107,069 research outputs found
Comparing a current-carrying circular wire with polygons of equal perimeter; Magnetic field versus magnetic flux
We compare the magnetic field at the center of and the self-magnetic flux
through a current-carrying circular loop, with those obtained for
current-carrying polygons with the same perimeter. As the magnetic field
diverges at the position of the wires, we compare the self-fluxes utilizing
several regularization procedures. The calculation is best performed utilizing
the vector potential, thus highlighting its usefulness in practical
applications. Our analysis answers some of the intuition challenges students
face when they encounter a related simple textbook example. These results can
be applied directly to the determination of mutual inductances in a variety of
situations.Comment: 9 pages, 4 figure
A Model of Growth with Intertemporal Knowledge Externalities, Augmented with Contemporaneous Knowledge Externalities
The present model is essentially Romerâs (1990) model of endogenous growth with intertemporal knowledge externalities, augmented with contemporaneous knowledge externalities to give a richer explanation of the growth process. Both types of knowledge spillovers seem essential to capturing the features of knowledge in a model of growth. Introducing synchronic complementarities and knowledge externalities across inventive firms immediately creates the possibility of multiple equilibria and threshold effects in the present model. Another advantage of this theoretical formulation is that it allows for an analysis of the effects on steady-state growth of a variety of technology policies relying on changing knowledge complementarities parameters.Endogenous growth, innovation, knowledge complementarities, knowledge externalities, general equilibrium
GRASP: A New Search Algorithm for Satisfiability
This paper introduces GRASP (Generic search Algorithm J3r the Satisfiabilily Problem), an integrated algorithmic J3amework 30r SAT that unifies several previously proposed searchpruning techniques and jcilitates identification of additional ones. GRASP is premised on the inevitability of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'ecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Einally, straighrward bookkeeping of the causali y chains leading up to conflicts a/lows GRASP to identij) assignments that are necessary jr a solution to be found. Experimental results obtained jom a large number of benchmarks, including many J3om the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely ejctive jr a large number of representative classes of SAT instances
Boolean Satisfiability in Electronic Design Automation
Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT âpackagesâ are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks
Light composite Higgs boson from the normalized Bethe-Salpeter equation
Scalar composite boson masses have been computed in QCD and Technicolor
theories with the help of the homogeneous Bethe-Salpeter equation (BSE),
resulting in a scalar mass that is twice the dynamically generated fermion or
technifermion mass (). We show that in the case of walking (or
quasi-conformal) technicolor theories, where the behavior with the
momenta may be quite different from the one predicted by the standard operator
product expansion, this result is incomplete and we must consider the effect of
the normalization condition of the BSE to determine the scalar masses. We
compute the composite Higgs boson mass for several groups with technifermions
in the fundamental and higher dimensional representations and comment about the
experimental constraints on these theories, which indicate that models based on
walking theories with fermions in the fundamental representation may, within
the limitations of our approach, have masses quite near the actual direct
exclusion limit.Comment: 9 pages, 4 figures, minor corrections, to appear in Physical Review
Pion mass dependence of the nucleon mass in the chiral quark soliton model
The dependence of the nucleon mass on the mass of the pion is studied in the
framework of the chiral quark-soliton model. A remarkable agreement is observed
with lattice data from recent full dynamical simulations. The possibility and
limitations to use the model results as a guideline for the chiral
extrapolation of lattice data are discussed.Comment: 14 pages, 12 figures, 4 tables. v2: References added, new figure
included, discussion improved, typos fixed, matches published versio
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