7,525 research outputs found

    The centripetal force law and the equation of motion for a particle on a curved hypersurface

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    It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once the fact be taken into consideration, the equation takes that same form as that for centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio

    Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force

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    In classical mechanics, a nonrelativistic particle constrained on an N−1N-1 curved hypersurface embedded in NN flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of the geometric potential. We demonstrate that the motion of the quantum particle is "driven" by not only the the centripetal force, but also a curvature induced force proportional to the Laplacian of the mean curvature, which is fundamental in the interface physics, causing curvature driven interface evolution.Comment: 4 page

    Incentive-Centered Design for User-Contributed Content

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    We review incentive-centered design for user-contributed content (UCC) on the Internet. UCC systems, produced (in part) through voluntary contributions made by non-employees, face fundamental incentives problems. In particular, to succeed, users need to be motivated to contribute in the first place ("getting stuff in"). Further, given heterogeneity in content quality and variety, the degree of success will depend on incentives to contribute a desirable mix of quality and variety ("getting \emph{good} stuff in"). Third, because UCC systems generally function as open-access publishing platforms, there is a need to prevent or reduce the amount of negative value (polluting or manipulating) content. The work to date on incentives problems facing UCC is limited and uneven in coverage. Much of the empirical research concerns specific settings and does not provide readily generalizable results. And, although there are well-developed theoretical literatures on, for example, the private provision of public goods (the "getting stuff in" problem), this literature is only applicable to UCC in a limited way because it focuses on contributions of (homogeneous) money, and thus does not address the many problems associated with heterogeneous information content contributions (the "getting \emph{good} stuff in" problem). We believe that our review of the literature has identified more open questions for research than it has pointed to known results.http://deepblue.lib.umich.edu/bitstream/2027.42/100229/1/icd4ucc.pdf7

    Dispersionless Toda hierarchy and two-dimensional string theory

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    The dispersionless Toda hierarchy turns out to lie in the heart of a recently proposed Landau-Ginzburg formulation of two-dimensional string theory at self-dual compactification radius. The dynamics of massless tachyons with discrete momenta is shown to be encoded into the structure of a special solution of this integrable hierarchy. This solution is obtained by solving a Riemann-Hilbert problem. Equivalence to the tachyon dynamics is proven by deriving recursion relations of tachyon correlation functions in the machinery of the dispersionless Toda hierarchy. Fundamental ingredients of the Landau-Ginzburg formulation, such as Landau-Ginzburg potentials and tachyon Landau-Ginzburg fields, are translated into the language of the Lax formalism. Furthermore, a wedge algebra is pointed out to exist behind the Riemann-Hilbert problem, and speculations on its possible role as generators of ``extra'' states and fields are presented.Comment: LaTeX 21 pages, KUCP-0067 (typos are corrected and a brief note is added

    Aerostructural Optimization of a Transonic Compressor Rotor

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77121/1/AIAA-15397-760.pd

    Numerical Study of the Poisson-Boltzmann Equation for Biomolecular Electrostatics

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    Electrostatics interaction plays a very important role in almost all biomolecular systems. The Poisson-Boltzmann equation is widely used to treat this electrostatic effect in an ionic solution. In this work, a simple mixed discrete-continuum model is considered and boundary element method is used to solve for the solution.Singapore-MIT Alliance (SMA

    Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules

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    The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the Kac table contribute. The theory involves unregularized divergences in some of correlators. We obtain the recursion relations which form a closed set among well-defined correlators on sphere, but they do not have a beautiful structure that the bosonized theory has and also give an inconsistent result when they include an ill-defined correlator with the divergence. We solve them and compute the several normalization independent ratios of the well-defined correlators, which agree with the matrix model results.Comment: Latex, 22 page
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