5,295 research outputs found

    A generalization of Turaev's virtual string cobracket and self-intersections of virtual strings

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    Previously we defined an operation µ that generalizes Turaev’s cobracket for loops on a surface. We showed that, in contrast to the cobracket, this operation gives a formula for the minimum number of self-intersections of a loop in a given free homotopy class. In this paper we consider the corresponding question for virtual strings, and conjecture that µ gives a formula for the minimum number of self-intersection points of a virtual string in a given virtual homotopy class. To support the conjecture, we show that µ gives a bound on the minimal self-intersection number of a virtual string which is stronger than a bound given by Turaev’s virtual string cobracket. We also use Turaev’s based matrices to describe a large set of strings α such that µ gives a formula for the minimal self-intersection number α. Finally, we construct an example that shows the bound on the minimal self-intersection number given by µ is always at least as good as, and sometimes stronger than, the bound ρ given by Turaev’s based matrix invariant

    Competition, R&D, and the Cost of Innovation.

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    This paper proposes a model in the spirit of Aghion et al. (2005) that encompasses the magnitude of the impact of competition on R&D according to the cost of the innovation. The effect of competition on R&D is an inverted U-shape. However, the shape is flatter and competition policy is therefore less relevant for innovation when innovations are relatively costly. Intuitively, if innovations are costly for a firm, competitive shocks have to be significant to alter its innovation decisions. Empirical investigations using a unique panel dataset from the Banque de France show that an inverted U-shaped relationship can be clearly evidenced for the largest firms, but the curve becomes flatter when the relative cost of R&D increases. For large costs, the relationship even vanishes. Consequently, in sectors in which innovations are costly, policy changes have to be on a very large scale for an impact to be expected; at the extreme end, in certain sectors, the curve is so at that competition policy is not an appropriate tool for boosting the research effort of firms.Competition ; R&D ; Innovation.

    Entropy production in phase field theories

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    Allen-Cahn (Ginzburg-Landau) dynamics for scalar fields with heat conduction is treated in rigid bodies using a non-equilibrium thermodynamic framework with weakly nonlocal internal variables. The entropy production and entropy flux is calculated with the classical method of irreversible thermodynamics by separating full divergences.Comment: 5 pages, no figure

    Two Stages in the evolution of binary alkali Bose-Einstein condensate mixtures towards phase segregation

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    Two stages of quantum spinodal decomposition is proposed and analyzed for this highly non-equilibrium process. Both time and spatial scales for the process are found. Qualitative agreement with existing data is found. Some cases the agreements are quantitative. Further experimental verifications are indicated.Comment: late

    Neutral atomic carbon in the globules of the Helix

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    We report detection of the 609u line of neutral atomic carbon in globules of the Helix nebula. The measurements were made towards the position of peak CO emission. At the same position, we obtained high-quality CO(2-1) and 13CO(2-1) spectra and a 135" x 135" map in CO(2-1). The velocity distribution of CI shows six narrow (1 -> 2 km/sec) components which are associated with individual globules traced in CO. The CI column densities are 0.5 -> 1.2 x 10^16/cm^2. CI is found to be a factor of ~6 more abundant than CO. Our estimate for the mass of the neutral envelope is an order of magnitude larger than previous estimates. The large abundance of CI in the Helix can be understood as a result of the gradual photoionisation of the molecular envelope by the central star's radiation field.Comment: 5 pages, Latex, AAS macros, 3 EPS figures, to appear in Astrophysical Journal Letter

    Two Modes of Solid State Nucleation - Ferrites, Martensites and Isothermal Transformation Curves

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    When a crystalline solid such as iron is cooled across a structural transition, its final microstructure depends sensitively on the cooling rate. For instance, an adiabatic cooling across the transition results in an equilibrium `ferrite', while a rapid cooling gives rise to a metastable twinned `martensite'. There exists no theoretical framework to understand the dynamics and conditions under which both these microstructures obtain. Existing theories of martensite dynamics describe this transformation in terms of elastic strain, without any explanation for the occurence of the ferrite. Here we provide evidence for the crucial role played by non-elastic variables, {\it viz.}, dynamically generated interfacial defects. A molecular dynamics (MD) simulation of a model 2-dimensional (2d) solid-state transformation reveals two distinct modes of nucleation depending on the temperature of quench. At high temperatures, defects generated at the nucleation front relax quickly giving rise to an isotropically growing `ferrite'. At low temperatures, the defects relax extremely slowly, forcing a coordinated motion of atoms along specific directions. This results in a twinned critical nucleus which grows rapidly at speeds comparable to that of sound. Based on our MD results, we propose a solid-state nucleation theory involving the elastic strain and non-elastic defects, which successfully describes the transformation to both a ferrite and a martensite. Our work provides useful insights on how to formulate a general dynamics of solid state transformations.Comment: 3 pages, 4 B/W + 2 color figure

    Dynamics of Phase Transitions: The 3D 3-state Potts model

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    In studies of the QCD deconfining phase transition or cross-over by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. In this paper we extend our previous study of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model, which serves as an effective model for some QCD properties. We investigate the linear theory of spinodal decomposition in some detail. It describes the early time evolution of the 3D model under a quench from the disordered into the ordered phase well, but fails in 2D. Further, the quench leads to competing vacuum domains, which are difficult to equilibrate, even in the presence of a small external magnetic field. From our hysteresis study we find, as before, a dynamics dominated by spinodal decomposition. There is evidence that some effects survive in the case of a cross-over. But the infinite volume extrapolation is difficult to control, even with lattices as large as 1203120^3.Comment: 12 pages; added references, corrected typo

    Azimuthal Correlation in Lepton-Hadron Scattering via Charged Weak-Current Processes

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    We consider the azimuthal correlation of the final-state particles in charged weak-current processes. This correlation provides a test of perturbative quantum chromodynamics. The azimuthal asymmetry is large in the semi-inclusive processes in which we identify a final-state hadron, say, a charged pion compared to that in the inclusive processes in which we do not identify final-state particles and use only the calorimetric information. In semi-inclusive processes the azimuthal asymmetry is more conspicuous when the incident lepton is an antineutrino or a positron than when the incident lepton is a neutrino or an electron. We analyze all the possible charged weak-current processes and study the quantitative aspects of each process. We also compare this result to the ep scattering with a photon exchange.Comment: 25 pages, 2 Postscript figures, uses RevTeX, fixes.st
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