Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “micro scale models”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Spherical tokamak physics research in preparation for the operation of NSTX-U

The National Spherical Torus Experiment Upgrade (NSTX-U) is preparing to resume operation, representing a crucial step toward realizing compact, cost-effective fusion pilot plants. In advance of this, extensive modeling and data analysis have been conducted to advance the physics basis for low-aspect-ratio, high-performance plasma regimes, focusing on three core objectives: confinement and stability, power and particle handling, and steady-state operation. Significant progress has been made in understanding the electron temperature flattening in high-β plasmas, which is shown to be driven by a complex interplay of magnetohydrodynamic instabilities (e.g. non-resonant infernal modes), fast-ion-driven Alfvén eigenmodes, and electron and ion-scale micro-instabilities, particularly Kinetic Ballooning Modes (KBMs), whose destabilization is strongly dependent on parallel magnetic field fluctuations (δB ∥ ). Furthermore, a new gyrokinetic critical pedestal model was developed, accurately predicting pedestal structure by identifying KBMs as the primary stability limit, offering a critical constraint for future high-confinement scenarios. To address the challenge of high heat flux, novel liquid lithium plasma-facing components were modeled. The analysis confirmed that lithium vapor shielding is a self-regulating mechanism for heat mitigation, while also emphasizing that strong main ion parallel flow is essential to minimize core lithium contamination. Finally, progress toward steady-state operation was anchored by developing the required physics basis and control tools. This includes predictive modeling for reversed magnetic shear sustainment, demonstrating that magnetic island-induced bootstrap current reduction is negligible in STs, and advancing real-time control and disruption avoidance capabilities. The development of high-speed surrogate models (e.g. MMMNet) provides computationally efficient tools vital for non-inductive scenario optimization and integrated, low-disruptivity operations planned for NSTX-U.

NSTX-U↗
DOE OSTI2026

Predicting U 3 O 8 powder processing conditions: An AI/ML approach analyzing deep learning embeddings of SEM micrographs

High-resolution SEM images of uranium-oxide powders encode micro- and nanoscale clues to their synthesis route and calcination temperature. We trained a ResNet-50 model on 11 commercial-scale U₃O₈ classes, ammonium diuranate (ADU) or uranyl peroxide (H₂O₂) precursors calcined at temperatures ranging from 400 to 750 °C and added a 256-D projection head before the classifier to analyze the learned representation. The best of eight seeds reached 92.4 % accuracy on reserved testing data, but our focus is the structure of the embedding space rather than the accuracy and labels. We quantify class relatedness in the original 256-D space using centroid similarity and distributional distances, and we use Uniform Manifold Approximation Projection (UMAP) for visualization. ‘Unknown’ images from different preparation methods, SEM operators, and from the literature localized near the expected classes under a nearest-centroid analysis without retraining, as well as clustered in similar UMAP space. In conclusion, this embedding-centered workflow complements black-box classification by providing quantitative, similarity-based comparisons of U₃O₈ morphologies and reduces storage space by up to 98 % for image data used in millisecond vector search comparisons.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Higher Efficiency, Demand Flexible Refrigerator with On-Demand Micro-Vibrational De-icing Technology

Refrigerator technology has advanced significantly over the last couple of decades. Today’s refrigerators use only about 25% of the energy that was required to power models built in 1975. Even as they continually improve efficiency to meet standards, refrigerators have increased in size by almost 20%, added energy-consuming features such as through-the-door ice, and provide more benefits than ever before. However, a few challenges and technology gaps are preventing further improvement of the demand responsiveness and efficiency of the refrigerators. One of the major technology gaps in existing refrigerators is their outdated de-icing process. When the evaporator generates frost, an old-fashioned resistive heating element melts the ice. Most refrigerators have a timed defrost cycle, rather than an active system that could monitor the state of the frost. In these systems, not only is the precious electricity used at its least efficient form of conversion (direct conversion of electricity to heat), but also all the latent heat associated with the ice is wasted during the melting process. On top of that, the refrigerator needs to work harder to pull the temperature down after defrosting, and, last but not least, the food quality is severely impacted by the temperature swings during the defrost cycle. According to a study, the EU alone wastes 89 million tons of food in the supply chain every year. Any temperature swing during defrosting (about 6F according to Emerson for low-temperature cases) can negatively impact the shelf life of meat and other products for multiple days. All these issues can happen during the peak demand time of the electric grid. Unlike the conventional systems, the proposed novel advanced micro-vibrational deicing process uses no heat for defrosting. Instead, it uses the micro vibrations generated by a piezoelectric or vibration-generating module to mechanically break ice from the heat exchanger almost instantaneously. The project titled “Higher Efficiency, Demand Flexible Refrigerator with On-Demand Micro-Vibrational De-icing Technology, performed by Ultrasonic Technology Solutions, LLC (UTS) of Knoxville, TN, in collaboration with Emerson (now Copeland), represents the final phase of a multi-year effort funded under the U.S. Department of Energy’s Building Technologies Office (BTO) BENEFIT FOA 2020. Initiated on October 1, 2021, and completed after a nine-month no-cost extension ending September 30, 2025, this project aimed to develop and validate a novel micro-vibrational mechanical defrosting system, achieving more than 25% improvement in defrosting energy efficiency over conventional baseline defrosting technologies. Over sixteen quarters, the project advanced from fundamental ice-mechanical characterization and prototype development to full-scale system integration and validation. Initial efforts established project management infrastructure and characterized ice adhesion properties, followed by the design and fabrication of early aluminum-based prototypes for resonance frequency testing. Subsequent quarters saw rapid technical progression, including the identification of optimal piezoelectric and motor-based vibration mechanisms, the demonstration of effective de-icing over 6x6-inch aluminum surfaces. The team achieved its Go/No-Go milestone by exceeding the 25% energy-efficiency improvement target—reaching up to 3,340% under optimized conditions—and later confirmed that motor-driven systems offered superior performance and energy efficiency compared to piezoelectric alternatives. Continued refinement led to the development of amplifier systems on printed circuit boards, improved control and instrumentation hardware, and integration into full-scale heat exchanger (HX) prototypes at both UTS and Copeland facilities. Multiple vibration-mounting studies and frost-growth experiments guided mechanical optimization and noise-mitigation strategies, achieving a 17.5 dB reduction in sound pressure level and verifying robust mechanical performance. Advanced analyses, including modal and harmonic simulations, established a quantitative understanding of vibrational behavior and de-icing efficiency across >1000 cm² systems. The final project phase successfully demonstrated scalable integration within reach-in and chest freezer prototypes, confirmed >25% efficiency improvements in large-area systems, and completed a comprehensive business model and scale-up strategy identifying electric defrost systems as the primary beachhead market. The culmination of this DOE-supported effort establishes micro-vibrational defrosting as a viable, high-efficiency, low-noise, and demand-flexible de-icing technology, paving the way for commercial deployment and broader application in next-generation refrigeration systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Large-scale physically accurate modelling of real proton exchange membrane fuel cell with deep learning

Proton exchange membrane fuel cells, consuming hydrogen and oxygen to generate clean electricity and water, suffer acute liquid water challenges. Accurate liquid water modelling is inherently challenging due to the multi-phase, multi-component, reactive dynamics within multi-scale, multi-layered porous media. In addition, currently inadequate imaging and modelling capabilities are limiting simulations to small areas (<1 mm 2 ) or simplified architectures. Herein, an advancement in water modelling is achieved using X-ray micro-computed tomography, deep learned super-resolution, multi-label segmentation, and direct multi-phase simulation. The resulting image is the most resolved domain (16 mm 2 with 700 nm voxel resolution) and the largest direct multi-phase flow simulation of a fuel cell. This generalisable approach unveils multi-scale water clustering and transport mechanisms over large dry and flooded areas in the gas diffusion layer and flow fields, paving the way for next generation proton exchange membrane fuel cells with optimised structures and wettabilities.

25 ENERGY STORAGE↗
DOE OSTI2021

The role of micro-inertia on the shock structure in porous metals

The behavior of porous materials under shock loading is a multi-scale problem bridging orders of magnitude across the macroscale geometry and the microscale pores. Under static loading, this problem is well understood, relating mechanisms of pore closure and crushing to the equivalent macroscale models. The dynamic response of porous solids under shock loading is related to the effects of viscoplasticity and micro-acceleration fields around the void boundaries. The significance of the micro-inertia effects in modeling the dynamic behavior of porous materials remains an open question. In this work, an experimental investigation on closed-cell porous aluminum with small porosity provides the evidence for the first time of micro-inertia’s fundamental role in describing the shock structure in these materials. Materials with different levels of porosity were manufactured using a modified process of additive manufacturing to achieve a mean pore size below 50$\mu$m. Plate impact experiments on porous aluminum samples were conducted at pressures in the range of 2 to 11 GPa. The structure of the steady shock was characterized as a function of porosity and shown to validate behavior revealed by an analytical approach (Czarnota et al. [J. Mech. Phys. Solids 107 (2017)]), highlighting the fundamental role of micro-inertia effects in such cases.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Modeling Flow and Transport in Fractured Rock using Machine Learning [Slides]

Fractured systems in the subsurface play a role in many natural and engineered applications such as geologic carbon sequestration, hydraulic fracturing and underground nuclear test detection. Structural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Traditional modeling approaches either ignore or idealize structural information at these larger scales because we lack a computational framework that utilizes it in its entirety. The work presented here integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning.

58 GEOSCIENCES↗
DOE OSTI2021

Review of Onsite Temperature and Solar Forecasting Models to Enable Better Building Design and Operations

Advanced building controls and energy optimization for new constructions and retrofits rely on accurate weather data. Traditionally, most studies utilize airport weather information as the decision inputs. However, most buildings are in environments that are quite different than those at the airport miles away. Tree cover, adjacent buildings, and micro-climate effects caused by the larger surrounding area can all yield deviations in air temperature, humidity, solar irradiance, and wind that are large enough to influence design and operation decisions. In order to overcome this challenge, there are many prior studies on developing weather forecasting algorithms from micro-to meso-scales. Additionally, this paper reviews and complies knowledge on common weather data resources, data processing methodologies and forecasting techniques of weather information. Commonly used statistical, machine learning and physical-based models are discussed and presented as two major categories: deterministic forecasting and probabilistic forecasting. Finally, evaluation metrics for forecasting errors are listed and discussed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Evaluating the Influence of Hemorheological Parameters on Circulating Tumor Cell Trajectory and Simulation Time

Extravasation of circulating tumor cells (CTCs) occurs primarily in the microvasculature, where flow and cell interactions significantly affect the blood rheology. Capturing cell trajectory at this scale requires the coupling of several interaction models, leading to increased computational cost that scales as more cells are added or the domain size is increased. In this work, we focus on micro-scale vessels and study the influence of certain hemorheological factors, including the presence of red blood cell aggregation, hematocrit level, microvessel size, and shear rate, on the trajectory of a circulating tumor cell. We determine which of the aforementioned factors significantly affect CTC motion and identify those which can potentially be disregarded, thus reducing simulation time. We measure the effect of these elements by studying the radial CTC movement and runtime at various combinations of these hemorheological parameters. To accurately capture blood flow dynamics and single cell movement, we perform high-fidelity hemodynamic simulations at a sub-micron resolution using our in-house fluid dynamics solver, HARVEY. We find that increasing hematocrit increases the likelihood of tumor cell margination, which is exacerbated by the presence of red blood cell aggregation. As microvessel diameter increases, there is no major CTC movement towards the wall; however, including aggregation causes the CTC to marginate quicker as the vessel size increases. Finally, as the shear rate is increased, the presence of aggregation has a diminished effect on tumor cell margination.

Roychowdhury, Sayan↗
DOE OSTI2022

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Heterogeneous materials and materials with complex microstructures pose a unique challenge in the development of accurate models of their response to external stimuli. These difficulties principally arise due to the difficulty in characterizing and modeling the constituents and their interactions. It is usually possible, though non-trivial, to construct an explicit representation of the microstructure (a direct numeric simulation or DNS) but the method by which the complex modes of deformation and other processes can be homogenized to a reduced-order approximation is frequently unclear. Many homogenization approaches are ad-hoc and lack a strong justification beyond ease of computation. Furthermore, the homogenization approach can, in some cases, not utilize the full breadth of information available in the computation of the macro-scale stresses and deformation measures. It is also noteworthy that homogenization, by its very nature, will tend to obfuscate details of processes occurring at the lower length-scale. It is therefore of interest to include as much information as possible in the construction of the reduced-order model so as to be predictive in a variety of loading environments. We here present a length-scale bridging technique based upon the micromorphic continuum mechanics of Eringen which incorporates volume and surface area averages as a part of its construction. This approach enforces the balance equations at the micro-scale and then studies the effect of the spatially varying nature on the macro-scale. This leads, naturally, to further balance equations which are solved at the macro-scale. This work details a homogenization framework which arises naturally from the micromorphic construction of Eringen attempting to introduce no definitions beyond which are justifiable from micro-structural considerations. One of the results of this effort is the so-called “micromorphic filter” which has been developed and applied to several DNS to demonstrate its effectively. In order to determine the macroscopic degrees of freedom we utilize the special case of an overlap coupling technique where the macro-scale is fully constrained to the micro-scale. This enables us to study the resulting material properties as expected but also allows us to further study the boundary conditions on the additional degrees of freedom at the macro-scale.

42 ENGINEERING↗
DOE OSTI2020

Molecular scale insight of pore morphology relation with mechanical properties of amorphous silica using ReaxFF

Porous materials are typically heterogeneous and they contain large variations of micro-/nano-pore structures, causing complicated behaviors. In continuum models, most mechanical properties of porous materials are estimated based on porosity, while the variations of micro/nano structures are ignored. That could be problematic as the microscopic heterogeneity may affect the mechanical response of porous materials. Thus, understanding micro/nano heterogeneity impact has been the focus in many scientific and engineering subjects. In the present study, we investigated the effect of nanopore structure (including pore shape and orientation) as well as porosity on mechanical properties of amorphous silica (a-SiO 2 ). The pore sizes in our simulations are comparable to the corresponding ones observed in a-SiO 2 based materials. We found that the existing of nanopores strongly influences Young’s modulus (E) and critical energy release rate (G IC ). These properties decrease with increasing porosity. Importantly, the impact of nanopores was characterized by structural parameters of porous materials. In addition to dependency on porosity, Young’s modulus also was found to vary as a function of potential energy per atom, which highly depends on nanopore shape. Furthermore, critical energy release rate was found to increase with increasing ligament length (also known as pore wall thickness). Finally, the results highlighted the importance of nanopore structures, which must be taken into account when studying fracture mechanisms in porous materials. Based on our findings, it was proposed that mechanical properties of porous materials can be controlled by nano-engineering pore structures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Session 3: Irradiation and Thermal Stesses - NRC Graphite Behavior Model

Graphite anisotropic microstructure Graphite crystal structure and basal planes Response to irradiation and temperature C-axis and a-axis behavior The effect of porosity Nano-and micro-length scale Microscopic to macroscopic response Material property changes Defect length-scale factors Internal stress build-up Irradiation induced dimensional change Temperature effects Stress increases & property changes

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Improving the W Coating Uniformity by a COMSOL Model-Based CVD Parameter Study for Denser W f /W Composites

Tungsten (W) has the unique combination of excellent thermal properties, low sputter yield, low hydrogen retention, and acceptable activation. Therefore, W is presently the main candidate for the first wall and armor material for future fusion devices. However, its intrinsic brittleness and its embrittlement during operation bears the risk of a sudden and catastrophic component failure. As a countermeasure, tungsten fiber-reinforced tungsten (W f /W) composites exhibiting extrinsic toughening are being developed. A possible W f /W production route is chemical vapor deposition (CVD) by reducing WF 6 with H 2 on heated W fabrics. The challenge here is that the growing CVD-W can seal gaseous domains leading to strength reducing pores. In previous work, CVD models for W f /W synthesis were developed with COMSOL Multiphysics and validated experimentally. In the present article, these models were applied to conduct a parameter study to optimize the coating uniformity, the relative density, the WF 6 demand, and the process time. A low temperature and a low total pressure increase the process time, but in return lead to very uniform W layers at the micro and macro scales and thus to an optimized relative density of the W f /W composite. High H 2 and low WF 6 gas flow rates lead to a slightly shorter process time and an improved coating uniformity as long as WF 6 is not depleted, which can be avoided by applying the presented reactor model.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Probing the Mechanical Performance of Micro-architected Porous Structures Through In Situ Characterization and Analysis

Micropores play critical roles in both natural and man-made materials. Such pores take on a variety of shapes and sizes ranging from spherical to irregular sphere-like voids with diameters spanning from the nanometer to millimeter scales. When porous structures are mechanically loaded, the pores direct the stress around their free surfaces, altering the material’s mechanical response relative to fully dense materials. In this study, for the first time, we create micro-architected porous samples using nanolithography and investigate the role of pore morphology by conducting a series of in situ micropillar compression tests in scanning electron microscopy. The findings demonstrate that porosity is the primary factor influencing the mechanical response of these micro-architected materials, as often seen on a macroscopic level. Additionally, we observed that pore geometry had a significant impact on Young’s modulus, yield stress, and strain energy density as a secondary parameter. Then, the extracted Young’s modulus was compared to macroscopic empirical models and determined the analytical models sufficiently described the impact of porosity in the microscopic scale but failed to capture the impact of second-order parameters. Furthermore, these results suggest how porous materials can be tailored to achieve desired mechanical properties based on the engineering applications of interest.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Permeability Hysteresis From Microchannels Opening During Dissolution/Reprecipitation Cycle

Abstract Permeability is a critical parameter for geological resources characterization. Its evolution with respect to porosity is particularly interesting and many research initiatives focus on deriving such relationships, to understand some hydraulic impacts of microstructure alteration. Permeability evolution from chemical reactions, for instance, can become complex as flow channels may open during rock dissolution. In this contribution, we show that this phenomenon can lead to irregular porosity‐permeability curves and permeability hysteresis after reprecipitation. Current approaches describing permeability as a simple function of porosity can therefore not capture this behavior, and we advocate instead the use of dynamic modeling for such scenarios. We demonstrate our approach by modeling a dissolution/precipitation cycle for a unit cell pore channel and quantify the process at larger scale on three different rock samples, whose microstructures are reconstructed from segmented micro‐Computerised Tomography scans.

Lesueur, Martin↗
DOE OSTI2025

Non-Destructive, Three-Dimensional Imaging of Processes in the Rhizosphere Utilizing High Energy Photons

Soil structure, which can be described as the aggregation and distribution of pore spaces, regulates carbon, nutrient, and water cycling across the Earth system. Yet the inability to make quantitative, dynamic, in situ measurements of soil structure and rhizosphere carbon flow has prevented meaningful incorporation of soil structural processes into Earth System Models (ESMs). The key limitations are: (i) Lack of scale integration between micron-scale soil structure and ecosystem-scale models, (ii) Poor functional linkage between soil structural properties and biogeochemical processes, and (iii) Absence of dynamic 3D measurements of rhizosphere structural changes and carbon transformations. To address these challenges, we developed a new integrated positron emission tomography (PET) - microcomputed tomography (CT) imaging platform that enables the first 4D (spatial 3D and time), non-invasive, quantitative imaging of carbon allocation and rhizosphere structural dynamics in living plants and intact soils. The system combines: • Rhizo-PET (R-PET): a high-resolution positron emission tomography scanner optimized for 11 CO 2 tracing in plant roots. • a-Se micro-CT: a high-contrast, high-spatial resolution CT system based on amorphous selenium (a-Se) direct conversion technology, enabling micron-scale visualization of soil structure and root–soil interfaces. Together, these advances allow us to quantify how carbon exudates move, transform, and stabilize within the rhizosphere, directly informing missing processes in BER-relevant carbon cycle models.

42 ENGINEERING↗
DOE OSTI2021

In vivo visualization of butterfly scale cell morphogenesis in Vanessa cardui

Many organisms exhibit functional micro- and nanoscale materials with structural definition and performance that challenge synthetic fabrication techniques, yet we know little about the processes that enable their formation. Using butterfly scales as a model system for functional biomaterials, we establish a timeline of scale formation and quantify relevant structural parameters for developing painted lady butterflies. We overcome challenges of previous efforts by imaging structure formation directly in living organisms, which allows us to continuously observe the evolving wing tissue and the fine details of individual scale cells. Visualization of scale structure formation in live butterflies forms the basis for modeling the underlying biomechanical processes and opens avenues for their translation into advanced fabrication strategies.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Understanding Low Level Jets in the US Atlantic Offshore

Low level jets (LLJs) in the atmosphere exhibit a local windspeed maximum in the boundary layer, with positive shear beneath the jet and negative shear above the jet. Wind turbines tend to experience increased loads with varying wake recovery characteristics in the presence of an LLJ, therefore understanding the mechanism and impact of LLJs is crucial to wind energy development. The US Mid-Atlantic offshore region is a huge potential wind energy resource, yet LLJs in this area are poorly understood. In particular, the coastal offshore environment does not exhibit the same diurnal cycle that leads to strong LLJs in the well-characterized Great Plains region. In this study, we use the Weather Research and Forecasting model (WRF) plus lidar buoy data to identify case studies for LLJ events in 2020 in the New York Bight. A reduced order model is presented to explain the onset of these events based on the competing effects of baroclinicity and eddy diffusivity. Finally, using the macro-scale WRF, we drive a micro-scale large eddy simulation (LES) to generate a more detailed characterization of the Marine Boundary Layer during an LLJ. Gaining a better understanding of LLJs and their impacts on offshore wind in the mid-Atlantic is crucial for a transition toward renewable energy.

atmospheric boundary layer↗
DOE OSTI2023

Atomistic simulations and machine learning of solute grain boundary segregation in Mg alloys at finite temperatures

Understanding solute segregation thermodynamics is the first step in investigating grain boundary (GB) properties, such as strong yttrium (Y) effects on grain growth and texture evolution in micro-scale polycrystalline magnesium (Mg) alloys. To estimate the average GB segregation behavior in low-solute-concentration Mg alloys (e.g., 2 at.% Y), a state-of-the-art spectral approach is applied based on a per-site segregation energy spectrum for Y solute atoms at zero K obtained from molecular statistics (MS) simulations of ~10 4 GB sites in Mg symmetric tilt GBs (STGBs). Although selected MS simulation results are consistent with verification by density functional theory (DFT) calculations, estimates of average segregation tendency based on the zero-K energy spectrum deviate from experimental observations. To resolve this problem, thermodynamic integration (TI) methods based on molecular dynamics (MD) simulations are used to determine the per-site segregation free energies of Y at representative GB sites, which show contributions beyond harmonic approximations can be important for certain GB sites at high temperatures. A surrogate model of per-site segregation free energy is constructed from a small set of TI data points using stacking cross-validation regressors and physics-informed descriptors. This model is applied to predict the Y segregation free energy spectra for thousands of GB sites in Mg STGBs with uncertainty quantification. Finally, the average segregation tendency predicted by the spectral approach based on the free energy spectra agrees well (within the uncertainty range) with experimental observations for micro-scale polycrystalline Mg alloys at typical thermomechanical processing temperatures (500 ~ 800 K), where thermodynamic equilibrium states are likely to be achieved due to fast diffusion.

Atomistic simulations↗