Vertex operator algebras and operads

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal to $0$, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of operads is presented. This reformulation shows that the rich geometric structure revealed in the study of conformal field theory and the rich algebraic structure of the theory of vertex operator algebras share a precise common foundation in basic operations associated with a certain kind of (two-dimensional) ``complex'' geometric object, in the sense in which classical algebraic structures (groups, algebras, Lie algebras and the like) are always implicitly based on (one-dimensional) ``real'' geometric objects. In effect, the standard analogy between point-particle theory and string theory is being shown to manifest itself at a more fundamental mathematical level.Comment: 16 pages. Only the definitions of "partial operad" and of "rescaling group" have been improve

Gamma-ray bursts: postburst evolution of fireballs

The postburst evolution of fireballs that produce $\gamma$-ray bursts is studied, assuming the expansion of fireballs to be adiabatic and relativistic. Numerical results as well as an approximate analytic solution for the evolution are presented. Due to adoption of a new relation among $t$, $R$ and $\gamma$ (see the text), our results differ markedly from the previous studies. Synchrotron radiation from the shocked interstellar medium is attentively calculated, using a convenient set of equations. The observed X-ray flux of GRB afterglows can be reproduced easily. Although the optical afterglows seem much more complicated, our results can still present a rather satisfactory approach to observations. It is also found that the expansion will no longer be highly relativistic about 4 days after the main GRB. We thus suggest that the marginally relativistic phase of the expansion should be investigated so as to check the afterglows observed a week or more later.Comment: 17 pages, 4 figures, MNRAS in pres

Coronal hole boundaries at small scales: IV. SOT view Magnetic field properties of small-scale transient brightenings in coronal holes

We study the magnetic properties of small-scale transients in coronal hole. We found all brightening events are associated with bipolar regions and caused by magnetic flux emergence followed by cancellation with the pre-existing and newly emerging magnetic flux. In the coronal hole, 19 of 22 events have a single stable polarity which does not change its position in time. In eleven cases this is the dominant polarity. The dominant flux of the coronal hole form the largest concentration of magnetic flux in terms of size while the opposite polarity is distributed in small concentrations. In the coronal hole the number of magnetic elements of the dominant polarity is four times higher than the non-dominant one. The supergranulation configuration appears to preserve its general shape during approximately nine hours of observations although the large concentrations in the network did evolve and were slightly displaced, and their strength either increased or decreased. The emission fluctuations seen in the X-ray bright points are associated with reoccurring magnetic cancellation in the footpoints. Unique observations of an X-ray jet reveal similar magnetic behaviour in the footpoints, i.e. cancellation of the opposite polarity magnetic flux. We found that the magnetic flux cancellation rate during the jet is much higher than in bright points. Not all magnetic cancellations result in an X-ray enhancement, suggesting that there is a threshold of the amount of magnetic flux involved in a cancellation above which brightening would occur at X-ray temperatures. Our study demonstrates that the magnetic flux in coronal holes is continuously recycled through magnetic reconnection which is responsible for the formation of numerous small-scale transient events. The open magnetic flux forming the coronal-hole phenomenon is largely involved in these transient features.Comment: 19 pages, 18 figures, A&A in pres

Understanding the aqueous phase ozonolysis of isoprene: distinct product distribution and mechanism from the gas phase reaction

The aqueous phase reaction of volatile organic compounds (VOCs) has not been considered in most analyses of atmospheric chemical processes. However, some experimental evidence has shown that, compared to the corresponding gas phase reaction, the aqueous chemical processes of VOCs in the bulk solutions and surfaces of ambient wet particles (cloud, fog, and wet aerosols) may potentially contribute to the products and formation of secondary organic aerosol (SOA). In the present study, we performed a laboratory experiment of the aqueous ozonolysis of isoprene at different pHs (3–7) and temperatures (4–25 °C). We detected three important kinds of products, including carbonyl compounds, peroxide compounds, and organic acids. Our results showed that the molar yields of these products were nearly independent of the investigated pHs and temperatures, those were (1) carbonyls: 56.7 ± 3.7 % formaldehyde, 42.8 ± 2.5 % methacrolein (MAC), and 57.7 ± 3.4 % methyl vinyl ketone (MVK); (2) peroxides: 53.4 ± 4.1 % hydrogen peroxide (H₂O₂) and 15.1 ± 3.1 % hydroxylmethyl hydroperoxide (HMHP); and (3) organic acids: undetectable (<1 % estimated by the detection limit). Based on the amounts of products formed and the isoprene consumed, the total carbon yield was estimated to be 94.8 ± 4.1 %. This implied that most of the products in the reaction system were detected. The combined yields of both MAC + MVK and H₂O₂ + HMHP in the aqueous isoprene ozonolysis were much higher than those observed in the corresponding gas phase reaction. We suggest that these unexpected high yields of carbonyls and peroxides are related to the greater capability of condensed water, compared to water vapor, to stabilize energy-rich Criegee radicals. This aqueous ozonolysis of isoprene (and possibly other biogenic VOCs) could potentially occur on the surfaces of ambient wet particles and plants. Moreover, the high-yield carbonyl and peroxide products might provide a considerable source of aqueous phase oxidants and SOA precursors

Modeling Vacuum Arcs

We are developing a model of vacuum arcs. This model assumes that arcs develop as a result of mechanical failure of the surface due to Coulomb explosions, followed by ionization of fragments by field emission and the development of a small, dense plasma that interacts with the surface primarily through self sputtering and terminates as a unipolar arc capable of producing breakdown sites with high enhancement factors. We have attempted to produce a self consistent picture of triggering, arc evolution and surface damage. We are modeling these mechanisms using Molecular Dynamics (mechanical failure, Coulomb explosions, self sputtering), Particle-In-Cell (PIC) codes (plasma evolution), mesoscale surface thermodynamics (surface evolution), and finite element electrostatic modeling (field enhancements). We can present a variety of numerical results. We identify where our model differs from other descriptions of this phenomenon.Comment: 4 pages, 5 figure

Parton Distributions at Hadronization from Bulk Dense Matter Produced at RHIC

We present an analysis of $\Omega$, $\Xi$, $\Lambda$ and $\phi$ spectra from Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV in terms of distributions of effective constituent quarks at hadronization. Consistency in quark ratios derived from various hadron spectra provides clear evidence for hadron formation dynamics as suggested by quark coalescence or recombination models. We argue that the constituent quark distribution reflects properties of the effective partonic degrees of freedom at hadronization. Experimental data indicate that strange quarks have a transverse momentum distribution flatter than that of up/down quarks consistent with hydrodynamic expansion in partonic phase prior to hadronization. After the AMPT model is tuned to reproduce the strange and up/down quark distributions, the model can describe the measured spectra of hyperons and $\phi$ mesons very well where hadrons are formed through dynamical coalescence.Comment: 5 pages, 3 figures, two more paragraph added to address the referee's comment, figure updated to include the KET scale. Accepted version to appear in Phys. Rev.