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DOE OSTI2020

Carbon nanotube porin diffusion in mixed composition supported lipid bilayers

Carbon nanotube porins (CNTPs), short pieces of carbon nanotubes capable of self-inserting into a lipid bilayer, represent a simplified model of biological membrane channels. We have used high-speed atomic force microscopy (HS-AFM) and all-atom molecular dynamics (MD) simulations to study the behavior of CNTPs in a mixed lipid membrane consisting of DOPC lipid with a variable percentage of DMPC lipid added to it. HS-AFM data reveal that the CNTPs undergo diffusive motion in the bilayer plane. Motion trajectories extracted from the HS-AFM movies indicate that CNTPs exhibit diffusion coefficient values broadly similar to values reported for membrane proteins in supported lipid bilayers. The data also indicate that increasing the percentage of DMPC leads to a marked slowing of CNTP diffusion. MD simulations reveal a CNTP-lipid assembly that diffuses in the membrane and show trends that are consistent with the experimental observations.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2020

The role of geography in the complex diffusion of innovations

The urban–rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with new insights into the spread of information, technological progress and economic development. In this work, we analyze the spatial adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and uncover empirical features about the spatial adoption in social networks. During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million friendship ties of 3 million users. We find that the number of adopters as a function of town population follows a scaling law that reveals a strongly concentrated early adoption in large towns and a less concentrated late adoption. We also discover a strengthening distance decay of spread over the life-cycle indicating high fraction of distant diffusion in early stages but the dominance of local diffusion in late stages. The spreading process is modelled within the Bass diffusion framework that enables us to compare the differential equation version with an agent-based version of the model run on the empirical network. Although both model versions can capture the macro trend of adoption, they have limited capacity to describe the observed trends of urban scaling and distance decay. We find, however that incorporating adoption thresholds, defined by the fraction of social connections that adopt a technology before the individual adopts, improves the network model fit to the urban scaling of early adopters. Controlling for the threshold distribution enables us to eliminate the bias induced by local network structure on predicting local adoption peaks. Finally, we show that geographical features such as distance from the innovation origin and town size influence prediction of adoption peak at local scales in all model specifications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Hybrid DFT investigation of the energetics of Mg ion diffusion in α-MoO 3

We report that rechargeable batteries that utilize divalent Mg ions as the charge carrier species can in principle achieve substantially greater volumetric energy densities than conventional Li-ion batteries. One significant impediment to the development of commercially viable Mg-ion batteries is the slow rate of Mg ion diffusion through otherwise promising cathode materials. Accurate prediction of the activation energies associated with this diffusion process using density functional theory (DFT) is especially challenging due to self-interaction errors intrinsic to DFT that lead to over-delocalization of the d-electrons. One effective but highly computationally demanding approach to reducing self-interaction errors is the use of hybrid functionals, which incorporate a fraction of exact Hartree–Fock exchange. In this work, we assess the effects of exact exchange on computed activation energies for ion diffusion in one potential cathode material, α-MoO 3 . In contrast to previous studies that primarily utilize non-hybrid functionals, we perform nudged elastic band calculations in which the nuclear coordinates are fully converged using both hybrid functionals and k-point sampling. Additionally, it is found that while non-hybrid functionals indicate the existence of thermodynamically accessible channels for bulk Mg ion diffusion in all three dimensions, hybrid functionals predict that some of these channels are largely inaccessible under typical charge/discharge conditions. Furthermore, it is demonstrated that certain commonly used approximations for incorporating the effects of Hartree–Fock exchange are inadequate for this system, including DFT+U calculations and the use of single-point hybrid calculations using atomic positions obtained using non-hybrid functionals.

25 ENERGY STORAGE↗

DOE OSTI2019

Diffusive ferromagnetic roller gas

An ensemble of actively rotating ferromagnetic particles is used to realize an active roller gas. Here, we investigate the diffusive properties of such a gas in experiments and simulations. We reveal that ferromagnetic rollers demonstrate a normal (Fickian) diffusion with a characteristic linear growth of the mean-squared displacement, while statistics of displacements stay non-Gaussian. At short times the system has a bimodal distribution of the displacements that transitions with time to a quasi-Gaussian distribution (Gaussian core with overpopulated tails) for a range of studied particle number densities. Inert particles introduced into the active roller gas exhibit similar diffusive behavior. Here, the results provide insights into diffusive properties of active colloidal systems with activity originating from spinning degrees of freedom.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Diffusion characteristics of water molecules in a lamellar structure formed by triblock copolymers

The distribution and diffusion of water molecules are playing important roles in determining self-assembly and transport properties of polymeric systems. Small-angle neutron scattering (SANS) experiments and molecular dynamics (MD) simulation have been applied to understand the distribution of water molecules and their dynamics in the lamellar membrane formed by Pluronic L62 block copolymers. Penetration of water molecules into the polyethylene oxide (PEO) layers of the membranes has been estimated using scattering length density (SLD) profiles obtained from SANS measurements, which agree well with the molecular distribution observed from MD simulations. The water diffusion coefficient at different regions of the lamellar membrane was further investigated using MD simulation. The diffusion characteristic shows a transition from normal to anomalous diffusion as the position of the water molecule changes from the bulk to PEO and to the polypropylene oxide (PPO) layer. Here we find that water molecules within the PEO or PPO layers follow subdiffusive dynamics, which can be interpreted by the model of fractional Brownian motion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Comprehensive evaluation and parametric sensitivity of interatomic potential models for diffusion kinetics of Cr 2 O 3 in molecular dynamics

While molecular dynamics (MD) has proven to be a promising approach to investigate the diffusion properties, the grand challenge resides in evaluating potential model parameters to accurately replicate experimentally measured properties. The Buckingham potential model with Columbic interaction is widely employed in MD simulations of chromia (Cr 2 O 3 ) systems, as it allows for reasonable computational cost and accuracy. However, considering the well-known limitation of classical potential models in simultaneous reproduction of various physical phenomena, further comprehensive evaluation of the potential is required for calculation of diffusion properties. In this study, we benchmark the performance of three different Buckingham models with the experimental data by calculating structural, thermodynamic, and mechanical properties of defect-free Cr 2 O 3 , and diffusion properties of Cr 2 O 3 with vacancy defects. Available Buckingham models display limited accuracies, consolidating the necessity of retraining the potential parameters for all properties impacting the diffusion dynamics. Oversimplification in parameterization procedures is suggested to impede the universal performance in property reproduction. Furthermore, this research also demonstrates effective guidelines for choosing a proper parameter set of current Buckingham potential for MD simulation with Cr 2 O 3 depending on properties and for potential reparameterization.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Solid-phase reactive inter-diffusion of Mg/B multilayers

A better understanding of the reaction of Mg and B in the solid-phase regime is needed for the low-temperature synthesis of MgB 2 films. Here in this paper, we study the kinetics of reactive inter-diffusion of Mg and B multilayers on glassy carbon substrates in the temperature range of 400-650°C. Results show that, at these temperatures, inter-diffusion is characterized by a single activation energy of ~0.45eV. The formation of the superconducting MgB 2 phase with critical temperatures of 25–31 K occurs at reaction temperatures of 450°C and above, with the rate of inter-diffusion obeying a power law with a kinetic exponent of ~0.3. This suggests that rate-limiting processes are the nucleation and growth of MgB 2 grains rather than diffusion and interfacial reactions. Implications of these results to the low-temperature synthesis of MgB 2 films are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

The impact of nanoparticle softness on its tracer diffusion coefficient in all polymer nanocomposites

The diffusion of nanoparticles in a polymer matrix is an area of current interest. However, a complete understanding is still limited as it is often difficult to quantify the much slower motion of nanoparticles in a polymer matrix. To combat this problem, we have developed a protocol to measure the diffusion coefficient of soft nanoparticles in a linear polymer matrix. Recently developed synthetic control over soft nanoparticle structures combined with this protocol provides a pathway to separately elucidate the effects of the molecular weight and nanoparticle softness on its diffusive behavior. These results indicate that the nanoparticle softness and deformability dictate its motion. Increasing the cross-linking density of the nanoparticle for all molecular weights increases its hardness and suppresses its motion in the linear matrix. Additionally, the nanoparticle molecular weight dependence deviates from the exponential dependence for star polymers suggesting that these nanoparticles benefit from the cooperative motion of the matrix to open pathways for the nanoparticle. Finally, comparison of these experimentally determined values to the Stokes–Einstein theory demonstrates that the nanoparticles diffuse much slower than a hard sphere. This is interpreted to indicate that there exist additional interactions between the nanoparticle and polymer matrix that are not captured by Stokes–Einstein, including threading or entanglement of the linear chain with the nanoparticle.

Rostom, Sahar↗

DOE OSTI2023

Diffusion of Sn donors in β-Ga 2 O 3

Diffusion of the n-type dopant Sn in β-Ga 2 O 3 is studied using secondary-ion mass spectrometry combined with hybrid functional calculations. The diffusion of Sn from a Sn-doped bulk substrate with surface orientation (001) into an epitaxial layer is observed after heat treatments in the temperature range of 1050–1250 °C. Calculated formation energies of Sn-related and intrinsic defects show that the migration of Sn is mediated by Ga vacancies ( V Ga ) through the formation and dissociation of intermittent mobile V Ga Sn Ga complexes. The evolution of the Sn concentration vs depth profiles after heat treatments can be well described by a reaction–diffusion model. Using model parameters guided by the hybrid functional calculations, we extract a V Ga Sn Ga complex migration barrier of 3.0 ± 0.4 eV with a diffusion coefficient of 2 × 10 –1 cm 2 /s. The extracted migration barrier is consistent with our theoretical predictions using the nudged elastic band method, which shows migration barriers of 3.42, 3.15, and 3.37 eV for the [100], [010], and [001] directions, respectively.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Ensemble flow reconstruction in the atmospheric boundary layer from spatially limited measurements through latent diffusion models

Due to costs and practical constraints, field campaigns in the atmospheric boundary layer typically only measure a fraction of the atmospheric volume of interest. Machine learning techniques have previously successfully reconstructed unobserved regions of flow in canonical fluid mechanics problems and two-dimensional geophysical flows, but these techniques have not yet been demonstrated in the three-dimensional atmospheric boundary layer. Here, we conduct a numerical analogue of a field campaign with spatially limited measurements using large-eddy simulation. We pose flow reconstruction as an inpainting problem, and reconstruct realistic samples of turbulent, three-dimensional flow with the use of a latent diffusion model. The diffusion model generates physically plausible turbulent structures on larger spatial scales, even when input observations cover less than 1% of the volume. Through a combination of qualitative visualization and quantitative assessment, we demonstrate that the diffusion model generates meaningfully diverse samples when conditioned on just one observation. These samples successfully serve as initial conditions for a large-eddy simulation code. We find that diffusion models show promise and potential for other applications for other turbulent flow reconstruction problems.

17 WIND ENERGY↗

DOE OSTI2025

Prediction of vacancy defect diffusion paths in high entropy alloys via machine learning on molecular dynamics data

Identifying the diffusion path of point defects is a critical step in understanding their evolution and the mechanisms of related phenomena. Defect diffusion occurs at small length and time scales, with impacts on material properties that may continue to evolve over ns to μs, ms, and the continuum scale (s, min, etc., and cm, m, etc.). The time scale accessible to molecular dynamics (MD) simulations is limited by small step sizes, typically in the fs range. Thus, surrogate models of MD simulations through machine learning (ML)-based algorithms are of great interest, especially for complex systems such as high entropy alloys (HEAs). In this work, dynamics governing vacancy migration in HEA were approximated with graph convolutional network (GCN) models as ansatzes for kinetic Monte Carlo (KMC) rate catalogs. Network design considered that diffusion in crystalline solids generally depends on interactions between defects and their immediate neighbor atoms. Graphs represented the vacancy surroundings, MD-generated trajectories provided training and comparison datasets, and unsupervised GCN models approximated interatomic dynamics governing vacancy migration in HEAs as ansatzes for KMC. A proof-of-concept model trained on MD data for the Fe, Ni, Cr, Co, and Cu HEA environment was used with two different neighbor interactions to assess the feasibility of training a GCN to predict vacancy defect transition rates in the HEA environment. The resulting setup rapidly generated MD-formatted synthetic trajectories based on dynamics learned from the MD training set, with a time acceleration of roughly two orders of magnitude and a similar diffusion coefficient to MD observations. Additionally, Nudged Elastic Band (NEB) calculations were performed on randomly generated FeNiCrCoCu HEA structures to determine vacancy migration barriers across nearest-neighbor sites. Transition probabilities for each jump, categorized by atomic type, were extracted from these calculations. NEB-based and GCN-based approaches led to similar outcomes.

Reimer, C↗

DOE OSTI2019

A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems

The Multilevel in Space and Energy Diffusion (MSED) method accelerates the iterative convergence of multigroup diffusion eigenvalue problems by performing work on lower-order equations with only one group and/or coarser spatial grids. It consists of two primary components: (1) a grey (one-group) diffusion eigenvalue problem that is solved via Wielandt-shifted power iteration (PI) and (2) a multigrid-in-space linear solver. In previous work, the efficiency of MSED was verified using Fourier analysis and numerical results from a one-dimensional multigroup diffusion code. Since that work, MSED has been implemented as a solver for the coarse-mesh finite difference (CMFD) system in the three-dimensional Michigan Parallel Characteristics Transport (MPACT) code. In this paper, the results from the implementation of MSED in MPACT are introduced, and the changes needed to make MSED more suitable for MPACT are described. For problems without feedback, the conclusions in this paper show that MSED can reduce the CMFD run time by an order of magnitude and the overall run time by a factor of 2 to 3 compared to the default CMFD solver in MPACT [PI with the generalized minimal residual (GMRES) method]. For problems with feedback, the convergence of the outer Picard iteration scheme is worsened by the well-converged CMFD solutions produced by the standard MSED method. To overcome this unintuitive deficiency, MSED may be run with looser convergence criteria (a modified version of the MSED method called MSED-L) to circumvent the issue until the multiphysics iteration in MPACT is improved. Results show that MSED-L can reduce the CMFD run time in MPACT by an order of magnitude, without negatively impacting the outer Picard iteration scheme.

3-D↗

DOE OSTI2024

A Second Moment Method for k -Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations

The second moment method is a linear acceleration technique that couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent of the transport discretization, unlike diffusion synthetic acceleration, and is symmetric positive definite, unlike quasidiffusion. While this method has been shown to be comparable to quasidiffusion in iterative performance for fixed source and time-dependent problems, it is largely unexplored as an eigenvalue problem acceleration scheme due to the belief that the resulting inhomogeneous source makes the problem ill posed. Recently, a preliminary feasibility study was performed on the second moment method for eigenvalue problems. The results suggested comparable performance to quasidiffusion and more robust performance than diffusion synthetic acceleration. This work extends the initial study to more realistic reactor problems using state-of-the-art discretization techniques. Finally, the results in this paper show that the second moment method is more computationally efficient than its alternatives on complex reactor problems with unstructured meshes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Search for a diffuse flux of photons with energies above tens of PeV at the Pierre Auger Observatory

Diffuse photons of energy above 0.1 PeV, produced through the interactions between cosmic rays and either interstellar matter or background radiation fields, are powerful tracers of the distribution of cosmic rays in the Galaxy. Furthermore, the measurement of a diffuse photon flux would be an important probe to test models of super-heavy dark matter decaying into gamma-rays. In this work, we search for a diffuse photon flux in the energy range between 50 PeV and 200 PeV using data from the Pierre Auger Observatory. For the first time, we combine the air-shower measurements from a 2 km 2 surface array consisting of 19 water-Cherenkov surface detectors, spaced at 433 m, with the muon measurements from an array of buried scintillators placed in the same area. Using 15 months of data, collected while the array was still under construction, we derive upper limits to the integral photon flux ranging from 13.3 to 13.8 km -2 sr -1 yr -1 above tens of PeV. We extend the Pierre Auger Observatory photon search program towards lower energies, covering more than three decades of cosmic-ray energy. This work lays the foundation for future diffuse photon searches: with the data from the next 10 years of operation of the Observatory, this limit is expected to improve by a factor of ∼20.

cosmic rays detectors↗

DOE OSTI2026

Effect of controlled magnetic island bifurcation on electron diffusion

Magnetic islands strongly influence cross-field electron transport in magnetized plasmas. In particular, bifurcations of the island topology modify the number and location of O-points, X-points, and separatrix boundaries, thereby altering diffusion pathways. In recent DIII-D experiments, external magnetic perturbations were used to rotate and periodically bifurcate the island on the q = 2 surface, causing a switchback between a q = 2/1-dominated structure and a narrower q = 4/2-dominated structure. To investigate how this topological change affects electron transport, we employ the field line tracing code TRIP3D with an implemented collisional operator. Thermal, tracer electrons launched from O-points, X-points, and outside separatrix boundaries reveal distinct diffusion regimes, including classical, subdiffusive, and superdiffusive behavior, depending on both the dominant island mode and launch location. These results suggest that island bifurcation can alter electron diffusion across rational surfaces, with direct implications for particle confinement. While the present work emphasizes diffusion as a general framework, the findings provide insight into the conditions under which electron trapping into an island or stochastization of the island's separatrix can enable additional mechanisms, such as the generation of energetic electrons.

DIII-D↗

DOE OSTI2026

Observation of the Jet Diffusion Wake Using Dijets in Heavy-Ion Collisions

Energetic quarks and gluons traversing a hot and dense quark-gluon plasma deposit energy and momentum into the medium before hadronizing to collimated sprays of particles, known as jets. This energy-momentum deposition is expected to produce medium responses, collectively known as jet wakes, with “diffusion wake” denoting a depletion of particles in the direction opposite to the propagating jet. The diffusion wake is studied by comparing dijet-hadron correlations measured in lead-lead (PbPb) and proton-proton (pp) collisions. The analysis uses PbPb and pp data recorded at a nucleon-nucleon (NN) center-of-mass energy s NN = 5.02 TeV with the CMS detector at the CERN LHC. By exploring how the dijet-hadron correlation distributions differ for various pseudorapidity separations of the two jets in the dijet, the presence of a jet diffusion wake is firmly established. The diffusion wake signal has a significance greater than 5 standard deviations for charged particles in the transverse momentum range 1 < p T < 2 GeV . The measurements are compared with model predictions with and without jet wake effects, providing new insights into quark-gluon plasma properties and the formation of jet-induced wakes.

Hayrapetyan, Aram [Yerevan Phys. Inst.]↗

DOE OSTI2026

Langevin and Fokker-Planck analyses for diffusion-mediated passing of circular and discorectangular species in two-dimensional channels

The propensity for pairs of diffusing species to pass each other within narrow channels or pores is of basic interest as a first-passage-type problem. It is also of relevance for solution-phase transport in nanoporous materials, and in particular for catalytic conversion reactions where high yield requires that product species can efficiently pass reactant species to exit the pores. Here, we analyze a two-dimensional model with nonoverlapping circular and discorectangular species confined to a rectangular channel, and where passing is mediated by Brownian dynamics in an implicit solvent. For narrower channels where passing is still possible, the discorectangle must align with the channel to pass the circular species. Behavior of the passing propensity, 𝑃, can be assessed by strongly damped Langevin simulations, or within an equivalent Fokker-Planck equation (FPE) formalism. The latter corresponds to a diffusion problem in a “higher-dimensional channel” with a constriction. We assess the variation of the passing propensity, 𝑃, for a broad range of channel width including its scaling just above the threshold where passing is sterically blocked. Analysis of 𝑃 versus the rotational diffusion coefficient 𝐷 𝑟 of the discorectangle reveals a significant decrease in 𝑃 for lower 𝐷 𝑟 for moderate channel width. This prompts a direct analysis of the regime where 𝐷 𝑟 → 0 , for which the FPE can be reduced to a three-dimensional diffusion problem, precise analysis of which is facilitated by adaptive-mesh finite element methods. The dependence of 𝑃 on the aspect ratio of the discorectangle is also assessed.

Rahman, Md Khaledur [Ames Laboratory (AMES), Ames,↗

DOE OSTI2019

Energy barriers for Pb adatom diffusion on stepped ultrathin Pb(111) quantum nanofilms: First-principles calculations

Various properties of Pb(111) nanofilms, prototypical quantum films, have been studied extensively. However, key ab initio -level energy barriers for Pb adatom diffusion on stepped Pb(111) nanofilm surfaces are still not available. Using first-principles density functional theory, we calculate these barriers for films with thicknesses of few monolayers (ML). We find that two-atom exchange is always much more favorable than direct hopping to cross A- or B-type steps. Ehrlich-Schwoebel (ES) barriers for downward transport to a higher-coordination step-edge site depend strongly on the film thickness. For such transport from 2- to 1-ML terraces, or from 4- to 3-ML terraces, there is no an ES barrier, but large ES barriers of more than 100 meV are found from 3- to 2-ML terraces. We also obtain the barriers for diffusion along the step edges and find that these step-edge barriers are significantly larger than terrace diffusion barriers. In addition, we analyze energetics for diffusion on the top flat surface of a nanofilm supported on a vicinal surface, and thus having underlying buried or ghost steps. We quantify the tilted potential energy surface in both ghost A- and B-step regions separating 2- and 3-ML (as well as 3- and 4-ML) terraces. Finally, consequences are discussed for the growth kinetics of supported Pb nanofilms, where the support does not strongly affect electronic states within the film.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗