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At least 109 records · Page 6

A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include the complex evolution of fault geometry, frictional contact, and off-fault damage over a wide range of spatial and temporal scales. Here, in this paper, we develop a phase-field model for quasi-dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off-fault damage processes with a single formulation. Built on a recently developed phase-field framework for shear fractures with frictional contact, the proposed formulation incorporates rate- and state-dependent friction, radiation damping, and their impacts on fault mechanics and off-fault damage. We show that the numerical results of the phase-field model are consistent with those obtained from well-verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g., the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase-field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods.

58 GEOSCIENCES↗

R-Adaptivity to Enable Compression of Elementary Computations in Extreme-Scale Finite Element Simulators

Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in processing power, the available system memory has not increased commensurately, and electrical power consumption continues to grow. A predominant approach to limit the memory usage in large-scale applications is to exploit the abundant processing power and continually recompute many low-level simulation quantities, rather than storing them. However, this approach can adversely impact the throughput of the simulation and diminish the benefits of modern computing architectures. We present three novel contributions to reduce the memory burden while maintaining, and sometimes improving, performance in simulations based on finite element discretizations. The first contribution develops dictionary-based data compression schemes that detect and exploit the structure of the discretization, due to redundancies across the finite element mesh. While these schemes are shown to reduce memory requirements by more than 99% on meshes with large numbers of identical mesh cells, there are applications where this structure does not exist. The second contribution leverages a recently developed augmented Lagrangian optimization algorithm to enable r-adaptivity for meshes with the goal of enhancing the redundancies in the mesh. The third contribution extends these methods to patch-based linear solvers and preconditioners by compressing local matrices. Numerical results demonstrate the effectiveness of the proposed methods to detect, enhance and exploit mesh structure on a suite of examples inspired by large-scale applications.

97 MATHEMATICS AND COMPUTING↗

Resolve the Clear-Sky Continuous Diurnal Cycle of High-Resolution ECOSTRESS Evapotranspiration and Land Surface Temperature

Although numerous evapotranspiration (ET) estimates have been developed from remote sensing measurements, a diurnally resolved product with high spatial resolution (<100 m) is still lacking, which is critically needed for agricultural and ecological monitoring. The ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) provides, for the first time, ET at 70 m resolution with diurnal samplings, enabling a step toward filling this data gap. This study developed the first framework to resolve the full diurnal cycle of ET and Land Surface Temperature (LST) from sporadic ECOSTRESS measurements. We first constructed 70 m diurnal LST utilizing a diurnal temperature cycle (DTC) model that fused ECOSTRESS and Geostationary Operational Environmental Satellite (GOES) LST. Next, we derived 70 m diurnal ET from the diurnally resolved LST, along with ancillary meteorological and reflectance data sets, using the Priestley-Taylor Jet Propulsion Laboratory (PT-JPL) algorithm. This framework was tested in two regions: A relatively homogeneous semiarid grassland landscape (centered at the US-Seg Ameriflux site) and a heterogeneous humid cropland landscape (centered at US-ARM). Our diurnally resolved LST and ET successfully reproduced the spatial patterns in the native ECOSTRESS measurements during overpasses for both landscapes (LST: r > 0.97, RMSE ~2°C; ET: r > 0.99, and RMSE = 1–7 W m -2 ). The constructed time series also well captured the temporal variability of the in situ measurements (especially under clear-sky conditions) at both US-Seg and US-ARM, albeit performance varying with availability and quality of ECOSTRESS samples. This study sets the stage for testing and applying our framework to broader climates, biomes, and landscapes toward eventually generating diurnally resolved 70 m global operational LST/ET products to enhance ecological/agricultural applications.

54 ENVIRONMENTAL SCIENCES↗

Learning continuous models for continuous physics

Abstract Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.

97 MATHEMATICS AND COMPUTING↗

Taking learning to another level

As a technical project manager at Los Alamos National Laboratory, Scott Boise works on programs and projects that make a big impact. Although he spends most of his days in a quiet office, he also makes a big impact on his team. He's well-known for his character and integrity because of the way he develops leadership skills on the team, promotes respect for others and lives a commitment to learning. Scott joined the Lab in June 2021, the period of the COVID-19 pandemic when most new employees began their careers without ever having stepped foot on-site. That experience has continued to serve as a reminder to him that new employees face numerous challenges no matter how and when they start. He's made it his aim to do what he can to lift some of that load. Coming to the Lab from a career in the biomedical industry, Scott arrived with years of project management experience but without a deep understanding of nuclear operations. His dedication to continuous learning has helped him pursue experiential opportunities and ask the proper questions to understand his role.

99 GENERAL AND MISCELLANEOUS↗

Universal Compiling and (No-)Free-Lunch Theorems for Continuous-Variable Quantum Learning

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete-variable hardware, less has been paid to compiling in the continuous-variable paradigm. Here we motivate several, closely related, short-depth continuous-variable algorithms for quantum compilation. We analyze the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr nonlinearities. We further make connections between this framework and quantum learning theory in the continuous-variable setting by deriving no-free-lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using two-mode-squeezed states.

97 MATHEMATICS AND COMPUTING↗

Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping

Here, we study the one-dimensional nearest-neighbor tight-binding model of electrons with independently distributed random hopping and no on-site potential (i.e., off-diagonal disorder with particle-hole symmetry, leading to sublattice symmetry, for each realization). For nonsingular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $ρ(E) ~ 1/|E\: \text{ln}^3 |E||$ and of the localization length $ξ(E) ~ |\text{ln}|E||$, near the band center $\textit{E}$ = 0 . (This singular behavior is also applicable to random $\textit{XY}$ and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain.) Simultaneously, the state at$\textit{E}$ = 0 shows a universal, subexponential decay at large distances $\sim \text{exp}[–\sqrt{r/r_0}]$. In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small $\textit{t}$ is of the form $\sim 1/[t \text{ln}^{λ+1}(1/t)]$, characterized by a single, continuously tunable parameter λ > 0. We find, using a combination of analytic and numerical methods, that while the universal result applies for λ > 2, it no longer holds in the interval 0 < λ < 2. In particular, we find that the form of the density of states singularity is enhanced (relative to the Dyson result) in a continuous manner depending on the nonuniversal parameter λ; simultaneously, the localization length shows a less divergent form at low energies and ceases to diverge below λ = 1. For λ < 2, the fall-off of the $\textit{E}$ = 0 state at large distances also deviates from the universal result and is of the form $\sim\text{exp}[–(r/r_0)^{1/λ}]$ , which decays faster than an exponential for λ < 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Formation of 6H-Ba 3 Ce 0.75 Mn 2.25 O 9 during Thermochemical Reduction of 12R-Ba 4 CeMn 3 O 12 : Identification of a Polytype in the Ba(Ce,Mn)O 3 Family

The resurgence of interest in a hydrogen economy and the development of hydrogen-related technologies has initiated numerous research and development efforts aimed at making the generation, storage, and transportation of hydrogen more efficient and affordable. Solar thermochemical hydrogen production (STCH) is a process that potentially exhibits numerous benefits such as high reaction efficiencies, tunable thermodynamics, and continued performance over extended cycling. Although CeO 2 has been the de facto standard STCH material for many years, more recently 12R-Ba 4 CeMn 3 O 12 (BCM) has demonstrated enhanced hydrogen production at intermediate H 2 /H 2 O conditions compared to CeO 2 , making it a contender for large-scale hydrogen production. However, the thermo-reduction stability of 12R-BCM dictates the oxygen partial pressure (pO 2 ) and temperature conditions optimal for cycling. In this study, we identify the formation of a 6H-BCM polytype at high temperature and reducing conditions, experimentally and computationally, as a mechanism and pathway for 12R-BCM decomposition. 12R-BCM was synthesized with high purity and then controllably reduced using thermogravimetric analysis (TGA). Synchrotron X-ray diffraction (XRD) data is used to identify the formation of a 6H-Ba 3 Ce 0.75 Mn 2.25 O 9 (6H-BCM) polytype that is formed at 1350 degrees C under strongly reducing pO 2 . Density functional theory (DFT) total energy and defect calculations show a window of thermodynamic stability for the 6H-polytype consistent with the XRD results. These data provide the first evidence of the 6H-BCM polytype and could provide a mechanistic explanation for the superior water-splitting behaviors of 12R-BCM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advances in Clayff Molecular Simulation of Layered and Nanoporous Materials and Their Aqueous Interfaces

As a general-purpose force field for molecular simulations of layered materials and their fluid interfaces, Clayff continues to see broad usage in atomistic computational modeling for numerous geoscience and materials science applications due to its (1) success in predicting properties of bulk nanoporous materials and their interfaces, (2) transferability to a range of layered and nanoporous materials, and (3) simple functional form which facilitates incorporation into a variety of simulation codes. Here, we review applications of Clayff to model bulk phases and interfaces not included in the original parameter set and recent modifications for modeling surface terminations such as hydroxylated nanoparticle edges. Overall, we conclude with a discussion of expectations for future developments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Confronting the Challenge of Modeling Cloud and Precipitation Microphysics

In the atmosphere, microphysics refers to the microscale processes that affect cloud and precipitation particles and is a key linkage among the various components of Earth’s atmospheric water and energy cycles. The representation of microphysical processes in models continues to pose a major challenge leading to uncertainty in numerical weather forecasts and climate simulations. In this paper, the problem of treating microphysics in models is divided into two parts: i) how to represent the population of cloud and precipitation particles, given the impossibility of simulating all particles individually within a cloud, and ii) uncertainties in the microphysical process rates owing to fundamental gaps in knowledge of cloud physics. The recently-developed Lagrangian particle-based method is advocated as a way to address several conceptual and practical challenges of representing particle populations using traditional bulk and bin microphysics parameterization schemes. For addressing critical gaps in cloud physics knowledge, sustained investment for observational advances from laboratory experiments, new probe development, and next-generation instruments in space is needed. Greater emphasis on laboratory work, which has apparently declined over the past several decades relative to other areas of cloud physics research, is argued to be an essential ingredient for improving process-level understanding. More systematic use of natural cloud and precipitation observations to constrain microphysics schemes is also advocated. Because it is generally difficult to quantify individual microphysical process rates from these observations directly, this presents an inverse problem that can be viewed from the standpoint of Bayesian statistics. Following this idea, a probabilistic framework is proposed that combines elements from statistical and physical modeling. Besides providing rigorous constraint of schemes, there is an added benefit of quantifying uncertainty systematically. Finally, a broader hierarchical approach is proposed to accelerate improvements in microphysics schemes, leveraging the advances described in this paper related to process modeling (using Lagrangian particle-based schemes), laboratory experimentation, cloud and precipitation observations, and statistical methods.

54 ENVIRONMENTAL SCIENCES↗

Review—Micro-Fuel Cell Principal Biosensors for Monitoring Transdermal Volatile Organic Compounds in Humans

Knowledge of transduction mechanisms in biosensing applications paves the way for ultrasensitive and dynamic detection in living systems. Real-world biosensing applications where ultra-sensitivity and dynamic detection are paramount include monitoring the anesthetic agent concentration during surgery; the slightest variation in concentration can potentially result in a life-threatening overdose or, on the other end of the spectrum, the patient’s awareness during the procedure. We review the benefits and functions of the transcutaneous biosensor device compared with other current technology and discuss the sensor’s capability to accurately measure volatile anesthetic gas concentration in blood using fuel cell technology. We review fundamental concepts of fuel-cell technology for wearable bio-sensing applications. The fuel cell sensor can also continuously monitor other volatile organic compounds making it versatile with numerous potential applications.

42 ENGINEERING↗

AmeriFlux FLUXNET-1F US-xJR NEON Jornada LTER (JORN)

This is the AmeriFlux Management Project (AMP) created FLUXNET-1F version of the carbon flux data for the site US-xJR NEON Jornada LTER (JORN). This is the FLUXNET version of the carbon flux data for the site US-xJR NEON Jornada LTER (JORN) produced by applying the standard ONEFlux (1F) software. Site Description - Land use at Jornada has contrasting livestock grazing histories (including ungrazed lands), dating back to 1902, which are representative of the pervasive land use in desert-southwest wildlands. Historical accounts of the region report significant changes in vegetation starting in the late 1800s coincident with the expansion of livestock grazing. By 1912, sufficiently dramatic changes lead area scientists and private landowners to convince the U.S. government to set aside Public Domain Lands for the Jornada Range Reserve for the purpose of scientific investigation on shrub invasion and subsequent loss of forage grasses. Much of this early research focused on quantifying utilization levels for forage species, developing livestock production strategies to deal with drought, and developing methods for shrub control and grass recovery. Exclosures were constructed and long-term plots were established throughout the range to monitor the continued expansion of shrubs across the landscape. Over the decades, numerous trials of various remediation approaches were implemented, from manual and mechanical shrub removal to herbicide application to construction of terraces or other means of redirecting surface flow of runoff.

Network), NEON (National Ecological Observatory↗

Climate Impact of Primary Plastic Production

Plastics show the strongest production growth of all bulk materials over the last decade. The industry’s current growth trajectory is exponential and plastic production is expected to double or triple by 2050. The rapidly increasing production of plastics and the continued reliance on fossil fuels for production, have contributed to numerous environmental problems and health harms. As a result, plastic pollution has become an increasing threat to natural ecosystems, human health and climate. However, there is a lack of granularity on the contribution of the primary plastics specifically to greenhouse gas (GHG) emissions and their impact on the remaining global carbon budget needed to stay below a 1.5°C or 2°C global average temperature rise. In this report, we explore the contribution of primary plastic production to climate change disaggregated by polymer and technology. To this end, we have developed comprehensive bottom-up modeling of GHG emissions from global primary plastic production, with a special focus on polymer value chains. We have analyzed the results under various growth scenarios in the context of carbon budgets compatible with a 1.5°C global trajectory. Modeling includes the material flows of all production stages, processes and technologies used in primary plastic production value chains, including from the extraction of fossil fuels required for production to shaping the final product. We specifically focus on nine major types of fossil fuelbased plastic polymers that are produced and consumed in large quantities: three types of polyethylene (PE) – low-density (LDPE), linear low-density (LLDPE), and high-density (HDPE) – as well as polypropylene (PP); polyethylene terephthalate (PET); polyvinyl chloride (PVC); polystyrene (PS) and other key styrene-based plastics such as styrene acrylonitrile (SAN) and acrylonitrile butadiene styrene (ABS), and polyurethane (PU). Together these account for about 80% of plastics production.

54 ENVIRONMENTAL SCIENCES↗

Climate Impact of Primary Plastic Production

Plastics show the strongest production growth of all bulk materials over the last decade. The industry’s current growth trajectory is exponential and plastic production is expected to double or triple by 2050. The rapidly increasing production of plastics and the continued reliance on fossil fuels for production, have contributed to numerous environmental problems and health harms. As a result, plastic pollution has become an increasing threat to natural ecosystems, human health and climate. However, there is a lack of granularity on the contribution of the primary plastics specifically to greenhouse gas (GHG) emissions and their impact on the remaining global carbon budget needed to stay below a 1.5°C or 2°C global average temperature rise. In this report, we explore the contribution of primary plastic production to climate change disaggregated by polymer and technology. To this end, we have developed comprehensive bottom-up modeling of GHG emissions from global primary plastic production, with a special focus on polymer value chains. We have analyzed the results under various growth scenarios in the context of carbon budgets compatible with a 1.5°C global trajectory. Modeling includes the material flows of all production stages, processes and technologies used in primary plastic production value chains, including from the extraction of fossil fuels required for production to shaping the final product. We specifically focus on nine major types of fossil fuel-based plastic polymers that are produced and consumed in large quantities: three types of polyethylene (PE) – low-density (LDPE), linear low-density (LLDPE), and high-density (HDPE) – as well as polypropylene (PP); polyethylene terephthalate (PET); polyvinyl chloride (PVC); polystyrene (PS) and other key styrene-based plastics such as styrene acrylonitrile (SAN) and acrylonitrile butadiene styrene (ABS), and polyurethane (PU). Together these account for about 80% of plastics production.

54 ENVIRONMENTAL SCIENCES↗

Tools and Methods for Optimization of Nuclear Plant Outages

Refueling outages are one of the most challenging phases in a nuclear power plants (NPP) operating cycle. Refueling outages are extremely costly for a NPP due to the large amount of required resources and because of lost revenue due to plant being off the grid. Outage durations have steadily decreased across the industry over that last few decades primarily due to improved planning and coordination, but there are still many plants that struggle to meet the performance metrics accomplished by other utilities. Schedule resilience is one of the issues. NPP outages require scheduling thousands of activities in a duration of around 30 days on average. Outage staff begin working on the schedule more than a year ahead of the outage start and make every effort to build a robust schedule. Despite the robust and detailed planning, once the outage starts, numerous emergent issues typically appear along with schedule delays requiring continuous replanning and adjusting. When schedule disruption occurs during an outage, plant staff make urgent efforts to recover but often not able to maintain the planned outage duration. These outage delays can cost a utility several million dollars per day. Tools that could help outage schedulers create a more resilient schedule and allow them to optimally reschedule emergent work could significantly reduce outage delays. One key aspect of creating a resilient schedule is to have accurate estimates for activity duration. Another important outage scheduling capability is the ability to schedule emergent work with minimal disruption. The Optimization of Outage Activities project under the Risk-Informed Systems Analysis Pathway (RISA) sponsored by Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) program focuses on developing tools and methods to support nuclear power plants with optimization of outage schedules. The goal of the outage optimization is the completion of all planned and emergent outage activities as fast as possible while maintaining highest level of safety. This report describes the initial development of tools to support outage management that leverage computational and machine learning methods developed in other RISA and LWRS projects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Methods and Tools To Assess Robustness of Nuclear Plant Outages

Refueling outages are one of the most challenging phases in a nuclear power plant (NPP) operating cycle. Refueling outages are extremely costly for an NPP due to the large amount of required resources and because of lost revenue due to plant being off the grid. Outage durations have steadily decreased across the industry over that last few decades primarily due to improved planning and coordination, but there are still many plants that struggle to meet the performance metrics accomplished by other utilities. Schedule resilience is one of the issues. NPP outages require scheduling thousands of activities within 30 days on average. Despite detailed planning, once the outage starts, numerous emergent issues typically appear along with schedule delays requiring continuous replanning and adjustment. When schedule disruption occurs during an outage, plant staff make urgent efforts to recover but are often not able to maintain the planned outage duration. These outage delays can cost a utility several million dollars per day. Tools that could help outage schedulers create a more resilient schedule and allow them to optimally reschedule emergent work could significantly reduce outage delays. One key aspect of creating a resilient schedule is to have accurate estimates for activity duration. Another important outage scheduling capability is the ability to schedule emergent work with minimal disruption. This paper focuses on developing tools and methods to support NPPs with outage schedule optimization and it describes the initial development of tools to support outage management that leverage computational and machine learning methods.

97 - MATHEMATICS AND COMPUTING↗

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Multi-scale Coupled Processes Modeling of Fractures as Porous, Interfacial and Granular Systems from Rock Images with the Numerical Manifold Method

Abstract The greatest challenges of rigorously modeling coupled hydro-mechanical processes in fractured rocks at different scales are associated with computational geometry. In addition, selections of continuous or discontinuous models, physical laws, and coupling priorities at different scales based on different geometric features determine the applicability of a numerical model for a certain type of problem. In this study, we present our multi-scale modeling capabilities that have been developed based on the numerical manifold method for analyzing coupled hydro-mechanical processes in fractured rocks. Based on their geometric features, the fractures are modeled as continua—finite-thickness porous zones, and discontinua—discontinuous interfaces and microscale asperities and granular systems. Different governing equations, physical laws, coupling priorities, and approaches for addressing fracture intersections and shearing are then applied to describe these. We applied these models to simulate coupled processes in fractured rocks using realistic geometry obtained from rock images at different scales. We first calculated shearing of a single fracture with different models and demonstrated the impacts of asperities on shearing. We then applied the continuous and discontinuous models to simulate a network of rough fractures, demonstrating that contact dynamics contribute significantly to the geometric, multi-physical evolution of systems where rough fractures are not mineral filled. For a discrete fracture network, our coupled processes modeling demonstrates that shearing of the discrete fractures can have a major impact on stress and pore pressure distribution. Lastly, we applied the discontinuous granular model to simulate evolution of a complex granular system with a deformation band, demonstrating that the deformation band can dominate contact dynamics, the structural and the stress evolution of the granular system.

58 GEOSCIENCES↗