Stress and heat flux via automatic differentiation

Machine-learning potentials provide computationally efficient and accurate approximations of the Born-Oppenheimer potential energy surface. This potential determines many materials properties and simulation techniques usually require its gradients, in particular forces and stress for molecular dynamics, and heat flux for thermal transport properties. Recently developed potentials feature high body order and can include equivariant semi-local interactions through message-passing mechanisms. Due to their complex functional forms, they rely on automatic differentiation (AD), overcoming the need for manual implementations or finite-difference schemes to evaluate gradients. This study demonstrates a unified AD approach to obtain forces, stress, and heat flux for such potentials, and provides a model-independent implementation. The method is tested on the Lennard-Jones potential, and then applied to predict cohesive properties and thermal conductivity of tin selenide using an equivariant message-passing neural network potential.Comment: 9 pages, 2 figures, 6 tables, excluding supplement (3 pages, 3 figures, 2 tables). Additional information at https://marcel.science/gl

Where's the Doughnut? LBV bubbles and Aspherical Fast Winds

In this paper we address the issue of the origin of LBV bipolar bubbles. Previous studies have explained the shapes of LBV nebulae, such as $\eta$ Car, by invoking the interaction of an isotropic fast wind with a previously deposited, slow aspherical wind (a ``slow torus''). In this paper we focus on the opposite scenario where an aspherical fast wind expands into a previously deposited isotropic slow wind. Using high resolution hydrodynamic simulations, which include the effects of radiative cooling, we have completed a series of numerical experiments to test if and how aspherical fast winds effect wind blown bubble morphologies. Our experiments explore a variety of models for the latitudinal variations of fast wind flow parameters. The simulations demonstrate that aspherical fast winds can produce strongly bipolar outflows. In addition the properties of outflows recover some important aspects of LBV bubbles which the previous "slow torus" models can not.Comment: 23 pages, 6 figures, to appear the Astrophysical Journa

Numerical Modeling of Eta Carinae Bipolar Outflows

In this paper, we present two-dimensional gas dynamic simulations of the formation and evolution of the eta-Car bipolar outflows. Adopting the interacting nonspherical winds model, we have carried out high-resolution numerical simulations, which include explicitly computed time-dependent radiative cooling, for different possible scenarios of the colliding winds. In our simulations, we consider different degrees of non-spherical symmetry for the pre-outburst wind and the great eruption of the 1840s presented by the eta-Car wind. From these models, we obtain important differences in the shape and kinematical properties of the Homunculus structure. In particular, we find an appropriate combination of the wind parameters (that control the degree of non-spherical symmetry) and obtain numerical experiments that best match both the observed morphology and the expansion velocity of the eta-Car bipolar shell. In addition, our numerical simulations show the formation of a bipolar nebula embedded within the Homunculus (the little Homunculus) developed from a secondary eruptive event suffered by the star in the 1890s, and also the development of tenuous, high velocity ejections in the equatorial region that result from the impact of the eruptive wind of the 1840s with the pre-outburst wind and that could explain some of the high speed features observed in the equatorial ejecta. The models were, however, unable to produce equatorial ejections associated to the second eruptive event.Comment: 33 pages, 9 figures, accepted by the Astrophysical Journa

Non-clasical Nucleation in Supercooled Nickel

The dynamics of homogeneous nucleation and growth of crystalline nickel from the super-cooled melt is examined during rapid quenching using molecular dynamics and a modified embedded atom method potential. The character of the critical nuclei of the crystallization transition is examined using common neighbor analysis and visualization. At nucleation the saddle point droplet consists of randomly stacked planar structures with an in plane triangular order. These results are consistent with previous theoretical results that predict that the nucleation process in some metals is non-classical due to the presence of long-range forces and a spinodal.Comment: 4 pages, 5 figure

Revisiting 2D Numerical Models for the 19th century outbursts of η\eta Carinae

We present here new results of two-dimensional hydrodynamical simulations of the eruptive events of the 1840s (the great) and the 1890s (the minor) eruptions suffered by the massive star $\eta$ Car. The two bipolar nebulae commonly known as the Homunculus and the little Homunculus were formed from the interaction of these eruptive events with the underlying stellar wind. As in previous work (Gonzalez et al. 2004a, 2004b), we assume here an interacting, nonspherical multiple-phase wind scenario to explain the shape and the kinematics of both Homunculi, but adopt a more realistic parametrization of the phases of the wind. During the 1890s eruptive event, the outflow speed {\it decreased} for a short period of time. This fact suggests that the little Homunculus is formed when the eruption ends, from the impact of the post-outburst $\eta$ Car wind (that follows the 1890s event) with the eruptive flow (rather than by the collision of the eruptive flow with the pre-outburst wind, as claimed in previous models; Gonzalez et al. 2004a, 2004b). Our simulations reproduce quite well the shape and the observed expansion speed of the large Homunculus. The little Homunculus (which is embedded within the large Homunculus) becomes Rayleigh-Taylor unstable and develop filamentary structures that resembles the spatial features observed in the polar caps. In addition, we find that the interior cavity between the two Homunculi is partially filled by material that is expelled during the decades following the great eruption. This result may be connected with the observed double-shell structure in the polar lobes of the $\eta$ Car nebula. Finally, as in previous work, we find the formation of tenuous, equatorial, high-speed features that seem to be related to the observed equatorial skirt of $\eta$ Car.Comment: accepted for publication in MNRA

The Evolution of Supernovae in Circumstellar Wind Bubbles II: Case of a Wolf-Rayet star

(Abridged) Mass-loss from massive stars leads to the formation of circumstellar wind-blown bubbles surrounding the star, bordered by a dense shell. When the star ends its life in a supernova (SN) explosion, the resulting shock wave will interact with this modified medium. In a previous paper we discussed the basic parameters of this interaction. In this paper we go a step further and study the evolution of SNe in the wind blown bubble formed by a 35 \msun star that starts off as an O star, goes through a red supergiant phase, and ends its life as a Wolf-Rayet star. We model the evolution of the CSM and then the expansion of the SN shock wave within this medium. Our simulations clearly reveal fluctuations in density and pressure within the surrounding medium. The SN shock interacting with these fluctuations, and then with the dense shell surrounding the wind-blown cavity, gives rise to a variety of transmitted and reflected shocks in the wind bubble. The interactions between these various shocks and discontinuities is examined, and its effects on the X-ray emission is noted. Our simulations reveal the presence of several hydrodynamic instabilities. They show that the turbulent interior, coupled with the large fluctuations in density and pressure, gives rise to an extremely corrugated SN shock wave. The shock shows considerable wrinkles as it impacts the dense shell, and the impact occurs in a piecemeal fashion, with some parts of the shock wave interacting with the shell before the others. Therefore different parts of the shell will `light-up' at different times. The non-spherical nature of the interaction means that it will occur over a prolonged period of time, and the spherical symmetry of the initial shock wave is destroyed.Comment: 50 pages, 19 figures. Accepted to the Astrophysical Journal. For a version with the original high-resolution color figures please download from http://astro.uchicago.edu/~vikram/sncsm.htm

Current-Induced Step Bending Instability on Vicinal Surfaces

We model an apparent instability seen in recent experiments on current induced step bunching on Si(111) surfaces using a generalized 2D BCF model, where adatoms have a diffusion bias parallel to the step edges and there is an attachment barrier at the step edge. We find a new linear instability with novel step patterns. Monte Carlo simulations on a solid-on-solid model are used to study the instability beyond the linear regime.Comment: 4 pages, 4 figure

Zero-bias anomaly in disordered wires

We calculate the low-energy tunneling density of states $\nu(\epsilon, T)$ of an $N$-channel disordered wire, taking into account the electron-electron interaction non-perturbatively. The finite scattering rate $1/\tau$ results in a crossover from the Luttinger liquid behavior at higher energies, $\nu\propto\epsilon^\alpha$, to the exponential dependence $\nu (\epsilon, T=0)\propto \exp{(-\epsilon^*/\epsilon)}$ at low energies, where $\epsilon^*\propto 1/(N \tau)$. At finite temperature $T$, the tunneling density of states depends on the energy through the dimensionless variable $\epsilon/\sqrt{\epsilon^* T}$. At the Fermi level $\nu(\epsilon=0,T) \propto \exp (-\sqrt{\epsilon^*/T})$.Comment: 5 pages, 1 figur

Progesterone From Ovulatory Menstrual Cycles Is an Important Cause of Breast Cancer

Many factors, including reproductive hormones, have been linked to a woman\u27s risk of developing breast cancer (BC). We reviewed the literature regarding the relationship between ovulatory menstrual cycles (MCs) and BC risk. Physiological variations in the frequency of MCs and interference with MCs through genetic variations, pathological conditions and or pharmaceutical interventions revealed a strong link between BC risk and the lifetime number of MCs. A substantial reduction in BC risk is observed in situations without MCs. In genetic or transgender situations with normal female breasts and estrogens, but no progesterone (P4), the incidence of BC is very low, suggesting an essential role of P4. During the MC, P4 has a strong proliferative effect on normal breast epithelium, whereas estradiol (E2) has only a minimal effect. The origin of BC has been strongly linked to proliferation associated DNA replication errors, and the repeated stimulation of the breast epithelium by P4 with each MC is likely to impact the epithelial mutational burden. Long-lived cells, such as stem cells, present in the breast epithelium, can carry mutations forward for an extended period of time, and studies show that breast tumors tend to take decades to develop before detection. We therefore postulate that P4 is an important factor in a woman\u27s lifetime risk of developing BC, and that breast tumors arising during hormonal contraception or after menopause, with or without menopausal hormone therapy, are the consequence of the outgrowth of pre-existing neoplastic lesions, eventually stimulated by estrogens and some progestins

Leading-effect vs. Risk-taking in Dynamic Tournaments: Evidence from a Real-life Randomized Experiment

Two 'order effects' may emerge in dynamic tournaments with information feedback. First, participants adjust effort across stages, which could advantage the leading participant who faces a larger 'effective prize' after an initial victory (leading-effect). Second, participants lagging behind may increase risk at the final stage as they have 'nothing to lose' (risk-taking). We use a randomized natural experiment in professional two-game soccer tournaments where the treatment (order of a stage-specific advantage) and team characteristics, e.g. ability, are independent. We develop an identification strategy to test for leading-effects controlling for risk-taking. We find no evidence of leading-effects and negligible risk-taking effects