Moving average fields, macro-scale response measures, and homogenizing micro-scale variation

There are two critical issues when deriving a macro-scale prediction model starting from a more complete, underlying model. The first is the precise relationship of the fields predicted by the more complete model and the fields predicted by the macro-scale model. The second is the manner of solving a closure problem that is invariably encountered in all such derivations. The understanding that moving averages of the fields predicted by the more complete model are the fields predicted by the macro-scale model is challenged on the grounds that accomplishing a moving average does not eliminate micro-scale variation, it only appears to do so in one representation of the moving average field. The solution of a closure problem by assumption is challenged on the grounds that the most common assumptions are demonstrably invalid, even while leading to prediction models that can provide reasonable estimates of the macro-scale response in some scenarios. In presenting the challenges, it is further shown how a multiresolution analysis by an orthogonal wavelet system provides a framework for both precisely defining macro-scale response fields, i.e., fields from which all micro-scale variation has been eliminated, and presenting a formally exact solution for a precisely described closure problem.     

Intensity-reversal in the donor bound exciton luminescence of GaAs

A self-reversal model is presented to explain the luminescence dependence of the donor bound exciton intensity. The line broadening mechanism is attributed to rotational interaction with non-rigid rotator states. Line reversal results from absorption by non-broadened states near the crystal surface. The absence of a similar excitation intensity dependence for acceptor bound excitons is explained.     

Temperature dependence in the Schumann-Runge photoabsorption continuum of oxygen

The photoabsorption cross section in the Schumann-Runge continuum of oxygen has been measured with high precision over the wavelength region 140–174 nm at temperatures in the range 295–575 K. Models for the upper state potential and the electronic transition moment were used in the calculation of the cross section and its temperature dependence. By comparing this theoretical cross section with measured values, curves for the upper state potential and the transition moment in the continuum region have been obtained independently for the first time.     

The evaluation identification in function spaces

A study is made of the natural function which maps each point x of a space X to the evaluation function e_x:Y^x→Y defined by $\text{e}{}_{\mathrm{x}}\text{(?)=?(x)}$. A consequence of the results is that βX and υX can both be considered as subspaces of spaces of continous functions from appropriate domain spaces into I or R, respectively.     

Rotational variation of predissociation linewidths for the Schumann-Runge bands of molecular oxygen

Predissociation linewidths are presented as a function of rotation for the (3-0)-(14-0) Schumann- Runge bands of molecular oxygen. While there may be a slight tendency overall for the linewidths to increase with rotation, it is shown that previous assumptions of linewidths constant with rotation are generally valid within the experimental error for the range of rotation studied, N_n ? 21. There is no evidence for the sudden increase in linewidth with rotation reported elsewhere.     

Experimentally determined oscillator strengths and linewidths for the Schumann-Runge band system of molecular oxygen—I. The (6-0)–(14-0) bands

Experimental oscillator strengths and predissociated linewidths have been measured at room temperature for the (6-0)–(14-0) Schumann-Runge bands of molecular oxygen using the Adelaide 6 m vacuum u.v. monochromator operated at a resolution of about 0.06 Å. Photoelectric detectors were used to measure the u.v. absorption at two different gas pressures for 138 groups of rotational lines distributed throughout the (6-0)–(14-0) bands and the resulting data were interpreted using an equivalent width type of analysis. Experimental measurements of the variation with N″ of the oscillator strengths within each band have been obtained for the first time. Measured oscillator strengths are found to be somwhat higher in general than previously reported values with a slightly faster decrease as N″ increases than is predicted theoretically. The mean predissociated linewidths obtained for each band show a smooth variation with v′, agreeing well with other results for v′=12?14 and lying between previously reported experimental and theoretical values for v′=6?9. The present work provides results which can be used to construct highly accurate synthetic absorption profiles for studies of the atmospheric absorption of u.v. radiation by the Schumann-Runge bands.     

Tunneling and transport problems for a quantum mechanical Brownian particle

The Kanai model of a quantum mechanical Brownian particle is used to examine the effect of interactions between particles and their environment. Random forces cause the thermalization of the particle. Reflection of a particle from a step barrier is analyzed. The problem of tunneling of the Brownian particle through a rectangular barrier is solved. Finally, a solution for a Brownian particle in a box is presented.     

Connection between the KdV equation and the two-dimensional Ising model

We construct the one-parameter family of solutions to d²w/dzsu2 = zw + 2w³ that tend to zero for z → +∞ by specializing an equation previously solved in connection with the two-dimensional Ising model. These solutions are intimately related to the KdV equation.     

Networks, dynamics, and modularity

The identification of general principles relating structure to dynamics has been a major goal in the study of complex networks. We propose that the special case of linear network dynamics provides a natural framework within which a number of interesting yet tractable problems can be defined. We report the emergence of modularity and hierarchical organization in evolved networks supporting asymptotically stable linear dynamics. Numerical experiments demonstrate that linear stability benefits from the presence of a hierarchy of modules and that this architecture improves the robustness of network stability to random perturbations in network structure. This work illustrates an approach to network science which is simultaneously structural and dynamical in nature.