Arc Phenomena in low-voltage current limiting circuit breakers

Circuit breakers are an important safety feature in most electrical circuits, and they act to prevent excessive currents caused by short circuits, for example. Low-voltage current limiting circuit breakers are activated by a trip solenoid when a critical current is exceeded. The solenoid moves two contacts apart to break the circuit. However, as soon as the contacts are separated an electric arc forms between them, ionising the air in the gap, increasing the electrical conductivity of air to that of the hot plasma that forms, and current continues to flow. The currents involved may be as large as 80,000 amperes. Critical to the success of the circuit breaker is that it is designed to cause the arc to move away from the contacts, into a widening wedge-shaped region. This lengthens the arc, and then moves it onto a series of separator plates called an arc divider or splitter. The arc divider raises the voltage required to sustain the arcs across it, above the voltage that is provided across the breaker, so that the circuit is broken and the arcing dies away. This entire process occurs in milliseconds, and is usually associated with a sound like an explosion and a bright ash from the arc. Parts of the contacts and the arc divider may melt and/or vapourise. The question to be addressed by the Study Group was to mathematically model the arc motion and extinction, with the overall aim of an improved understanding that would help the design of a better circuit breaker. Further discussion indicated that two key mechanisms are believed to contribute to the movement of the arc away from the contacts, one being self-magnetism (where the magnetic field associated with the arc and surrounding circuitry acts to push it towards the arc divider), and the other being air flow (where expansion of air combined with the design of the chamber enclosing the arc causes gas flow towards the arc divider). Further discussion also indicated that a key aspect of circuit breaker design was that it is desirable to have as fast a quenching of the arc as possible, that is, the faster the circuit breaker can act to stop current flow, the better. The relative importance of magnetic and air pressure effects on quenching speed is of central interest to circuit design

Multilayered folding with voids

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers results in geometrically-induced curvature singularities. When voids are penalized by external pressure, the system is forced to trade off these competing effects, leading to sometimes striking periodic patterns. In this paper we construct a simple model of geometrically nonlinear multi-layered structures under axial loading and pressure confinement, with non-interpenetration conditions separating the layers. Energy minimizers are characterized as solutions of a set of fourth-order nonlinear differential equations with contact-force Lagrange multipliers, or equivalently of a fourth-order free-boundary problem. We numerically investigate the solutions of this free boundary problem, and compare them with the periodic solutions observed experimentally

Interplay of Mre11 Nuclease with Dna2 plus Sgs1 in Rad51-Dependent Recombinational Repair

The Mre11/Rad50/Xrs2 complex initiates IR repair by binding to the end of a double-strand break, resulting in 5′ to 3′ exonuclease degradation creating a single-stranded 3′ overhang competent for strand invasion into the unbroken chromosome. The nuclease(s) involved are not well understood. Mre11 encodes a nuclease, but it has 3′ to 5′, rather than 5′ to 3′ activity. Furthermore, mutations that inactivate only the nuclease activity of Mre11 but not its other repair functions, mre11-D56N and mre11-H125N, are resistant to IR. This suggests that another nuclease can catalyze 5′ to 3′ degradation. One candidate nuclease that has not been tested to date because it is encoded by an essential gene is the Dna2 helicase/nuclease. We recently reported the ability to suppress the lethality of a dna2Δ with a pif1Δ. The dna2Δ pif1Δ mutant is IR-resistant. We have determined that dna2Δ pif1Δ mre11-D56N and dna2Δ pif1Δ mre11-H125N strains are equally as sensitive to IR as mre11Δ strains, suggesting that in the absence of Dna2, Mre11 nuclease carries out repair. The dna2Δ pif1Δ mre11-D56N triple mutant is complemented by plasmids expressing Mre11, Dna2 or dna2K1080E, a mutant with defective helicase and functional nuclease, demonstrating that the nuclease of Dna2 compensates for the absence of Mre11 nuclease in IR repair, presumably in 5′ to 3′ degradation at DSB ends. We further show that sgs1Δ mre11-H125N, but not sgs1Δ, is very sensitive to IR, implicating the Sgs1 helicase in the Dna2-mediated pathway

On the Solution of Convection-Diffusion Boundary Value Problems Using Equidistributed Grids

The effect of using grid adaptation on the numerical solution of model convection-diffusion equations with a conservation form is studied. The grid adaptation technique studied is based on moving a fixed number of mesh points to equidistribute a generalization of the arc-length of the solution. In particular, a parameter-dependent monitor function is introduced which incorporates fixed meshes, approximate arc-length equidistribution, and equidistribution of the absolute value of the solution, in a single framework. Thus the resulting numerical method is a coupled nonlinear system of equations for the mesh spacings and the nodal values. A class of singularly perturbed problems, including Burgers's equation in the limit of small viscosity, is studied. Singular perturbation and bifurcation techniques are used to analyze the solution of the discretized equations, and numerical results are compared with the results from the analysis. Computation of the bifurcation diagram of the system is performed numerically using a continuation method and the results are used to illustrate the theory. It is shown that equidistribution does not remove spurious solutions present on a fixed mesh and that, furthermore, the spurious solutions can be stable for an appropriate moving mesh method

On asymptotic nonlocal symmetry of nonlinear Schr\"odinger equations

A concept of asymptotic symmetry is introduced which is based on a definition of symmetry as a reducibility property relative to a corresponding invariant ansatz. It is shown that the nonlocal Lorentz invariance of the free-particle Schr\"odinger equation, discovered by Fushchych and Segeda in 1977, can be extended to Galilei-invariant equations for free particles with arbitrary spin and, with our definition of asymptotic symmetry, to many nonlinear Schr\"odinger equations. An important class of solutions of the free Schr\"odinger equation with improved smoothing properties is obtained

Role of bulk and surface phonons in the decay of metal surface states

We present a comprehensive theoretical investigation of the electron-phonon contribution to the lifetime broadening of the surface states on Cu(111) and Ag(111), in comparison with high-resolution photoemission results. The calculations, including electron and phonon states of the bulk and the surface, resolve the relative importance of the Rayleigh mode, being dominant for the lifetime at small hole binding energies. Including the electron-electron interaction, the theoretical results are in excellent agreement with the measured binding energy and temperature dependent lifetime broadening.Comment: 4 pages, 3 figure

Mutation Testing as a Safety Net for Test Code Refactoring

Refactoring is an activity that improves the internal structure of the code without altering its external behavior. When performed on the production code, the tests can be used to verify that the external behavior of the production code is preserved. However, when the refactoring is performed on test code, there is no safety net that assures that the external behavior of the test code is preserved. In this paper, we propose to adopt mutation testing as a means to verify if the behavior of the test code is preserved after refactoring. Moreover, we also show how this approach can be used to identify the part of the test code which is improperly refactored