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Three-dimensional CP-DNS of reacting iron particle dust clouds in a turbulent mixing layer are conducted. The simulation approach considers the Eulerian transport equations for the reacting gas phase and resolves all scales of turbulence, whereas the particle boundary layers are modelled employing the Lagrangian point-particle framework for the dispersed phase. The CP-DNS employs an existing sub-model for iron particle combustion that considers the oxidation of iron to FeO and that accounts for both diffusion- and kinetically-limited combustion. At first, the particle sub-model is validated against experimental results for single iron particle combustion considering various particle diameters and ambient oxygen concentrations. Subsequently, the CP-DNS approach is employed to predict iron particle cloud ignition and combustion in a turbulent mixing layer. The upper stream of the mixing layer is initialised with cold particles in air, while the lower stream consists of hot air flowing in the opposite direction. Simulation results show that turbulent mixing induces heating, ignition and combustion of the iron particles. Significant increases in gas temperature and oxygen consumption occur mainly in regions where clusters of iron particles are formed. Over the course of the oxidation, the particles are subjected to different rate-limiting processes. While initially particle oxidation is kinetically-limited it becomes diffusion-limited for higher particle temperatures and peak particle temperatures are observed near the fully-oxidised particle state. Comparing the present non-volatile iron dust flames to general trends in volatile-containing solid fuel flames, non-vanishing particles at late simulation times and a stronger limiting effect of the local oxygen concentration on particle conversion is found for the present iron dust flames in shear-driven turbulence.

We calculate murmuration densities for two families of Dirichlet characters. The first family contains complex Dirichlet characters normalized by their Gauss sums. Integrating the first density over a geometric interval yields a murmuration function compatible with experimental observations. The second family contains real Dirichlet characters weighted by a smooth function with compact support. We show that the second density exhibits a universality property analogous to Zubrilina's density for holomorphic newforms, and it interpolates the phase transition in the the $1$-level density for a symplectic family of $L$-functions., Comment: 21 pages, 9 figures. Significant updates since first upload

We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separating class numbers of matching/different parity from a data-scientific perspective, apply the methodology of feature analysis and principal component analysis, and use symbolic classification to develop machine-learned formulas for class numbers 1, 2 and 3 that apply to our dataset., Comment: 26 pages, 20 figures

Diketopyrrolopyrroles are a popular class of electron-withdrawing unit in optoelectronic materials. When combined with electron donating side-chain functional groups such as thiophenes, they form a very broad class of donor-acceptor molecules: thiophene-diketopyrrolopyrroles (TDPPs). Despite their widescale use in biosensors and photovoltaic materials, studies have yet to establish the important link between the electronic structure of the specific TDPP and the critical optical properties. To bridge this gap, ultrafast transient absorption with 22 fs time resolution has been used to explore the photophysics of three prototypical TDPP molecules: a monomer, dimer and polymer in solution. These studies show that the photophysics of these molecular prototypes under visible photoexcitation are determined by just two excited electronic states, having very different electronic characters (one is optically bright, the other dark), their relative energetic ordering and the timescales for internal conversion from one to the other and/or to the ground state. The underlying difference in electronic structure alters the branching between these excited states and their associated dynamics. In turn, these factors dictate the fluorescence quantum yields, which are shown to vary by ~1-2 orders of magnitude across the TDPP prototypes investigated here. The fast non-radiative transfer of molecules from the bright to dark states is mediated by conical intersections. Remarkably, wavepacket signals in the measured transient absorption data carry signatures of the nuclear motions that enable mixing of the electronic-nuclear wavefunction and facilitate non-adiabatic coupling between the bright and dark states., Comment: 65 pages, 27 figures

We investigate the average value of the $p$th Dirichlet coefficients of elliptic curves for a prime p in a fixed conductor range with given rank. Plotting this average yields a striking oscillating pattern, the details of which vary with the rank. Based on this observation, we perform various data-scientific experiments with the goal of classifying elliptic curves according to their ranks., Comment: 25 pages, 16 figures, 2 tables

We establish everywhere convergence in a natural domain for Eisenstein series on a symmetrizable Kac--Moody group over a function field. Our method is different from that of the affine case which does not directly generalize. In comparison with the analogous result over the real numbers, everywhere convergence is achieved without any additional condition on the root system., Comment: 11 pages

We show that standard machine-learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around one hundred thousand, we demonstrate the utility of machine-learning in classification problems pertaining to the BSD invariants of an elliptic curve (including its rank and torsion subgroup), and the analogous invariants of a genus 2 curve. Our results show that a trained machine can efficiently classify curves according to these invariants with high accuracies (>0.97). For problems such as distinguishing between torsion orders, and the recognition of integral points, the accuracies can reach 0.998., Comment: 21 pages, 1 figure, 9 tables

We show that standard machine-learning algorithms may be trained to predict certain invariants of algebraic number fields to high accuracy. A random-forest classifier that is trained on finitely many Dedekind zeta coefficients is able to distinguish between real quadratic fields with class number 1 and 2, to 0.96 precision. Furthermore, the classifier is able to extrapolate to fields with discriminant outside the range of the training data. When trained on the coefficients of defining polynomials for Galois extensions of degrees 2, 6, and 8, a logistic regression classifier can distinguish between Galois groups and predict the ranks of unit groups with precision >0.97., Comment: 20 pages, 1 figure, 3 tables

We apply some of the latest techniques from machine-learning to the arithmetic of hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence (between 99 and 100 percent precision), and in very short time (matter of seconds on an ordinary laptop), a Bayesian classifier can distinguish between Sato-Tate groups given a small number of Euler factors for the L-function. Our observations are in keeping with the Sato-Tate conjecture for curves of low genus. For elliptic curves, this amounts to distinguishing generic curves (with Sato-Tate group SU(2)) from those with complex multiplication. In genus 2, a principal component analysis is observed to separate the generic Sato-Tate group USp(4) from the non-generic groups. Furthermore in this case, for which there are many more non-generic possibilities than in the case of elliptic curves, we demonstrate an accurate characterisation of several Sato-Tate groups with the same identity component. Throughout, our observations are verified using known results from the literature and the data available in the LMFDB. The results in this paper suggest that a machine can be trained to learn the Sato-Tate distributions and may be able to classify curves much more efficiently than the methods available in the literature., Comment: 21 pages, 1 table, 5 figures

We prove various converse theorems for automorphic forms on \Gamma_0(N), each assuming fewer twisted functional equations than the last. We show that no twisting at all is needed for holomorphic modular forms in the case that N is 18, 20, or 24 - these integers are the smallest multiples of 4 or 9 not covered by earlier work of Conrey-Farmer. This development is a consequence of finding generating sets for \Gamma_0(N) such that each generator can be written as a product of special matrices. As for real-analytic Maass forms of even (resp. odd) weight we prove the analogous statement for N=1,...12,16,18 (resp. N=1,...,12,14,15,16,17,18,20,23,24)., Comment: 17 pages, 2 tables

A correction factor naturally arises in the theory of p-adic Kac--Moody groups. In this paper, we expand the correction factor into a sum of irreducible characters of the underlying Kac--Moody algebra. We derive a formula for the coefficients, which lie in the ring of power series with integral coefficients. In the case that the Weyl group is a universal Coxeter group, we show that the coefficients are actually polynomials., Comment: 20 pages, 4 tables

We show that certain quotients of Artin L-functions have infinitely many poles. Our result follows from a converse theorem for Maass forms of Laplace eigenvalue 1/4 in which the twisted L-functions are not assumed to be entire. We do not require the conjectural automorphy of Artin L-functions, only their established meromorphic continuation and functional equation., Comment: 35 pages

We prove two principal results. Firstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that the twists are allowed to be meromorphic. This weakened analytic assumption applies in the context of our second theorem, which shows that the quotient of the symmetric square L-function of a Maass newform and the Riemann zeta function has infinitely many poles., Comment: Updated introduction