In this article, continuous Galerkin finite elements are applied to perform full waveform inversion (FWI) for seismic velocity model building. A time-domain FWI approach is detailed that uses meshes composed of variably sized triangular elements to d
iscretize the domain. To resolve both the forward and adjoint-state equations, and to calculate a mesh-independent gradient associated with the FWI process, a fully-explicit, variable higher-order (up to degree $k=5$ in $2$D and $k=3$ in 3D) mass lumping method is used. By adapting the triangular elements to the expected peak source frequency and properties of the wavefield (e.g., local P-wavespeed) and by leveraging higher-order basis functions, the number of degrees-of-freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both $2$D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material proprieties. Software developments are implemented an open source code built on top of Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite element method.
The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet also features significant variability reflecting the stochastic nature of disease spread. The interplay of biological, social, s
tructural and random factors makes disease forecasting extraordinarily complex. In this work, we reframe a stochastic branching process analysis in terms of probability generating functions and compare it to continuous time epidemic simulations on networks. In doing so, we predict the diversity of emerging epidemic courses on both homogeneous and heterogeneous networks. We show how the challenge of inferring the early course of an epidemic falls on the randomness of disease spread more so than on the heterogeneity of contact patterns. We provide an analysis which helps quantify, in real time, the probability that an epidemic goes supercritical or conversely, dies stochastically. These probabilities are often assumed to be one and zero, respectively, if the basic reproduction number, or R0, is greater than 1, ignoring the heterogeneity and randomness inherent to disease spread. This framework can give more insight into early epidemic spread by weighting standard deterministic models with likelihood to inform pandemic preparedness with probabilistic forecasts.
Two popular approaches to model-free continuous control tasks are SAC and TD3. At first glance these approaches seem rather different; SAC aims to solve the entropy-augmented MDP by minimising the KL-divergence between a stochastic proposal policy an
d a hypotheical energy-basd soft Q-function policy, whereas TD3 is derived from DPG, which uses a deterministic policy to perform policy gradient ascent along the value function. In reality, both approaches are remarkably similar, and belong to a family of approaches we call `Off-Policy Continuous Generalized Policy Iteration. This illuminates their similar performance in most continuous control benchmarks, and indeed when hyperparameters are matched, their performance can be statistically indistinguishable. To further remove any difference due to implementation, we provide OffCon$^3$ (Off-Policy Continuous Control: Consolidated), a code base featuring state-of-the-a
Magnetars are slowly-rotating neutron stars with extremely strong magnetic fields ($10^{13-15}$ G), episodically emitting $sim100$ ms long X-ray bursts with energies of $sim10^{40-41}$ erg. Rarely, they produce extremely bright, energetic giant flare
s that begin with a short ($sim0.2$ s), intense flash, followed by fainter, longer lasting emission modulated by the magnetar spin period (typically 2-12 s), thus confirming their origin. Over the last 40 years, only three such flares have been observed in our local group; they all suffered from instrumental saturation due to their extreme intensity. It has been proposed that extra-galactic giant flares likely constitute a subset of short gamma-ray bursts, noting that the sensitivity of current instrumentation prevents us from detecting the pulsating tail, while the initial bright flash is readily observable out to distances $sim 10-20$ Mpc. Here, we report X- and gamma-ray observations of GRB 200415A, which exhibits a rapid onset, very fast time variability, flat spectra and significant sub-millisecond spectral evolution. These attributes match well with those expected for a giant flare from an extra-galactic magnetar, noting that GRB 200415A is directionally associated with the galaxy NGC 253 ($sim$3.5 Mpc away). The detection of $sim3$ MeV photons provides definitive evidence for relativistic motion of the emitting plasma. The observed rapid spectral evolution can naturally be generated by radiation emanating from such rapidly-moving gas in a rotating magnetar.
Co$^{2+}$ ions in an octahedral crystal field, stabilise a j$_{eff}$ = 1/2 ground state with an orbital degree of freedom and have been recently put forward for realising Kitaev interactions, a prediction we have tested by investigating spin dynamics
in two cobalt honeycomb lattice compounds, Na$_2$Co$_2$TeO$_6$ and Na$_3$Co$_2$SbO$_6$, using inelastic neutron scattering. We used linear spin wave theory to show that the magnetic spectra can be reproduced with a spin Hamiltonian including a dominant Kitaev nearest-neighbour interaction, weaker Heisenberg interactions up to the third neighbour and bond-dependent off-diagonal exchange interactions. Beyond the Kitaev interaction that alone would induce a quantum spin liquid state, the presence of these additional couplings is responsible for the zigzag-type long-range magnetic ordering observed at low temperature in both compounds. These results provide evidence for the realization of Kitaev-type coupling in cobalt-based materials, despite hosting a weaker spin-orbit coupling than their 4d and 5d counterparts.
Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is computed in s
mall patches spread across the space-time domain, with patch coupling conditions bridging the unsimulated space. For accurate simulations, care must be taken in designing the patch coupling conditions. Here we construct novel coupling conditions which preserve translational invariance, rotational invariance, and self-adjoint symmetry, thus guaranteeing that conservation laws associated with these symmetries are preserved in the macroscale simulation. Spectral and algebraic analyses of the proposed scheme in both one and two dimensions reveal mechanisms for further improving the accuracy of the simulations. Consistency of the patch schemes macroscale dynamics with the original microscale model is proved. This new self-adjoint patch scheme provides an efficient, flexible, and accurate computational homogenisation in a wide range of multiscale scenarios of interest to scientists and engineers.
Neutron scattering, specific heat and magnetisation measurements on both powders and single crystals reveal that Dy$_2$Ir$_2$O$_7$ realizes the fragmented monopole crystal state in which antiferromagnetic order and a Coulomb phase spin liquid co-inha
bit. The measured residual entropy is that of a hard core dimer liquid, as predicted. Inclusion of Coulomb interactions allows for a quantitative description of both the thermodynamic data and the magnetisation dynamics, with the energy scale given by deconfined defects in the emergent ionic crystal. Our data reveal low energy excitations, as well as a large distribution of energy barriers down to low temperatures, while the magnetic response to an applied field suggests that domain wall pinning is important; results that call for further theoretical modelling.
We review more than 10 years of continuous monitoring of accreting X-ray pulsars with the all-sky Gamma-ray Burst Monitor (GBM) aboard the Fermi Gamma-ray Space Telescope. Our work includes data from the start of GBM operations in August 2008, throug
h to November 2019. Pulsations from 39 accreting pulsars are observed over an energy range of $10-50,$keV by GBM. The GBM Accreting Pulsars Program (GAPP) performs data reduction and analysis for each accreting pulsar and makes histories of the pulse frequency and pulsed flux publicly available. We examine in detail the spin histories, outbursts and torque behaviors of the persistent and transient X-ray pulsars observed by GBM. The spin period evolution of each source is analyzed in the context of disk-accretion and quasi-spherical settling accretion driven torque models. Long-term pulse frequency histories are also analyzed over the GBM mission lifetime and compared to those available from the previous BATSE all-sky monitoring mission, revealing previously unnoticed episodes in some of the analyzed sources (such as a torque reversal in 2S 1845-024). We obtain new, or update known, orbital solutions for three sources. Our results demonstrate the capabilities of GBM as an excellent instrument for monitoring accreting X-ray pulsars and its important scientific contribution to this field.
Scientists and engineers often create accurate, trustworthy, computational simulation schemes - but all too often these are too computationally expensive to execute over the time or spatial domain of interest. The equation-free approach is to marry s
uch trusted simulations to a framework for numerical macroscale reduction - the patch dynamics scheme. This article extends the patch scheme to scenarios in which the trusted simulation resolves abrupt state changes on the microscale that appear as shocks on the macroscale. Accurate simulation for problems in these scenarios requires extending the patch scheme by capturing the shock within a novel patch, and also modifying the patch coupling rules in the vicinity in order to maintain accuracy. With these two extensions to the patch scheme, straightforward arguments derive consistency conditions that match the usual order of accuracy for patch schemes. The new scheme is successfully tested on four archetypal problems. This technique will empower scientists and engineers to accurately and efficiently simulate, over large spatial domains, multiscale multiphysics systems that have rapid transition layers on the microscale.
In this paper, we report on numerical calculations of the spontaneous emission rates and Lamb shifts of a $^{87}text{Rb}$ atom in a Rydberg-excited state $left(nleq30right)$ located close to a silica optical nanofiber. We investigate how these quanti
ties depend on the fibers radius, the distance of the atom to the fiber, the direction of the atomic angular momentum polarization as well as the different atomic quantum numbers. We also study the contribution of quadrupolar transitions, which may be substantial for highly polarizable Rydberg states. Our calculations are performed in the macroscopic quantum electrodynamics formalism, based on the dyadic Greens function method. This allows us to take dispersive and absorptive characteristics of silica into account; this is of major importance since Rydberg atoms emit along many different transitions whose frequencies cover a wide range of the electromagnetic spectrum. Our work is an important initial step towards building a Rydberg atom-nanofiber interface for quantum optics and quantum information purposes.
