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At least 253 records · Page 14

A fully-integrated lattice Boltzmann method for fluid–structure interaction

Here we present a fully-integrated lattice Boltzmann (LB) method for fluid–structure interaction (FSI) simulations that efficiently models deformable solids in complex suspensions and active systems. Our Eulerian method (LBRMT) couples finite-strain solids to the LB fluid on the same fixed computational grid with the reference map technique (RMT). An integral part of the LBRMT is a new LB boundary condition for moving deformable interfaces across different densities. With this fully Eulerian solid–fluid coupling, the LBRMT is well-suited for parallelization and simulating multi-body contact without remeshing or extra meshes. We validate its accuracy via a benchmark of a deformable solid in a lid-driven cavity, then showcase its versatility through examples of soft solids rotating and settling. The LBRMT achieves a spatial convergence rate between first-order and second-order for FSI simulations and is designed for low to intermediate Reynolds number flows with finite inertia at small Mach numbers. With simulations of complex suspensions mixing, we highlight the potential of the LBRMT for studying collective behavior in soft matter and biofluid dynamics.

97 MATHEMATICS AND COMPUTING↗

From 2D to 4D: a containerized workflow and browser to explore dynamic chromatin architecture

Background Characterizing the physical organization of the genome is essential for understanding long-range gene regulation, chromatin compartmentalization, and epigenetic accessibility. Hi-C experiments generate two-dimensional (2D) genome-wide contact maps of chromatin interactions by capturing the spatial proximity between genomic loci, which reveal interaction frequencies but lack the spatial resolution needed to interpret the three-dimensional (3D) genome structure(s). Emerging evidence suggests that epigenetic regulation is closely linked to 3D genome architecture, and that structural changes over time (4D) drive key biological processes in development, disease, and environmental response. Thus, integrating 3D structure with functional data is critical for a more complete understanding of genome regulation. Previous work, most notably the 4DHiC chromosome modeling framework, has shown that physical multi-dimensional modeling approaches rooted in polymer physics and molecular dynamics can resolve these structures at biologically meaningful resolutions by integrating temporal Hi-C data with physical constraints to uncover dynamic chromosome reorganization. Thus, molecular dynamics simulations, constrained by Hi-C contact matrices, can resolve fine-scale structural changes and reveal functionally significant transitions in chromatin conformation. Results Herein, we present the 4D Genome Browser Workflow (4DGBWorkflow) and the 4D Genome Browser (4DGB). The algorithm is based on the 4DHiC method, and the containerized tool is an end-to-end workflow that can transform, filter, and view 4D epigenomics and chromatin datasets, allowing non-specialists to apply three-dimensional modeling principles to diverse datasets and experimental conditions. The software executes on a laptop running macOS, Linux or Windows. From input Hi-C files (.hic), the 4DGBWorkflow produces 3D reconstructions of chromosomes, integrates the reconstruction with track data (e.g., epigenetic marks, transcriptome profiles), and provides comparative visualization of the results in a single workflow. Conclusions The 4DGBWorkflow and 4D Genome Browser are open-source tools for comparative analysis and visualization of 4D chromosome datasets, including chromatin architecture and epigenomic signals. Automatic integration of Hi-C data with molecular dynamics democratizes the construction of time resolved 3D genome structures, simplifying complex simulations and data integration schemes.

3D Genome Browser↗

Selective deuteration of an RNA:RNA complex for structural analysis using small-angle scattering

The structures of RNA:RNA complexes regulate many biological processes. Despite their importance, protein-free RNA:RNA complexes represent a tiny fraction of experimentally determined structures. Here, we describe a joint small-angle X-ray and neutron scattering (SAXS/SANS) approach to structurally interrogate conformational changes in a model RNA:RNA complex. Using SAXS, we measured the solution structures of the individual RNAs and of the overall RNA:RNA complex. With SANS, we demonstrate, as a proof of principle, that isotope labeling and contrast matching (CM) can be combined to probe the bound state structure of an RNA within a selectively deuterated RNA:RNA complex. Furthermore, we show that experimental scattering data can validate and improve predicted AlphaFold 3 RNA:RNA complex structures to reflect its solution structure. In conclusion, our work demonstrates that in silico modeling, SAXS, and CM-SANS can be used in concert to directly analyze conformational changes within RNAs when in complex, enhancing our understanding of RNA structure in functional assemblies.

HIV-1 dimerization initiation site↗

Integrated experimental studies of pore structure and fluid uptake in the Bossier Shale in eastern Texas, USA

Within the Haynesville-Bossier Shale complex, the Bossier Shale has not been extensively studied by either industry and academia, despite it being an unconventional gas reservoir and a potential caprock for carbon storage in the underlaying Haynesville Shale. The lack of knowledge of the complex pore structures and fluid-rock interactions hinders the effective extraction of gas and the characterization of fluid reservoirs and sealing capacity. Integrated experimental studies of pore structure and fluid-rock interactions were conducted in seven Bossier Shale core samples collected in eastern Texas. Petrographic, geochemical, and petrophysical properties such as mineral composition, organic richness, thermal maturity, porosity, pore/pore throat diameter distribution, water-accessible pores, liquid water imbibition, and water vapor adsorption were characterized using complementary approaches of thin-section petrography, scanning electron microscopy, X-ray diffraction, total organic matter, pyrolysis, mercury intrusion porosimetry, nuclear magnetic resonance, (Ultra-) small angle X-rays scattering as well as small angle neutron scattering with deuterated liquids and contrast variation. Further, the results show that the thermally mature Bossier Shales are composed of mixed argillaceous mudstone, mixed mudstone, and mixed carbonate mudstone. The shale contains both organic and inorganic pores, with porosities of 3.24-9.37 %, pore-to-throat ratios of 1.65 to 19.4, and water-accessible pores accounting for 28.7-72.6 % of total pores. Approaches of liquid water imbibition and water vapor adsorption, with and without direct contact of water with shale samples, indicate that liquid water first enters the nano-sized pores under high capillary pressures, and water vapor adsorption is mainly controlled by both clay minerals and pores with diameters less than 10 nm. These findings contribute to a better understanding of pore structures and water-shale interactions and their controlling factors in the Bossier Shale.

58 GEOSCIENCES↗

Flux Upcycling of Degraded Layered Cathodes to LiNi x Mn y Co z O 2 (NMCs) with Gradient Transition Metal Distribution

The rising demand for lithium-ion batteries (LIBs) has intensified the need for efficient recycling methods to address both supply chain constraints and environmental impacts. Direct upcycling, distinguished by its ability to achieve both the structural and compositional integrity of cathode materials, has gained prominence as a sustainable alternative to conventional pyrometallurgical and hydrometallurgical processes. However, the current direct upcycling methods are typically limited by incorporating Li and/or Ni, significantly constraining the adaptability across diverse LiNi x Mn y Co z O 2 (NMCs). Here, in this study, a versatile molten salt approach is reported that expands the scope of direct upcycling by enabling simultaneous incorporation of Li, Ni, and Mn. This methodology facilitates flexible conversion among diverse NMC compositions, including non-stoichiometric Co/Mn systems such as upcycling degraded LiCoO 2 (D-LCO), LiNi 1/3 Mn 1/3 Co 1/3 O 2 (D-NMC111), LiNi 0.8 Mn 0.1 Co 0.1 O 2 (D-NMC811) to surface Mn enriched NMC111, LiNi 0.5 Mn 0.3 Co 0.2 O 2 (NMC532), and NMC811, respectively. The gradient transition metal distribution in upcycled products, characterized by Mn-enriched outer layers and Co/Ni-enriched cores enhances the interfacial stability of NMC cathodes, addressing critical challenges in long-term performance and structural integrity. These results highlight the potential of flux methods for advancing the upcycling of spent cathodes and producing high-performance materials for next-generation LIBs applications.

lithium -ion batteries↗

Strong Zero Modes in Integrable Quantum Circuits

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this Letter, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Furthermore, our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

1-dimensional spin chains↗

Enhancing sorption kinetics by oriented and single crystalline array-structured ZSM-5 film on monoliths

Abstract To enhance the reaction kinetics without sacrificing activity in porous materials, one potential solution is to utilize the anisotropic distribution of pores and channels besides enriching active centers at the reactive surfaces. Herein, by designing a unique distribution of oriented pores and single crystalline array structures in the presence of abundant acid sites as demonstrated in the ZSM-5 nanorod arrays grown on monoliths, both enhanced dynamics and improved capacity are exhibited simultaneously in propene capture at low temperature within a short duration. Meanwhile, the ZSM-5 array also helps mitigate the long-chain HCs and coking formation due to the enhanced diffusion of reactants in and reaction products out of the array structures. Further integrating the ZSM-5 array with Co 3 O 4 nanoarray enables comprehensive propene removal throughout a wider temperature range. The array structured film design could offer energy-efficient solutions to overcome both sorption and reaction kinetic restrictions in various solid porous materials for various energy and chemical transformation applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modular DC circuit breaker with integrated energy storage for future DC networks

A T-breaker is an all-in-one solution for dc microgrid fault protection, power flow control, and power quality improvement. A T-breaker features a modular multilevel “T” structure with integrated energy storage devices. The two horizontal arms of the T-breaker realize fault current breaking, load voltage compensation, and power flow control; and the vertical arm of the T-breaker realizes shunt compensation. The configuration provides excellent voltage scalability and relaxes the requirements on the switching signal synchronization during fault transients. The local energy storage in sub-modules eases the fault energy dissipation requirement placed on the traditionally-adopted surge arrestors. The modular multilevel structure also offers immense control flexibility for all types of targeted functions of the provided T-breaker.

Wang, Jin↗

Infrared thermography NDT for in-situ defect detection in sandwich composite panel manufacturing

Composite manufacturing presents numerous challenges, as defects can arise from various sources throughout the process. In sandwich composite structures, the integration of a foam core introduces additional complexity and increases the likelihood of defect formation like delamination. To mitigate these issues and reduce the risk of future structural failures, in-situ monitoring during manufacturing is essential. This study investigates infrared (IR) thermography as a non-destructive technique for detecting manufacturing defects in foam-core sandwich composite panels under thermally excited conditions representative of in-situ processing. A stationary FLIR A8590 IR camera (640 × 512 pixels, 30Hz, 17mm lens, 9 ft stand-off distance) was used to monitor prefabricated panels subjected to controlled external heating simulating compression molding and resin cure exotherm. Interlaminar delamination defects with characteristic sizes ranging from 0.25 × 0.25in² to 5 × 5in² produced measurable surface temperature depressions of approximately 4–10°C during transient cooling, exceeding the effective noise floor of the camera by more than two standard deviations. Thicker laminates exhibited prolonged defect detectability windows due to increased thermal diffusion time. In contrast, embedded Teflon inclusions generated weak thermal contrasts of ≤ 3°C, approaching the measurement noise floor, due to limited thermal property contrast with the surrounding glass fiber composite. These results establish quantitative detectability limits for stationary thermographic inspection of sandwich composite panels under manufacturing-representative thermal cycles.

Barakat, Abdallah [ORNL] (ORCID:0000000296141398)↗

Combining coordination and chelation moieties to engineer a new linker for lanthanide coordination chemistry

Organic linkers play a crucial role in constructing lanthanide (Ln) coordination polymers (CPs), influencing structural topologies and physicochemical properties. Herein, we introduce 6-oxo-1,6-dihydro-2,5-pyridinedicarboxylic acid (2,5-H 3 PODC) as a new ligand for constructing lanthanide coordination polymers that integrates the structural features of terephthalic acid with the chelation capabilities of pyridinone-based functional groups. Six lanthanide-based coordination polymers were synthesized with 2,5-H 3 PODC, forming two types of CPs – type 1: [Ln(HPODC)(Ox) 0.5 (H 2 O) 2 ] (where (Ox) = oxalic acid and Ln = Pr 3+ (1), Nd 3+ (2)) and type 2: [Ln(H 2 PODC)(HPODC)(H 2 O)] (Ln = Eu 3+ (3), Gd 3+ (4), Dy 3+ (5), Er 3+ (6)). All compounds were structurally characterized by single-crystal and powder X-ray diffraction, and both compound types are 2D ladder-like networks with cem topologies where the trivalent metal centers are bridged via HPODC 2− and Ox 2− ligands in type 1 structures and H 2 PODC − and HPODC 2− linkers in type 2 structures. Thermogravimetric analysis (TGA) demonstrated that the metal–organic networks of type 1 and type 2 compounds exhibit distinct decomposition patterns, and the photoluminescent properties of 3 were also examined, revealing efficient ligand based sensitization and characteristic emission bands for Eu(III).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Allosteric prediction via convolutional neural networks and protein structural and dynamical features

Allostery is the phenomenon whereby a binding event or covalent modification at one site in a protein modulates function at a distal site, thus changing a protein’s functional state. As such, it is a ubiquitous aspect of protein functional regulation. Computationally predicting allosteric states is important as part of the broader challenge of functional annotation, but it also has practical implications for drug development, as targeting an allosteric site often affords greater specificity compared with targeting an orthosteric site. This study introduces a machine learning approach to predict the allosteric functional state using the small G-protein KRas as the model system, due to its implication in many types of cancer and being well studied as a result with many x-ray crystallographic structures of KRas available with different mutations and ligands bound. Using structural and dynamical features that can be cast as images, namely interatomic distances, contact maps, covariance, and mutual information, supervised learning was performed using convolutional neural networks. Two pretrained convolutional neural network architectures, GoogLeNet and ResNet18, were fine-tuned to classify KRas into active or inactive states based on these features. Across training regimes, atomic contact maps emerged as the most effective structural feature, whereas linearized mutual information outperformed covariance in capturing dynamical correlations relevant to allostery. Models achieved significant validation accuracy, with atomic contact maps yielding up to 90% accuracy. In conclusion, the findings suggest that integrating global structural rearrangements and correlated motion patterns with deep learning can reliably predict protein allosteric states, offering a promising framework for understanding allosteric regulation and developing targeted therapeutics.

Rajeshwar T., Rajitha [Oak Ridge National Laborato↗

Influence of Powder Characteristics and Processing Methods on Creep Performance of Powder Metallurgy Hot Isostatic Pressed SS316

The U.S. nuclear energy expansion goals are driving the demand for manufacturing routes that can rapidly produce large, complex, near net shape components. Powder metallurgy hot isostatic pressing (PM HIP) is an advanced manufacturing technique that can be economically scaled-up, while alleviating the supply chain challenges that forging and casting face in terms of cost and lead time constraints. This makes PM-HIP a viable technology to aid and accelerate large-scale part manufacturing for nuclear applications. However, large-scale qualification and deployment of this technology require a thorough understanding of the influence of powder feedstock quality, powder handling history, hot isostatic pressing (HIP) parameters, and subsequent heat treatment on microstructural evolution and elevated temperature mechanical performance. The present work focusses on 316 austenitic stainless steel (SS316) which is most commonly used in high temperature environments for nuclear applications Results from this study show that PM HIPed SS316 meets ASME tensile requirements at room temperature and at elevated temperature. However, creep performance of PM-HIPed SS316 remains inferior to its wrought counterpart, demonstrating that tensile performance alone is not a reliable metric for long duration high temperature integrity. Further, this report delineates powder derived microstructural features that govern creep damage, with key evidences pointing to “microstructural inheritance” from gas atomized powder feedstocks. Commercial SS316 powders of varying chemical compositions and recycling histories were studies, and the results showed large differences in elemental segregation, oxide surface layers and secondary phase distributions. Multi-scale characterization revealed segregation of chromium, molybdenum, manganese and silicon at the boundaries and the precipitation of manganese-, silicon-, and molybdenum-oxides. During HIP consolidation, these surface oxides transform into decorated prior particle boundaries (PPBs) and grain boundary inclusions that persist through conventional post-HIP solution annealing treatment. The retained oxides in post-HIP microstructures were found to influence grain growth, precipitation behavior, and ultimately creep cavitation and fracture. Such post-HIP heat treatments are therefore limited by a complex trade-off between grain growth, and oxide coarsening which aggravate creep damage by acting as nucleation sites for cavities. The objective of this work is to establish an integrated processing–structure–property framework for PM-HIP 316 stainless steel by investigating the influence of powder feedstock characteristics in pre- and post-HIP processing as well as to understand the significance of post-HIP heat treatment on microstructural evolution and creep properties. The results from this report emphasize the significance of powder feedstock integrity in improving creep performance of PM-HIPed SS316, by highlight the effect of rapid solidification, elemental segregation, oxide formation and powder recycling on microstructural defect inheritance following HIP consolidation. Rather than considering HIP processing, solution annealing, and mechanical performance independently, this report treats powder production, HIP consolidation, post-HIP thermal processing, and creep deformation as interconnected stages within a continuous metallurgical process. The resulting framework will provide a scientific basis for developing feedstock engineering strategies capable of improving long-term reliability of PM-HIP stainless steels and accelerating their qualification for advanced nuclear applications.

Ajjarapu, Pavan [Oak Ridge National Laboratory (OR↗

Developing cathode infiltration processes for all-solid-state bilayer LLZO cells

To realize the bilayer architecture of lithium lanthanum zirconate (LLZO) for application in solid-state batteries (SSBs), the scaffold structure must be optimized, and effective cathode infiltration strategies must be established. In this study, we fabricate a modified bilayer LLZO using a sacrificial layer to enhance surface porosity, and systematically investigate various cathode infiltration techniques to fill the scaffold with oxide cathode active materials (CAM). Structural characterizations showed that the sacrificial layer significantly increased open surface porosity, enabling the surface of the scaffold to be filled with CAM. To further increase infiltration depth, applying vacuum or vibration was compared, with the full-depth infiltration achieved using a sonicator-based vibration. Full cells prepared using the modified bilayer LLZO and vibration-assisted technique demonstrated successful operation. This work demonstrates a practical and scalable approach for engineering bilayer LLZO structures and integrating oxide cathodes into porous scaffolds, offering a promising pathway toward high-performance solid-state batteries.

Bilayer↗

Yesterday’s extremes, today’s new normal: flood risk in the Kathmandu Valley, Nepal

Unplanned urban growth has left many cities increasingly vulnerable to extreme rainfall events, particularly in regions with inadequate drainage infrastructures and development encroaching on natural floodplains. Here, in this perspective paper, we examine the September 2024 floods that struck Central Nepal, triggered by a persistent low-pressure system and enhanced by converging moisture flows from the Arabian Sea and the Bay of Bengal which led to widespread catastrophic damage. In the Kathmandu Valley, floodwaters expanded to more than 2.5 times the bankfull water extent, causing significant damage to housing, transportation network, and critical infrastructure, displacing thousands of residents, and severely disrupting urban services. This event highlights the urgent need for improved flood management strategies that integrate both structural and non-structural measures into the infrastructure development. While early warning systems provided critical lead time, challenges remain in reducing forecasting uncertainties and improving communication across government agencies and with local communities. A forward-looking approach is essential, including probabilistic flood forecasting systems, sustainable floodplain management, risk-sensitive land use planning, climate- and disaster- resilient infrastructure development, and the integration of nature-based solutions like urban green and blue spaces to mitigate flood impacts. By involving local communities in planning and preparedness efforts, particularly through citizen science initiatives, and engagement with underserved and disadvantaged communities, Nepal can better adapt to the growing risks posed by extreme rainfall and urban flooding and enhance long-term disaster resilience in rapidly urbanizing areas like Kathmandu Valley.

Kathmandu Valley↗

Electric-Field-Driven Localization of Molecular Nanowires in Wafer-Scale Nanogap Electrodes

As integrated circuits continue to scale toward the atomic limit, bottom-up processes, such as epitaxial growth, have come to feature prominently in their fabrication. At the same time, chemistry has developed highly tunable molecular semiconductors that can perform the functions of ultimately scaled circuit components. Hybrid techniques that integrate programmable structures comprising molecular components into devices however are sorely lacking. Here we demonstrate a wafer-scale process that directs the localization of a conductive polymer, M w = 20 kg mol –1 polyaniline, from dilute solutions into 50 nm vertical nanogap device architectures using electric-field-driven self-assembly. The resulting metal–polymer–metal junctions were characterized by electron microscopy, Raman spectroscopy and transport measurements demonstrating that our technique is highly selective, assembling conductive polymers only in electrically activated nanogaps. Our results represent a step toward scalable hybrid nanoelectronics that seamlessly integrate established lithographic top-down fabrication with bottom-up synthesized molecular functional circuit components.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

The Factors Governing Metal Dependence of an Emergent Superfamily of Bimetallic Oxygenases

Metalloenzyme superfamilies are typically defined by their protein scaffolds and active sites. Owing to the high tunability of protein structures, members of a single superfamily can catalyze diverse reactions with the same metallocofactor. Some superfamilies, such as amidohydrolase-related dinuclear oxygenases (AROs), display further versatility by utilizing multiple metallocofactors. We have shown that certain AROs catalyze monooxygenation reactions with diiron, dimanganese, and/or mixed manganese−iron cofactors, but the molecular factors governing the selection of a particular cofactor remain unknown, and the extent of this superfamily in biology is unclear. Here, we report bioinformatic analyses that expand the ARO superfamily to approximately 17,000 unique UniProt sequences, far exceeding the number of previously characterized enzymes. Through the integration of structural, spectroscopic, and thermodynamic analyses of representative proteins with a bioinformatic pipeline that identifies key secondary- and tertiary-sphere residues, we can predict in silico the metal preference for the majority of reported ARO sequences. These annotations were validated via the characterization of multiple new AROs, including ones implicated in key oxidative steps of natural product biosyntheses. This study establishes the key structure−function relationships governing metal preferences in AROs and highlights their vastly underappreciated role in myriad biological processes.

Liu, Chang [University of California, Berkeley, CA↗

Dissolution zone model of the oxide structure in additively manufactured dispersion-strengthened alloys

The structural evolution of oxides in dispersion-strengthened superalloys during laser-powder bed fusion is considered in detail. Alloy chemistry and process parameter effects on oxide structure are assessed through a parameter study on the model alloy Ni-20Cr, doped with varying concentrations of Y 2 O 3 and Al. Small angle neutron scattering measurements of the dispersoid size distribution show the dispersoid size increases with higher laser power, slower scan speed, and increasing Y 2 O 3 and Al content. Complementary electron microscopy measurements reveal reactions between Y 2 O 3 and Al, even in nanoscale dispersoids, and the presence of micron-scale oxide slag inclusions in select specimens. A scaling analysis of mass and momentum transport within the melt pool, presented here, establishes that diffusional structural evolution mechanisms dominate for nanoscale dispersoids, while fluid forces and advection become significant for larger slag inclusions. These findings are developed into a theory of dispersoid structural evolution, integrating quantitative models of diffusional processes – dispersoid dissolution, nucleation, growth, coarsening – with a reduced order model of time-temperature trajectories of fluid parcels within the melt pool. Calculations of the dispersoid size in single-pass melting reveal a zone in the center of the melt track in which the oxide feedstock fully dissolves. Within this zone the final Y 2 O 3 size is independent of feedstock size and determined by nucleation and growth kinetics. If the dissolution zones of adjacent melt tracks overlap sufficiently with each other to dissolve large oxides, formed during printing or present in the powder feedstock, then the dispersoid structure throughout the build volume is homogeneous and matches that from a single pass within the dissolution zone. Gaps between adjacent dissolution zones result in oxide accumulation into larger slag inclusions. Predictions of final dispersoid size and slag formation using this dissolution zone model match the present experimental data and explain process-structure linkages speculated in the open literature.

36 MATERIALS SCIENCE↗

Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory

The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3 , ζ 5 to the cusp anomalous dimension.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗