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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗
DOE OSTI2024

Unidirectional amplification in the frozen mode regime enabled by a nonlinear defect

A stationary inflection point (SIP) is a spectral singularity of the Bloch dispersion relation ω(k) of a periodic structure where the first and the second derivatives of ω with respect to k vanish. An SIP is associated with a third-order exceptional point degeneracy in the spectrum of the unit-cell transfer matrix, where there is a collapse of one propagating and two evanescent Bloch modes. At the SIP frequency, the incident wave can be efficiently converted into the frozen mode with greatly enhanced amplitude and vanishing group velocity. This can be very attractive for applications, including light amplification. Due to its non-resonant nature, the frozen mode regime (FMR) has fundamental advantages over common cavity resonances. Furthermore, we propose, a novel, to the best of our knowledge, scheme for FMR-based unidirectional amplifiers by leveraging a tailored amplification/attenuation mechanism and a single nonlinear defect. The defect breaks the directional symmetry of the periodic structure and enables nonlinearity-related unidirectional amplification/attenuation in the vicinity of the SIP frequency. We demonstrate the robustness of the amplification mechanism to local impurities and parasitic nonlinearity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Stabilization of high-performance rock-salt LiMnSbTe3 thermoelectrics with embedded van der Waals-like gaps

Rock-salt-structured compounds like lead chalcogenides are promising thermoelectrics, as their high symmetry, strong anharmonicity, and favorable phase behavior collectively lead to high performance by enabling large power factors and ultralow thermal conductivity. Here, we report LiMnSbTe 3 , a new rock-salt semiconductor stabilized through targeted chemical design by combining hexagonal MnTe with cubic LiSbTe 2 . Embedded in the highsymmetry matrix, van der Waals-like gaps form due to Sb 2 Te 3 nanoscale segregation, which acts as effective phonon-scattering centers, leading to a low lattice thermal conductivity of 0.37Wm- 1 K -1 at 873 K with alloy scattering from disordered cations. The ordered local structure of Sb2Te 3 -type vdW-like gaps and the cross-gap interaction facilitate the carrier transport. Aided by energyconverged valence bands and a paramagnon drag effect, high Seebeck coefficients and enhanced power factor can be achieved, leading to a high ZT of 1.2 at 873 K. Furthermore, introducing Mn deficiency increases ZT to 1.5, highlighting the potential for higher performance through optimized doping or alloying. A segmented single-leg thermoelectric module achieves an output power density of 0.52 Wcm -2 and an efficiency of 8.7% under ΔT of 478 K, further demonstrating its promising thermoelectric applications.

42 ENGINEERING↗
DOE OSTI2024

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Analytical and EZmock covariance validation for the DESI 2024 results

The estimation of uncertainties in cosmological parameters is an important challenge in Large-Scale-Structure (LSS) analyses. For standard analyses such as Baryon Acoustic Oscillations (BAO) and Full-Shape two approaches are usually considered. First: analytical estimates of the covariance matrix use Gaussian approximations and (nonlinear) clustering measurements to estimate the matrix, which allows a relatively fast and computationally cheap way to generate matrices that adapt to an arbitrary clustering measurement. On the other hand, sample covariances are an empirical estimate of the matrix based on an ensemble of clustering measurements from fast and approximate simulations. While more computationally expensive due to the large amount of simulations and volume required, these allow us to take into account systematics that are impossible to model analytically. In this work we compare these two approaches in order to enable DESI's key analyses. We find that the configuration space analytical estimate performs satisfactorily in BAO analyses and its flexibility in terms of input clustering makes it the fiducial choice for DESI's 2024 BAO analysis. On the contrary, the analytical computation of the covariance matrix in Fourier space does not reproduce the expected measurements in terms of Full-Shape analyses, which motivates the use of a corrected mock covariance for DESI's 2024 Full Shape analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Semi-inclusive deep-inelastic scattering on a polarized spin-1 target. I. Cross section and spin observables

We develop the theoretical framework for semi-inclusive deep-inelastic scattering on a polarized spin-1 target and apply it to scattering on the polarized deuteron with spectator nucleon tagging. In Part I (this article) we present the general form of the semi-inclusive cross section and polarization observables for the spin-1 target. A relativistically covariant formulation in terms of four-vectors and invariant polarization parameters is employed. The target polarization is described by a spin density matrix with vector and tensor polarization. The spin and azimuthal angle dependence of the semi-inclusive cross section is derived and parametrized in terms of invariant structure functions. To validate the result, the structure functions are expressed as photon-target helicity amplitudes with known symmetry properties. The expressions presented here are kinematic (no assumptions about particle production dynamics) and valid in all regions of the deep-inelastic final state (current and target fragmentation regions). In Part II (following article), we consider deep-inelastic scattering on the polarized deuteron with spectator nucleon tagging as a special case of target fragmentation. The semi-inclusive structure functions are computed by separating nuclear and hadronic structure, and the polarization observables are explored as functions of the tagged nucleon momentum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Detector alignment for X-ray crystallography using Millepede-II

I describe a method for accurately refining the geometrical parameters of segmented X-ray area detectors on the basis of serial crystallography data, using 'Millepede' – an algorithm created for a very similar problem in high-energy physics. The Millepede method for serial crystallography builds on the approach of Brewster et al. [Acta Cryst. (2018), D74, 877–894], in which the detector parameters are refined simultaneously with the parameters for each individual crystal. This accounts for the mutual dependency between the parameters and thereby avoids the bias and slow convergence problems that have afflicted older approaches in which the deviations between observed and calculated Bragg peak positions were taken directly as the updates for the detector panel positions. The Millepede method uses the special structure of the least-squares normal equations to reduce them to a much smaller form that can be solved very quickly, even compared with the sparse matrix methods used previously. This makes it practical to refine the detector geometry frequently and thereby maintain accurate calibration without specialized alignment campaigns. Tilts of detector panels out of the plane can be reliably refined, as can the overall distance of the detector in the beam direction. With a simulated test case, the new method produced panel shifts within 7% of the correct values with only one iteration, and produced almost exactly correct shifts after a second iteration. A simulated out-of-plane panel rotation was correctly determined to within 0.001°. Applied to experimental data from an X-ray free-electron laser, the method increased the indexable fraction of frames from 30% to 91% in a single iteration, and to 96% after two further iterations. Computing the geometry updates on the basis of 2060 crystals took only 0.819 s on desktop computing hardware, including the time taken to read the required data from disk. The scaling was found to be very close to linear for up to 100 980 sets of crystal parameters, which took only 78.2 s to process under the same conditions. The method has been applied as part of a real-time feedback system at a synchrotron radiation beamline, in which an out-of-plane detector tilt of 0.04° was detected and corrected. Possible further applications are also described here.

Millepede-II↗
DOE OSTI2026

Fundamentals of Solar PV Bolted Joint Loosening and Prevention

The photovoltaic (PV) industry has long reported anecdotal accounts of systems exhibiting intermittent or chronic fastener loosening, including joints that fail to maintain preload despite multiple re-tightening attempts. These occurrences are frequently, and often incorrectly, attributed to installer errors, vibration, or loading beyond design expectations (e.g., extreme weather events). Loose fasteners have serious implications and can significantly impact solar PV systems’ performance, reliability, and safety. However, effective bolted joint design and proper assembly practices can mitigate or eliminate loosening. Until the US Department of Energy’s Solar Energy Technologies Office (SETO) funded research on fasteners and solar PV structures, there was a notable gap in understanding the causes of loosening in solar PV systems.

14 SOLAR ENERGY↗
DOE OSTI2025

Damage progression and failure of SiC/SiC composite tubes under hard-contact radial expansion

The response of silicon carbide (SiC) fiber-reinforced SiC matrix (SiC/SiC) composite cladding to mechanical interaction with fissile fuel is a knowledge gap that must be overcome to design and assess SiC-based cladding systems for advanced nuclear applications. This study developed the relevant mechanical testing capability and identified the failure behavior and the critical microstructural features and processing defects. Sections of SiC composite tube were subjected to a modified expansion-due-to-compression (EDC) test in an X-ray computed tomography microscope: a polyurethane plug pressed surrogate Al 2 O 3 into the inner walls of the SiC/SiC composite tubes to achieve hard contact. A pure EDC test with just a polyurethane plug was also performed as a reference. Through the use of displacement fields, digital volume correlation revealed inhomogeneous deformation fields in the tubes, even for pure EDC, which was related to the inherent defects in the structure. Deep learning–aided segmentation and systematic data analysis revealed that the presence of inhomogeneous deformation applied by the hard contact was exaggerated by the presence of inner surface imperfections left behind from the matrix densification process. In conclusion, the findings provide insights into the applications, highlighting the necessity for improvements in inner surface roughness and the incorporation of localized contacts in pellet–cladding mechanical interaction computational models.

Composites↗
DOE OSTI2025

Structural and Dynamical Insights into the Formation Process of a Cross-Linked Polymer Network in Acrylic Adhesives During Thermal Curing

Many modern adhesives, sealants, and coatings rely on the controlled transition from a liquid to a solid state by forming a three-dimensional cross-linked polymer network, often referred to as curing. The curing process, which is initiated by the mixing of reactive components or an external trigger, defines the structure of a network and further controls the final mechanical properties of cured materials. However, the curing mechanism is not fully understood yet due to the lack of experimental tools capable of directly probing the structure and dynamics of a network over relevant time- and length scales. Here, in this paper, we report the curing process of a commercial two-component methyl methacrylate (MMA) adhesive using in operando X-ray photon correlation spectroscopy (XPCS), a method that closely simulates the target manufacturing environment of the adhesive. The results are then integrated with those obtained by rheology, differential scanning calorimetry (DSC), and transmission electron microscopy to establish the structure–dynamics–process–property relationship. The XPCS results identify four distinct stages in the curing process after the mixing, extrusion, and deposition of the acrylic adhesive: (i) At a cure time (or “aging time”, t age ) of less than 1 min, nanodomains of polymerized MMA are formed within a liquid monomeric MMA matrix. The average size is several nm and remains constant over t age , while the dynamics of the nanodomains are slowed down with t age due to an increase in the viscosity of the MMA matrix. (ii) After t age > 1 min, the size of the nanodomains increases with t age until the gel point (= 6.3 min after mixing as determined by rheology). The dynamics of the nanodomains also increase due to the heat generated by the exothermic reaction. (iii) At the gel point, the nanodomains begin to interconnect each other, resulting in a network structure with a characteristic length of about 100 nm. This characteristic network size does not change for the rest of the curing process up to t age = 500 min. The dynamics of the network structure, however, show a rapid slowing down with t age up to t age ≈ 12 min, corresponding to the onset of vitrification (as determined by rheology). (iv) At t age > 12 min, when the DSC and rheology data can no longer provide meaningful information, the XPCS data show a further slowing down of the network dynamics associated with vitrification. Our results provide rich and complex insights into the physics and material design of thermosets in commercially relevant processes, which are essential for future industrial applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Direct ink writing of shear exfoliated two-dimensional nanomaterial- elastomeric multifunctional nanocomposite

Direct ink writing (DIW) of polymer nanocomposites with high loadings of two-dimensional (2D) nanofillers (graphene and hexagonal boron nitride (hBN)) is challenging because of potential clogging, use of hazardous solvents, and agglomeration. Here, in this work, a shear exfoliation and sieving method to prepare DIW ink with high loading of nanofillers produced from low-cost bulk layered materials such as graphite and bulk hBN powder for successful DIW printing without the use of any solvents, binders, or plasticizers. The single-step exfoliation technique resulted in a composite with substantial layer reduction along the c-axis, as confirmed by SEM, TEM, XRD, and Raman analysis. Incorporating exfoliated graphene (40 wt%) increased viscosity by ∼6 orders of magnitude due to enhanced particle–matrix interactions, leading to pronounced yield stress behavior and a yield stress of approximately 1598 Pa, which enabled excellent shape retention during extrusion. Using the DIW technique, porous structures such as desalination membranes, self-sensing bone scaffolds, thermal management coating, and serpentine strain sensors were fabricated. When tested in a direct contact membrane distillation setup, the fabricated membrane demonstrated a promising permeate flux of 21.85 Lm −2 h −1 and a salt rejection of 74.3 %. The fabricated serpentine sensor exhibited stable signal variations under cyclic tensile loading, with a working range of 0–200 % strain and a maximum gauge factor of 43,735. A cell culture test using the printed bone scaffold demonstrated promising cell attachment and proliferation. The DIW printed hBN nanocomposite exhibited reversible shape change under heat, demonstrating potential 4D printing capability and efficient thermal management when exposed to high heat or flame.

Desalination↗
DOE OSTI2024

X-ray scattering based scanning tomography for imaging and structural characterization of cellulose in plants

X-ray and neutron scattering have long been used for structural characterization of cellulose in plants. Due to averaging over the illuminated sample volume, these measurements traditionally overlooked the compositional and morphological heterogeneity within the sample. Here, a scanning tomographic imaging method is described, using contrast derived from the X-ray scattering intensity, for virtually sectioning the sample to reveal its internal structure at a resolution of a few micrometres. This method provides a means for retrieving the local scattering signal that corresponds to any voxel within the virtual section, enabling characterization of the local structure using traditional data-analysis methods. This is accomplished through tomographic reconstruction of the spatial distribution of a handful of mathematical components identified by non-negative matrix factorization from the large dataset of X-ray scattering intensity. Joint analysis of multiple datasets, to find similarity between voxels by clustering of the decomposed data, could help elucidate systematic differences between samples, such as those expected from genetic modifications, chemical treatments or fungal decay. The spatial distribution of the microfibril angle can also be analyzed, based on the tomographically reconstructed scattering intensity as a function of the azimuthal angle.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Calculation of ion–ion mutual neutralization rate constants using Landau–Zener theory coupled with trajectory simulations for Ar + –Cl − , Br − , I −

In this computational study, we self-consistently calculate the rate constants of mutual neutralization reactions by incorporating the electron transfer probability, using Landau–Zener state transition theory with inputs derived from ab initio quantum chemistry calculations, into classical trajectory simulations. Electronic structure calculations are done using correlation consistent basis sets with multi-reference configuration interaction to map all the molecular electronic states below the ion-dissociation limit as a function of the distance between the reacting species. Our electronic structure calculations have been significantly improved from our previous work through improved selection of molecular electronic configurations maintaining a fine grid of 1a 0 over a wide range of bond lengths and accurate treatment of spin–orbit couplings. Non-adiabatic coupling matrix elements are calculated with the three-point central difference method near each avoided crossing to estimate the exact crossing point R x and coupling parameter H if , which are inputs to the multi-channel Landau–Zener theory to calculate the electron transition probability. Our approach is applied to estimate the mutual neutralization rate constants for the following ion pairs: Ar + –Cl − , Ar + –Br − , Ar + –I − at ∼133 Pa. Furthermore, our predictions are compared against the experimental data reported. It is seen that the improvement in the electronic structure calculation results in excellent agreement between the simulation results and the available experimental data to within a factor of ∼2 or ∼±50%.

Complete-active space self-consistent field↗
DOE OSTI2024

Structure of Low-spin States in \(^{45}\)Sc Studied via Coulomb Excitation

The electromagnetic structure of 45 Sc at low excitation energy was investigated via low-energy Coulomb excitation at the Heavy Ion Laboratory (HIL) of the University of Warsaw and at the Inter-University Accelerator Centre (IUAC) in New Delhi. A set of reduced E2, E3, and M1 matrix elements was extracted from the collected data using the GOSIA code. The reduced transition probability B(E2; 11/2 – → 7/2 – ) has been determined, allowing us to deduce the lifetime of the 11/2 – state at 1237 keV. In addition, the upper limit on the reduced transition probability B(E3; 7/2 – → 5/2 + ) has been determined for the first time. Finally, new large-scale shellmodel and beyond-mean-field calculations were performed to interpret the structure of this nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Towards exact finite temperature electronic structure in solids and molecules (Final Technical Report)

This report describes the University of Iowa portion of a project that is now continuing at Michigan State University. We are developing novel methods, algorithms, and software to enable simulations of molecules and materials at high temperature. This is a key challenge in chemistry and materials science. By refining an approach called Density Matrix Quantum Monte Carlo (DMQMC), we developed faster and more accurate ways to conduct these simulations. These advances will help us understand how temperature affects the behavior of electrons, chemical bonds, and phase transitions in solids and molecules. These breakthroughs are especially important for applications where light and heat drive chemical reactions, superconductivity, and materials used in energy and sensing. In addition, this project involved the development of the open-source HANDE-QMC software package, supporting the broader community in benchmarking and developing finite-temperature electronic structure methods.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Interface instabilities in hafnium hydride entrained iron metal matrix composites

The chemical interactions in Fe–HfH 2 metal matrix composites (MMCs) are studied across multiple length scales to elucidate the decomposition of the parent phases and corresponding reaction zone physics during direct current sintering. Fe–HfH 2 composites were synthesized with increasing as-mixed hydride contents of Fe–25% HfH 2 , Fe–40% HfH 2 , Fe–55% HfH 2 , and Fe–70% HfH 2 (all in vol. %) to demonstrate the ability to achieve sintered MMCs with target hydride contents. Samples were probed across multiple length scales through a multi-modal workflow employing x-ray diffraction, scanning electron microscopy and segmentation analysis, and synchrotron techniques including hard x-ray fluorescence mapping and nanoprobe x-ray absorption near-edge structure measurements. Under the selected sintering temperature and pressure conditions, hydrogen evolution is seen to evolve through parallel paths: thermal decomposition from during the transformation of HfH 2 to HfH x<2 and through subsequent reaction with the Fe matrix leading to intermetallic phase formation. Specifically, HfFe and HfFe 2 intermetallic formation accelerates the release of hydrogen with a subsequent HfO 2 phase forming at grain boundaries. For this MMC, the consumption or loss of hydrogen can be considerable in compacts with initial hydride loading of 25%–40% HfH 2 approaching 83% hydrogen loss for the lower volume fraction composites. Increasing the volume fraction of HfH 2 to 70% enhanced the retained hydrogen content to 53% and attributed to the reduced interfacial area intrinsic to the increased HfH 2 loading in this MMC.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Quantum entropy as a harbinger of factorizability

Deeply inelastic scattering (DIS) is a powerful probe for investigating the QCD structure of hadronic matter and testing the standard model (SM). DIS can be described through QCD factorization theorems which separate contributions to the scattering interaction arising from disparate scales — e.g ., with nonperturbative matrix elements associated with long distances and a perturbative hard scattering kernel applying to short-distance parton-level interactions. The fundamental underpinnings of factorization may be recast in the quantum-theoretic terms of entanglement, (de)coherence, and system localization in a fashion which sheds complementary light on the dynamics at work in DIS from QCD bound states. In this Letter, we propose and quantitatively test such a quantum-information theoretic approach for dissecting factorization in DIS and its domain of validity; we employ metrics associated with quantum entanglement such as a differential quantum entropy and associated Kullback-Leibler (KL) divergences in numerical tests. We deploy these methods on an archetypal quark-spectator model of the proton, for which we monitor quantum decoherence in DIS as underlying model parameters are varied. On this basis, we demonstrate quantitatively how factorization-breaking effects may be imprinted on quantum entropies in a kinematic regime where leading-twist factorization increasingly receives large corrections from finite- Q 2 effects; our findings suggest potential applications of quantum simulation to QCD systems and their interactions.

Deep inelastic scattering↗