Quantum deformed magnon kinematics

The dispersion relation for planar N=4 supersymmetric Yang-Mills is identified with the Casimir of a quantum deformed two-dimensional kinematical symmetry, E_q(1,1). The quantum deformed symmetry algebra is generated by the momentum, energy and boost, with deformation parameter q=e^{2\pi i/\lambda}. Representing the boost as the infinitesimal generator for translations on the rapidity space leads to an elliptic uniformization with crossing transformations implemented through translations by the elliptic half-periods. This quantum deformed algebra can be interpreted as the kinematical symmetry of a discrete integrable model with lattice spacing given by the BMN length a=2\pi/\sqrt{\lambda}. The interpretation of the boost generator as the corner transfer matrix is briefly discussed

Modeling dust emission in PN IC 418

We investigated the infrared (IR) dust emission from PN IC 418, using a detailed model controlled by a previous determination of the stellar properties and the characteristics of the photoionized nebula, keeping as free parameters the dust types, amounts and distributions relative to the distance of the central star. The model includes the ionized region and the neutral region beyond the recombination front (Photodissociation region, or PDR), where the [OI] and [CII] IR lines are formed. We succeeded in reproducing the observed infrared emission from 2 to 200~\mm. The global energy budget is fitted by summing up contributions from big grains of amorphous carbon located in the neutral region and small graphite grains located in the ionized region (closer to the central star). Two emission features seen at 11.5 and 30~\mm are also reproduced by assuming them to be due to silicon carbide (SiC) and magnesium and iron sulfides (Mg$_x$Fe$_{1-x}$S), respectively. For this, we needed to consider ellipsoidal shapes for the grains to reproduce the wavelength distribution of the features. Some elements are depleted in the gaseous phase: Mg, Si, and S have sub-solar abundances (-0.5 dex below solar by mass), while the abundance of C+N+O+Ne by mass is close to solar. Adding the abundances of the elements present in the dusty and gaseous forms leads to values closer to but not higher than solar, confirming that the identification of the feature carriers is plausible. Iron is strongly depleted (3 dex below solar) and the small amount present in dust in our model is far from being enough to recover the solar value. A remaining feature is found as a residue of the fitting process, between 12 and 25~\mm, for which we do not have identification.Comment: Accepted for publication in Astronomy & Astrophysics. V2: adding reference

One Step at a Time: The Origins of Sequential Simulation and Beyond

[EN] In the mid-1980s, still in his young 40s, Andre Journel was already recognized as one of the giants of geostatistics. Many of the contributions from his new research program at Stanford University had centered around the indicator methods that he developed: indicator kriging and multiple indicator kriging. But when his second crop of graduate students arrived at Stanford, indicator methods still lacked an approach to conditional simulation that was not tainted by what Andre called the 'Gaussian disease'; early indicator simulations went through the tortuous path of converting all indicators to Gaussian variables, running a turning bands simulation, and truncating the resulting multi-Gaussian realizations. When he conceived of sequential indicator simulation (SIS), even Andre likely did not recognize the generality of an approach to simulation that tackled the simulation task one step at a time. The early enthusiasm for SIS was its ability, in its multiple-indicator form, to cure the Gaussian disease and to build realizations in which spatial continuity did not deteriorate in the extreme values. Much of Stanford's work in the 1980s focused on petroleum geostatistics, where extreme values (the high-permeability fracture zones and the low-permeability shale barriers) have much stronger anisotropy, and much longer ranges of correlation in the maximum continuity direction, than mid-range values. With multi-Gaussian simulations necessarily imparting weaker continuity to the extremes, SIS was an important breakthrough. The generality of the sequential approach was soon recognized, first through its analogy with multi-variate unconditional simulation achieved using the lower triangular matrix of an LU decomposition of the covariance matrix as the multiplier of random normal deviates. Modifying LU simulation so that it became conditional gave rise to sequential Gaussian simulation (SGS), an algorithm that shared much in common with SIS. With nagging implementation details like the sequential path and the search neighborhood being common to both methods, improvements in either SIS or SGS often became improvements to the other. Almost half of the contributors to this Special Issue became students of Andre in the classes of 1984-1988, and several are the pioneers of SIS and SGS. Others who studied later with Andre explored and developed the first multipoint statistics simulation procedures, which are based on the same concept that underlies sequential simulation. Among his many significant intellectual accomplishments, one of the cornerstones of Andre Journel's legacy was sequential simulation, built one step at a time.The first author wishes to acknowledge the financial contribution of the Spanish Ministry of Science and Innovation through Project Number PID2019-109131RB-I00.Gómez-Hernández, JJ.; Srivastava, RM. (2021). One Step at a Time: The Origins of Sequential Simulation and Beyond. Mathematical Geosciences. 53(2):193-209. https://doi.org/10.1007/s11004-021-09926-0S19320953