Large Deviations and Transient Multiplexing at a Buffered Resource

In this paper we discuss asymptotics associated with a large number of sources using a resource in a compact time interval. A large deviations condition is placed on the sum of the vectors that describe the stochastic behaviour of the sources and large deviations results deduced about the probability of exhaustion of the resource. This approach allows us to consider sources which are highly non-stationary in time. The examples in mind are a single server queue and a form of the Cramer-Lundburg model from risk theory. Connection is made with past work on stability of queues and effective bandwidths. A number of examples are presented to illustrate the strengths of this approach

Frequency pulling and mixing of relaxation oscillations in superconducting nanowires

Many superconducting technologies such as rapid single flux quantum computing (RSFQ) and superconducting quantum interference devices (SQUIDs) rely on the modulation of nonlinear dynamics in Josephson junctions for functionality. More recently, however, superconducting devices have been developed based on the switching and thermal heating of nanowires for use in fields such as single photon detection and digital logic. In this paper, we use resistive shunting to control the nonlinear heating of a superconducting nanowire and compare the resulting dynamics to those observed in Josephson junctions. We show that interaction of the hotspot growth with the external shunt produces high frequency relaxation oscillations with similar behavior as observed in Josephson junctions due to their rapid time constants and ability to be modulated by a weak periodic signal. In particular, we use a microwave drive to pull and mix the oscillation frequency, resulting in phase locked features that resemble the AC Josephson effect. New nanowire devices based on these conclusions have promising applications in fields such as parametric amplification and frequency multiplexing

Bridging the gap between nanowires and Josephson junctions: a superconducting device based on controlled fluxon transfer across nanowires

The basis for superconducting electronics can broadly be divided between two technologies: the Josephson junction and the superconducting nanowire. While the Josephson junction (JJ) remains the dominant technology due to its high speed and low power dissipation, recently proposed nanowire devices offer improvements such as gain, high fanout, and compatibility with CMOS circuits. Despite these benefits, nanowire-based electronics have largely been limited to binary operations, with devices switching between the superconducting state and a high-impedance resistive state dominated by uncontrolled hotspot dynamics. Unlike the JJ, they cannot increment an output through successive switching, and their operation speeds are limited by their slow thermal reset times. Thus, there is a need for an intermediate device with the interfacing capabilities of a nanowire but a faster, moderated response allowing for modulation of the output. Here, we present a nanowire device based on controlled fluxon transport. We show that the device is capable of responding proportionally to the strength of its input, unlike other nanowire technologies. The device can be operated to produce a multilevel output with distinguishable states, which can be tuned by circuit parameters. Agreement between experimental results and electrothermal circuit simulations demonstrates that the device is classical and may be readily engineered for applications including use as a multilevel memory

Stability of the nonlinear dynamics of an optically injected VCSEL

Automated protocols have been developed to characterize time series data in terms of stability. These techniques are applied to the output power time series of an optically injected vertical cavity surface emitting laser (VCSEL) subject to varying injection strength and optical frequency detuning between master and slave lasers. Dynamic maps, generated from high resolution, computer controlled experiments, identify regions of dynamic instability in the parameter space. © 2012 Optical Society of America

Advances in seismic imaging of magma and crystal mush

Seismic imaging methods have provided detailed three-dimensional constraints on the physical properties of magmatic systems leading to invaluable insight into the storage, differentiation and dynamics of magma. These constraints have been crucial to the development of our modern understanding of magmatic systems. However, there are still outstanding knowledge gaps resulting from the challenges inherent in seismic imaging of volcanoes. These challenges stem from the complex physics of wave propagation across highly heterogeneous low-velocity anomalies associated with magma reservoirs. Ray-based seismic imaging methods such as travel-time and surface-wave tomography lead to under-recovery of such velocity anomalies and to under-estimation of melt fractions. This review aims to help the volcanologist to fully utilize the insights gained from seismic imaging and account for the resolution limits. We summarize the advantages and limitations of the most common imaging methods and propose best practices for their implementation and the quantitative interpretation of low-velocity anomalies. We constructed and analysed a database of 277 seismic imaging studies at 78 arc, hotspot and continental rift volcanoes. Each study is accompanied by information about the seismic source, part of the wavefield used, imaging method, any detected low-velocity zones, and estimated melt fraction. Thirty nine studies attempted to estimate melt fractions at 22 different volcanoes. Only five studies have found evidence of melt storage at melt fractions above the critical porosity that separates crystal mush from mobile magma. The median reported melt fraction is 13% suggesting that magma storage is dominated by low-melt fraction crystal mush. However, due to the limits of seismic resolution, the seismological evidence does not rule out the presence of small (<10 km3) and medium-sized (<100 km3) high-melt fraction magma chambers at many of the studied volcanoes. The combination of multiple tomographic imaging methods and the wider adoption of methods that use more of the seismic wavefield than the first arriving travel-times, promise to overcome some of the limitations of seismic tomography and provide more reliable constraints on melt fractions. Wider adoption of these new methods and advances in data collection are needed to enable a revolution in imaging magma reservoirs

A superconducting nanowire spiking element for neural networks

As the limits of traditional von Neumann computing come into view, the brain's ability to communicate vast quantities of information using low-power spikes has become an increasing source of inspiration for alternative architectures. Key to the success of these largescale neural networks is a power-efficient spiking element that is scalable and easily interfaced with traditional control electronics. In this work, we present a spiking element fabricated from superconducting nanowires that has pulse energies on the order of ~10 aJ. We demonstrate that the device reproduces essential characteristics of biological neurons, such as a refractory period and a firing threshold. Through simulations using experimentally measured device parameters, we show how nanowire-based networks may be used for inference in image recognition, and that the probabilistic nature of nanowire switching may be exploited for modeling biological processes and for applications that rely on stochasticity.Comment: 5 main figures; 7 supplemental figure