Minimum Arc Research Articles

Voltage-Current Characteristics of Breaking Arc at Constant Opening Speed in the Air

Voltage-Current (VI) characteristics of breaking arc between electrical contacts have been investigated for several contact materials (Au, Ag, Cu, Pt, and Ni). The purpose of this paper is to investigate the VI-characteristics and minimum arc voltages of the breaking arcs that occur between slowly opening (1.0 cm/s) contacts, and compare these results with those of Holm. Experimental circuit is resistive, which has 5-/spl Omega/ circuit resistance. Experiments were carried out in the air at atmospheric pressure for supply voltages 30, 42, and 54V. The time evolutions of arc voltage, arc current and gap length were measured simultaneously. The VI-characteristics and minimum arc voltages were obtained from those measured values. The results showed that minimum arc voltages for each contact material (Au, Ag, Cu, Pt, and Ni) agreed with those of Holm. On the other hand, VI-characteristics of Au, Ag, Cu, and Pt contacts agreed with those of Holm, but VI-characteristics of Ni electrical contacts disagreed with those of Holm. The difference for VI-characteristics between Ni electrical contacts and the others was because of lower electric field of the arc column for the case of nickel electrical contacts.

Disengaging Connectors Under Automotive 42-VDC Loads

Connectors are designed to pass current but are generally not designed to disconnect electrical loads under power. In some circumstances, however, connectors are mated and unmated under load, as for instance during repairs, diagnostic procedures, or when blown fuses are replaced under short circuit conditions. With the present 14-VDC automotive power network no serious consequences are associated with plugging and unplugging under load due to very short break arcs (the system voltage is approximately the same as the minimum arc voltage of the contact material). For the 42-VDC PowerNet, however, serious consequences may result; impacting the reliability of the connection, the electrical distribution system, and automotive safety. The authors show component design approaches, which minimize damage when connectors are disengaged under dc loads. The connector damage is evaluated employing insertion force readings, and contact resistance measurements as part of a field correlated life test for automotive connections.

Complete classification of tournaments having a disjoint union of directed paths as a minimum feedback arc set

AbstractA feedback arc set of a digraph is a set of arcs whose reversal makes the resulting digraph acyclic. Given a tournament with a disjoint union of directed paths as a feedback arc set, we present necessary and sufficient conditions for this feedback arc set to have minimum size. We will present a construction for tournaments where the difference between the size of a minimum feedback arc set and the size of the largest collection of arc disjoint cycles can be made arbitrarily large. We will also make a connection to a problem found in [Barthélemy et al., 2]. The reversing number of a digraph was defined to be $r(D)\, = |V(T)|-|V(D)|$ where T is a smallest tournament having the arc set of D as a minimum feedback arc set. As a consequence of our classification of all tournaments having a disjoint union of directed paths as a minimum feedback arc set, we will obtain a new result involving the reversing number. We obtain precise reversing numbers for all digraphs consisting of a disjoint union of directed paths. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 28–47, 2004

Solving problems for maximal reducible flowgraphs

In this paper, the family of Maximal Reducible Flowgraphs (MRFs) is recursively defined, based on a decomposition theorem. A one-to-one association between MRFs and extended binary trees allows to deduce some numerical properties of the family. Hamiltonian problems, testing isomorphism and finding a minimum cardinality feedback arc set are efficiently solved for MRFs. The results concerning hamiltonian paths and cycles also hold for reducible flowgraphs.

Algorithm of capacity expansion on networks optimization

The paper points out the relationship between the bottleneck and the minimum cutset of the network, and presents a capacity expansion algorithm of network optimization to solve the network bottleneck problem. The complexity of the algorithm is also analyzed. As required by the algorithm, some virtual sources are imported through the whole positive direction subsection in the network, in which a certain capacity value is given. Simultaneously, a corresponding capacity-expanded network is constructed to search all minimum cutsets. For a given maximum flow value of the network, the authors found an adjustment value of each minimum cutset arc’s group with gradually reverse calculation and marked out the feasible flow on the capacity-extended networks again with the adjustment value increasing. All this has been done repeatedly until the original topology structure is resumed. So the algorithm can increase the capacity of networks effectively and solve the bottleneck problem of networks.

Application of Steenbeck's minimum principle for three-dimensional modelling of DC arc plasma torches

In this paper, physical/mathematical models for the three-dimensional, quasi-steady modelling of the plasma flow and heat transfer inside a non-transferred DC arc plasma torch are described in detail. The Steenbeck's minimum principle (Finkelnburg W and Maecker H 1956 Electric arcs and thermal plasmas Encyclopedia of Physics vol XXII (Berlin: Springer)) is employed to determine the axial position of the anode arc-root at the anode surface. This principle postulates a minimum arc voltage for a given arc current, working gas flow rate, and torch configuration. The modelling results show that the temperature and flow fields inside the DC non-transferred arc plasma torch show significant three-dimensional features. The predicted anode arc-root attachment position and the arc shape by employing Steenbeck's minimum principle are reasonably consistent with experimental observations. The thermal efficiency and the torch power distribution are also calculated in this paper. The results show that the thermal efficiency of the torch always ranges from 30% to 45%, i.e. more than half of the total power input is taken away by the cathode and anode cooling water. The special heat transfer mechanisms at the plasma–anode interface, such as electron condensation, electron enthalpy and radiative heat transfer from the bulk plasma to the anode inner surface, are taken into account in this paper. The calculated results show that besides convective heat transfer, the contributions of electron condensation, electron enthalpy and radiation to the anode heat transfer are also important (∼30% for parameter range of interest in this paper). Additional effects, such as the non-local thermodynamic equilibrium plasma state near the electrodes, the transient phenomena, etc, need to be considered in future physical/mathematical models, including corresponding measurements.

Combinatorial algorithms for feedback problems in directed graphs

Given a weighted directed graph G=( V, A), the minimum feedback arc set problem consists of finding a minimum weight set of arcs A′⊆ A such that the directed graph ( V, A⧹ A′) is acyclic. Similarly, the minimum feedback vertex set problem consists of finding a minimum weight set of vertices containing at least one vertex for each directed cycle. Both problems are NP-complete. We present simple combinatorial algorithms for these problems that achieve an approximation ratio bounded by the length, in terms of number of arcs, of a longest simple cycle of the digraph.

Factors influencing the minimum arc sustaining electric field and associated current for a high-pressure-vortex-water-wall-arc lamp

Pulsed high pressure arc lamps are often operated with a small sustaining current during the interpulse period in order to minimize the arc expansion time, to increase the lamps' operating lifetime and to enable operation at higher repetition frequencies. It is common to select a sustaining current level associated with an arc voltage which lies between the maximum DC source voltage and the minimum sustaining voltage. This paper shows that the radius of the arc tube, the amount of convection and radiation and the assumptions regarding the nature of the radiation model strongly influence the current value associated with the minimum sustaining voltage. Pressure and boundary temperature have only a slight effect on the current associated with the minimum sustaining voltage but affect the minimum sustaining voltage. Heat conduction plays the primary role in tubes with a small radius while optically thin radiation plays the primary role in tubes with a large radius. The simulation results were obtained using Patankar's control volume algorithm along with boundary conditions. The extended Ellenbass-Heller equation in cylindrical coordinates was solved. The numerical results for the electric field as a function of current are somewhat smaller than the experimentally derived results. Convection appears to be the reason for this difference.

Breaking cycles for minimizing crossings

We consider the one-sided crossing minimization problem (CP): given a bipartite graph G and a permutation x 0 of the vertices on a layer, find a perumuation x 1 of the vertices on the other layer which minimizes the number of edge crossings in any straightline drawing of G where vertices are placed on two parallel lines and sorted according to x 0 and x 1 . Solving CP represents a fundamental step in the construction of aesthetically pleasing layouts of heirarchies and directed graphs, but unfortunately this problem has been proved to be NP-complete. In this paper we address the strong relation between CP and the problem of computing minimum feedback arc sets in directed graphs and we devise a enw approximation algorithm for CP, called PM, that exploits this dependency. We experimantally and visually compare the performance of PM with the performance of well-known algorithms and of recent attractive strategies. Experiments are carried out on different families of randomly generated graphs, on pathological instances, and on real test sets. Performance indicators include both number of edge crossings and running time, as well as structural measures of the problem instances. We found CP to be a very interesting and rich problem from a combinatorial point of view. Our results clearly separate the behavior of the algorithms, proving the effectiveness of PM on most test sets and showing tradeoffs between quality of the solutions and running time. However, if the visual complexity of the drawings is considered, we found no clear winner. This confirms the importance of optimizing also other aesthetic criteria such as symmetry, edge length, and angular resolution.

Solving Problems for Maximal Reducible Flowgraphs

In this paper, the family of Maximal Reducible Flowgraphs (MRFs) is recursively defined, based on a decomposition theorem. A one-to-one association between MRFs and extended binary trees allows to deduce some numerical properties of the family. Hamiltonian problems, testing isomorphism and finding a minimum cardinality feedback arc set are efficiently solved for MRFs. The results concerning hamiltonian paths and cycles also hold for reducible flowgraphs.

Modeling the effects of an axial magnetic field on the vacuum arc

A quantitative two-dimensional model of a vacuum arc in an applied magnetic field is presented. For the particular case, a uniform axial magnetic field B/sub Z/, it provides a unified condition for the two regimes of arc voltage versus B/sub Z/, i.e. ? the steeply falling voltage branch (low B/sub Z/), and the slowly rising voltage branch (high B/sub Z/, which characterizes the diffuse arc mode). The transition to the high-B/sub Z/ regime is complete when the average mixing distance of the individual expanding cathode-spot plasma jets, measured from the cathode plane, is equal to the contact gap length. The model also predicts the observed smooth transition and minimum arc voltage between the two branches, and the independence of the are voltage on the arc current in the high-B/sub Z/ regime. Calculated results are found to be in good agreement with reported experimental data from several independent investigations over a wide range of gap, B/sub Z/ and arc current I/sub ARC/.

Short arc duration laws and distributions at low current (>1 A) and voltage (14-42 VDC)

In the automobile industry, safety and comfort equipment require more and more switches which are operated over a wide range of electrical, mechanical and ambient conditions. In the low electrical power range, i.e., near minimum current and voltage, shorts and fluctuating arcing may occur. Using a testing apparatus capable of rapid measurements with high temporal resolution (0.2 ns) we have measured and analyzed arc durations on break in a pure resistive circuit near minimum arc current and voltage O < I < 1 A, and V = 14 VDC. For all contact materials tested (Ag, Cu, Pd, Au, Sn, Ni), average arc duration values versus current are grouped around two exponential curves corresponding to two anodic arc regimes. The analytical expressions for these curves are found to be in good agreement with the multiburst arc operating model [T = t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> exp(I//i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> )]. The lifetime and current intensity of the burst (t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> , i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> ) are deduced for various contact materials. In addition, the histogram of arc duration fluctuations is well fitted by multiGaussian distributions centered around a multiple of the burst time. This confirms the burst mechanism and introduces the concept that arc duration values are discrete. On the other hand, the plot of arc occurrence in the first regime clarifies the significance of the minimum arc current (100%) and yields the current limit for arc appearance (0%). Finally, high voltages (14-28-42 V) and inductances (1 μH-10 mH) can produce long arc durations with the result that we may enter into the cathodic arc.

On Integrality, Stability and Composition of Dicycle Packings and Covers

Given a digraph D, the minimum integral dicycle cover problem (known also as the minimum feedback arc set problem) is to find a minimum set of arcs that intersects every dicycle; the maximum integral dicycle packing problem is to find a maximum set of pairwise arc disjoint dicycles. These two problems are NP-complete.

Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms

In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by the min-cut. The result (which is existentially optimal) establishes an important analogue of the famous 1-commodity max-flow min-cut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use the flow result to design the first polynomial-time (polylog n-times-optimal) approximation algorithms for well-known NP-hard optimization problems such as graph partitioning, min-cut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems, network reconfiguration, communication in distributed networks, scientific computing and rapidly mixing Markov chains are also described in the paper. Categories and Subject Descriptors: F.2.2 (Analysis of Algorithms and Problem Complexity):

Robust output tracking of constrained nonlinear systems

The problem of output tracking for constrained nonlinear systems in the presence of uncertainties is studied. The concepts of input/output (I/O) linearization, relative degree, hyporbolically minimum phase and matching condition arc reviewed. A sliding mode control (SMC) law is developed which achieves asymptotically tracking despite the uncertainties while maintaining the boundness of all signals inside the loop.

Parallel Algorithms for Reducible Flow Graphs

We present parallel NC algorithms for recognizing a reducible flow graph (rfg) and for finding dominators, minimum feedback vertex sets, and a depth first search tree in an rfg. On ann-node rfg, all of these algorithms run inpolylog(n) time usingM(n) processors, whereM(n) is the number of processors needed to multiply twon×nmatrices in polylog time. We show that finding a minimum feedback vertex set in vertex-weighted rfg's or finding a minimum feedback arc set in arc-weighted rfg's is P-complete. For arc or vertex weights in unary, we present RNC algorithms for these problems and show that the problems are in NC if and only if the problem of finding a minimum cut in a flow network is in NC.

High-Pressure ( 2000 MPa) Kyanite- and Glaucophane-bearing Pelitic Schist and Eclogite from Cordillera de la Costa Belt, Venezuela

In the Cretaceous melange of the Cordillera de la Costa belt, INTRODUCTION north–central Venezuela, there are knockers of eclogite, barroisiteTwo belts of high-pressure (HP)–low-temperature (LT) bearing eclogite, and pelitic glaucophane schist. These occur in a metamorphic rocks are exposed in the Caribbean Mounmetamorphic melange matrix that locally consists of marble, sertain system of northern Venezuela, which is part of the pentinite, amphibolite, actinolite schist, feldspathic schist and gneiss, complex east–west-trending boundary zone between the graphitic schist, chloritoid schist, and garnet-bearing mica schist. Caribbean and South American plates (e.g. Menendez, The protoliths for these various rock types exhibit a wide age range 1966, 1967). These two belts are the Cordillera de la (Cambrian to Early Cretaceous?). Recently discovered knockers of Costa and Villa de Cura belts, both of which were pelitic glaucophane schist contain Mg-glaucophane + paragonite metamorphosed during the mid-Cretaceous, presumably + kyanite + garnet + talc + graphite + rutile + quartz. in a subduction zone related to the mid-Cretaceous The coexistence of kyanite and Mg-glaucophane suggests minimum Leeward Antilles volcanic arc (e.g. Pindell, 1993). From P ~2000 MPa at T > 600°C. Eclogite knockers from the same Jurassic to Eocene time North and South America were outcrop contain garnet and clinopyroxene which yield ~500°C for diverging and new proto-Caribbean sea-floor was created cores, ~700°C for rims, and P [ 1200 MPa. The assemblage between them (e.g. Pindell, 1993). Therefore, the Leegarnet–biotite–phengite–albite within schists of the melange matrix ward Antilles arc, as well as the entire Caribbean Mounof this locality indicates metamorphic conditions of T = tain system, are allochthonous and formed far to the 450–520°C at P = 1800 MPa. Because all lithologies in this west as part of the Farallon–North/South American plate outcrop record high-P conditions, this metamorphic melange formed boundary zone (e.g. Pindell, 1993). before or during peak metamorphism in a mid-Cretaceous subduction Although the two HP–LT belts have similar metazone. morphic ages, they differ greatly in lithology and metamorphic history. The Cordillera de la Costa belt consists of oceanic and passive continental-margin rocks intermixed with Paleozoic granites and granitic gneisses. In this belt, the eclogites and blueschists were retrograded to epidote–amphiboliteand greenschist-facies assemblages following an apparent P–T path typical for

Using the residual area criterion for signal reconstruction from noiseless and noisy samples

We consider reconstruction of a signal from a univariate data set. A problem that is often observed using existing techniques is overshoots between data samples. We propose a criterion, called the residual area criterion, which addresses this problem. The curve of minimum arc length that interpolates the data is the piecewise linear curve connecting the data points. Our criterion is to minimize the /spl Lscr//sup 2/ distance to this curve from the chosen set of functions. We discuss the use of this criterion for both noisy and noiseless samples. The main point of our paper is that a significant improvement is realized by minimizing our criterion rather than requiring continuity of high order derivatives (which is the usual method employed for noiseless data) or minimizing curvature (which is the usual criterion for noisy data). A comparison of our method to existing methods is included.

Tournaments as Feedback Arc Sets

We examine the size $s(n)$ of a smallest tournament having the arcs of an acyclic tournament on $n$ vertices as a minimum feedback arc set. Using an integer linear programming formulation we obtain lower bounds $s(n) \geq 3n - 2 - \lfloor \log_2 n \rfloor$ or $s(n) \geq 3n - 1 - \lfloor \log_2 n \rfloor$, depending on the binary expansion of $n$. When $n = 2^k - 2^t$ we show that the bounds are tight with $s(n) = 3n - 2 - \lfloor \log_2 n \rfloor$. One view of this problem is that if the 'teams' in a tournament are ranked to minimize inconsistencies there is some tournament with $s(n)$ 'teams' in which $n$ are ranked wrong. We will also pose some questions about conditions on feedback arc sets, motivated by our proofs, which ensure equality between the maximum number of arc disjoint cycles and the minimum size of a feedback arc set in a tournament.

Faster Approximation Algorithms For the Unit Capacity Concurrent Flow Problem with Applications to Routing and Finding Sparse Cuts

This paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities. These algorithms are much faster than algorithms discovered previously. Besides being an important problem in its own right, the uniform-capacity concurrent flow problem has many interesting applications. Leighton and Rao used uniform-capacity concurrent flow to find an approximately “sparsest cut” in a graph and thereby approximately solve a wide variety of graph problems, including minimum feedback arc set, minimum cut linear arrangement, and minimum area layout. However, their method appeared to be impractical as it required solving a large linear program. This paper shows that their method might be practical by giving an $O(m^2 \log m)$ expected-time randomized algorithm for their concurrent flow problem on an m-edge graph. Raghavan and Thompson used uniform-capacity concurrent flow to solve approximately a channel width minimization problem in very large scale integration. An $O(k^{{3 / 2}} (m + n\log n)$ expected-time randomized algorithm and an $O(k\min \{ n,k\} (m + n\log n)\log k)$ deterministic algorithm is given for this problem when the channel width is $\Omega (\log n)$, where k denotes the number of wires to be routed in an n-node, m-edge network.