Publications

Many active biological particles, such as swimming microorganisms or motor-proteins, do work on their environment by going though a periodic sequence of shapes. Interactions between particles can lead to the phase-synchronization of their duty cycles. Here we consider collective dynamics in a suspension of such active particles coupled through hydrodynamics. We demonstrate that the emergent non-equilibrium states feature stationary patterned flows and robust unidirectional pumping states under confinement. Moreover the phase-synchronized state of the suspension exhibits spatially robust chimera patterns in which synchronized and phase-isotropic regions coexist within the same system. These findings demonstrate a new route to pattern formation and could guide the design of new active materials.

Recovering the birth radii of observed stars in the Milky Way is one of the ultimate goals of Galactic Archaeology. One method to infer the birth radius and the evolution of the interstellar medium (ISM) metallicity assumes a linear relation between the ISM metallicity with radius at any given look-back time. Here, we test the reliability of this assumption by using four zoom-in cosmological hydrodynamic simulations from the NIHAO-UHD project. We find that one can infer precise birth radii only when the stellar disc starts to form, which for our modelled galaxies happens ∼10 Gyr ago, in agreement with recent estimates for the Milky Way. With a current day measurement of ISM metallicity gradient of −0.05 dex and a dispersion of 0.03 dex, the intrinsic uncertainty in inferring Rbirth is ∼0.6 kpc. At later times, the linear correlation between the ISM metallicity and radius increases, as stellar motions become more ordered and the azimuthal variations of the ISM metallicity start to drop. The formation of a central bar and perturbations from mergers can increase this uncertainty in the inner and outer disc, respectively.

With the funding provided by this award, we developed numerical codes for the study of magnetically confined plasmas for fusion applications. Accordingly, our work can be divided into two separate categories: 1) the design and analysis of novel numerical methods providing high accuracy and high efficiency; 2) the study of the equilibrium and stability of magnetically confined plasmas with some of these numerical codes, as well as the study of the nature of the turbulent behavior which may arise in the presence of instabilities. We first developed new numerical schemes based on integral equation methods for the computation of steady-state magnetic configurations in fusion experiments, providing high accuracy for the magnetic field and its derivatives, which are required for stability and turbulence calculations. We employed different integral formulations depending on the application of interest: axisymmetric or non-axisymmetric equilibria, force-free or magnetohydrodynamic equilibria, fixed-boundary equilibria or free-boundary equilibria. While efficient, these methods do not yet apply to plasma boundaries which are not smooth, a situation which is fairly common in magnetic confinement experiments. To address this temporary weakness, we also constructed a new steady-state solver based on the Hybridizable Discontinuous Galerkin (HDG) method, which provides full geometric flexibility. In addition to these numerical tools focused on steady-states, we also contributed to the improvement of the speed and accuracy of codes simulating the plasma dynamics of fusion plasmas, by developing a novel velocity space representation for the efficient solution of kinetic equations, which most accurately describe the time evolution of hot plasmas in fusion experiments. Using the tools discussed above, we studied several questions pertaining to the equilibrium and stability of magnetically confined plasmas. In particular, we derived a new simple model for axisymmetric devices called tokamaks, to predict how elongated a fusion plasma can be before it becomes unstable and collapses. We also looked at the effect of the shape of the outer plasma surface on key properties of the steady-state magnetic configurations, and how these properties impact turbulence in fusion plasmas, and the corresponding transport of momentum. Likewise, we studied the role of large localized flows on the steady-state magnetic configurations, and how they may influence plasma stability and turbulence. Non-axisymmetric steady-state magnetic configurations are inherently more complex than axisymmetric steady-state configurations, and the subject of ongoing controversies regarding the regularity of the equations determining such steady-states, and their solutions. Implementing an existing NYU code in a new geometry, we studied the nature of the singularity of the solutions observed in the code, and methods to eliminate them. Our main conclusion is that by appropriately tailoring the plasma boundary, it is possible to eliminate the singularities otherwise appearing in our simulations, and to obtain steady-states which appear to be smooth. To gain further insights on incompletely understood turbulence phenomena, we proposed a new reduced model capturing most of these phenomena, which is simple enough to not require expensive numerical simulations on massive supercomputers to investigate them. We demonstrated the strong similarity between our simulations and published results obtained from computationally expensive simulations, and plan to rely on our reduced model to identify the key mechanisms determining the evolution and strength turbulent driven transport in fusion plasmas. Finally, we proposed a new framework for tokamak reactor design studies, enabling us to consider the relative merits of steady-state versus pulsed fusion reactors. We found that pulsed fusion reactors may benefit most from recent advances in magnet technology, and the availability of very high field magnets. As such, they may become more desirable than steady-state tokamak reactors for cost efficient electricity generation.

A new scheme is proposed to construct a $\mathcal{C}^n\$ function extension for smooth functions defined on a smooth domain $D\in \mathbb{R}^d$. Unlike the PUX scheme, which requires the extrapolation of the volume grid via an expensive ill-conditioned least squares fitting, the scheme relies on an explicit formula consisting of a linear combination of function values in $D,$ which only extends the function along the normal direction. To be more precise, the $\mathcal{C}^n$ extension requires only $n+1$ function values along the normal directions in the original domain and ensures $\mathcal{C}^n$ smoothness by construction. When combined with a shrinking function and a smooth window function, the scheme can be made stable and robust for a broad class of domains with complex smooth boundary.

Both the core collapse of rotating massive stars, and the coalescence of neutron star (NS) binaries, result in the formation of a hot, differentially rotating NS remnant. The timescales over which differential rotation is removed by internal angular-momentum transport processes ("viscosity") has key implications for the remnant's long-term stability and the NS equation-of-state (EOS). Guided by a non-rotating model of a cooling proto-NS, we estimate the dominant sources of viscosity using an externally imposed angular velocity profile Ω(r). Although the magnetorotational instability provides the dominant source of effective viscosity at large radii, convection and/or the Spruit-Tayler dynamo dominate in the core of merger remnants where dΩ/dr≥0. Furthermore, the viscous timescale in the remnant core is sufficiently short that solid body rotation will be enforced faster than matter is accreted from rotationally-supported outer layers. Guided by these results, we develop a toy model for how the merger remnant core grows in mass and angular momentum due to accretion. We find that merger remnants with sufficiently massive and slowly rotating initial cores may collapse to black holes via envelope accretion, even when the total remnant mass is less than the usually considered threshold ≈1.2MTOV for forming a stable solid-body rotating NS remnant (where MTOV is the maximum non-rotating NS mass supported by the EOS). This qualitatively new picture of the post-merger remnant evolution and stability criterion has important implications for the expected electromagnetic counterparts from binary NS mergers and for multi-messenger constraints on the NS EOS.

According to the standard model of cosmology, the arrangement of matter in the cosmos on scales much larger than galaxies is entirely specified by the initial conditions laid down during inflation. But zooming in by dozens of orders of magnitude to microscopic (and human?) scales, quantum randomness reigns, independent of the initial conditions. Where is the boundary of determinism, and how does that interplay with chaos? Here, we make a first attempt at answering this question in an astronomical context, including currently understood processes. The boundary is a function, at least, of length scale, position, and matter type (dark matter being more simply predictable). In intergalactic voids, the primordial pattern of density fluctuations is largely preserved. But we argue that within galaxies, the conditions are at minimum chaotic, and may even be influenced by non-primordial information, or randomness independent of the initial conditions. Randomness could be supplied by events such as supernovae and jets from active galactic nuclei (AGN) and other accretion disks, which, with the help of chaotic dynamics, could broadcast any possible microscopic randomness to larger scales, eventually throughout a galaxy. This may be generated or amplified by a recently investigated process called spontaneous stochasticity, or effective randomness in turbulent systems arising from arbitrarily small perturbations.

In this paper, the random iterative method is introduced to massive multiple-input multiple-output (MIMO) systems for the efficient downlink linear precoding. By adopting the random sampling into the traditional iterative methods, the matrix inversion within the linear precoding schemes can be approximated statistically, which not only achieves a faster exponential convergence with low complexity but also experiences a global convergence without suffering from the various convergence requirements. Specifically, based on the random iterative method, the randomized iterative precoding algorithm (RIPA) is firstly proposed and we show its approximation error decays exponentially and globally along with the number of iterations. Then, with respect to the derived convergence rate, the concept of conditional sampling is introduced, so that further optimization and enhancement are carried out to improve both the convergence and the efficiency of the randomized iterations. After that, based on the equivalent iteration transformation, the modified randomized iterative precoding algorithm (MRIPA) is presented, which achieves a better precoding performance with low-complexity for various scenarios of massive MIMO. Finally, simulation results based on downlink precoding in massive MIMO systems are given to show the system gains of RIPA and MRIPA in terms of performance and complexity.

We present an analytic model for clustered supernovae (SNe) feedback in galaxy disks, incorporating the dynamical evolution of superbubbles formed from spatially overlapping SNe remnants. We propose two realistic outcomes for the evolution of superbubbles in galactic disks: (1) the expansion velocity of the shock front falls below the turbulent velocity dispersion of the ISM in the galaxy disk, whereupon the superbubble stalls and fragments, depositing its momentum entirely within the galaxy disk, or (2) the superbubble grows in size to reach the gas scale height, breaking out of the galaxy disk and driving galactic outflows/fountains. In either case, we find that superbubble breakup/breakout almost always occurs before the last Type-II SN (≲40 Myr) in the recently formed star cluster, assuming a standard high-end IMF slope, and scalings between stellar lifetimes and masses. The threshold between these two cases implies a break in the effective strength of feedback in driving turbulence within galaxies, and a resulting change in the scalings of, e.g., star formation rates with gas surface density (the Kennicutt-Schmidt relation) and the star formation efficiency in galaxy disks.

Dust plays a pivotal role in determining the observed spectral energy distribution (SED) of galaxies. Yet our understanding of dust attenuation is limited and our observations suffer from the dust-metallicity-age degeneracy in SED fitting (single galaxies), large individual variances (ensemble measurements), and the difficulty in properly dealing with uncertainties (statistical considerations). In this study, we create a population Bayesian model to rigorously account for correlated variables and non-Gaussian error distributions and demonstrate the improvement over a simple Bayesian model. We employ a flexible 5-D linear interpolation model for the parameters that control dust attenuation curves as a function of stellar mass, star formation rate (SFR), metallicity, redshift, and inclination. Our setup allows us to determine the complex relationships between dust attenuation and these galaxy properties simultaneously. Using Prospector fits of nearly 30,000 3D-HST galaxies, we find that the attenuation slope (n) flattens with increasing optical depth (τ), though less so than in previous studies. τ increases strongly with SFR, though when log SFR≲0, τ remains roughly constant over a wide range of stellar masses. Edge-on galaxies tend to have larger τ than face-on galaxies, but only for log M∗≳10, reflecting the lack of triaxiality for low-mass galaxies. Redshift evolution of dust attenuation is strongest for low-mass, low-SFR galaxies, with higher optical depths but flatter curves at high redshift. Finally, n has a complex relationship with stellar mass, highlighting the intricacies of the star-dust geometry. We have publicly released software (this https URL) for users to access our population model.

We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.