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DOE OSTI2025

Molecular Origin of Nanoscale Anion Ordering of LiTFSI Electrolytes Revealed through SAXS/WAXS and Molecular Dynamics Simulations

Recent developments in “water-in-salt” electrolytes have precipitated a renewed effort to study imide-based electrolytes. While previous small-/wide-angle X-ray scattering (SAXS/WAXS) studies have attributed the emergence of a low-Q peak in the SAXS profile of aqueous LiTFSI electrolytes to nanometer-scale anion clustering, a molecular-level understanding of the root of these clusters remains unclear. Here, in this study, we combined molecular dynamics simulations and SAXS/WAXS to study the solvation structures of LiTFSI in acetonitrile, methanol, and water. We concluded that hydrogen bonding in water and MeOH stabilizes anion clusters, while nonpolar methyl groups on methanol and acetonitrile interrupt the nanoscale ordering of TFSI anions. This causes LiTFSI in water and MeOH electrolytes to exhibit two low-Q SAXS profile peaks while LiTFSI in acetonitrile exhibits only a single peak below Q = 1 Å –1 . These findings shed light on the underlying molecular origins of nanoscale anion clusters, which may help in the design of the next generation of electrolyte chemistries.

Trojanowski, Lucas [Univ. of Michigan, Ann Arbor, ↗

DOE OSTI2025

Porous and Amorphous Mn x Mo 3 S 13 Chalcogel Electrode for High-Capacity Conversion-Based Lithium-Ion Batteries

While Li-ion batteries (LIBs) are a leading energy storage technology, their energy densities are limited by the low capacity of conventional intercalation cathodes, driving interest in high energy-density Li–S batteries that make use of conversion chemistry. Achieving high capacity, reversibility, and cycle stability, and controlling volume changes in conversion batteries during the charge–discharge process, however, remains challenging. Here, in this study, we present a porous, amorphous, sulfide-based Mn x Mo 3 S 13 chalcogel, which concurrently offers high capacity and cycle stability. The solution-processable room temperature synthesized Mn x Mo 3 S 13 (x = 0.25) chalcogel exhibits a local structure that resembles the Mo 3 S 13 cluster with Mn 2+ distributed across the Mo 3 S 13 matrix, as determined by synchrotron X-ray pair distribution function (PDF) and extended X-ray absorption fine structure (EXAFS). Ab initio molecular dynamics (AIMD) simulations reveal that Mn 2+ incorporation shortens the polysulfide chain in the gel matrix compared to the Mo 3 S 13 chalcogel, while forming a coordination environment with disulfide groups, analogous to the experimental findings. A Li/Mn 0.25 Mo 3 S 13 half-cell delivers 897 mAh g –1 capacity during the first discharge and retains 571 mAh g –1 capacity after 100 cycles at a C/3 rate. Distribution of relaxation time (DRT) unveils a stable solid–electrolyte interphase (SEI) formation upon cycling that enables charge–discharge reversibility. Here, the enhanced capacity retention and cycle stability compared to those of the Li/Mo 3 S 13 cell are attributed to the reduced dissolution of active mass into the electrolyte, facilitated by the formation of shorter polysulfide chains within the Mn 0.25 Mo 3 S 13 structure and the strong affinity of Lewis-acidic Mn 2+ for polysulfide anions generated during the charge–discharge process of the Li/Mn 0.25 Mo 3 S 13 cell. Thus, this work illustrates a design principle of material for high-capacity and cycle-stable Li-metal sulfide batteries.

25 ENERGY STORAGE↗

DOE OSTI2025

Simulating Marine Ecosystem Dynamics and Biogeochemical Cycling With Multiple Plankton Functional Types

Current representations of marine ecosystems in Earth System Models are greatly simplified, neglecting key interactions between dynamic food webs, biogeochemistry, and climate change. We use the Marine Biogeochemistry Library code base within the Community Earth System Model 2.2.2 to create an expanded ecosystem model with eight phytoplankton groups and four zooplankton size classes (MARBL-8P4Z). Incorporating more specific plankton types and size classes has the potential to capture a wider range of possible behaviors of the ecosystem, its complex interactions with biogeochemistry, and its feedback to climate change. It also permits stronger observational constraints, including in situ group-specific biomass and various observational estimates of plankton community composition. MARBL-8P4Z broadly captures observed global-scale patterns in biomass and community composition for both phytoplankton and zooplankton, with a good performance in simulating broad biogeochemistry fields. The model shows comparable spatial patterns and magnitudes to the observed picophytoplankton biomass (Prochlorococcus, Synechococcus, picoeukaryotes), and captures the seasonal cycle of mesozooplankton biomass. Picophytoplankton groups and microzooplankton dominate biomass and production in oligotrophic, subtropical regions, while nano-phytoplankton, diatoms and the larger zooplankton groups prevail at higher latitudes and within upwelling zones. The model simulates reasonable energy transfer efficiency through the food web, with tight linkages between the phytoplankton community composition, zooplankton grazing, and carbon export, with the potential to link to fisheries models. Thus, MARBL-8P4Z has the potential to account for key climate-driven ecological shifts in the plankton that will modify ocean biogeochemistry in the future.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Asymmetric drift in MaNGA: mass and radially dependent stratification rates in galaxy discs

ABSTRACT We measure the age–velocity relationship from the lag between ionized gas and stellar tangential speeds in ∼500 nearby disc galaxies from MaNGA in Sloan Digital Sky Survey IV (SDSS-IV). Selected galaxies are kinematically axisymmetric. Velocity lags are asymmetric drift, seen in the Milky Way’s (MW) solar neighbourhood and other Local Group galaxies; their amplitude correlates with stellar population age. The trend is qualitatively consistent in rate ($\dot{\sigma }$) with a simple power-law model where σ ∝ tb that explains the dynamical phase-space stratification in the solar neighbourhood. The model is generalized based on disc dynamical times to other radii and other galaxies. We find in-plane radial stratification parameters σ0,r (dispersion of the youngest populations) in the range of 10–40 km s−1 and 0.2 < br < 0.5 for MaNGA galaxies. Overall, brincreases with galaxy mass, decreases with radius for galaxies above 10.4 dex (M⊙) in stellar mass, but is ∼constant with radius at lower mass. The measurement scatter indicates the stratification model is too simple to capture the complexity seen in the data, unsurprising given the many possible astrophysical processes that may lead to stellar population dynamical stratification. None the less, the data show dynamical stratification is broadly present in the galaxy population, with systematic trends in mass and density. The amplitude of the asymmetric drift signal is larger for the MaNGA sample than the MW, and better represented in the mean by what is observed in the discs of M31 and M33. Either typical discs have higher surface-density or, more likely, are dynamically hotter (hence thicker) than the MW.

Bershady, Matthew A. (ORCID:0000000231314374)↗

DOE OSTI2025

Controlled Reaction Dynamics of Binary Hexafluorides to Explore New Chemical Signatures

Conclusions • Successfully halted the UF6 hydrolysis reaction and trapped intermediate complexes • Simple alcohol instead of water leads to shifting of bands in UF6 likely from change in matrix effects • MoF6 reaction shows some potential for methyl group being present in structure of intermediates • Future work with bulkier R-groups will hopefully reveal further information as to the reaction pathway and intermediate structure via kinetics and peak shifting

Dorris, Austin L. [Savannah River National Laborat↗

DOE OSTI2026

Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems

Here, we present a perspective on recent progress in machine-learning (ML) force-field approaches for large-scale Landau–Lifshitz–Gilbert (LLG) simulations of metallic spin systems. Building on a generalization of the Behler–Parrinello (BP) architecture originally developed for quantum molecular dynamics, we develop scalable and transferable ML models that faithfully capture the complex, environment-dependent electron-mediated exchange fields characteristic of itinerant magnets. A central ingredient of this framework is the implementation of symmetry-aware magnetic descriptors based on group-theoretical bispectrum formalisms. Leveraging these ML force fields, LLG simulations faithfully reproduce hallmark non-collinear magnetic orders—such as the 120° and tetrahedral states—on the triangular lattice, and successfully capture the complex spin textures emerging in the mixed-phase states of a square-lattice double-exchange model under thermal quench. We further discuss a generalized potential theory that extends the BP formalism to incorporate both conservative and nonconservative electronic torques, thereby enabling ML models to learn nonequilibrium exchange fields from computationally demanding microscopic approaches such as nonequilibrium Green’s-function techniques. This extension yields quantitatively accurate predictions of voltage-driven domain-wall motion and establishes a foundation for quantum-accurate, multiscale modeling of nonequilibrium spin dynamics and spintronic functionalities.

Descriptors↗

DOE OSTI2024

An improved stochastic weighted particle method for boundary driven flows

Here, the stochastic weighted particle method (SWPM) is a generalization of the Direct Simulation Monte Carlo (DSMC) method where particle weights are variable and dynamic. SWPM is backed by a strong theoretical foundation but has not been critically evaluated for problems of practical interest. A thorough assessment of SWPM for boundary-driven flows reveals significant numerical artifacts near the boundary, notably a diverging heat flux. To correct the boundary heat flux, two modifications to SWPM are proposed: separated grouping and a spatially-dependent weight transfer function. To gauge the relative efficiency of SWPM in comparison to DSMC, a high-Mach-number wheel flow which forms a strong density gradient is also simulated.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Missing baryons recovered: A measurement of the gas fraction in galaxies and groups with the kinematic Sunyaev-Zel’dovich effect and CMB lensing

We present new constraints on the halo masses and matter density profiles of DESI galaxy groups by cross-correlating samples of luminous red galaxies (LRGs) and bright galaxy survey (BGS) galaxies with the publicly available CMB lensing convergence map from ACT DR6. This provides an independent, lensing-based calibration of halo masses, complementary to methods relying on clustering or dynamics. We derive constraints on the mean halo mass for three DESI-selected samples, finding log⁡(𝑀 halo /(𝑀 ⊙ /ℎ)) ≈ 13.18, 13.03 and 13.02 for the main LRG, extended LRG, and BGS samples, respectively. Using a halo model approach, we also compare the projected galaxy-matter density profiles with previously reported gas profiles inferred from measurements of the kinematic Sunyaev-Zel’dovich (kSZ) effect. This work addresses one of the key uncertainties in interpreting kSZ signals—the unknown host halo mass distribution—by providing an independent and consistent mass calibration. The agreement between the gas and total mass profiles at large aperture suggests that sufficiently far from the group center (2–3 virial radii), we recover all the baryons, offering a resolution to the missing baryon problem. We further study the cumulative gas fractions for all galaxies as well as for the most massive galaxy groups in the sample [log⁡(𝑀 halo /(𝑀 ⊙ /ℎ)) ≈ 13.5], finding values that are physically sensible and in agreement with previous findings using kSZ and x-ray data: compared to the TNG300 simulation, the observed gas fractions are systematically lower at fixed radius by ≳ 4⁢𝜎, providing compelling, independent evidence for stronger baryonic feedback in the real Universe. These findings highlight the power of combining CMB lensing with galaxy surveys to probe the interplay between baryons and dark matter in group-sized halos.

Hadzhiyska, Boryana [Lawrence Berkeley National La↗

DOE OSTI2025

Entanglement asymmetry and symmetry defects in boundary conformal field theory

A state in a quantum system with a given global symmetry, G, can be sensitive to the presence of boundaries, which may either preserve or break this symmetry. In this work, we investigate how conformal invariant boundary conditions influence the G-symmetry breaking through the lens of the entanglement asymmetry, a quantifier of the “distance” between a symmetry-broken state and its symmetrized counterpart. By leveraging 2D boundary conformal field theory (BCFT), we investigate the symmetry breaking for both finite and compact Lie groups. Beyond the leading order term, we also compute the subleading corrections in the subsystem size, highlighting their dependence on the symmetry group G and the BCFT operator content. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian. In this dynamical setting, we compute the entanglement asymmetry by extending the method of images to a BCFT with non-local objects such as invertible symmetry defects.

Field Theories in Lower Dimensions↗

DOE OSTI2025

Shear Response of Ionizable Polymer Melts at the Crossover from Ionomers to Polyelectrolytes

Nonlinear shear response of polymers is affected by inherent barriers for diffusive motion, including entanglements and topology. In ionizable polymers, ionic clusters further constrain the intrinsic dynamics of the polymers, significantly enhancing their viscosity. Here, using fully atomistic molecular dynamics simulations, the nonlinear shear response of ionizable polymers is presented, across the transition from the ionomer regime where distinctive clusters dominate the structure to the polyelectrolyte regime where clusters percolate, in polystyrene randomly sulfonated with fractions of SO 3 − groups of f = 0.20 and 0.35, in pristine and tetrahydrofuran (THF) swollen polyelectrolyte melts. For f = 0.20, the ionic clusters first fracture into smaller clusters followed by splitting into individual ionic groups and eventually reform. At higher f, the clusters morph in shape but do not break under high shear. At very high shear rates, all of the chains stretch and recoil rapidly. As the shear rate is reduced, some chains stretch and recoil, while others remain largely unaffected by the shear. Macroscopically, for all systems, the shear viscosity displays initially an elastic response, followed by nonlinear shear stress overshoot and, eventually, a steady state. The evolution of viscosity with time and shear reflects that of the ionizable domains.

cluster chemistry↗

DOE OSTI2025

Filling data analysis gaps in time-resolved crystallography by machine learning

There is a growing understanding of the structural dynamics of biological molecules fueled by x-ray crystallography experiments. Time-resolved serial femtosecond crystallography (TR-SFX) with x-ray Free Electron Lasers allows the measurement of ultrafast structural changes in proteins. Nevertheless, this technique comes with some limitations. One major challenge is the quality of data from TR-SFX measurements, which often faces issues like data sparsity, partial recording of Bragg reflections, timing errors, and pixel noise. To overcome these difficulties, conventionally, large volumes of data are collected and grouped into a few temporal bins. The data in each bin are then averaged and paired with the mean of their corresponding jittered timestamps. This procedure provides one structure per bin, resulting in a limited number of averaged structures for the entire time interval spanned by the experiment. Therefore, the information on ultrafast structural dynamics at high temporal resolution is lost. This has initiated research for advanced methods of analyzing experimental TR-SFX data beyond the standard binning and averaging method. To address this problem, we use a machine learning algorithm called Nonlinear Laplacian Spectral Analysis (NLSA), which has emerged as a promising technique for studying the dynamics of complex systems. In this work, we demonstrate the power of this algorithm using synthetic x-ray diffraction snapshots from a protein with significant data incompleteness, timing uncertainties, and noise. Our study confirms that NLSA is a suitable approach that effectively mitigates the effects of these artifacts in TR-SFX data and recovers accurate structural dynamics information hidden in such data.

Trujillo, Justin (ORCID:0000000285505360)↗

DOE OSTI2025

Host population dynamics influence Leptospira spp. transmission patterns among Rattus norvegicus in Boston, Massachusetts, US

Leptospirosis (caused by pathogenic bacteria in the genus Leptospira ) is prevalent worldwide but more common in tropical and subtropical regions. Transmission can occur following direct exposure to infected urine from reservoir hosts, or a urine-contaminated environment, which then can serve as an infection source for additional rats and other mammals, including humans. The brown rat, Rattus norvegicus , is an important reservoir of Leptospira spp. in urban settings. We investigated the presence of Leptospira spp. among brown rats in Boston, Massachusetts and hypothesized that rat population dynamics in this urban setting influence the transportation, persistence, and diversity of Leptospira spp. We analyzed DNA from 328 rat kidney samples collected from 17 sites in Boston over a seven-year period (2016–2022); 59 rats representing 12 of 17 sites were positive for Leptospira spp. We used 21 neutral microsatellite loci to genotype 311 rats and utilized the resulting data to investigate genetic connectivity among sampling sites. We generated whole genome sequences for 28 Leptospira spp. isolates obtained from frozen and fresh tissue from some of the 59 positive rat kidneys. When isolates were not obtained, we attempted genomic DNA capture and enrichment, which yielded 14 additional Leptospira spp. genomes from rats. We also generated an enriched Leptospira spp. genome from a 2018 human case in Boston. We found evidence of high genetic structure among rat populations that is likely influenced by major roads and/or other dispersal barriers, resulting in distinct rat population groups within the city; at certain sites these groups persisted for multiple years. We identified multiple distinct phylogenetic clades of L. interrogans among rats that were tightly linked to distinct rat populations. This pattern suggests L. interrogans persists in local rat populations and its transportation is influenced by rat population dynamics. Finally, our genomic analyses of the Leptospira spp. detected in the 2018 human leptospirosis case in Boston suggests a link to rats as the source. These findings will be useful for guiding rat control and human leptospirosis mitigation efforts in this and other similar urban settings.

Stone, Nathan E.↗

DOE OSTI2024

Generalized symmetry in dynamical gravity

We explore generalized symmetry in the context of nonlinear dynamical gravity. Our basic strategy is to transcribe known results from Yang-Mills theory directly to gravity via the tetrad formalism, which recasts general relativity as a gauge theory of the local Lorentz group. By analogy, we deduce that gravity exhibits a one-form symmetry implemented by an operator U α labeled by a center element α of the Lorentz group and associated with a certain area measured in Planck units. The corresponding charged line operator W ρ is the holonomy in a spin representation ρ, which is the gravitational analog of a Wilson loop. The topological linking of U α and W ρ has an elegant physical interpretation from classical gravitation: the former materializes an exotic chiral cosmic string defect whose quantized conical deficit angle is measured by the latter. We verify this claim explicitly in an AdS-Schwarzschild black hole background. Notably, our conclusions imply that the standard model exhibits a new symmetry of nature at scales below the lightest neutrino mass. More generally, the absence of global symmetries in quantum gravity suggests that the gravitational one-form symmetry is either gauged or explicitly broken. The latter mandates the existence of fermions. Finally, we comment on generalizations to magnetic higher-form or higher-group gravitational symmetries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Longitudinal Solid P Longitudinal Solid Polarized Target for CL get for CLAS12 and Study of Spin AS12 and Study of Spin Structure of Nucleons

A suite of experiments measuring target-spin observables in electron-nucleon scattering (dubbed Run Group C) was conducted at Jefferson Lab's Hall B in Newport News, VA with a new polarized nuclear target known as 'APOLLO' (Ammonia POLarized LOngitudinally). This innovative target is engineered to seamlessly integrate with the advanced 12GeV CEBAF (Continuous Electron Beam Accelerator Facility) accelerator and the Hall B CLAS12 (12 GeV CEBAF Large Acceptance Spectrometer) detector array. The 'APOLLO' target harnesses the power of Dynamic Nuclear Polarization (DNP) to achieve longitudinal polarization of solid ammonia, thereby creating a net polarization in both protons (NH3) and deuterons (ND3). These samples are subjected to a 5 Tesla magnetic field produced by the CLAS12 spectrometer central solenoid, cooled to 1 K using helium evaporation, and subsequently exposed to microwave radiation at a frequency of 140 GHz. This project was made possible through a collaborative partnership between the Jefferson Lab Target Group, Old Dominion University, University of Virginia, Christopher Newport University, and the CLAS Collaboration. Integrating the APOLLO target into CLAS12 presented unique challenges because of its specific spatial and dimensional constraints. This dissertation will highlight the innovative solutions developed to address these challenges, including the creation of a new target material transport system, the incorporation of superconducting magnetic correction coils, and the development of a customized Nuclear Magnetic Resonance (NMR) system. In addition to a detailed description of the development and operation of APOLLO, and an overview of RGC, this document also describes the global data fitting of proton asymmetries in the Deep Inelastic scattering (DIS) and the Resonance regions, and it offers insights into the comprehensive analysis of target polarization data.

Pandey, Pushpa↗

DOE OSTI2024

Sliceable, Moldable, and Highly Conductive Electrolytes for All-Solid-State Batteries

All-solid-state batteries (ASSBs) require solid electrolytes with high ionic conductivity, stability, and deformability for optimal energy and power density. Here, we developed lithium-deficient lithium yttrium bromide (LYB) solid electrolytes, Li 3–x YBr 6–x (0 ≤ x ≤ 0.50), using a comelting method with controlled lithium deficiency. These electrolytes exhibit favorable mechanical properties such as high moldability and sliceability. The Li 2.65 YBr 5.65 composition has an ionic conductivity of 4.49 mS cm –1 at 25 °C and an activation energy of 0.28 eV. Compared to Li 3 YBr 6 , Li 2.65 YBr 5.65 demonstrates improved rate performance and cycling stability in ASSBs. High-resolution X-ray diffraction confirms the formation of the LYB phase with a C2/m space group. Structural analysis reveals increased cation disorder and larger polyhedral volumes for x > 0 in Li 3–x YBr 6–x , contributing to reduced Li + migration energy barriers. Bond valence site energy calculations and molecular dynamics simulations reveal enhanced 3D lithium-ion transport. NMR spectroscopy further highlights increased Li + dynamics and impurity elimination.

Poudel, Tej P. [Florida State Univ., Tallahassee, ↗

DOE OSTI2025

Dynamics modeling of molten salt reactor with reduced and expanded representations of delayed neutron precursors

Molten salt reactors (MSRs) present unique challenges in dynamic behavior due to the mobility of their fuel. In these reactors, delayed neutron precursors (DNPs) drift with the fuel circulation through the primary loop. As a result, a fraction of DNPs decays outside the core, effectively reducing the available delayed neutron population for reactivity control. Consequently, precise modeling of the distribution and behavior of DNPs is critical for accurate reactor dynamics simulations. In this study, the System Dynamics Analysis Tool (SDAT) was used to simulate a thermal-spectrum MSR under steady-state conditions and following transients. The effects of using reduced and expanded representations of DNPs with fewer or more groups than the conventional 6-group model were investigated. Their impact on the simulated distribution of precursors in the primary loop, reactivity loss value, and reactor response to transients was analyzed. Simulation results showed that reduced models lead to the loss of the actual DNPs distribution data, resulting in less accurate estimates of reactivity loss. Reactor power predictions using these reduced models showed significant deviations compared to those using the conventional 6-group model in transient simulations. Expanded models offered a more accurate representation of the distribution of DNPs and reactivity loss estimates. Reactor power predictions using expanded models showed minimal deviation from the conventional 6-group model during the simulated transients.

analysis↗

DOE OSTI2025

Affinity for OH – Produces Four-Coordinated Zn 2+ Impurities in Hydrated Amorphous Calcium Carbonate

Using ab initio based molecular dynamics and electronic structure calculations, we show that Zn impurities in hydrated amorphous calcium carbonate (ACC) have a much lower coordination number than other divalent impurities due to covalent interactions between the 3d Zn shell and the oxygen atoms of the carbonate and water groups. Further, the local structure around Zn in ACC, including the predicted low coordination number, is confirmed by X-ray absorption spectroscopy of synthetic Zn-bearing ACC. The strong Zn–O chemical interaction leads to substantial water dissociation and slightly disrupts the hydrogen bonding network. Implications of Zn 2+ incorporation for ACC stability are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Isochronous and period-doubling diagrams for symplectic maps of the plane

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the interpretation of how systems evolve under varying conditions. While the area-preserving quadratic Hénon map has received significant theoretical attention, a comprehensive description of its mixed parameter-space dynamics remain lacking. This limitation arises from early attempts to reduce the full two-dimensional phase space to a one-dimensional projection, a simplification that resulted in the loss of important dynamical features. Consequently, there is a clear need for a more thorough understanding of the underlying qualitative aspects. This paper aims to address this gap by revisiting the foundational concepts of reversibility and associated symmetries, first explored in the early works of G.D. Birkhoff. We extend the original framework proposed by Hénon by adding a period-doubling diagram to his isochronous diagram, which allows to represents the system’s bifurcations and the groups of symmetric periodic orbits that emerge in typical bifurcations of the fixed point. A qualitative and quantitative explanation of the main features of the region of parameters with bounded motion is provided, along with the application of this technique to other symplectic mappings, including cases of multiple reversibility. Modern chaos indicators, such as the Reversibility Error Method (REM) and the Generalized Alignment Index (GALI), are employed to distinguish between various dynamical regimes in the mixed space of variables and parameters. These tools prove effective in differentiating regular and chaotic dynamics, as well as in identifying twistless orbits and their associated bifurcations. Additionally, we discuss the application of these methods to real-world problems, such as visualizing dynamic aperture in accelerator physics, where our findings have direct relevance.

43 PARTICLE ACCELERATORS↗