Time Quasilattices in Dissipative Dynamical Systems

We establish the existence of `time quasilattices' as stable trajectories in dissipative dynamical systems. These tilings of the time axis, with two unit cells of different durations, can be generated as cuts through a periodic lattice spanned by two orthogonal directions of time. We show that there are precisely two admissible time quasilattices, which we term the infinite Pell and Clapeyron words, reached by a generalization of the period-doubling cascade. Finite Pell and Clapeyron words of increasing length provide systematic periodic approximations to time quasilattices which can be verified experimentally. The results apply to all systems featuring the universal sequence of periodic windows. We provide examples of discrete-time maps, and periodically-driven continuous-time dynamical systems. We identify quantum many-body systems in which time quasilattices develop rigidity via the interaction of many degrees of freedom, thus constituting dissipative discrete `time quasicrystals'.Comment: 38 pages, 14 figures. This version incorporates "Pell and Clapeyron Words as Stable Trajectories in Dynamical Systems", arXiv:1707.09333. Submission to SciPos

New Symmetric and Planar Designs of Reversible Full-Adders/Subtractors in Quantum-Dot Cellular Automata

Quantum-dot Cellular Automata (QCA) is one of the emerging nanotechnologies, promising alternative to CMOS technology due to faster speed, smaller size, lower power consumption, higher scale integration and higher switching frequency. Also, power dissipation is the main limitation of all the nano electronics design techniques including the QCA. Researchers have proposed the various mechanisms to limit this problem. Among them, reversible computing is considered as the reliable solution to lower the power dissipation. On the other hand, adders are fundamental circuits for most digital systems. In this paper, Innovation is divided to three sections. In the first section, a method for converting irreversible functions to a reversible one is presented. This method has advantages such as: converting of irreversible functions to reversible one directly and as optimal. So, in this method, sub-optimal methods of using of conventional reversible blocks such as Toffoli and Fredkin are not used, having of minimum number of garbage outputs and so on. Then, Using the method, two new symmetric and planar designs of reversible full-adders are presented. In the second section, a new symmetric, planar and fault tolerant five-input majority gate is proposed. Based on the designed gate, a reversible full-adder are presented. Also, for this gate, a fault-tolerant analysis is proposed. And in the third section, three new 8-bit reversible full-adder/subtractors are designed based on full-adders/subtractors proposed in the second section. The results are indicative of the outperformance of the proposed designs in comparison to the best available ones in terms of area, complexity, delay, reversible/irreversible layout, and also in logic level in terms of garbage outputs, control inputs, number of majority and NOT gates

New Symmetric and Planar Designs of Reversible Full-Adders/Subtractors in Quantum-Dot Cellular Automata

Quantum-dot Cellular Automata (QCA) is one of the emerging nanotechnologies, promising alternative to CMOS technology due to faster speed, smaller size, lower power consumption, higher scale integration and higher switching frequency. Also, power dissipation is the main limitation of all the nano electronics design techniques including the QCA. Researchers have proposed the various mechanisms to limit this problem. Among them, reversible computing is considered as the reliable solution to lower the power dissipation. On the other hand, adders are fundamental circuits for most digital systems. In this paper, Innovation is divided to three sections. In the first section, a method for converting irreversible functions to a reversible one is presented. This method has advantages such as: converting of irreversible functions to reversible one directly and as optimal. So, in this method, sub-optimal methods of using of conventional reversible blocks such as Toffoli and Fredkin are not used, having of minimum number of garbage outputs and so on. Then, Using the method, two new symmetric and planar designs of reversible full-adders are presented. In the second section, a new symmetric, planar and fault tolerant five-input majority gate is proposed. Based on the designed gate, a reversible full-adder are presented. Also, for this gate, a fault-tolerant analysis is proposed. And in the third section, three new 8-bit reversible full-adder/subtractors are designed based on full-adders/subtractors proposed in the second section. The results are indicative of the outperformance of the proposed designs in comparison to the best available ones in terms of area, complexity, delay, reversible/irreversible layout, and also in logic level in terms of garbage outputs, control inputs, number of majority and NOT gates

Exploration of Majority Logic Based Designs for Arithmetic Circuits

Since its inception, Moore\u27s Law has been a reliable predictor of computational power. This steady increase in computational power has been due to the ability to fit increasing numbers of transistors in a single chip. A consequence of increasing the number of transistors is also increasing the power consumption. The physical properties of CMOS technologies will make this powerwall unavoidable and will result in severe restrictions to future progress and applications. A potential solution to the problem of rising power demands is to investigate alternative low power nanotechnologies for implementing logic circuits. The intrinsic properties of these emerging nanotechnologies result in them being low power in nature when compared to current CMOS technologies. This thesis specifically highlights quantum dot celluar automata (QCA) and nanomagnetic logic (NML) as just two possible technologies. Designs in NML and QCA are explored for simple arithmetic units such as full adders and subtractors. A new multilayer 5-input majority gate design is proposed for use in NML. Designs of reversible adders are proposed which are easily testable for unidirectional stuck at faults

Technology Mapping, Design for Testability, and Circuit Optimizations for NULL Convention Logic Based Architectures

Delay-insensitive asynchronous circuits have been the target of a renewed research effort because of the advantages they offer over traditional synchronous circuits. Minimal timing analysis, inherent robustness against power-supply, temperature, and process variations, reduced energy consumption, less noise and EMI emission, and easy design reuse are some of the benefits of these circuits. NULL Convention Logic (NCL) is one of the mainstream asynchronous logic design paradigms that has been shown to be a promising method for designing delay-insensitive asynchronous circuits. This dissertation investigates new areas in NCL design and test and is made of three sections. The first section discusses different CMOS implementations of NCL gates and proposes new circuit techniques to enhance their operation. The second section focuses on mapping multi-rail logic expressions to a standard NCL gate library, which is a form of technology mapping for a category of NCL design automation flows. Finally, the last section proposes design for testability techniques for a recently developed low-power variant of NCL called Sleep Convention Logic (SCL)

κ\kappa-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations

We consider $\kappa$-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincar\'e algebra is unaltered, while the other is a general extension where the Poincar\'e algebra is deformed. As an example we fix the Jordanian twist and the corresponding realization of noncommutative coordinates, coproduct of momenta and addition of momenta. An extension with a one-parameter family of realizations of the Lorentz generators, dilatation and momenta closing the Poincar\'e-Weyl algebra is considered. The corresponding physical interpretation depends on the way the Lorentz algebra is implemented in phase space. We show how the spectrum of the relativistic hydrogen atom depends on the realization of the generators of the Poincar\'e-Weyl algebra.Comment: Title changed and minor changes in the tex

Custom Integrated Circuits

Contains reports on ten research projects.Analog Devices, Inc.IBM CorporationNational Science Foundation/Defense Advanced Research Projects Agency Grant MIP 88-14612Analog Devices Career Development Assistant ProfessorshipU.S. Navy - Office of Naval Research Contract N0014-87-K-0825AT&TDigital Equipment CorporationNational Science Foundation Grant MIP 88-5876

Control theoretic models of pointing

This article presents an empirical comparison of four models from manual control theory on their ability to model targeting behaviour by human users using a mouse: McRuer’s Crossover, Costello’s Surge, second-order lag (2OL), and the Bang-bang model. Such dynamic models are generative, estimating not only movement time, but also pointer position, velocity, and acceleration on a moment-to-moment basis. We describe an experimental framework for acquiring pointing actions and automatically fitting the parameters of mathematical models to the empirical data. We present the use of time-series, phase space, and Hooke plot visualisations of the experimental data, to gain insight into human pointing dynamics. We find that the identified control models can generate a range of dynamic behaviours that captures aspects of human pointing behaviour to varying degrees. Conditions with a low index of difficulty (ID) showed poorer fit because their unconstrained nature leads naturally to more behavioural variability. We report on characteristics of human surge behaviour (the initial, ballistic sub-movement) in pointing, as well as differences in a number of controller performance measures, including overshoot, settling time, peak time, and rise time. We describe trade-offs among the models. We conclude that control theory offers a promising complement to Fitts’ law based approaches in HCI, with models providing representations and predictions of human pointing dynamics, which can improve our understanding of pointing and inform design

Modified Gravity and Dark Energy models Beyond w(z)w(z)CDM Testable by LSST

One of the main science goals of the Large Synoptic Survey Telescope (LSST) is to uncover the nature of cosmic acceleration. In the base analysis, possible deviations from the Lambda-Cold-Dark-Matter ($\Lambda$CDM) background evolution will be probed by fitting a $w(z)$CDM model, which allows for a redshift-dependent dark energy equation of state with $w(z)$, within general relativity (GR). A rich array of other phenomena can arise due to deviations from the standard $\Lambda$CDM+GR model though, including modifications to the growth rate of structure and lensing, and novel screening effects on non-linear scales. Concrete physical models are needed to provide consistent predictions for these (potentially small) effects, to give us the best chance of detecting them and separating them from astrophysical systematics. A complex plethora of possible models has been constructed over the past few decades, with none emerging as a particular favorite. This document prioritizes a subset of these models along with rationales for further study and inclusion into the LSST Dark Energy Science Collaboration (DESC) data analysis pipelines, based on their observational viability, theoretical plausibility, and level of theoretical development. We provide references and theoretical expressions to aid the integration of these models into DESC software and simulations, and give justifications for why other models were not prioritized. While DESC efforts are free to pursue other models, we provide here guidelines on which theories appear to have higher priority for collaboration efforts due to their perceived promise and greater instructional value.Comment: 61 pages. Some acknowledgments and references added. This is version-1.1 of an internal collaboration document of LSST-DESC that is being made public and is not planned for submission to a journa