On polynomial digraphs

Let $\Phi(x,y)$ be a bivariate polynomial with complex coefficients. The zeroes of $\Phi(x,y)$ are given a combinatorial structure by considering them as arcs of a directed graph $G(\Phi)$. This paper studies some relationship between the polynomial $\Phi(x,y)$ and the structure of $G(\Phi)$.Comment: 13 pages, 6 figures, See also http://www-ma2.upc.edu/~montes

ρ\rho and K∗K^* resonances on the lattice at nearly physical quark masses and Nf=2N_f=2

Working with a pion mass $m_\pi \approx 150$ MeV, we study $\pi\pi$ and $K\pi$ scattering using two flavours of non-perturbatively improved Wilson fermions at a lattice spacing $a\approx 0.071$ fm. Employing two lattice volumes with linear spatial extents of $N_s=48$ and $N_s=64$ points and moving frames, we extract the phase shifts for p-wave $\pi\pi$ and $K\pi$ scattering near the $\rho$ and $K^*$ resonances.Comparing our results to those of previous lattice studies, that used pion masses ranging from about 200 MeV up to 470 MeV, we find that the coupling $g_{\rho\pi\pi}$ appears to be remarkably constant as a function of $m_{\pi}$.Comment: 16 pages, 8 figures, v2: "and $N_f=2$" added to the title, references updated, some figures replaced, including improved summary plots, alternative parametrizations are considered and analytical continations are performed to determine pole positions on the second Riemann shee

DK and ππ Scattering from Lattice QCD

Lüscher's formalism and its generalisations enables the access of scattering properties of particles by perfoming numerical computations on the lattice. The formalism is applied to ππ, Kπ, DK and DK* elastic scattering with angular momentum-parity combinations of 0⁺, 1⁺, 1⁻ and 1⁻, respectively. Masses and couplings of the resonances and bound states which couple to these channels are determined. The weak decay constants of the scalar and axialvector charmed-strange bound states are also computed. The simulation stands out for the close-to-physical pion mass and the high-statistics employed

A Learned Born Series for Highly-Scattering Media

A new method for solving the wave equation is presented, called the learned Born series (LBS), which is derived from a convergent Born Series but its components are found through training. The LBS is shown to be significantly more accurate than the convergent Born series for the same number of iterations, in the presence of high contrast scatterers, while maintaining a comparable computational complexity. The LBS is able to generate a reasonable prediction of the global pressure field with a small number of iterations, and the errors decrease with the number of learned iterations.Comment: 6 pages, 1 figur

Cloudlet Capture Model for the Accretion Streamer onto the disk of DG Tau

DG Tau is a nearby T Tauri star associated with a collimated jet, a circumstellar disk and a streamer a few hundred au long. The streamer connects to the disk at $\sim$50 au from DG Tau. At this location SO emission is observed, likely due to the release of sulphur from dust grains caused by the shock of the impact of the accretion streamer onto the disk. We investigate the possibility that the DG Tau streamer was produced via cloudlet capture on the basis of hydrodynamic simulations, considering a cloudlet initiating infall at 600 au from DG Tau with low angular momentum so that the centrifugal force is smaller than the gravitational force, even at 50 au. The elongation of the cloudlet into a streamer is caused by the tidal force when its initial velocity is much less than the free-fall velocity. The elongated cloudlet reaches the disk and forms a high density gas clump. Our hydrodynamic model reproduces the morphology and line-of-sight velocity of CS ($5-4$) emission from the Northern streamer observed with ALMA. We discuss the conditions for forming a streamer based on the simulations. We also show that the streamer should perturb the disk after impact for several thousands of years.Comment: 12 page, 11 figure

A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound

Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict the acoustic field passing through the skull (e.g., to account for subject-specific dose and targeting variations). As a step towards real-time predictions, in the current work, a fast iterative solver for the heterogeneous Helmholtz equation in 2D is developed using a fully-learned optimizer. The lightweight network architecture is based on a modified UNet that includes a learned hidden state. The network is trained using a physics-based loss function and a set of idealized sound speed distributions with fully unsupervised training (no knowledge of the true solution is required). The learned optimizer shows excellent performance on the test set, and is capable of generalization well outside the training examples, including to much larger computational domains, and more complex source and sound speed distributions, for example, those derived from x-ray computed tomography images of the skull.Comment: 23 pages, 13 figure

On Cox rings of K3-surfaces

We study Cox rings of K3-surfaces. A first result is that a K3-surface has a finitely generated Cox ring if and only if its effective cone is polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3-surfaces of Picard number two, and explicitly compute the Cox rings of generic K3-surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.Comment: minor corrections, to appear in Compositio Mathematica, 32 page