arXiv subjects

Pierson Guthrey

Publications and source records attributed to Pierson Guthrey.

5 recordsLinked to original sources

arXiv2026

A Local Macroscopic Conservative Low-Rank Discontinuous Galerkin Method for the Vlasov-Poisson Equation with Dougherty-Fokker-Planck Collisions

In this paper, we construct a low-rank, structure preserving discontinuous Galerkin (DG) method to simulate the Vlasov-Poisson (VP) system coupled with the Dougherty Fokker-Planck (DFP) collision operator. When Coulomb collisions occur in dense or weakly-collisional plasmas, electrons get pushed to a low-rank steady state. In many cases, the plasma arrives to this steady state quickly, meaning that for most of the run-time, the plasma consists mainly of numerical low-rank structures. Our new low-rank scheme is constructed to exploit these numerical low-rank structures to greatly reduce the needed storage complexity of simulations for the VP-DFP system. It is constructed as an extension of the previously established Local Macroscopic Conservative (LoMaC) method by incorporating Coulomb collisions into the system. The LoMaC property ensures local conservation of macroscopic mass, momentum, and energy at the discrete level. Details of the new method are discussed in this paper. Numerical experiments are performed to show the efficacy of the method.

math.NA↗

arXiv2026

Tensor Train Representation of High-Dimensional Unsteady Flamelet Manifolds

This study, for the first time, investigates the use of tensor trains (TTs) to represent high-dimensional unsteady flamelet progress variable (UFPV) manifolds in chemically reacting computational fluid dynamics (CFD). The UFPV framework captures the thermochemical state of reacting flows using a reduced set of parameters and pre-computed manifolds, avoiding the need to transport all species or solve large stiff reaction systems. High-dimensional manifolds enhance accuracy by resolving coupled thermochemical effects critical in high-speed reacting flows but impose substantial memory demands. Here, a five-dimensional UFPV manifold is constructed and stored in the TT format to address this limitation. Several chemical mechanisms and table sizes are examined to evaluate TT compression performance and accuracy. The TT representation achieves significant memory reduction while preserving manifold fidelity and combustion behavior. A one-dimensional reacting-flow case using the discontinuous Galerkin (DG)-based JENRE Multiphysics Framework confirms that TT-compressed manifolds are interchangeable with standard UFPV tables. In addition to memory reduction, benchmark tests show that TT-based manifold sampling can achieve up to 2.4X speedup relative to dense tensor evaluation. Although demonstrated for UFPV combustion models, the proposed TT framework is broadly applicable to other tabulation-based combustion methodologies and provides a scalable alternative to machine learning (ML)-based approaches for representing high-dimensional combustion manifolds.

physics.comp-ph↗

arXiv2026

Efficient SN-like and PN-like Dynamic Low Rank methods for Thermal Radiative Transfer

Dynamic Low Rank (DLR) methods are a promising way to reduce the computational cost and memory footprint of the high-dimensional thermal radiative transfer (TRT) equations. The TRT equations are a system of nonlinear PDEs that model the energy exhchange between the material temperature and the radiation energy density; due to their high dimensionality, solving the TRT equations is often bottleneck in multi-physics simulations. DLR methods represent the solution in terms of time-evolving SVD-like factors of angle and space. Although previous work has explored DLR methods for TRT, most of the methods have limitations that make them impractical for realistic scenarios and uncompetitive with current non-DLR production codes. Here we develop new PN-like and SN-like Dynamic Low Rank (DLR) methods for TRT. In the SN-like DLR method, we use the time-evolving angular basis functions to select time-evolving angles; this DLR formulation enables us to use the highly optimized SN transport sweep as our main computational kernel, and results in a practical way of leveraging low-rank methods in production TRT codes. In contrast, our PN-like DLR method uses an even-parity formulation and results in positive-definite linear systems to solve for each time step. We demonstrate the methods on several challenging, highly heterogenous problems in two spatial dimensions $(4$D) that these DLR schemes can give significant reduction in angular artifacts (``ray effects'') with the same cost as gold-standard SN methods.

math.NA↗

arXiv2025

Tensor Networks for Liquids in Heterogeneous Systems

Many-body correlations in strongly coupled liquids and plasmas are critical for many applications in nanofluids, biology, and fusion-related plasma physics, but their description in fully heterogeneous environments remains challenging due to the high-dimensional equations involved. Recently, tensor network decompositions have emerged as powerful tools for tackling such equations by reducing memory usage and computational complexity. In this paper, we solve for equilibrium density and density-density correlation functions of liquids in confined heterogeneous environments using tensor network methods. We demonstrate that these functions admit high compression when their lengthscale dependence is encoded via quantized tensor trains or when their spatial-coordinate dependence is represented in standard tensor-train format, but not with respect to their dependence on distinct particle coordinates.

physics.comp-ph↗

arXiv2014

Atomic form factor for twisted vortex photons interacting with atoms

The relatively new atomic form factor for twisted (vortex) beams, which carry orbital angular momentum (OAM), is considered and compared to the conventional atomic form factor for plane wave beams that carry only spin angular momentum (SAM). Since the vortex symmetry of a twisted photon is more complex that that of a plane-wave, evaluation of the atomic form factor is also more complex for twisted photons. On the other hand, the twisted photon has additional parameters, including the OAM quantum number, $\ell$, the nodal radial number, $p$, and the Rayleigh range, $z_R$ that determines the cone angle of the vortex. This Rayleigh range may be used as a variable parameter to control, in new ways, the interaction of twisted photons with matter. Here we address: i) normalization of the vortex atomic form factor, ii) displacement of target atoms away from the center of the beam vortex, and iii) formulation of transition probabilities for a variety of photon-atom processes. We attend to features related to new experiments that can test the range of validity and accuracy of calculations of these variations of the atomic form factor. Using the absolute square of the form factor for vortex beams, we introduce a vortex factor that can be directly measured.

quant-ph↗