5,295 research outputs found

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

Previously we defined an operation Â” that generalizes Turaevâs 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 Â” 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 Â” gives a bound on the minimal self-intersection number of a virtual string which is stronger than a bound given by Turaevâs virtual string cobracket. We also use Turaevâs based matrices to describe a large set of strings Î± such that Â” gives a formula for the minimal self-intersection number Î±. Finally, we construct an example that shows the bound on the minimal self-intersection number given by Â” is always at least as good as, and sometimes stronger than, the bound Ï given by Turaevâs based matrix invariant

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

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

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

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

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

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

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 $120^3$.Comment: 12 pages; added references, corrected typo

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

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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