Handbook of the I-T-E circuit breaker. Series K.

Mode of access: Internet.

Survey of ground fault circuit interrupter usage for protection against hazardous shock /

Includes bibliographical references.

Sneak circuit analysis : a means of verifying design integrity.

"July 1986."

Modeling and analysis of a tunable piezoelectric structure for transverse shear wave generation

An analytical investigation of the transverse shear wave mode tuning with a resonator mass (packing mass) on a Lead Zirconium Titanate (PZT) crystal bonded together with a host plate and its equivalent electric circuit parameters are presented. The energy transfer into the structure for this type of wave modes are much higher in this new design. The novelty of the approach here is the tuning of a single wave mode in the thickness direction using a resonator mass. First, a one-dimensional constitutive model assuming the strain induced only in the thickness direction is considered. As the input voltage is applied to the PZT crystal in the thickness direction, the transverse normal stress distribution induced into the plate is assumed to have parabolic distribution, which is presumed as a function of the geometries of the PZT crystal, packing mass, substrate and the wave penetration depth of the generated wave. For the PZT crystal, the harmonic wave guide solution is assumed for the mechanical displacement and electric fields, while for the packing mass, the former is solved using the boundary conditions. The electromechanical characteristics in terms of the stress transfer, mechanical impedance, electrical displacement, velocity and electric field are analyzed. The analytical solutions for the aforementioned entities are presented on the basis of varying the thickness of the PZT crystal and the packing mass. The results show that for a 25% increase in the thickness of the PZT crystal, there is ~38% decrease in the first resonant frequency, while for the same change in the thickness of the packing mass, the decrease in the resonant frequency is observed as ~35%. Most importantly the tuning of the generated wave can be accomplished with the packing mass at lower frequencies easily. To the end, an equivalent electric circuit, for tuning the transverse shear wave mode is analyzed.

Slightly slanting impact on an elastic cantilever column-an experimental study

Experiments concerning slightly slanting impact between a flat-ended rigid body and a flat-ended elastic cantilever column with a rectangular cross-section have been performed. The experimental results are compared with the theoretical ones. The small angle of incidence was measured by using an optical method. The impact process was studied by using a split disc for the rigid body, with the two halves bonded together and electrically insulated from each other. The disc and the column were parts of an electric circuit. Different contact states could be distinguished according to different voltage levels. Reasonably good agreement between theory and experiment was found. Thus, the impact duration has its minimum under perfectly axial impact as predicted by the theory. Also, the predicted process of alternating line and surface contact was observed. Furthermore, the existence of a small critical angle of incidence was verified. This critical angle of incidence divides the impact processes into two categories: (1) The rigid body and the column end come into surface contact before separation. (2) They separate without surface contact. Comparison of axial strains between theory and experiment shows good agreement.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Spontaneous DC Current Generation in a Resistively Shunted Semiconductor Superlattice Driven by a TeraHertz Field

We study a resistively shunted semiconductor superlattice subject to a high-frequency electric field. Using a balance equation approach that incorporates the influence of the electric circuit, we determine numerically a range of amplitude and frequency of the ac field for which a dc bias and current are generated spontaneously and show that this region is likely accessible to current experiments. Our simulations reveal that the Bloch frequency corresponding to the spontaneous dc bias is approximately an integer multiple of the ac field frequency.

Surface determination of the air-earth electrical current density using co-located sensors of different geometry

A vertical conduction current flows in the atmosphere as a result of the global atmospheric electric circuit. The current at the surface consists of the conduction current and a locally generated displacement current, which are often approximately equal in magnitude. A method of separating the two currents using two collectors of different geometry is investigated. The picoammeters connected to the collectors have a RC time constant of approximately 3 s, permitting the investigation of higher frequency air-earth current changes than previously achieved. The displacement current component of the air-earth current derived from the instrument agrees with calculations using simultaneous data from a co-located fast response electric field mill. The mean value of the nondisplacement current measured over 9 h was 1.76 +/- 0.002 pA m(-2). (c) 2006 American Institute of Physics.

High performance blocking filters for the region 1µm to 20µm

A set of filters based on the sequence of semiconductor edges is described which offers continuity of short-wave infrared blocking. The rejection throughout the stop region is greater than 103 for each filter and the transmission better than 70% through one octave with a square cutoff. The cutoff points are located at intervals of about two-thirds of an octave. Filters at 2.6 ,µm, 5.5 µm, and 12 µm which use a low-passing multilayer in combination with a semiconductor absorption edge are described in detail. The design of multilayers for optimum performance is discussed by analogy with the synthesis of electric circuit filters.

Experimental determination of layer cloud edge charging from cosmic ray ionisation

The cloud-air transition zone at stratiform cloud edges is an electrically active region where droplet charging has been predicted. Cloud edge droplet charging is expected from vertical flow of cosmic ray generated atmospheric ions in the global electric circuit. Experimental confirmation of stratiform cloud edge electrification is presented here, through charge and droplet measurements made within an extensive layer of supercooled stratiform cloud, using a specially designed electrostatic sensor. Negative space charge up to 35 pC m−3 was found in a thin (<100 m) layer at the lower cloud boundary associated with the clear air-cloud conductivity gradient, agreeing closely with space charge predicted from the measured droplet concentration using ion-aerosol theory. Such charge levels carried by droplets are sufficient to influence collision processes between cloud droplets.

Extraction of Tschebysheff design data for the low pass dielectric multilayer

The extraction of design data for the lowpass dielectric multilayer according to Tschebysheff performance is described. The extraction proceeds initially by analogy with electric-circuit design, and can then be given numerical refinement which is also described. Agreement with the Tschebysheff desideratum is satisfactory. The multilayers extracted by this procedure are of fractional thickness, symmetric with regard to their central layers.

Another Proof of the Preceding Theory

Another Proof of the Preceding Theory was produced as part of a residency run by Artists in Archeology in conjunction with the Stonehenge Riverside project. The film explores the relationship between science, work and ritual, imagining archaeology as a future cult. As two robed disciples stray off from the dig, they are drawn to the drone of the stones and proceed to play the henge like a gigantic Theremin. Just as a Theremin is played with the hand interfering in an electric circuit and producing sound without contact, so the stones respond to the choreographed bodily proximity. Finally, one of the two continues alone to the avenue at Avebury, where the magnetic pull of the stones reaches its climax. Shot on VHS, the film features a score by Zuzushi Monkey, with percussion and theremin sounds mirroring the action. The performers are mostly artists and archeologists from the art and archaeology teams. The archeologists were encouraged to perform their normal work in the robes, in an attempt to explore the meeting points of science and ritual and interrogate our relationship to an ultimately unknowable prehistoric past where activities we do not understand are relegated to the realm of religion. Stonehenge has unique acoustic properties, it’s large sarsen stones are finely worked on the inside, left rough on the outside, intensifying sound waves within the inner horseshoe, but since their real use, having been built over centuries, remains ambiguous, the film proposes that our attempts to decode them may themselves become encoded in their cumulative meaning for future researchers.

Charge measurements in stratiform cloud from a balloon based sensor

Abstract. The electrification of stratiform clouds has is little investigated in comparison with thunderstorms and fair weather atmospheric electricity. Theory indicates that, at the upper and lower horizontal boundaries of layer clouds, charging will arise from vertical flow of cosmogenic ions in the global atmospheric electric circuit. Charge is transferred to droplets and particles, affecting cloud microphysical processes such as collision and droplet activation. Due to the lack of in-situ measurements, the magnitude and distribution of charge in stratiform clouds is not well known. A sensitive, inexpensive, balloon borne charge sensor has been developed to make in-situ measurements of edge charging in stratiform cloud using a standard meteorological radiosonde system. The charge sensor has now been flown through over 20 stratiform clouds and frequently detected charge up to 200 pC m-3 near cloud edges. These results are compared with measurements from the same sensor used to investigate charge in particle layers, such as volcanic ash from the Eyjafjallajökull eruption, and Saharan dust in the Cape Verde Isles. 1.