Frequency tuning, nonlinearities and mode coupling in circular graphene resonators

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to geometrical nonlinearity these can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for eigenfrequencies and nonlinear coefficients as functions of radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings.Comment: 21 pages, 7 figures, 3 table

Pseudo-digital quantum bits

Quantum computers are analog devices; thus they are highly susceptible to accumulative errors arising from classical control electronics. Fast operation--as necessitated by decoherence--makes gating errors very likely. In most current designs for scalable quantum computers it is not possible to satisfy both the requirements of low decoherence errors and low gating errors. Here we introduce a hardware-based technique for pseudo-digital gate operation. We perform self-consistent simulations of semiconductor quantum dots, finding that pseudo-digital techniques reduce operational error rates by more than two orders of magnitude, thus facilitating fast operation.Comment: 4 pages, 3 figure

Meta-tools for software development and knowledge acquisition

The effectiveness of tools that provide support for software development is highly dependent on the match between the tools and their task. Knowledge-acquisition (KA) tools constitute a class of development tools targeted at knowledge-based systems. Generally, KA tools that are custom-tailored for particular application domains are more effective than are general KA tools that cover a large class of domains. The high cost of custom-tailoring KA tools manually has encouraged researchers to develop meta-tools for KA tools. Current research issues in meta-tools for knowledge acquisition are the specification styles, or meta-views, for target KA tools used, and the relationships between the specification entered in the meta-tool and other specifications for the target program under development. We examine different types of meta-views and meta-tools. Our current project is to provide meta-tools that produce KA tools from multiple specification sources--for instance, from a task analysis of the target application