Dynamics and stability of the Godel universe

We use covariant techniques to describe the properties of the Godel universe and then consider its linear response to a variety of perturbations. Against matter aggregations, we find that the stability of the Godel model depends primarily upon the presence of gradients in the centrifugal energy, and secondarily on the equation of state of the fluid. The latter dictates the behaviour of the model when dealing with homogeneous perturbations. The vorticity of the perturbed Godel model is found to evolve as in almost-FRW spacetimes, with some additional directional effects due to shape distortions. We also consider gravitational-wave perturbations by investigating the evolution of the magnetic Weyl component. This tensor obeys a simple plane-wave equation, which argues for the neutral stability of the Godel model against linear gravity-wave distortions. The implications of the background rotation for scalar-field Godel cosmologies are also discussed.Comment: Revised version, to match paper published in Class. Quantum Gra

Pressure reconstruction from Lagrangian particle tracking with FFT integration

Volumetric time-resolved pressure gradient fields in unsteady flows can be estimated through flow measurements of the material acceleration in the fluid and the assumption of the governing momentum equation. In order to derive pressure, almost exclusively two numerical methods have been used to spatially integrate the pressure gradient until now: first, direct path integration in the spatial domain, and second, the solution of the Poisson equation with numerical methods. We propose an alternative method by integrating the pressure gradient field directly in Fourier space with a standard FFT function. The method is fast and easy to implement. We demonstrate the accuracy of the integration scheme on a synthetic pressure field and apply it to an experimental example based on acceleration data from Lagrangian particle tracking with high seeding density (Shake-The-Box method)

Cosmology with inhomogeneous magnetic fields

We review spacetime dynamics in the presence of large-scale electromagnetic fields and then consider the effects of the magnetic component on perturbations to a spatially homogeneous and isotropic universe. Using covariant techniques, we refine and extend earlier work and provide the magnetohydrodynamic equations that describe inhomogeneous magnetic cosmologies in full general relativity. Specialising this system to perturbed Friedmann-Robertson-Walker models, we examine the effects of the field on the expansion dynamics and on the growth of density inhomogeneities, including non-adiabatic modes. We look at scalar perturbations and obtain analytic solutions for their linear evolution in the radiation, dust and inflationary eras. In the dust case we also calculate the magnetic analogue of the Jeans length. We then consider the evolution of vector perturbations and find that the magnetic presence generally reduces the decay rate of these distortions. Finally, we examine the implications of magnetic fields for the evolution of cosmological gravitational waves.Comment: Typos corrected. Version to appear in Physics Report

Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change

Flow and pressure measurement using phase-contrast MRI : experiments in stenotic phantom models.

Peripheral Arterial Disease (PAD) is a progressive atherosclerotic disorder which is defined as any pathologic process obstructing the blood flow of the arteries supplying the lower extremities. Moderate stenoses mayor may not be hemodynamically significant, and intravascular pressure measurements have been recommended to evaluate whether these lesions are clinically significant. Phase-contrast MRI (PC-MRI) provides a powerful and non-invasive method to acquire spatially registered blood velocity. The velocity field, then, can be used to derive other clinically useful hemodynamic parameters, such as blood flow and blood pressure gradients. Herein, a series of detailed experiments are reported for the validation of MR measurements of steady and pulsatile flows with stereoscopic particle image velocimetry (SPIV). Agreement between PC-MRI and SPIV was demonstrated for both steady and pulsatile flow measurements at the inlet by evaluating the linear regression between the two methods, which showed a correlation coefficient of\u3e 0.99 and\u3e 0.96 for steady and pulsatile flows, respectively. Experiments revealed that the most accurate measures of flow by PC-MRI are found at the throat of the stenosis (error \u3c 5% for both steady and pulsatile mean flows). The flow rate error distal to the stenosis was shown to be a function of narrowing severity. Furthermore, pressure differences across an axisymmetric stenotic phantom model were estimated by solving the pressure-Poisson equation (iterative method) and a non-iterative method based on harmonics-based orthogonal projection using PC-MRI velocity data. Results were compared with the values obtained from other techniques including SPIV, computational fluid dynamic (CFD) simulations, and direct pressure measurements. Using the pressure obtained from CFD as the ground truth and PC-MRI velocity data as the input, the relative error in pressure drop for iterative and non-iterative techniques were 13.1 % and 12.5% for steady flow, 4.0% and 22.1 % for pulsatile flow at peak-systole, and 194.5% and 155.2% at end-diastole, respectively. It was concluded that pressure drop calculation using PC-MRI is more promising for steady cases and pulsatile cases at peak-systole compared to pulsatile flow cases at end-diastole