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At least 1,153 records · Page 64

Utah FORGE 3-2514: Strain Sensing Array for Deformation Characterization - 2024 Annual Workshop Presentation

This is a presentation on the Strain Sensing Array to characterize deformation at the FORGE site project by Clemson University, presented by Lawrence Murdoch. The project's objective was to evaluate the feasibility of measuring and interpreting tensor strain data to improve the performance of EGS. This presentation was featured in the Utah FORGE R&D Annual Workshop on August 23, 2024.

15 GEOTHERMAL ENERGY↗

A Low-Rank QTT-based Finite Element Method for Elasticity Problems

We present an efficient and robust numerical algorithm for solving the linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve the linear elasticity problem on a computational domain that is more general than a square. By integrating Z-ordering and subdomain concatenation, our method substantially decreases memory usage and achieves a notable reduction in rank compared to established Finite Element implementations like the FEniCS platform. This efficiency is maintained while still guaranteeing exponential convergence with respect to the number of degrees of freedom. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented. This includes changes to mesh discretization, node and degree of freedom ordering, stiffness matrix and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this work, we discuss all these aspects in detail and assess the method’s performance in the numerical approximation of three representative test cases.

97 MATHEMATICS AND COMPUTING↗

Comparison of DeePMD, MTP, GAP, ACE and MACE Machine‐Learned Potentials for Radiation‐Damage Simulations: A User Perspective

Accurate and efficient interatomic potentials are essential for molecular dynamics (MD) simulations of radiation damage, gas diffusion, and phase stability in complex ceramics such as LiAlO 2 , especially under extreme conditions relevant to tritium production. Here, we evaluate the performance of six machine-learned interatomic potentials (MLIPs), moment tensor potential (MTP), Gaussian approximation potential, deep potential (DeePMD), atomic cluster expansion (ACE), message-passing ACE (multilayer atomic cluster expansion (MACE) pretrained) and MACE (trained from-scratch), all trained on the same density functional theory dataset with inclusion of tritium. The MLIPs are benchmarked against traditional Buckingham and ReaxFF potentials in terms of energy accuracy, density predictions, thermal equilibration behavior, threshold displacement energy (E d ), tritium diffusivity, and computational cost. Among the models, MTP shows the best overall balance between efficiency and accuracy, with low force and energy errors and realistic E d values for Li and Al. The ACE and MACE (pretrained and trained from scratch) models exhibit high E d (>200 eV) and unphysical pair interactions. DeePMD underestimates Ed due to overly repulsive behavior even at equilibrium distances. All models over-estimate tritium diffusion but the pretrained MACE model behaves well during tritium-diffusion simulations up to 500 K, maintaining diffusivities in the physically consistent 10 −11 m 2 /s range. Finally, we quantify the computational cost of each potential in large-scale atomic/molecular massively parallel simulator, finding that only MTP is more efficient than traditional empirical potentials, while others are significantly more expensive. These findings explain the trade-offs between accuracy and computational cost in MLIP development and provide essential guidance for use in high-throughput radiation damage and gas diffusion simulations in nuclear ceramics.

74 ATOMIC AND MOLECULAR PHYSICS↗

Nanoscale lattice strains in self-ion implanted tungsten

Developing a comprehensive understanding of the modification of material properties by neutron irradiation is important for the design of future fission and fusion power reactors. Self-ion implantation is commonly used to mimic neutron irradiation damage, however an interesting question concerns the effect of ion energy on the resulting damage structures. The reduction in the thickness of the implanted layer as the implantation energy is reduced results in the significant quandary: Does one attempt to match the primary knock-on atom energy produced during neutron irradiation or implant at a much higher energy, such that a thicker damage layer is produced? In this work, we address this question by measuring the full strain tensor for two ion implantation energies, 2 MeV and 20 MeV in self-ion implanted tungsten, a critical material for the first wall and divertor of fusion reactors. A comparison of 2 MeV and 20 MeV implanted samples is shown to result in similar lattice swelling. Multi-reflection Bragg coherent diffractive imaging (MBCDI) shows that implantation induced strain is in fact heterogeneous at the nanoscale, suggesting that there is a non-uniform distribution of defects, an observation that is not fully captured by micro-beam Laue diffraction. At the surface, MBCDI and high-resolution electron back-scattered diffraction (HR-EBSD) strain measurements agree quite well in terms of this clustering/non-uniformity of the strain distribution. However, MBCDI reveals that the heterogeneity at greater depths in the sample is much larger than at the surface. This combination of techniques provides a powerful method for detailed investigation of the microstructural damage caused by ion bombardment, and more generally of strain related phenomena in micro-volumes that are inaccessible via any other technique.

36 MATERIALS SCIENCE↗

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp ( t H ) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. Here, we provide optimized decompositions up to order t 6 . The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Post-Newtonian kinetic theory

A kinetic theory for relativistic gases in the presence of gravitational fields is developed in the second post-Newtonian approximation. The corresponding Boltzmann equation is determined from the evolution of the one-particle distribution function with respect to the proper time along the world line of the particle. From the knowledge of the equilibrium Maxwell–Jüttner distribution function in the second post-Newtonian approximation the components of the particle four-flow and energy–momentum tensor are obtained. The Eulerian hydrodynamic equations for the mass density, mass-energy density and momentum density in the second post-Newtonian approximation are determined from the Boltzmann equation. It is shown that the combination of the hydrodynamic equations of mass and mass-energy densities leads to the hydrodynamic equation for the internal energy density in the first post-Newtonian approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Casimir effect in Very Special Relativity at finite temperature

Recently a great deal of interest in field theories formulated in a Lorentz violating framework has been developed. Here the Very Special Relativity (VSR) is considered. The main aspect in the VSR proposal is that laws of physics are invariant under the subgroups of the Poincaré group preserving the basic elements of special relativity. An important point is that the photon acquires a mass. In this context, the energy–momentum tensor for the electromagnetic field is calculated. From this, the Stefan–Boltzmann law and Casimir effect at finite temperature in VSR are obtained. The effects of temperature are introduced using the Thermo Field Dynamics (TFD) formalism. A comparative analysis with the Casimir effect for the standard electromagnetic case is developed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Anisotropy of localized states in an anisotropic disordered medium

Highlights: • Mobility edges of the Anderson transition are unaffected by anisotropy alone. • The critical exponent of the Anderson localization transition is also unaffected. • Anderson localized eigenstates in an anisotropic medium retain substantial anisotropy. • Their anisotropy is weaker than expected from purely geometric considerations. • Modes with the longest lifetimes are found to be the most anisotropic. We study Anderson localization of a scalar wave in an ensemble of resonant point scatterers embedded in an anisotropic background medium. For uniaxial anisotropy of moderate strength, the mobility edges and the critical exponent of the localization transition are found to be unaffected by the anisotropy provided that the determinant of the anisotropy tensor is kept equal to one upon introducing the anisotropy. Localized modes have anisotropic spatial shapes although their anisotropy is weaker than the one expected from purely geometric considerations. The modes with the longest lifetimes are found to be the most anisotropic and their anisotropy increases with the size of the disordered medium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gravity effects on Hawking radiation from charged black strings in Rastall theory

Highlights: • Introductory review of charged black strings in Rastall theory. • Detailed description of Hawking temperature. • Graphically Analysis of Hawking temperature. • Discuss the stability of charged black strings. The Rastall theory of gravity is the generalized form of the Einstein theory which describes the conservation law of energy and momentum tensor. In our work, we compute the charged black strings solution in the background of Rastall theory by applying the Newman–Janis approach. After computing the charged black strings solution in the background of Rastall theory, we study the thermodynamical property (i.e., Hawking temperature) for the charged black strings. Furthermore, we investigate the graphical representation of Hawking temperature via event horizon to check the stability conditions of charged black strings under the influence of Rastall theory. Moreover, we examine the modified Hawking temperature for charged black strings in Rastall theory by taking into account the quantum gravity effects. We also discuss the physical state of charged black strings under the effects of quantum gravity and spin parameter (appears due to Rastall theory in charged black strings solution).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quasinormal modes for non-minimally coupled scalar fields in regular black hole spacetimes: Grey-body factors, area spectrum and shadow radius

Black hole perturbation theory is a useful approach to study interactions between black holes and fundamental fields. A particular class of black hole solutions arising out of modification of Einstein’s general theory of relativity are regular black holes (RBHs) which can be constructed using a nonlinear electrodynamic Lagrangian. Because of their importance, we are interested in studying the behavior of three kinds of such RBHs under perturbations generated by an external field. Indeed, we investigate the quasinormal modes (QNMs) of a massive scalar field propagating near the RBHs which is non-minimally coupled to the Ricci scalar-tensor of background geometry. We will attempt to find the low-lying quasinormal frequencies of the perturbations by using WKB approximation. We shall also study the relationship between the QNMs and some characteristic properties of black holes such as grey-body factors, area quantization, and shadow radius.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Current-conserving relativistic linear response for collisional plasmas

Here we investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi–Dirac equilibrium distribution in terms of the average relaxation rate k. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on k. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for k >2ω p , where ω p is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, k$\ll$ ω p , the propagating plasma modes are weakly damped.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Restricting loop expansions in gauge theories coupled to matter

Highlights: • Lagrange multiplier fields are used to restrict radiative effects to one-loop order. • This approach is exemplified in the Yang-Mills theory coupled to a scalar matter field. • We showed that it can be used with the Einstein–Hilbert action coupled to matter. • The resulting quantum gravity theory is both renormalizable and unitary. Quantizing any model in which a Lagrange multiplier (LM) field is used to restrict field configurations to those that satisfy the classical equations of motion, leads to at most one-loop radiative corrections. This approach can be used with both the Yang–Mills (YM) and Einstein–Hilbert (EH) action; the resulting theory is both renormalizable and unitary, has a positive energy spectrum and has no negative norm states contributing to physical processes. Although this approach cannot be consistently used with scalar fields alone, scalar fields can be coupled to gauge fields so that loop effects in the gauge sector are restricted to one-loop order in a way that satisfies the usual criterion for a consistent quantum field theory. The tree-level diagrams are those of the classical theory in which the metric couples to the energy–momentum tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A low-rank solver for the stochastic unsteady Navier–Stokes problem

Here we study a low-rank iterative solver for the unsteady Navier–Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once formulation where the algebraic systems at all the time steps are collected and solved simultaneously. The problem is linearized with Picard’s method. To efficiently solve the linear systems at each step, we use low-rank tensor representations within the Krylov subspace method, which leads to significant reductions in storage requirements and computational costs. Combined with effective mean-based preconditioners and the idea of inexact solve, we show that only a small number of linear iterations are needed at each Picard step. The proposed algorithm is tested with a model of flow in a two-dimensional symmetric step domain with different settings to demonstrate the computational efficiency.

97 MATHEMATICS AND COMPUTING↗

Terahertz EPR spectroscopy using a 36-tesla high-homogeneity series-connected hybrid magnet

Electron Paramagnetic Resonance (EPR) is a powerful technique to study materials and biological samples on an atomic scale. High-field EPR in particular enables extracting very small g-anisotropies in organic radicals and half-filled 3d and 4f metal ions such as Mn II (3d 5 ) or Gd III (4f 7 ), and resolving EPR signals from unpaired spins with very close g-values, both of which provide high-resolution details of the local atomic environment. Before the recent commissioning of the high-homogeneity Series Connected Hybrid magnet (SCH, superconducting + resistive) at the National High Magnetic Field Laboratory (NHMFL), the highest-field, high-resolution EPR spectrometer available was limited to 25 T using a purely resistive “Keck” magnet at the NHMFL. Herein, we report the first EPR experiments performed using the SCH magnet capable of reaching the field of 36 T, corresponding to an EPR frequency of 1 THz for g = 2. The magnet’s intrinsic homogeneity (25 ppm, that is 0.9 mT at 36 T over 1 cm diameter, 1 cm length cylinder) was previously established by NMR. We characterized the magnet’s temporal stability (5 ppm, which is 0.2 mT at 36 T over one-minute, the typical acquisition time) using 2,2-diphenyl-1-picrylhydrazyl (DPPH). This high resolution enables resolving the weak g-anisotropy of 1,3-bis(diphenylene)-2-phenylallyl (BDPA), Δg = 2.5 × 10 –4 obtained from measurements at 932 GHz and 33 T. Subsequently, we recorded EPR spectra at multiple frequencies for two Gd III complexes with potential applications as spin labels. In conclusion, we demonstrated a significant reduction in line broadening in Gd[DTPA], attributed to second order zero field splitting, and a resolution enhancement of g-tensor anisotropy for Gd[sTPATCN]-SL.

47 OTHER INSTRUMENTATION↗

Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of φ $-$functions of matrices via quadrature

Here, in this article, we propose an algorithm for approximating the action of φ $-$ functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum structure, which arise from problems admitting a tensor product representation. The method is based on quadrature approximations of the integral form of the φ $-$ functions combined with a scaling and modified squaring method. Owing to the Kronecker sum representation, only actions of 1D matrix exponentials are needed at each quadrature node and assembly of the full matrix can be avoided. Additionally, we derive a priori bounds for the quadrature error, which show that, as expected by classical theory, the rate of convergence of our method is supergeometric. Guided by our analysis, we construct a fast and robust method for estimating the optimal scaling factor and number of quadrature nodes that minimizes the total cost for a prescribed error tolerance. We investigate the performance of our algorithm by solving several linear and semilinear time-dependent problems in 2D and 3D. The results show that our method is accurate and orders of magnitude faster than the current state-of-the-art.

97 MATHEMATICS AND COMPUTING↗

Adiabatic fast passage spin manipulation measurements in solid polarized targets

Adiabatic fast passage (AFP) is a rapid method for reversing nuclear polarization and manipulating spin populations in polarized solid targets, avoiding the long repolarization times associated with dynamic nuclear polarization (DNP). We report AFP measurements in a 5 T, 1 K polarized-target system for irradiated 15 NH 3 , irradiated 14 ND 3 , and butanol-based materials prepared either with TEMPO doping or by irradiation. We also present a joint manipulated-lineshape analysis for spin-1 targets and demonstrate that vector and tensor polarizations can be extracted from AFP-manipulated deuteron NMR spectra even when the populations are not described by a single Boltzmann spin temperature. In conclusion, we report a reproducible polarization- and direction-dependent AFP response in a large irradiated 15 NH 3 sample. These ammonia results are presented as empirical observations under the specific sample–coil conditions of the experiment, with possible circuit-mediated mechanisms such as radiation damping or superradiant behavior discussed but not assigned as a definitive cause.

Adiabatic fast passage↗

Planar, longitudinal, compressive waves in solids: Thermodynamics and uniaxial strain restrictions

A new tri-axial pressure-based constitutive expression has been found using Cauchy's stress tensor. This stress state emphasizes pressure and shear stress. The description is a pressure plus an effective shear stress allowing for a constitutive law based on atomic solid-state phase changes in crystalline cells due to pressure plus shear-based dislocation motion commonly associated with plasticity. Pressure has a new role in the material's constitutive response as it is separated from plasticity. The thermo-mechanical system describes third-order Gibbs’ expressions without specific volume restrictions placed upon the material. Isothermally, the ratio of heat to shear work in elastic copper is shown to approach zero at a very low temperature and become larger than one as temperature approaches melting. Wave compression models investigated are elastic and plastic: in fully elastic materials, the planar wave is restricted by Poisson's effect although plastic shear changes this constraint. Plastic deformation, dominated by dissipative shear stresses in uniaxial strain, heats the material while excluding phase changes from hydrostatic pressures. The material properties per se across Hugoniot shocks are described with entropy concepts. Shock waves are exceedingly complex since the constitutive laws are linked at extreme temperatures, pressures, and shear stresses. Isothermal, isentropic, isochoric, and iso-shear conditions are used throughout with Jacobian algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗