Spontaneous Scaling Emergence in Generic Stochastic Systems

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range ($\alpha < -2.$) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents $\alpha > -2$ there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos and bursts/intermitency.Comment: latex, 11 page

Power Laws are Logarithmic Boltzmann Laws

Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.Comment: latex, 9 pages with 3 figure

An economic analysis of five selected LANDSAT assisted information systems in Oregon

A comparative cost analysis was performed on five LANDSAT-based information systems. In all cases, the LANDSAT system was found to have cost advantages over its alternative. The information sets generated by LANDSAT and the alternative method are not identical but are comparable in terms of satisfying the needs of the sponsor. The information obtained from the LANDSAT system in some cases is said to lack precision and detail. On the other hand, it was found to be superior in terms of providing information on areas that are inaccessible and unobtainable through conventional means. There is therefore a trade-off between precision and detail, and considerations of costs. The projects examined were concerned with locating irrigation circles in Morrow County; monitoring tansy ragwort infestation; inventoring old growth Douglas fir near Spotted Owl habitats; inventoring vegetation and resources in all state-owned lands; and determining and use for Columbia River water policies

Stereo and motion parallax cues in human 3D vision: can they vanish without a trace?

In an immersive virtual reality environment, subjects fail to notice when a scene expands or contracts around them, despite correct and consistent information from binocular stereopsis and motion parallax, resulting in gross failures of size constancy (A. Glennerster, L. Tcheang, S. J. Gilson, A. W. Fitzgibbon, & A. J. Parker, 2006). We determined whether the integration of stereopsis/motion parallax cues with texture-based cues could be modified through feedback. Subjects compared the size of two objects, each visible when the room was of a different size. As the subject walked, the room expanded or contracted, although subjects failed to notice any change. Subjects were given feedback about the accuracy of their size judgments, where the “correct” size setting was defined either by texture-based cues or (in a separate experiment) by stereo/motion parallax cues. Because of feedback, observers were able to adjust responses such that fewer errors were made. For texture-based feedback, the pattern of responses was consistent with observers weighting texture cues more heavily. However, for stereo/motion parallax feedback, performance in many conditions became worse such that, paradoxically, biases moved away from the point reinforced by the feedback. This can be explained by assuming that subjects remap the relationship between stereo/motion parallax cues and perceived size or that they develop strategies to change their criterion for a size match on different trials. In either case, subjects appear not to have direct access to stereo/motion parallax cues

Predictions of spray combustion interactions

Mean and fluctuating phase velocities; mean particle mass flux; particle size; and mean gas-phase Reynolds stress, composition and temperature were measured in stationary, turbulent, axisymmetric, and flows which conform to the boundary layer approximations while having well-defined initial and boundary conditions in dilute particle-laden jets, nonevaporating sprays, and evaporating sprays injected into a still air environment. Three models of the processes, typical of current practice, were evaluated. The local homogeneous flow and deterministic separated flow models did not provide very satisfactory predictions over the present data base. In contrast, the stochastic separated flow model generally provided good predictions and appears to be an attractive approach for treating nonlinear interphase transport processes in turbulent flows containing particles (drops)

Structure of Evaporating and Combusting Sprays: Measurements and Predictions

Complete measurements of the structure of nonevaporating, evaporating and combusting sprays for sufficiently well defined boundary conditions to allow evaluation of models of these processes were obtained. The development of rational design methods for aircraft combustion chambers and other devices involving spray combustion were investigated. Three methods for treating the discrete phase are being considered: a locally homogeneous flow (LHF) model, a deterministic separated flow (DSF) model, and a stochastic separated flow (SSF) model. The main properties of these models are summarized

One Hour of Chemical Demonstrations

This article describes a diverse set of chemistry demonstrations especially selected to encourage student interaction and to be easily transported. The demonstrations may be presented at a level that can be tailored to any audience– from very young children to high school students planning careers in science. An ideal environment is a small classroom with 20-30 students where everyone can take part in the discussion. Once the chemicals are prepared, the collection of demonstrations takes about ten minutes to set-up, and one hour (or less) to perform. Very little is needed at the visiting site, no more than a table and a pitcher of water. A single electrical outlet is useful, but not essential. In Table 2 th