Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, sometimes by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We review, discuss and benchmark state-of-the-art representations and relations between them, including smooth overlap of atomic positions, many-body tensor representation, and symmetry functions. For this, we use a unified mathematical framework based on many-body functions, group averaging and tensor products, and compare energy predictions for organic molecules, binary alloys and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method and hyper-parameter optimization

A microscopic model for solidification

We present a novel picture of a non isothermal solidification process starting from a molecular level, where the microscopic origin of the basic mechanisms and of the instabilities characterizing the approach to equilibrium is rendered more apparent than in existing approaches based on coarse grained free energy functionals \`a la Landau. The system is composed by a lattice of Potts spins, which change their state according to the stochastic dynamics proposed some time ago by Creutz. Such a method is extended to include the presence of latent heat and thermal conduction. Not only the model agrees with previous continuum treatments, but it allows to introduce in a consistent fashion the microscopic stochastic fluctuations. These play an important role in nucleating the growing solid phase in the melt. The approach is also very satisfactory from the quantitative point of view since the relevant growth regimes are fully characterized in terms of scaling exponents.Comment: 7 pages Latex +3 figures.p

Evolution, Explosion and Nucleosynthesis of Core Collapse Supernovae

We present a new set of presupernova evolutions and explosive yields of massive stars of initial solar composition (Y=0.285, Z=0.02) in the mass range 13-35 Msun. All the models have been computed with the latest version (4.97) of the FRANEC code that now includes a nuclear network extending from neutrons to Mo98. The explosive nucleosynthesis has been computed twice: a first one with an hydro code and a second one following the simpler radiation dominated shock approximation (RDA).Comment: 20 pages, 10 figures, 12 tables. Accepted for publication on Ap

Gamma-Ray Burst Environments and Progenitors

Likely progenitors for the GRBs (gamma-ray bursts) are the mergers of compact objects or the explosions of massive stars. These two cases have distinctive environments for the GRB afterglow: the compact object explosions occur in the ISM (interstellar medium) and those of massive stars occur in the preburst stellar wind. We calculate the expected afterglow for a burst in a Wolf-Rayet star wind and compare the results to those for constant, interstellar density. The optical afterglow for the wind case is generally expected to decline more steeply than in the constant density case, but this effect may be masked by variations in electron spectral index, and the two cases have the same evolution in the cooling regime. Observations of the concurrent radio and optical/X-ray evolution are especially useful for distinguishing between the two cases. The different rates of decline of the optical and X-ray afterglows of GRB 990123 suggest constant density interaction for this case. We have previously found strong evidence for wind interaction in SN 1998bw/GRB 980425 and here present a wind model for GRB 980519. We thus suggest that there are both wind type GRB afterglows with massive star progenitors and ISM type afterglows with compact binary star progenitors. The wind type bursts are likely to be accompanied by a supernova, but not the ISM type.Comment: 11 pages, 1 figure, revised version, ApJ Letters, in pres

Asymmetric supernova remnants generated by Galactic, massive runaway stars

After the death of a runaway massive star, its supernova shock wave interacts with the bow shocks produced by its defunct progenitor, and may lose energy, momentum, and its spherical symmetry before expanding into the local interstellar medium (ISM). We investigate whether the initial mass and space velocity of these progenitors can be associated with asymmetric supernova remnants. We run hydrodynamical models of supernovae exploding in the pre-shaped medium of moving Galactic core-collapse progenitors. We find that bow shocks that accumulate more than about 1.5 Mo generate asymmetric remnants. The shock wave first collides with these bow shocks 160-750 yr after the supernova, and the collision lasts until 830-4900 yr. The shock wave is then located 1.35-5 pc from the center of the explosion, and it expands freely into the ISM, whereas in the opposite direction it is channelled into the region of undisturbed wind material. This applies to an initially 20 Mo progenitor moving with velocity 20 km/s and to our initially 40 Mo progenitor. These remnants generate mixing of ISM gas, stellar wind and supernova ejecta that is particularly important upstream from the center of the explosion. Their lightcurves are dominated by emission from optically-thin cooling and by X-ray emission of the shocked ISM gas. We find that these remnants are likely to be observed in the [OIII] lambda 5007 spectral line emission or in the soft energy-band of X-rays. Finally, we discuss our results in the context of observed Galactic supernova remnants such as 3C391 and the Cygnus Loop.Comment: 21 pages, 16 figure

Coalescence in the 1D Cahn-Hilliard model

We present an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition. We have identified all the intermediate profiles, stationary solutions of the noiseless Cahn-Hilliard equation. Using properties of the soliton lattices, periodic solutions of the Ginzburg-Landau equation, we have construct a family of ansatz describing continuously the processus of destabilization and period doubling predicted in Langer's self similar scenario

Localized induction equation and pseudospherical surfaces

We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A: Mathematical and Genera