Using both analytic and numerical methods, we study the radial growth probability distribution P (r, M ) for large scale off lattice diffusion limited aggregation (DLA) clusters. If the form of P (r, M ) is a Gaussian, we show analytically that the width ξ(M ) of the distribution can not scale as the radius of gyration R G of the cluster. We generate about 1750 clusters of masses M up to 500, 000 particles, and calculate the distribution by sending 10 6 further random walkers for each cluster. We give strong support that the calculated distribution has a power law tail in the interior (r ∼ 0) of the cluster, and can be described by a scaling Ansatz P (r, M ) ∝ r α ξ · g r−r 0 ξ , where g(x) denotes some scaling function which is centered around zero and has a width of order unity. The exponent α is determined to be ≈ 2, which is now substantially smaller than values measured earlier. We show, by including the power-law tail, that the width can scale as R G , if α > D f − 1.

The stress exponent in the power-law creep of niobium at 1985 °C was measured by a noncontact technique using an electrostatic levitation facility at NASA MSFC. This method employs a distribution of stress to allow the stress exponent to be determined from each test, rather than from the curve fit through measurements from multiple samples that is required by conventional methods. The sample is deformed by the centripetal acceleration from the rapid rotation, and the deformed shapes are analyzed to determine the strain. Based on a mathematical proof, which revealed that the stress exponent was determined uniquely by the ratio of the polar to equatorial strains, a series of finite-element analyses with the models of different stress exponents were also performed to determine the stress exponent corresponding to the measured strain ratio. The stress exponent from the ESL experiment showed a good agreement with those from the literature and the conventional creep test.