Hopping conductivity in the quantum Hall effect -- revival of universal scaling

We have measured the temperature dependence of the conductivity $\sigma_{xx}$ of a two-dimensional electron system deep into the localized regime of the quantum Hall plateau transition. Using variable-range hopping theory we are able to extract directly the localization length $\xi$ from this experiment. We use our results to study the scaling behavior of $\xi$ as a function of the filling factor distance $|\delta \nu|$ to the critical point of the transition. We find for all samples a power-law behavior $\xi\propto|\delta\nu|^{-\gamma}$ with a universal scaling exponent $\gamma = 2.3$ as proposed theoretically

Conductance fluctuations at the quantum Hall plateau transition

We analyze the conductance fluctuations observed in the quantum Hall regime for a bulk two-dimensional electron system in a Corbino geometry. We find that characteristics like the power spectral density and the temperature dependence agree well with simple expectations for universal conductance fluctuations in metals, while the observed amplitude is reduced. In addition, the dephasing length $L_\Phi \propto T^{-1/2}$, which governs the temperature dependence of the fluctuations, is surprisingly different from the scaling length $L_{sc}\propto T^{-1}$ governing the width of the quantum Hall plateau transition

A large scale software system for simulation and design optimization of mechanical systems

The concept of an advanced integrated, networked simulation and design system is outlined. Such an advanced system can be developed utilizing existing codes without compromising the integrity and functionality of the system. An example has been used to demonstrate the applicability of the concept of the integrated system outlined here. The development of an integrated system can be done incrementally. Initial capabilities can be developed and implemented without having a detailed design of the global system. Only a conceptual global system must exist. For a fully integrated, user friendly design system, further research is needed in the areas of engineering data bases, distributed data bases, and advanced user interface design

High Frequency Conductivity in the Quantum Hall Regime

We have measured the complex conductivity $\sigma_{xx}$ of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that $\sigma_{xx}$ can be scaled to a single function for different frequencies and for all investigated transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length $\xi$. Even for large filing factor distances $\delta \nu$ from the critical point we find $\xi \propto \delta \nu^{-\gamma}$ with a scaling exponent $\gamma=2.3$

Design sensitivity analysis and optimization of built-up structures

Developments during the course of the research in design sensitivity analysis and optimization of built-up structures, with both sizing and shape design variables, show clearly that a unified variational approach to design sensitivity analysis can yield derivatives of structural response with respect to design. Rigorous and practically computable results for structural components and built-up structures have been demonstrated and used to solve design optimization problems