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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.

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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Diffusion anisotropy of poor metal solute atoms in hcp-Ti

Atom migration mechanisms influence a wide range of phenomena: solidification kinetics, phase equilibria, oxidation kinetics, precipitation of phases, and high-temperature deformation. In particular, solute diffusion mechanisms in α-Ti alloys can help explain their excellent high-temperature behaviour. The purpose of this work is to study self- and solute diffusion in hexagonal close-packed (hcp)-Ti, and its anisotropy, from first-principles using the 8-frequency model. The calculated diffusion coefficients show that diffusion energy barriers depend more on bonding characteristics of the solute rather than the size misfit with the host, while the extreme diffusion anisotropy of some solute elements in hcp-Ti is a result of the bond angle distortion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Indium and gallium diffusion through zirconia in the TiN/ZrO{sub 2}/InGaAs stack

Angle-resolved X-ray Photoelectron Spectroscopy (ARXPS) was applied to the TiN/ZrO{sub 2}/InGaAs stack to assess its thermal stability. Through a robust ARXPS analysis, it was possible to observe subtle effects such as the thermally induced diffusion of substrate atomic species (In and Ga) through the dielectric layer. The detailed characterization of the film structure allowed for assessing the depth profiles of the diffused atomic species by means of the scenarios-method. Since the quantification for the amount of diffused material was done at different temperatures, it was possible to obtain an approximate value of the activation energy for the diffusion of indium through zirconia. The result is very similar to the previously reported values for indium diffusion through alumina and through hafnia.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Reaction rates for reaction-diffusion kinetics on unstructured meshes

The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. Here in this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmor radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Accelerated kinetic Monte Carlo: A case study; vacancy and dumbbell interstitial diffusion traps in concentrated solid solution alloys

Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and $\langle$100$\rangle$ dumbbell interstitials in Ni–Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy’s non-monotonic behavior. In contrast, the difference between formation energies of Ni–Ni, Ni–Fe, and Fe–Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition—based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one—is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Robust estimation of charge carrier diffusivity using transient photoluminescence microscopy

Transient microscopy has emerged as a powerful tool for imaging the diffusion of excitons and free charge carriers in optoelectronic materials. In many excitonic materials, extraction of diffusion coefficients can be simplified because of the linear relationship between signal intensity and local excited state population. However, in materials where transport is dominated by free charge carriers, extracting diffusivities accurately from multidimensional data is complicated by the nonlinear dependence of the measured signal on the local charge carrier density. To obtain accurate estimates of charge carrier diffusivity from transient microscopy data, statistically robust fitting algorithms coupled to efficient 3D numerical solvers that faithfully relate local carrier dynamics to raw experimental measurables are sometimes needed. Here, we provide a detailed numerical framework for modeling the spatiotemporal dynamics of free charge carriers in bulk semiconductors with significant solving speed reduction and for simulating the corresponding transient photoluminescence microscopy data. To demonstrate the utility of this approach, we apply a fitting algorithm using a Markov chain Monte Carlo sampler to experimental data on bulk CdS and methylammonium lead bromide (MAPbBr 3 ) crystals. Parameter analyses reveal that transient photoluminescence microscopy can be used to obtain robust estimates of charge carrier diffusivities in optoelectronic materials of interest, but that other experimental approaches should be used for obtaining carrier recombination constants. Additionally, simplifications can be made to the fitting model depending on the experimental conditions and material systems studied. Our open-source simulation code and fitting algorithm are made freely available to the scientific community.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Diffusion–convection model of runaway electrons due to large magnetohydrodynamic perturbations in post-thermal quench plasmas

Systematic test particle tracing simulations for runaway electrons (REs) are performed for six post-thermal quench equilibria from DIII-D and ITER, where large scale, kink-like n = 1 (n is the toroidal mode number) magnetohydrodynamic (MHD) instabilities are found. The modeled particle guiding center orbits allow extraction of the effective diffusion–convection coefficients of REs in the presence of large three-dimensional (3D) perturbations up to 10% of the equilibrium toroidal field. With a fixed spatial distribution of the field perturbation, the RE transport coefficients along the plasma radial coordinate track reasonably well with the surface-averaged perturbation level. A substantial variation in the value of the transport coefficients—by three orders of magnitude in most cases, however, occurs with varying launching location of REs along the plasma radius. Large 3D perturbations almost always lead to comparable diffusion and convection processes, meaning that diffusion alone is insufficient to describe the particle motion. At lower (but still high) level of perturbation, the RE convection is found to be dominant over diffusion. A similar observation is made when the perturbation is too strong. In the presence of large perturbation, the dependence of the RE transport on the particle energy is sensitive to the spatial distribution of the perturbation. Based on numerically obtained RE transport coefficients, an analytic fitting model is proposed to quantify the particle diffusion and convection processes due to large MHD events in post-thermal quench plasmas. The model is shown to reasonably well reproduce the direct test particle tracing results for the RE loss fraction and can, thus, be useful for incorporating into other kinetic RE codes in order to simulate the RE beam evolution in the presence of large 3D perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Onset of kinetic effects on Rayleigh–Taylor instability: Advective–diffusive asymmetry

In nature and engineering applications, the Rayleigh–Taylor instability (RTI) occurs over a wide range of Atwood, Reynolds, Mach, and Knudsen numbers. At low Atwood, Mach, and Knudsen numbers, the classic advective instability causes quasi-symmetric bubble and spike growth on the two sides of the interface. However, recent findings suggest that at high degrees of rarefaction, advective effects are suppressed and molecular diffusion leads to planar growth of the density fronts on either side of the interface. This study aims to investigate the flow physics of the transition from advective to diffusive behavior, focusing on the onset of the kinetic effects. Using the gas kinetic methodology, RTI is simulated over a range of Knudsen and Mach numbers in the transition regime. The simulation results reveal the various stages of transformation from advective instability to diffusive transport. For the first time, the study demonstrates the existence of a Knudsen–Mach parameter regime where the bubble side exhibits advective instability, while the other side shows a planar density front due to molecular diffusion, rather than the canonical advective spike shape. The dominance of different mechanisms on the two sides of the interface leads to the advective–diffusive asymmetry. In conclusion, the findings of this study can lead to a more comprehensive understanding of RTI over a wide range of Mach and Knudsen numbers.

42 ENGINEERING↗
DOE OSTI2013

DIFFUSE HARD X-RAY EMISSION IN STARBURST GALAXIES AS SYNCHROTRON FROM VERY HIGH ENERGY ELECTRONS

The origin of the diffuse hard X-ray (2-10 keV) emission from starburst galaxies is a long-standing problem. We suggest that synchrotron emission of 10-100 TeV electrons and positrons (e {sup {+-}}) can contribute to this emission, because starbursts have strong magnetic fields. We consider three sources of e {sup {+-}} at these energies: (1) primary electrons directly accelerated by supernova remnants, (2) pionic secondary e {sup {+-}} created by inelastic collisions between cosmic ray (CR) protons and gas nuclei in the dense interstellar medium of starbursts, and (3) pair e {sup {+-}} produced between the interactions between 10 and 100 TeV {gamma}-rays and the intense far-infrared (FIR) radiation fields of starbursts. We create one-zone steady-state models of the CR population in the Galactic center (R {<=} 112 pc), NGC 253, M82, and Arp 220's nuclei, assuming a power-law injection spectrum for electrons and protons. We consider different injection spectral slopes, magnetic field strengths, CR acceleration efficiencies, and diffusive escape times, and include advective escape, radiative cooling processes, and secondary and pair e {sup {+-}}. We compare these models to extant radio and GeV and TeV {gamma}-ray data for these starbursts, and calculate the diffuse synchrotron X-ray and inverse Compton (IC) luminosities of these starbursts in the models which satisfy multiwavelength constraints. If the primary electron spectrum extends to {approx}PeV energies and has a proton/electron injection ratio similar to the Galactic value, we find that synchrotron emission contributes 2%-20% of their unresolved, diffuse hard X-ray emission. However, there is great uncertainty in this conclusion because of the limited information on the CR electron spectrum at these high energies. IC emission is likewise a minority of the unresolved X-ray emission in these starbursts, from 0.1% in the Galactic center to 10% in Arp 220's nuclei, with the main uncertainty being the starbursts' magnetic field. We also model generic starbursts, including submillimeter galaxies, in the context of the FIR-X-ray relation, finding that anywhere between 0% and 16% of the total hard X-ray emission is synchrotron for different parameters, and up to 2% in the densest starbursts assuming an E {sup -2.2} injection spectrum and a diffusive escape time of 10 Myr (E/3 GeV){sup -1/2} (h/100 pc). Neutrino observations by IceCube and TeV {gamma}-ray data from HESS, VERITAS, and CTA can further constrain the synchrotron X-ray emission of starbursts. Our models do not constrain the possibility of hard, second components of primary e {sup {+-}} from sources like pulsars in starbursts, which could enhance the synchrotron X-ray emission further.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

The diffuse gamma-ray flux associated with sub-PEV/PEV neutrinos from starburst galaxies

One attractive scenario for the excess of sub-PeV/PeV neutrinos recently reported by IceCube is that they are produced by cosmic rays in starburst galaxies colliding with the dense interstellar medium. These proton-proton (pp) collisions also produce high-energy gamma rays, which finally contribute to the diffuse high-energy gamma-ray background. We calculate the diffuse gamma-ray flux with a semi-analytic approach and consider that the very high energy gamma rays will be absorbed in the galaxies and converted into electron-positron pairs, which then lose almost all of their energy through synchrotron radiation in the strong magnetic fields in the starburst region. Since the synchrotron emission goes into energies below GeV, this synchrotron loss reduces the diffuse high-energy gamma-ray flux by a factor of about two, thus leaving more room for other sources to contribute to the gamma-ray background. For an E{sub ν}{sup −2} neutrino spectrum, we find that the diffuse gamma-ray flux contributes about 20% of the observed diffuse gamma-ray background in the 100 GeV range. However, for a steeper neutrino spectrum, this synchrotron loss effect is less important, since the energy fraction in absorbed gamma rays becomes lower.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Diffuse γ-ray emission from galactic pulsars

Millisecond pulsars (MSPs) are old fast-spinning neutron stars that represent the second most abundant source population discovered by the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope (Fermi). As guaranteed γ-ray emitters, they might contribute non-negligibly to the diffuse emission measured at high latitudes by Fermi-LAT (i.e., the Isotropic Diffuse γ-Ray Background (IDGRB)), which is believed to arise from the superposition of several components of galactic and extragalactic origin. Additionally, γ-ray sources also contribute to the anisotropy of the IDGRB measured on small scales by Fermi-LAT. In this manuscript we aim to assess the contribution of the unresolved counterpart of the detected MSPs population to the IDGRB and the maximal fraction of the measured anisotropy produced by this source class. To this end, we model the MSPs' spatial distribution in the Galaxy and the γ-ray emission parameters by considering observational constraints coming from the Australia Telescope National Facility pulsar catalog and the Second Fermi-LAT Catalog of γ-ray pulsars. By simulating a large number of MSP populations through a Monte Carlo simulation, we compute the average diffuse emission and the anisotropy 1σ upper limit. We find that the emission from unresolved MSPs at 2 GeV, where the peak of the spectrum is located, is at most 0.9% of the measured IDGRB above 10° in latitude. The 1σ upper limit on the angular power for unresolved MSP sources turns out to be about a factor of 60 smaller than Fermi-LAT measurements above 30°. Our results indicate that this galactic source class represents a negligible contributor to the high-latitude γ-ray sky and confirm that most of the intensity and geometrical properties of the measured diffuse emission are imputable to other extragalactic source classes (e.g., blazars, misaligned active galactic nuclei, or star-forming galaxies). Nevertheless, because MSPs are more concentrated toward the galactic center, we expect them to contribute significantly to the γ-ray diffuse emission at low latitudes. Because, along the galactic disk, the population of young pulsars overcomes in number that of MSPs, we compute the γ-ray emission from the whole population of unresolved pulsars, both young and millisecond, in two low-latitude regions: the inner Galaxy and the galactic center.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A Herschel/HIFI legacy survey of HF and H{sub 2}O IN the galaxy: Probing diffuse molecular cloud chemistry

We combine Herschel observations for a total of 12 sources to construct the most uniform survey of HF and H{sub 2}O in our Galactic disk. Both molecules are detected in absorption along all sight lines. The high spectral resolution of the Heterodyne Instrument for the Far-infrared (HIFI) allows us to compare the HF and H{sub 2}O distributions in 47 diffuse cloud components sampling the disk. We find that the HF and H{sub 2}O velocity distributions follow each other almost perfectly and establish that HF and H{sub 2}O probe the same gas-phase volume. Our observations corroborate theoretical predictions that HF is a sensitive tracer of H{sub 2} in diffuse clouds, down to molecular fractions of only a few percent. Using HF to trace H{sub 2} in our sample, we find that the N(H{sub 2}O)-to-N(HF) ratio shows a narrow distribution with a median value of 1.51. Our results further suggest that H{sub 2}O might be used as a tracer of H{sub 2}—within a factor of 2.5—in the diffuse interstellar medium (ISM). We show that the measured factor of ∼2.5 variation around the median is driven by true local variations in the H{sub 2}O abundance relative to H{sub 2} throughout the disk. The latter variability allows us to test our theoretical understanding of the chemistry of oxygen-bearing molecules in the diffuse gas. We show that both gas-phase and grain-surface chemistry are required to reproduce our H{sub 2}O observations. This survey thus confirms that grain surface reactions can play a significant role in the chemistry occurring in the diffuse ISM (n{sub H} ⩽ 1000 cm{sup −3}).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Evidence for superionic H 2 O and diffusive He–H 2 O at high temperature and high pressure

In this work, we present the evidence of superionic phase formed in H 2 O and, for the first time, diffusive H 2 O–He phase, based on time-resolved x-ray diffraction experiments performed on ramp-laser-heated samples in diamond anvil cells. The diffraction results signify a similar bcc-like structure of superionic H 2 O and diffusive He–H 2 O, while following different transition dynamics. Based on time and temperature evolution of the lattice parameter, the superionic H 2 O phase forms gradually in pure H 2 O over the temperature range of 1350–1400 K at 23 GPa, but the diffusive He–H 2 O phase forms abruptly at 1300 K at 26 GPa. We suggest that the faster dynamics and lower transition temperature in He–H 2 O are due to a larger diffusion coefficient of interstitial-filled He than that of more strongly bound H atoms. This conjecture is then consistent with He disordered diffusive phase predicted at lower temperatures, rather than H-disordered superionic phase in He–H 2 O.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Investigations on a fuzzy process: effect of diffusion on calibration and particle identification in Liquid Argon Time Projection Chambers

Ionization electron diffusion in Liquid Argon Time Projection Chambers (LArTPCs) has typically been considered at the detector design stage, but little attention has been given to its effects on calibration and particle identification. We use a GEANT4-based simulation to study how diffusion impacts these techniques, and give consideration to how this effect is simulated. We find that diffusion can cause a drift-dependent bias to both the median and Most Probable Value (MPV) of dQ/dx distributions. The bias is estimated to be ~2.5% (median) and ~5.0% (MPV) for typical maximum drift times in currently running LArTPCs before adding detector specific considerations such as electric field non-uniformities. This information indicates that these metrics should not be used for calibration without care, contrary to the conventional wisdom. The impact of diffusion on the ability of LArTPCs to separate muons and protons is small, and not expected to pose any problems in future detectors. Diffusion may however be a significant source of systematic uncertainty when separating particles of more similar masses (muons and pions, kaons and protons). Separation of such populations may be improved by implementation of a drift-time dependent particle identification.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Escape and finite-size scaling in diffusion-controlled annihilation

In this paper, we study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial dimensions d>2 where a finite number of particles typically survive the annihilation process. Using scaling techniques we investigate the average number of surviving particles, M, as a function of the initial number of particles, N. In three dimensions, for instance, we find the scaling law M ~ N 1/3 in the asymptotic regime N»1. We show that two time scales govern the reaction kinetics: the diffusion time scale, T ~ N 2/3 , and the escape time scale, τ ~ N 4/3 . The vast majority of annihilation events occur on the diffusion time scale, while no annihilation events occur beyond the escape time scale.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Superresolution Diffuse Optical Imaging by Localization of Fluorescence

The multiple scattering of light presents major challenges in realizing useful in vivo imaging at tissue depths of more than about one millimeter, where many answers to health questions lie. Visible through near-infrared photons can be readily and safely detected through centimeters of tissue; however, limited information is available for image formation. One strategy for obtaining images is to model the photon transport and a simple incoherent model is the diffusion equation approximation to the Boltzmann transport equation. Such an approach provides a prediction of the mean intensity of heavily scattered light and hence provides a forward model for optimization-based computational imaging. While diffuse optical imaging methods have received substantial attention, they remain restricted in terms of resolution because of the loss of high-spatial-frequency information that is associated with the multiple scattering of photons. Consequently, only relatively large inhomogeneities, such as tumors or organs in small animals, can be effectively resolved. We introduce a superresolution imaging approach based on point localization in a diffusion framework that enables over two orders of magnitude improvement in the spatial resolution of diffuse optical imaging. The method is demonstrated experimentally by localizing a fluorescent inhomogeneity in a highly scattering slab and characterizing the localization uncertainty. The approach allows imaging through centimeters of tissue with a resolution of tens of microns, thereby enabling cells or cell clusters to be resolved. More generally, this high-resolution imaging approach could be applied with any physical transport or wave model and hence to a broad class of physical problems. Finally, paired with a suitable optical contrast mechanism, as can be realized with targeted fluorescent molecules or genetically modified animals, superresolution diffuse imaging should open alternative dimensions for in vivo applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Multicomponent mutual diffusion in the warm, dense matter regime

In this work, we present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Protein drift-diffusion dynamics and phase separation in curved cell membranes and dendritic spines: Hybrid discrete-continuum methods

We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Furthermore, our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.

97 MATHEMATICS AND COMPUTING↗