arXiv subjects

Christian Y. Cardall

Publications and source records attributed to Christian Y. Cardall.

At least 19 recordsLinked to original sources

arXiv2026

A unified perspective on Poincaré and Galilei relativity: I. Special relativity

A semantic adjustment to what physicists mean by the terms `special relativity' and `general relativity' is suggested, which prompts a conceptual shift to a more unified perspective on physics governed by the Poincaré group and physics governed by the Galilei group. After exploring the limits of a unified perspective available in the setting of 4-dimensional spacetime, a particular central extension of the Poincaré group -- analogous to the Bargmann group that is a central extension of the Galilei group -- is presented that deepens a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting. The immediate focus of this paper is classical physics on affine 4-dimensional and 5-dimensional spacetimes (`special relativity' as redefined here), including the electrodynamics that gave rise to Poincaré physics in the first place; but the results here may suggest the existence of a `Galilei general relativity' more extensive than generally known, to be pursued in the sequel.

physics.gen-ph↗

arXiv2026

GenASiS: General Astrophysical Simulation System. II. Self-gravitating Baryonic Matter

GenASiS (General Astrophysical Simulation System) is a code being developed initially and primarily, though not exclusively, for the simulation of core-collapse supernovae on the world's leading capability supercomputers. This paper -- the second in a series -- documents capabilities for Newtonian self-gravitating fluid dynamics, including tabulated microphysical equations of state treating nuclei and nuclear matter (`baryonic matter'). Computation of the gravitational potential of a spheroid, and simulation of the gravitational collapse of dust and of an ideal fluid, provide tests of self-gravitation against known solutions. In multidimensional computations of the adiabatic collapse, bounce, and explosion of spherically symmetric pre-supernova progenitors -- which we propose become a standard benchmark for code comparisons -- we find that the explosions are prompt and remain spherically symmetric (as expected), with an average shock expansion speed and total kinetic energy that are inversely correlated with the progenitor mass at the onset of collapse and the compactness parameter.

astro-ph.HE↗

arXiv2026

thornado+Flash-X: A Hybrid DG-IMEX and Finite-Volume Framework for Neutrino-Radiation Hydrodynamics in Core-Collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement (AMR)-based multiphysics simulation framework Flash-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $O(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino-matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino-electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved with a hybrid DG-FV representation of the fluid variables and operator-split evolution in Flash-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within Flash-X. thornado's neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

astro-ph.IM↗

arXiv2023

GenASiS Basics: Object-oriented utilitarian functionality for large-scale physics simulations (Version 4)

GenASiS Basics provides modern Fortran classes furnishing extensible object-oriented utilitarian functionality for large-scale physics simulations on distributed memory supercomputers. This functionality includes physical units and constants; display to the screen or standard output device; message passing; I/O to disk; and runtime parameter management and usage statistics. This revision -- Version 4 of GenASiS Basics -- includes a name change and additions to functionality, including the facilitation of direct communication between GPUs.

astro-ph.IM↗

arXiv2023

Combining 3-momentum and kinetic energy on Galilei/Newton spacetime

Without the mass-energy equivalence available on Minkowski spacetime $\mathbb{M}$, it is not possible on 4-dimensional non-relativistic Galilei/Newton spacetime $\mathbb{G}$ to combine 3-momentum and total mass-energy in a single tensor object. However, given a fiducial frame, it is possible to combine 3-momentum and kinetic energy into a linear form (particle) or $(1,1)$ tensor (continuum) in a manner that exhibits increased unity of classical mechanics on flat relativistic and non-relativistic spacetimes $\mathbb{M}$ and $\mathbb{G}$. As on $\mathbb{M}$, for a material continuum on $\mathbb{G}$, the First Law of Thermodynamics can be considered a consequence of a unified dynamical law for energy-momentum rather than an independent postulate.

physics.gen-ph↗

arXiv2023

Towards full `Galilei general relativity': Bargmann-Minkowski and Bargmann-Galilei spacetimes

Galilei-Newton spacetime $\mathbb{G}$ with its Galilei group can be understood as a `degeneration' as $c \rightarrow \infty$ of Minkowski spacetime $\mathbb{M}$ with its Poincaré group. $\mathbb{G}$ does not have a spacetime metric and its Galilei symmetry transformations do not include energy; but Bargmann-Galilei spacetime $B\mathbb{G}$, a 5-dimensional extension that preserves Galilei physics, remedies these infelicities. Here an analogous Bargmann-Minkowski spacetime $B\mathbb{M}$ is described. While not necessary for Poincaré physics, it may illuminate a path towards a more extensive `Galilei general relativity' than is presently known, which would be a useful -- and conceptually and mathematically sound -- approximation in astrophysical scenarios such as core-collapse supernovae.

physics.gen-ph↗

arXiv2022

Fluid Dynamics in Curvilinear Coordinates without Fictitious Forces

Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in three dimensions, these fictitious forces can be eliminated by solving for rectangular (Cartesian) momentum components on a curvilinear mesh. A thoroughly geometric approach to fluid dynamics on spacetime demonstrates this transparently, while also giving insight into a greater unity of the relativistic and nonrelativistic cases than is usually appreciated.

physics.flu-dyn↗

arXiv2019

Targeting GPUs with OpenMP Directives on Summit: A Simple and Effective Fortran Experience

We use OpenMP to target hardware accelerators (GPUs) on Summit, a newly deployed supercomputer at the Oak Ridge Leadership Computing Facility (OLCF), demonstrating simplified access to GPU devices for users of our astrophysics code GenASiS and useful speedup on a sample fluid dynamics problem. We modify our workhorse class for data storage to include members and methods that significantly streamline the persistent allocation of and association to GPU memory. Users offload computational kernels with OpenMP target directives that are rather similar to constructs already familiar from multi-core parallelization. In this initial example we ask, "With a given number of Summit nodes, how fast can we compute with and without GPUs?", and find total wall time speedups of $\sim 12\mathrm{X}$. We also find reasonable weak scaling up to 8000 GPUs (1334 Summit nodes). We make available the source code from this work at https://github.com/GenASiS/GenASiS_Basics.

physics.comp-ph↗

arXiv2019

Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3+1 Spacetime Perspective

A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases on as common a footing as possible reveals that the particle four-momentum is better regarded as comprising momentum and \textit{inertia} rather than momentum and energy; and consequently, that the object now known as the stress-energy or energy-momentum tensor is more properly understood as a stress-\textit{inertia} or \textit{inertia}-momentum tensor. In dealing with both fiducial and comoving frames as fluid dynamics requires, tensor decompositions in terms of the four-velocities of observers associated with these frames render use of coordinate-free geometric notation not only fully viable, but conceptually simplifying. A particle number four-vector, three-momentum $(1,1)$ tensor, and kinetic energy four-vector characterize a simple fluid and satisfy balance equations involving spacetime divergences on both Minkowski and Galilei/Newton spacetimes. Reduced to a fully $3+1$ form, these equations yield the familiar conservative formulations of special relativistic and non-relativistic hydrodynamics as partial differential equations in inertial coordinates, and in geometric form will provide a useful conceptual bridge to arbitrary-Lagrange-Euler and general relativistic formulations.

astro-ph.HE↗

arXiv2018

Relativistic Analogue of the Newtonian Fluid Energy Equation with Nucleosynthesis

In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. A relativistic equation in conservative form for total fluid energy, obtained from the spacetime divergence of the stress-energy tensor, in principle encompasses such energy generation; but it is not explicitly manifest. An alternative relativistic energy equation in conservative form---in which the nuclear energy generation appears explicitly, and that reduces directly to the Newtonian internal + kinetic energy in the appropriate limit---emerges naturally and self-consistently from the difference of the equation for total fluid energy and the equation for baryon number conservation multiplied by the average baryon mass $m$, when $m$ is expressed in terms of contributions from the nuclear species in the fluid, and allowed to be mutable.

astro-ph.HE↗

arXiv2017

GenASiS Mathematics: Object-oriented manifolds, operations, and solvers for large-scale physics simulations

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a `finite-volume' approach in which space is partitioned into a large number of small `cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual `unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GenASiS (General Astrophysical Simulation System), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

physics.comp-ph↗

arXiv2015

Stochasticity and efficiency of simplified core-collapse supernova explosions

We present an initial report on 160 simulations of a highly simplified model of the post-bounce core-collapse supernova environment in three spatial dimensions (3D). We set different values of a parameter characterizing the impact of nuclear dissociation at the stalled shock in order to regulate the post-shock fluid velocity, thereby determining the relative importance of convection and the stationary accretion shock instability (SASI). While our convection-dominated runs comport with the paradigmatic notion of a `critical neutrino luminosity' for explosion at a given mass accretion rate (albeit with a nontrivial spread in explosion times just above threshold), the outcomes of our SASI-dominated runs are much more stochastic: a sharp threshold critical luminosity is `smeared out' into a rising probability of explosion over a $\sim 20\%$ range of luminosity. We also find that the SASI-dominated models are able to explode with 3 to 4 times less efficient neutrino heating, indicating that progenitor properties, and fluid and neutrino microphysics, conducive to the SASI would make the neutrino-driven explosion mechanism more robust.

astro-ph.HE↗

arXiv2015

Accelerating Our Understanding of Supernova Explosion Mechanism via Simulations and Visualizations with GenASiS

Core-collapse supernovae are among the most powerful explosions in the Universe, releasing about $10^{53}~\mbox{erg}$ of energy on timescales of a few tens of seconds. These explosion events are also responsible for the production and dissemination of most of the heavy elements, making life as we know it possible. Yet exactly how they work is still unresolved. One reason for this is the sheer complexity and cost of a self-consistent, multi-physics, and multi-dimensional core-collapse supernova simulation, which is impractical, and often impossible, even on the largest supercomputers we have available today. To advance our understanding we instead must often use simplified models, teasing out the most important ingredients for successful explosions, while helping us to interpret results from higher fidelity multi-physics models. In this paper we investigate the role of instabilities in the core-collapse supernova environment. We present here simulation and visualization results produced by our code GenASiS.

astro-ph.IM↗

arXiv2015

GenASiS: General Astrophysical Simulation System. II. Nonrelativistic Hydrodynamics

In this paper, the second in a series, we document the algorithms and solvers for compressible nonrelativistic hydrodynamics implemented in GenASiS (General Astrophysical Simulation System)---a new code being developed initially and primarily, though by no means exclusively, for the simulation of core-collapse supernovae. In the Mathematics division of GenASiS we introduce Solvers, which includes finite-volume updates for generic hyperbolic BalanceEquations and ordinary differential equation integration Steps. We also introduce the Physics division of GenASiS; this extends the Manifolds division of Mathematics into physical Spaces, defines StressEnergies, and combines these into Universes. We benchmark the hydrodynamics capabilities of GenASiS against many standard test problems; the results illustrate the basic competence of our implementation, demonstrate the manifest superiority of the HLLC over the HLL Riemann solver in a number of interesting cases, and provide preliminary indications of the code's ability to scale and to function with cell-by-cell fixed-mesh refinement.

astro-ph.IM↗

arXiv2015

GenASiS: General Astrophysical Simulation System. I. Refinable Mesh and Nonrelativistic Hydrodynamics

GenASiS (General Astrophysical Simulation System) is a new code being developed initially and primarily, though by no means exclusively, for the simulation of core-collapse supernovae on the world's leading capability supercomputers. This paper---the first in a series---demonstrates a centrally refined coordinate patch suitable for gravitational collapse and documents methods for compressible nonrelativistic hydrodynamics. We benchmark the hydrodynamics capabilities of GenASiS against many standard test problems; the results illustrate the basic competence of our implementation, demonstrate the strengths and limitations of the HLLC relative to the HLL Riemann solver in a number of interesting cases, and provide preliminary indications of the code's ability to scale and to function with cell-by-cell fixed-mesh refinement.

astro-ph.IM↗

arXiv2013

Conservative 3+1 General Relativistic Variable Eddington Tensor Radiation Transport Equations

We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These equations are intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are the lab frame coordinate basis spacetime position coordinates and the particle energy measured in the comoving frame. With an eye towards astrophysical applications---such as core-collapse supernovae and compact object mergers---in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles are neutrinos, we pay special attention to the consistency of four-momentum and lepton number exchange between neutrinos and the fluid, showing the term-by-term cancellations that must occur for this consistency to be achieved.

astro-ph.HE↗

arXiv2013

Conservative 3+1 General Relativistic Boltzmann Equation

We present a new derivation of the conservative form of the general relativistic Boltzmann equation and specialize it to the 3+1 metric. The resulting transport equation is intended for use in simulations involving numerical relativity, particularly in the absence of spherical symmetry. The independent variables are lab frame coordinate basis spacetime position components and comoving frame curvilinear momentum space coordinates. With an eye towards astrophysical applications---such as core-collapse supernovae and compact object mergers---in which the fluid includes nuclei and/or nuclear matter at finite temperature, and in which the transported particles are neutrinos, we examine the relationship between lepton number and four-momentum exchange between neutrinos and the fluid.

astro-ph.HE↗

arXiv2012

Conservative Moment Equations for Neutrino Radiation Transport with Limited Relativity

We derive conservative, multidimensional, energy-dependent moment equations for neutrino transport in core-collapse supernovae and related astrophysical systems, with particular attention to the consistency of conservative four-momentum and lepton number transport equations. After taking angular moments of conservative formulations of the general relativistic Boltzmann equation, we specialize to a conformally flat spacetime, which also serves as the basis for four further limits. Two of these---the multidimensional special relativistic case, and a conformally flat formulation of the spherically symmetric general relativistic case---are given in appendices for the sake of comparison with extant literature. The third limit is a weak-field, `pseudo-Newtonian' approach \citep{kim_etal_2009,kim_etal_2012} in which the source of the gravitational potential includes the trace of the stress-energy tensor (rather than just the mass density), and all orders in fluid velocity $v$ are retained. Our primary interest here is in the fourth limit: `$\mathcal{O}(v)$' moment equations for use in conjunction with Newtonian self-gravitating hydrodynamics. We show that the concept of `$\mathcal{O}(v)$' transport requires care when dealing with both conservative four-momentum and conservative lepton number transport, and present two self-consistent options: `$\mathcal{O}(v)$-plus' transport, in which an $\mathcal{O}(v^2)$ energy equation combines with an $\mathcal{O}(v)$ momentum equation to give an $\mathcal{O}(v^2)$ number equation; and `$\mathcal{O}(v)$-minus' transport, in which an $\mathcal{O}(v)$ energy equation combines with an $\mathcal{O}(1)$ momentum equation to give an $\mathcal{O}(v)$ number equation.

astro-ph.SR↗