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Molecular dynamic (MD) simulations are used to probe molecular systems in regimes not accessible to physical experiments. A common goal of these simulations is to compute the power spectral density (PSD) of some component of the system such as particle velocity. In certain MD simulations, only a few time locations are observed, which makes it difficult to estimate the autocorrelation and PSD. This work develops a novel nuclear norm minimization-based method for this type of sub-sampled data, based on a parametric representation of the PSD as the sum of Lorentzians. We show results on both synthetic data and a test system of methanol. 

Abstract One of the classical approaches for estimating the frequencies and damping factors in a spectrally sparse signal is the MUltiple SIgnal Classification (MUSIC) algorithm, which exploits the low-rank structure of an autocorrelation matrix. Low-rank matrices have also received considerable attention recently in the context of optimization algorithms with partial observations, and nuclear norm minimization (NNM) has been widely used as a popular heuristic of rank minimization for low-rank matrix recovery problems. On the other hand, it has been shown that NNM can be viewed as a special case of atomic norm minimization (ANM), which has achieved great success in solving line spectrum estimation problems. However, as far as we know, the general ANM (not NNM) considered in many existing works can only handle frequency estimation in undamped sinusoids. In this work, we aim to fill this gap and deal with damped spectrally sparse signal recovery problems. In particular, inspired by the dual analysis used in ANM, we offer a novel optimization-based perspective on the classical MUSIC algorithm and propose an algorithm for spectral estimation that involves searching for the peaks of the dual polynomial corresponding to a certain NNM problem, and we show that this algorithm is in fact equivalent to MUSIC itself. Building on this connection, we also extend the classical MUSIC algorithm to the missing data case. We provide exact recovery guarantees for our proposed algorithms and quantify how the sample complexity depends on the true spectral parameters. In particular, we provide a parameter-specific recovery bound for low-rank matrix recovery of jointly sparse signals rather than use certain incoherence properties as in existing literature. Simulation results also indicate that the proposed algorithms significantly outperform some relevant existing methods (e.g., ANM) in frequency estimation of damped exponentials. 

Abstract Heavy quark production provides a unique probe of the quark-gluon plasma transport properties in heavy ion collisions. Experimental observables like the nuclear modification factor $$R_\mathrm{AA}$$ R AA and elliptic anisotropy $$v_\mathrm{2}$$ v 2 of heavy flavor mesons are sensitive to the heavy quark diffusion coefficient. There now exist an extensive set of such measurements, which allow a data-driven extraction of this coefficient. In this work, we make such an attempt within our recently developed heavy quark transport modeling framework (Langevin-transport with Gluon Radiation, LGR). A question of particular interest is the temperature dependence of the diffusion coefficient, for which we test a wide range of possibility and draw constraints by comparing relevant charm meson data with model results. We find that a relatively strong increase of diffusion coefficient from crossover temperature $$T_c$$ T c toward high temperature is preferred by data. We also make predictions for Bottom meson observables for further experimental tests.