Surviving an avalanche of data

Open the sports or business section of your daily newspaper, and you are immediately bombarded with an array of graphs, tables, diagrams, and statistical reports that require interpretation. Across all walks of life, the need to understand statistics is fundamental. Given that our youngsters’ future world will be increasingly data laden, scaffolding their statistical understanding and reasoning is imperative, from the early grades on. The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council’s professional development “Focus of the Year” for 2007–2008. We need such a focus, especially given the results of the statistics items from the 2003 NAEP. As Shaughnessy (2007) noted, students’ performance was weak on more complex items involving interpretation or application of items of information in graphs and tables. Furthermore, little or no gains were made between the 2000 NAEP and the 2003 NAEP studies. One approach I have taken to promote young children’s statistical reasoning is through data modeling. Having implemented in grades 3 –9 a number of model-eliciting activities involving working with data (e.g., English 2010), I observed how competently children could create their own mathematical ideas and representations—before being instructed how to do so. I thus wished to introduce data-modeling activities to younger children, confi dent that they would likewise generate their own mathematics. I recently implemented data-modeling activities in a cohort of three first-grade classrooms of six year- olds. I report on some of the children’s responses and discuss the components of data modeling the children engaged in.

Analysis of avalanche breakdown in bipolar transistors based on majority carrier transportation

This paper describes a new analysis of the avalanche breakdown phenomenon in bipolar transistors for different bias conditions of the emitter-base junction. This analysis revolves around the transportation and storage of majority carriers in the base region. Using this analysis one can compute all the voltage-current characteristics of a transistor under avalanche breakdown.

Tombstone for Fritz Gottschalk who died in an avalanche in 1935; Bothfeld Cemetery; Hannover.

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Tombstone for Fritz Gottschalk who died in an avalanche in 1935; Bothfeld Cemetery; Hannover.

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Tombstone for Fritz Gottschalk who died in an avalanche in 1935; Bothfeld Cemetery; Hannover.

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Tombstone for Fritz Gottschalk who died in an avalanche in 1935; Bothfeld Cemetery; Hannover.

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Avalanche behavior and statistical properties in a microcrack coalescence process

Fracture owing to the coalescence of numerous microcracks can be described by a simple statistical model, where a coalescence event stochastically occurs as the number density of nucleated microcracks increases. Both numerical simulation and statistical analysis reveal that a microcrack coalescence process may display avalanche behavior and that the final failure is catastrophic. The cumulative distribution of coalescence events in the vicinity of critical fracture follows a power law and the fracture profile has self-affine fractal characteristic. Some macromechanical quantities may be traced back and extracted from the mesoscopic process based on the statistical analysis of coalescence events.

Gigacount/second photon detection with InGaAs avalanche photodiodes

We demonstrate high count rate single photon detection at telecom wavelengths using a thermoelectrically-cooled semiconductor diode. Our device consists of a single InGaAs avalanche photodiode driven by a 2 GHz gating frequency signal and coupled to a tuneable self-differencing circuit for enhanced detection sensitivity. We find the count rate is linear with the photon flux in the single photon detection regime over approximately four orders of magnitude, and saturates at 1 gigacount/s at high photon fluxes. This result highlights promising potential for APDs in high bit rate quantum information applications.

Integrated avalanche diode for 600 v Trench IGBT over-voltage protection

Avalanche multiplication has been one of the major destructive failure mechanisms in IGBTs; in order to avoid operating an IGBT under abnormal conditions, it is desirable to develop peripheral protecting circuits monolithically integrated without compromising the operation and performance of the IGBT. In this paper, a monolithically integrated avalanche diode (D av) for 600V Trench IGBT over-voltage protection is proposed. The mix-mode transient simulation proves the clamping capability of the D av when the IGBT is experiencing over-voltage stress in unclamped inductive switching (UIS) test. The spread of avalanche energy, which prevents hot-spot formation, through the help of the avalanche diode feeding back a large fraction of the avalanche current to a gate resistance (R G) is also explained. © 2011 IEEE.

X-ray observation of micro-failures in granular piles approaching an avalanche

An X-ray imaging technique is used to probe the stability of 3-dimensional granular packs in a slowly rotating drum. Well before the surface reaches the avalanche angle, we observe intermittent plastic events associated with collective rearrangements of the grains located in the vicinity of the free surface. The energy released by these discrete events grows as the system approaches the avalanche threshold. By testing various preparation methods, we show that the pre-avalanche dynamics is not solely controlled by the difference between the free surface inclination and the avalanche angle. As a consequence, the measure of the pre-avalanche dynamics is unlikely to serve as a tool for predicting macroscopic avalanches.