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Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion -- the time-dependent Schr\"odinger equation (TDSE) -- is numerically intractable. We present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances., Comment: 8 pages, 2 figures

We study the stellar mass function (SMF) and the co-evolution with dark matter halos via abundance matching in the largest redshift range to date $0.25$, we find increased abundances of massive (log$\, M_{\star}/M_{\odot}>10.5$) implying integrated star formation efficiencies (SFE) $\epsilon_{\star}\equiv M_{\star}\, f_{\rm b}^{-1} M_{\rm halo}^{-1} \gtrsim 0.5$. We find a flattening of the SMF at the high-mass end that is better described by a double power law at $z>5.5$. At $z \lesssim 5.5$ it transitions to a Schechter law which coincides with the emergence of the first massive quiescent galaxies in the Universe. We trace the cosmic stellar mass density (SMD) and infer the star formation rate density (SFRD), which at $z>7.5$ agrees remarkably with recent \JWST{} UV luminosity function-derived estimates. However, at $z \lesssim 3.5$, we find significant tension ($\sim 0.3$ dex) with the cosmic star formation (SF) history from instantaneous SF measures, the causes of which remain poorly understood. We infer the stellar-to-halo mass relation (SHMR) and the SFE from abundance matching out to $z=12$, finding a non-monotonic evolution. The SFE has the characteristic strong dependence with mass in the range of $0.02 - 0.2$, and mildly decreases at the low mass end out to $z\sim3.5$. At $z\sim3.5$ the SFE increases sharply from $\sim 0.1$ to approach high SFE of $0.8-1$ by $z\sim 10$ for log$(M_{\rm h}/M_{\odot})\approx11.5$, albeit with large uncertainties. Finally, we use the SHMR to track the SFE and stellar mass growth throughout the halo history and find that they do not grow at the same rate -- from the earliest times up until $z\sim3.5$ the halo growth rate outpaces galaxy assembly, but at $z>3.5$ halo growth stagnates and accumulated gas reservoirs keep the SF going and galaxies outpace halos.

The stellar mass-star formation rate (M$_\star$ - SFR) plane is essential for distinguishing galaxy populations, but how galaxies move within this plane over cosmic time remains unclear. This study aims to describe galaxy migrations in the M$_\star$ - SFR plane by reconstructing star formation histories (SFHs) for a sample of galaxies out to redshift $z < 4$. This provides insights into the physical processes driving star formation. We use data from the COSMOS field, selecting 299131 galaxies at $z < 4$ with COSMOS-Web NIRCam data (m$_\mathrm{F444W} < 27$) over 0.54 deg$^2$. Using the SED modeling code CIGALE with non-parametric SFHs, we derive physical properties and migration vectors for these galaxies. These vectors describe the direction and velocity of evolutionary paths across the M$_\star$ - SFR plane. To assess the accuracy of these vectors, we compare them to results from the Horizon-AGN simulation. Galaxies within the main sequence show low migration amplitudes and dispersed movement directions, indicating oscillation within the main sequence. Most progenitors were already on the main sequence a billion years earlier. Starburst galaxies assembled half their mass in the last 350 Myr and originated from the main sequence. Passive galaxies show uniformly declining SFHs and include massive galaxies already in the passive region at $z = 3.5-4$, with increasing density over time. Using reconstructed SFHs up to $z < 4$, we propose a coherent picture of how galaxies migrate over cosmic time in the M$_\star$ - SFR plane, highlighting the connection between major phases in the star-formation history.

We propose a framework to learn the time-dependent Hartree-Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Though the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange-correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to $60 \times 60 \times 60 \times 60$. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training., Comment: 25 pages, 8 figures

In this paper, a hydrogen-based energy storage system (ESS) is proposed for DC microgrids, which can potentially be integrated with battery ESS to meet the needs of future grids with high renewable penetration. Hydrogen-based ESS can provide a stable energy supply for a long time but has a slower response than battery ESSs. However, a combination of battery and hydrogen storage provides stable energy for an extended period of time and can easily handle the sudden demands and surpluses of the microgrid. One of the main challenges in this system is the integration of power electronics with fuel cell technology to convert renewable energy into electricity seamlessly. This paper proposes a system that uses an isolated DC-DC converter to activate clean hydrogen production using an electrolyzer and then pressurize the hydrogen to store in a tank. The pressured hydrogen becomes an essential input to the fuel cell, which regulates and transforms it into electricity. The electricity produced is then transferred to the grid using a DC-DC boost converter. A Simulink model of the hybrid system with a 1 kV DC bus voltage is used to demonstrate the hydrogen production and fuel cell behavior based on the demand and surplus power of the loads. The proposed system simulates aspects of the power conversion, electrolyzer, storage tank, and fuel cell needed for the proposed hybrid ESS. Due to its economic feasibility, the polymer electrolyte membrane (PEM) is the primary technology considered for the electrolyzer and fuel cell., Comment: A 5-pages Digest paper summarizes in detail the work done

We study of the role of galaxy-galaxy interactions and disk instabilities in producing starburst activity in galaxies out to z = 4. For this, we use a sample of 387 galaxies with robust total star formation rate measurements from Herschel, gas masses from ALMA, stellar masses and redshifts from multi-band photometry, and JWST/NIRCam rest-frame optical imaging. Using mass-controlled samples, we find an increased fraction of interacting galaxies in the starburst regime at all redshifts out to z = 4. This increase correlates with star formation efficiency (SFE), but not with gas fraction. However, the correlation is weak (and only significant out to z = 2), which could be explained by the short duration of SFE increase during interaction. In addition, we find that isolated disk galaxies make up a significant fraction of the starburst population. The fraction of such galaxies with star-forming clumps ("clumpy disks") is significantly increased compared to the main-sequence disk population. Furthermore, this fraction directly correlates with SFE. This is direct observational evidence for a long-term increase of SFE maintained due to disk instabilities, contributing to the majority of starburst galaxies in our sample and hence to substantial mass growth in these systems. This result could also be of importance for explaining the growth of the most massive galaxies at z > 6., Comment: 16 pages, 6 figures. Accepted by ApJ

For any linear system with unreduced dynamics governed by invertible propagators, we derive a closed, time-delayed, linear system for a reduced-dimensional quantity of interest. This method does not target dimensionality reduction: rather, this method helps shed light on the memory-dependence of $1$-electron reduced density matrices in time-dependent configuration interaction (TDCI), a scheme to solve for the correlated dynamics of electrons in molecules. Though time-dependent density functional theory has established that the $1$-electron reduced density possesses memory-dependence, the precise nature of this memory-dependence has not been understood. We derive a symmetry/constraint-preserving method to propagate reduced TDCI electron density matrices. In numerical tests on two model systems ($\text{H}_2$ and $\text{HeH}^+$), we show that with sufficiently large time-delay (or memory-dependence), our method propagates reduced TDCI density matrices with high quantitative accuracy. We study the dependence of our results on time step and basis set. To implement our method, we derive the $4$-index tensor that relates reduced and full TDCI density matrices. Our derivation applies to any TDCI system, regardless of basis set, number of electrons, or choice of Slater determinants in the wave function., Comment: 35 pages, 7 figures

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a method to learn a continuous-time Markov chain's transition rate functions from fully observed time series. In contrast with existing methods, our method allows for transition rates to depend nonlinearly on both state variables and external covariates. The Gillespie algorithm is used to generate trajectories of stochastic systems where propensity functions (reaction rates) are known. Our method can be viewed as the inverse: given trajectories of a stochastic reaction network, we generate estimates of the propensity functions. While previous methods used linear or log-linear methods to link transition rates to covariates, we use neural networks, increasing the capacity and potential accuracy of learned models. In the chemical context, this enables the method to learn propensity functions from non-mass-action kinetics. We test our method with synthetic data generated from a variety of systems with known transition rates. We show that our method learns these transition rates with considerably more accuracy than log-linear methods, in terms of mean absolute error between ground truth and predicted transition rates. We also demonstrate an application of our methods to open-loop control of a continuous-time Markov chain., Comment: 8 pages, 6 figures