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DOE OSTI2021

Leading nonlinear tidal effects and scattering amplitudes

We present the two-body Hamiltonian and associated eikonal phase, to leading post-Minkowskian order, for infinitely many tidal deformations described by operators with arbitrary powers of the curvature tensor. Scattering amplitudes in momentum and position space provide systematic complementary approaches. For the tidal operators quadratic in curvature, which describe the linear response to an external gravitational field, we work out the leading post-Minkowskian contributions using a basis of operators with arbitrary numbers of derivatives which are in one-to-one correspondence with the worldline multipole operators. Explicit examples are used to show that the same techniques apply to both bodies interacting tidally with a spinning particle, for which we find the leading contributions from quadratic in curvature tidal operators with an arbitrary number of derivatives, and to effective field theory extensions of general relativity. We also note that the leading post-Minkowskian order contributions from higher-dimension operators manifest double-copy relations. Finally, we comment on the structure of higher-order corrections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗
DOE OSTI2022

Combining PCA and nonlinear fitting of peak models to re-evaluate C 1s XPS spectrum of cellulose

Cellulose is an example of a material that responds to XPS by the creation of new chemistry not present in the as-received sample. While improvements in instrumentation may be seen in general as beneficial to surface science, recent studies have shown that the consequences for some materials are detrimental. Here, in this work, these problems are illustrated through an analysis of cellulose spectra obtained during a degradation study. C 1s spectra are decomposed into two well-formed component curves that are open to chemical interpretation. In particular, a component-curve representative of pure cellulose is obtained as well as a second component curve that implies cellulose is degraded through the creation of carbon chemistry involving C—O, C$=$O and O—C$=$O. Since cellulose is a crystalline material, formed through the alignment of molecules under the influence of hydrogen bonds, the analysis and findings presented in this paper are relevant to any material analyzed by XPS whose properties are dependent on hydrogen bonds. The analysis techniques are based on an informed vectorial approach, which extracts directly from data spectral shapes that are used to monitor sample degradation via linear least squares optimization. Related mathematics of Principal Component Analysis and linear analysis are presented.

36 MATERIALS SCIENCE↗