease than it did two decades – or even one decade – ago, but new insights have been plentiful. Clinical trials should be seen more as experiments on pathogenic mechanisms. A medication or combination of medications that targets more than one pathogenic pathway may slow disease progression in an additive or synergistic fashion