The Hot-Spot Phenomenon and its Countermeasures in Bipolar Power Transistors by Analytical Electro-Thermal Simulation

This communication deals with a theoretical study of the hot spot onset (HSO) in cellular bipolar power transistors. This well-known phenomenon consists of a current crowding within few cells occurring for high power conditions, which significantly decreases the forward safe operating area (FSOA) of the device. The study was performed on a virtual sample by means of a fast, fully analytical electro-thermal simulator operating in the steady state regime and under the condition of imposed input base current. The purpose was to study the dependence of the phenomenon on several thermal and geometrical factors and to test suitable countermeasures able to impinge this phenomenon at higher biases or to completely eliminate it. The power threshold of HSO and its localization within the silicon die were observed as a function of the electrical bias conditions as for instance the collector voltage, the equivalent thermal resistance of the assembling structure underlying the silicon die, the value of the ballasting resistances purposely added in the emitter metal interconnections and the thickness of the copper heat spreader placed on the die top just to the aim of making more uniform the temperature of the silicon surface.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up

We introduce the new space $BV^{\alpha}(\mathbb{R}^n)$ of functions with bounded fractional variation in $\mathbb{R}^n$ of order $\alpha \in (0, 1)$ via a new distributional approach exploiting suitable notions of fractional gradient and fractional divergence already existing in the literature. In analogy with the classical $BV$ theory, we give a new notion of set $E$ of (locally) finite fractional Caccioppoli $\alpha$-perimeter and we define its fractional reduced boundary $\mathscr{F}^{\alpha} E$. We are able to show that $W^{\alpha,1}(\mathbb{R}^n)\subset BV^\alpha(\mathbb{R}^n)$ continuously and, similarly, that sets with (locally) finite standard fractional $\alpha$-perimeter have (locally) finite fractional Caccioppoli $\alpha$-perimeter, so that our theory provides a natural extension of the known fractional framework. Our main result partially extends De Giorgi's Blow-up Theorem to sets of locally finite fractional Caccioppoli $\alpha$-perimeter, proving existence of blow-ups and giving a first characterisation of these (possibly non-unique) limit sets.Comment: 46 page

Fast inactivation in Shaker K+ channels. Properties of ionic and gating currents.

Fast inactivating Shaker H4 potassium channels and nonconducting pore mutant Shaker H4 W434F channels have been used to correlate the installation and recovery of the fast inactivation of ionic current with changes in the kinetics of gating current known as "charge immobilization" (Armstrong, C.M., and F. Bezanilla. 1977. J. Gen. Physiol. 70:567-590.). Shaker H4 W434F gating currents are very similar to those of the conducting clone recorded in potassium-free solutions. This mutant channel allows the recording of the total gating charge return, even when returning from potentials that would largely inactivate conducting channels. As the depolarizing potential increased, the OFF gating currents decay phase at -90 mV return potential changed from a single fast component to at least two components, the slower requiring approximately 200 ms for a full charge return. The charge immobilization onset and the ionic current decay have an identical time course. The recoveries of gating current (Shaker H4 W434F) and ionic current (Shaker H4) in 2 mM external potassium have at least two components. Both recoveries are similar at -120 and -90 mV. In contrast, at higher potentials (-70 and -50 mV), the gating charge recovers significantly more slowly than the ionic current. A model with a single inactivated state cannot account for all our data, which strongly support the existence of "parallel" inactivated states. In this model, a fraction of the charge can be recovered upon repolarization while the channel pore is occupied by the NH2-terminus region

Spatial composition in the multi-channel domain: aesthetics and techniques

This paper outlines technical and aesthetic approaches to sound spatialisation for electroacoustic music composition. In particular, the paper discusses how spatialisation (sound diffusion) is used to realise specific musical objectives. Technological solutions to problems associated with adapting multichannel compositions for live spatialisation are explored, with particular reference to the open-source Resound system [2, 3]. Examples of Resound applications are provided to illustrate the potential of the system for controlling complex spatial behaviour during live performance

Reversals in nature and the nature of reversals

The asymmetric shape of reversals of the Earth's magnetic field indicates a possible connection with relaxation oscillations as they were early discussed by van der Pol. A simple mean-field dynamo model with a spherically symmetric $\alpha$ coefficient is analysed with view on this similarity, and a comparison of the time series and the phase space trajectories with those of paleomagnetic measurements is carried out. For highly supercritical dynamos a very good agreement with the data is achieved. Deviations of numerical reversal sequences from Poisson statistics are analysed and compared with paleomagnetic data. The role of the inner core is discussed in a spectral theoretical context and arguments and numerical evidence is compiled that the growth of the inner core might be important for the long term changes of the reversal rate and the occurrence of superchrons.Comment: 24 pages, 12 figure

Fractional divergence-measure fields, Leibniz rule and Gauss–Green formula

Given a E (0, 1] and p E [1, +co], we define the space DMa,p(R-n) of L-p vector fields whose a-divergence is a finite Radon measure, extending the theory of divergence-measure vector fields to the distributional fractional setting. Our main results concern the absolute continuity properties of the a-divergence-measure with respect to the Hausdorff measure and fractional analogues of the Leibniz rule and the Gauss-Green formula. The sharpness of our results is discussed via some explicit examples

On sets with finite distributional fractional perimeter

We continue the study of the fine properties of sets having locally finite distributional fractional perimeter. We refine the characterization of their blow-ups and prove a Leibniz rule for the intersection of sets with locally finite distributional fractional perimeter with sets with finite fractional perimeter. As a byproduct, we provide a description of non-local boundaries associated with the distributional fractional perimeter.Comment: 18 page

Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula

Given $\alpha\in[0,1]$ and $p\in[1,+\infty]$, we define the space $\mathcal{DM}^{\alpha,p}(\mathbb R^n)$ of $L^p$ vector fields whose $\alpha$-divergence is a finite Radon measure, extending the theory of divergence-measure vector fields to the distributional fractional setting. Our main results concern the absolute continuity properties of the $\alpha$-divergence-measure with respect to the Hausdorff measure and fractional analogues of the Leibniz rule and the Gauss-Green formula. The sharpness of our results is discussed via some explicit examples.Comment: 22 page

Control system design using optimization techniques Final report

Optimization techniques for control of fuel valve systems for air breathing jet engines and 40-60 inlet control problem