Probability Distribution Of Displacement Research Articles

Direct loss‐based seismic design of low‐rise base‐isolated reinforced concrete buildings

AbstractThis paper proposes a procedure to design low‐rise base‐isolated structures achieving a specific target level of earthquake‐induced loss (e.g., dollars, downtime) while complying with a predefined minimum level of structural reliability. The procedure is “direct” since the target loss is specified at the first step of the process, and virtually no design iterations are required. Direct loss‐based design (DLBD) is enabled by a simplified loss assessment module involving: (1) surrogate probabilistic seismic demand models representing the probability distribution of peak horizontal displacements and accelerations on top of the isolation layer conditional on different ground‐motion intensity levels; (2) approximations of the superstructure response; (3) simplified consequence models for isolation system and superstructure based on damage‐to‐loss ratios (economic loss or repair time); (4) simplified consequence models for acceleration‐ and drift‐sensitive non‐structural components, based on storey loss functions of a potential inventory of components. Given some basic geometrical parameters of the superstructure, DLBD provides the isolation system's force‐displacement curve and the required superstructure's strength complying with a selected loss target. The members' structural detailing follows the principles of direct displacement‐based design, sectional analysis, and the general theory of base isolation. The procedure is illustrated by designing six reinforced concrete wall buildings (two‐, three‐, and four‐storeys) base isolated with lead rubber bearings, to achieve predefined targets of expected repair time. Repair time is benchmarked against a more refined method adopting a cloud‐based non‐linear time history analysis, finding a maximum underestimation of 17%, thus confirming the dependability of DLBD. Such error is almost entirely attributable to the simplified estimation of peak floor accelerations, and it could be potentially eliminated by refining such estimation.

Experimental study of confined diffusion of rough and smooth ellipsoidal colloids

The study of diffusion in complex confined environments has received great attention in the field of condensed matter physics. The emergence of colloidal systems provides an excellent experimental model system for quantitatively studying the confined diffusion of microscopic particles. When colloidal particles change from spherical to ellipsoidal shape, the system presents anisotropic diffusion dynamics. Recent studies have found that rough surfaces, another important physical parameter of colloids, can lead to unusual rotational dynamics in spherical colloidal systems. However, due to the lack of a suitable experimental system, little is known about the effect of rough surfaces on the confined diffusion of ellipsoidal colloidal particles. In this work, rough colloidal spheres, rough colloidal ellipsoids, and smooth colloidal ellipsoids are prepared, and then monolayer colloidal samples are prepared to study the confined diffusions of these two types of ellipsoids in dense packing of the rough sphere colloids. By calculating the mean square displacement, intermediate self-scattering function, and orientation correlation function of the ellipsoids, we quantitatively characterize the diffusion dynamics of rough and smooth ellipsoids in varying concentrations of rough spheres. The results indicate that the translational diffusion and rotational diffusion of rough ellipsoids and smooth ellipsoids slow down as the concentration of rough spheres increases. This is due to the confinement of the ellipsoid by the surrounding spheres. At low stacking fractions of spheres, smooth and rough ellipsoids show similar translational diffusion and rotational diffusion. However, as the stacking fraction of spheres increases, there is a significant difference in advection diffusion between rough ellipsoids and smooth ellipsoids. The advection diffusion of rough ellipsoids is significantly slower than that of smooth ellipsoids. This is because the rough surface strongly inhibits rotation, meaning that the rotational diffusion of the rough ellipsoids is significantly slower than that of the smooth ellipsoids. By extracting the diffusion coefficients for translation and rotation from the ellipsoid's long-time mean-square displacements, we find that at <i>ϕ</i> = 0.60 and 0.65, the diffusion coefficients of rough ellipsoids are smaller than those of smooth ellipsoids. The translational diffusion coefficient of the rough ellipsoids is notably smaller than that of the smooth ellipsoids. However, the rotation diffusion coefficient of the rough ellipsoids is not significantly different from that of the smooth ellipsoids. This suggests that the rough surface mainly affect translational diffusion, strongly suppressing the translational diffusion of the ellipsoids. By calculating the displacement probability distribution for ellipsoidal motion, we find that at <i>ϕ</i> = 0.65, the translational displacements of rough ellipsoids have a relatively narrow distribution. This suggests that the translational motion of particles is suppressed by the rough surface. However, the distributions of rotation displacement for smooth ellipsoids and rough ellipsoids are very similar, indicating that the rough surface has less influence on particle rotation. At <i>ϕ</i> = 0.74, the rough surface suppresses both the translation and the rotation of the ellipsoid, resulting in a narrower displacement distribution than in the case of smooth ellipsoid. These findings suggest that rough surfaces significantly impede ellipsoidal diffusion, leading the translational and rotational motions not to occur simultaneously. This study provides an in-depth understanding of the role of rough surfaces of colloidal particles in confined diffusion, as well as an experimental basis for explaining the diffusion laws of rough materials.

Nano-particle motion in a monolithic silica column using the single-particle tracking method.

Porous materials are used in a variety of industrial applications owing to their large surface areas, large pore volumes, hierarchical porosities, and low densities. The motion of particles inside the pores of porous materials has attracted considerable attention. We investigated nano-particle motion in a porous material using the single-particle tracking method. Particle motion such as absorption and desorption at the wall was observed. The displacement probability distribution deviated from the Gaussian distribution at the tail, indicating non-Gaussian motion of the particles. Moreover, an analysis of the relative angle between three consecutive particle positions revealed that the probability of the particle moving backward was approximately twice that of the particle moving forward. These results indicate that particle motion inside porous materials is highly complex and that a single-particle study is essential for fabricating a structure that is suitable for applications.

Fault slip behavior and segmentation revealed by geomorphic offset clusters: An example from the middle Riganpei Co fault, central Tibet

High-resolution topographic datasets are useful for revealing offset features of fault geomorphology and are thus important for reconstructing the evolution history of faults. The Riganpei Co fault, located in the central Tibetan Plateau, is an important active fault on the northern boundary of the Bangong-Nujiang suture zone. In this study, WorldView-2 stereo images were used to generate high-resolution topographic data in a 1 km range on both flanks of the middle section of the Riganpei Co fault. We interpreted the tectonic geomorphology along the fault, classified it into distinct units, and measured the horizontal displacement of each unit. Within approximately 70 km along the fault, we obtained 396 displacement measurements ranging from 0 to 60 m. Given the evident uneven distribution of displacement, the fault was divided into four segments. In each fault segment, the reconstructed slip distributions revealed a tendency of larger displacements in the center and smaller displacements toward the ends. The cumulative offset probability distribution (COPD) of displacements displays 4–5 offset clusters in the range of 0–30 m for each segment, suggesting that at least four large earthquakes ruptured this fault. The binned COPD demonstrated that there are differences in the displacement accumulation modes among these fault segments, where the middle segment follows a characteristic slip accumulation mode. Reconstructed cumulative slip profiles revealed a complex pattern of strong earthquake activities along the Riganpei Co fault.

Temperature-mediated diffusion of nanoparticles in semidilute polymer solutions.

The temperature is often a critical factor affecting the diffusion of nanoparticles in complex physiological media, but its specific effects are still to be fully understood. Here, we constructed a temperature-regulated model of semidilute polymer solution and experimentally investigated the temperature-mediated diffusion of nanoparticles using the particle tracking method. By examining the ensemble-averaged mean square displacements (MSDs), we found that the MSD grows gradually as the temperature increases while the transition time from sublinear to linear stage in MSD decreases. Meanwhile, the temperature-dependent measured diffusivity of the nanoparticles shows an exponential growth. We revealed that these temperature-mediated changes are determined by the composite effect of the macroscale property of polymer solution and the microscale dynamics of polymer chain as well as nanoparticles. Furthermore, the measured non-Gaussian displacement probability distributions were found to exhibit non-Gaussian fat tails, and the tailed distribution is enhanced as the temperature increases. The non-Gaussianity was calculated and found to vary in the same trend with the tailed distribution, suggesting the occurrence of hopping events. This temperature-mediated non-Gaussian feature validates the recent theory of thermally induced activated hopping. Our results highlight the temperature-mediated changes in diffusive transport of nanoparticles in polymer solutions and may provide the possible strategy to improve drug delivery in physiological media.

Cobble Tracking Observations at Torrey Pines State Beach, CA, USA

AbstractCobbles provide a nature‐based method to help generate beach stability. However, few detailed cobble movement observations exist. This study deployed 344 radio‐frequency identification tagged cobbles in a California beach in November–December 2020. Coincident LiDAR surveys quantified beach morphology. Cobbles were mapped daily for 10 days and then ∼ monthly until January 2023. Cobble detection rates ranged 17%–92%, and generally declined with time (with slight increases during winter months). Cobble movement exhibited complex patterns, sometimes moving in opposing directions during the same time period. Large winter waves (up to ∼4 m) resulted in average displacements of 40 m per month between November 2020 and April 2021. From April 2021 to August 2022, most cobbles were located high on the beach and net alongshore movements were relatively low, despite several moderate size (∼2 m) wave events. The largest wave event in January 2023 (>4 m) moved cobbles to the highest elevations of the study period. The initial release location and accommodation space in the back beach influenced cobble movement and final position. Cobbles high on the beach were relatively stable compared to lower elevation cobbles, and more than half of all cobble detections were within 50 m of the initial release location. However, three cobbles moved >500 m. The probability distribution of displacement was approximately exponential. Statistically, alongshore cobble spreading followed a non‐Gaussian subdiffusive process. Despite myriad sources of noise, the results suggest that cobble shape and mass were related to maximum cobble displacement. Overall, displacements increased with incident wave energy and depended on elevation relative to total water level.

Size-Dependent Diffusion and Dispersion of Particles in Mucin.

Mucus, composed significantly of glycosylated mucins, is a soft and rheologically complex material that lines respiratory, reproductive, and gastrointestinal tracts in mammals. Mucus may present as a gel, as a highly viscous fluid, or as a viscoelastic fluid. Mucus acts as a barrier to the transport of harmful microbes and inhaled atmospheric pollutants to underlying cellular tissue. Studies on mucin gels have provided critical insights into the chemistry of the gels, their swelling kinetics, and the diffusion and permeability of molecular constituents such as water. The transport and dispersion of micron and sub-micron particles in mucin gels and solutions, however, differs from the motion of small molecules since the much larger tracers may interact with microstructure of the mucin network. Here, using brightfield and fluorescence microscopy, high-speed particle tracking, and passive microrheology, we study the thermally driven stochastic movement of 0.5-5.0 μm tracer particles in 10% mucin solutions at neutral pH, and in 10% mucin mixed with industrially relevant dust; specifically, unmodified limestone rock dust, modified limestone, and crystalline silica. Particle trajectories are used to calculate mean square displacements and the displacement probability distributions; these are then used to assess tracer diffusion and transport. Complex moduli are concomitantly extracted using established microrheology techniques. We find that under the conditions analyzed, the reconstituted mucin behaves as a weak viscoelastic fluid rather than as a viscoelastic gel. For small- to moderately sized tracers with a diameter of lessthan 2 μm, we find that effective diffusion coefficients follow the classical Stokes-Einstein relationship. Tracer diffusivity in dust-laden mucin is surprisingly larger than in bare mucin. Probability distributions of mean squared displacements suggest that heterogeneity, transient trapping, and electrostatic interactions impact dispersion and overall transport, especially for larger tracers. Our results motivate further exploration of physiochemical and rheological mechanisms mediating particle transport in mucin solutions and gels.

Gaussian process regression-based surrogate modelling for direct loss-based seismic design of low-rise base-isolated structures

Seismic base isolation has gained popularity in the last decades. As a result, many structures are now equipped with base isolation systems to offer enhanced seismic performance and meet the needs of risk-aware stakeholders. However, a robust performance-based seismic design of these types of structures is generally not carried out due to the iterative nature of common design approaches and the time/computational resources required for such iterations, which are incompatible with the preliminary design phase. Indeed, seismic risk/loss is often just assessed at the end of the design process as a final verification step. This paper offers an overview of a simplified methodology for the seismic design of low-rise structures equipped with a base isolation system to achieve a predefined level of earthquake-induced economic loss while complying with a predefined minimum level of structural reliability. The main advantage of the proposed methodology is that it requires no design iterations. The procedure is enabled by Gaussian-process-regression-based surrogate probabilistic seismic demand modelling of equivalent single degree of freedom systems (i.e., the probability distribution of peak horizontal displacements and accelerations on top of the isolation layer conditional on different ground-motion intensity levels). Combined with simplified loss models for the base isolation system and the structural and non-structural components of the superstructure, this approach allows mapping a range of structural configurations to their resulting seismic loss. A designer can then select one of the identified combinations of the strength of the superstructure and properties of the isolation system conforming with the loss target, and reliability requirements, and consequently detail the superstructure and isolation system accordingly. This paper introduces the implemented surrogate probabilistic seismic demand models and provides an overview of a tentative Direct Loss-based Design procedure for low-rise base-isolated structures.

Quantum uncertainty effects in the dynamics of supercooled liquids: A molecular dynamics study.

Dynamics of density fluctuations in quantum supercooled liquids is analyzed using molecular dynamics simulations. In contrast to the classical case, the uncertainty in the particle position (delocalization of quantum particle in space) leads to significant differences in the dynamics of quantum liquids, both in the short- and long-time limits. The effect of uncertainty is found to be significant for length scales smaller than the uncertainty itself, and diminishes as the length scale grows. The dynamic heterogeneity of the system at short times is enhanced due to uncertainty. In the intermediate (β-relaxation) time regime, the heterogeneity tends to get suppressed due to quantum uncertainty. The probability distribution of particle displacements shows highly nonclassical behavior with double-peak structure at short timescales.

Understanding the diffusive transport of nanoparticles in agarose hydrogels

The enhanced delivery of nanoparticle (NP) drugs in the human system is a revolutionary approach for various diseases, e.g., cancer therapy, in which nanoparticle diffusion is one of the main routes of transport. The diffusive transport of nanoparticles in complex tumor microenvironments is intriguing, while its complete understanding is still nascent. Herein, we experimentally report a systematic study of nanoparticle diffusion in model porous media, i.e., agarose (AG) hydrogels. By examining both the time-averaged and ensemble-averaged mean square displacements (MSDs), the heterogeneous and spatially dependent mobility, as well as the significant hydrodynamic damping effect, are identified. The concept of ergodicity breaking (EB) is employed and correlated with the measured non-Gaussian displacement probability distributions (DPDs). The non-Gaussian profile is clarified to be attributed to the superposition of the coexisted Gaussian and non-Gaussian motions of the individual nanoparticles. Furthermore, the interstitial viscosity is found to only affect the probed heterogeneity temporarily but never modify the intrinsic non-ergodicity of the porous media. Our results give a comprehensive understanding of anomalous diffusion in spatially heterogeneous porous media and could provide the imperative knowledge to improve drug delivery in physiological media.

Hopping Behavior Mediates the Anomalous Confined Diffusion of Nanoparticles in Porous Hydrogels.

Diffusion is an essential means of mass transport in porous materials such as hydrogels, which are appealing in various biomedical applications. Herein, we investigate the diffusive motion of nanoparticles (NPs) in porous hydrogels to provide a microscopic view of confined diffusion. Based on the mean square displacement from particle tracking experiments, we elucidate the anomalous diffusion dynamics of the embedded NPs and reveal the heterogeneous pore structures in hydrogels. The results demonstrate that diffusive NPs can intermittently escape from single pores through void connective pathways and exhibit non-Gaussian displacement probability distribution. We simulate this scenario using the Monte Carlo method and clarify the existence of hopping events in porous diffusion. The resultant anomalous diffusion can be fully depicted by combining the hopping mechanism and the hydrodynamic effect. Our results highlight the hopping behavior through the connective pathways and establish a hybrid model to predict NP transport in porous environments.

Heterogeneous Nanostructures Cause Anomalous Diffusion in Lipid Monolayers.

The diffusion and mobility in biomembranes are crucial for various cell functions; however, the mechanisms involved in such processes remain ambiguous due to the complex membrane structures. Herein, we investigate how the heterogeneous nanostructures cause anomalous diffusion in dipalmitoylphosphatidylcholine (DPPC) monolayers. By identifying the existence of condensed nanodomains and clarifying their impact, our findings renew the understanding of the hydrodynamic description and the statistical feature of the diffusion in the monolayers. We find a universal characteristic of the multistage mean square displacement (MSD) with an intermediate crossover, signifying two membrane viscosities at different scales: the short-time scale describes the local fluidity and is independent of the nominal DPPC density, and the long-time scale represents the global continuous phase taking into account nanodomains and increases with DPPC density. The constant short-time viscosity reflects a dynamic equilibrium between the continuous fluid phase and the condensed nanodomains in the molecular scale. Notably, we observe an "anomalous yet Brownian" phenomenon exhibiting an unusual double-peaked displacement probability distribution (DPD), which is attributed to the net dipolar repulsive force from the heterogeneous nanodomains around the microdomains. The findings provide physical insights into the transport of membrane inclusions that underpin various biological functions and drug deliveries.

Self-propulsion with speed and orientation fluctuation: Exact computation of moments and dynamical bistabilities in displacement.

We consider the influence of active speed fluctuations on the dynamics of a d-dimensional active Brownian particle performing a persistent stochastic motion. The speed fluctuation brings about a dynamical anisotropy even in the absence of shape anisotropy. We use the Laplace transform of the Fokker-Planck equationto obtain exact expressions for time-dependent dynamical moments. Our results agree with direct numerical simulations and show several dynamical crossovers determined by the activity, persistence, and speed fluctuation. The dynamical anisotropy leads to a subdiffusive scaling in the parallel component of displacement fluctuation at intermediate times. The kurtosis remains positive at short times determined by the speed fluctuation, crossing over to a negative minimum at intermediate times governed by the persistence before vanishing asymptotically. The probability distribution of particle displacement obtained from numerical simulations in two dimensions shows two crossovers between compact and extended trajectories via two bimodal distributions at intervening times. While the speed fluctuation dominates the first crossover, the second crossover is controlled by persistence like in the wormlike chain model of semiflexible polymers.

Extreme value statistics and arcsine laws for heterogeneous diffusion processes.

Heterogeneous diffusion with a spatially changing diffusion coefficient arises in many experimental systems such as protein dynamics in the cell cytoplasm, mobility of cajal bodies, and confined hard-sphere fluids. Here, we showcase a simple model of heterogeneous diffusion where the diffusion coefficient D(x) varies in a power-law way, i.e., D(x)∼|x|^{-α} with the exponent α>-1. This model is known to exhibit anomalous scaling of the mean-squared displacement (MSD) of the form ∼t^{2/2+α} and weak ergodicity breaking in the sense that ensemble averaged and time averaged MSDs do not converge. In this paper, we look at the extreme value statistics of this model and derive, for all α, the exact probability distributions of the maximum spatial displacement M(t) and arg-maximum t_{m}(t) (i.e., the time at which this maximum is reached) till duration t. In the second part of our paper, we analyze the statistical properties of the residence time t_{r}(t) and the last-passage time t_{ℓ}(t) and compute their distributions exactly for all values of α. Our study unravels that the heterogeneous version (α≠0) displays many rich and contrasting features compared to that of the standard Brownian motion (BM). For example, while for BM (α=0), the distributions of t_{m}(t),t_{r}(t), and t_{ℓ}(t) are all identical (á la "arcsine laws" due to Lévy), they turn out to be significantly different for nonzero α. Another interesting property of t_{r}(t) is the existence of a critical α (which we denote by α_{c}=-0.3182) such that the distribution exhibits a local maximum at t_{r}=t/2 for α<α_{c} whereas it has minima at t_{r}=t/2 for α≥α_{c}. The underlying reasoning for this difference hints at the very contrasting natures of the process for α≥α_{c} and α<α_{c} which we thoroughly examine in our paper. All our analytical results are backed by extensive numerical simulations.

Anisotropic diffusion of ellipsoidal tracers in microswimmer suspensions

Tracer particles immersed in suspensions of biological microswimmers such as E. coli or C. reinhardtii display phenomena unseen in conventional equilibrium systems, including strongly enhanced diffusivity relative to the Brownian value and non-Gaussian displacement statistics. In dilute, 3-dimensional suspensions, these phenomena have typically been explained by the hydrodynamic advection of point tracers by isolated microswimmers, while, at higher concentrations, correlations between pusher microswimmers such as E. coli can increase the effective diffusivity even further. Anisotropic tracers in active suspensions can be expected to exhibit even more complex behaviour than spherical ones, due to the presence of a nontrivial translation-rotation coupling. Using large-scale lattice Boltzmann simulations of model microswimmers described by extended force dipoles, we study the motion of ellipsoidal point tracers immersed in 3-dimensional microswimmer suspensions. We find that the rotational diffusivity of tracers is much less affected by swimmer-swimmer correlations than the translational diffusivity. We furthermore study the anisotropic translational diffusion in the particle frame and find that, in pusher suspensions, the diffusivity along the ellipsoid major axis is higher than in the direction perpendicular to it, albeit with a smaller ratio than for Brownian diffusion. Thus, we find that far field hydrodynamics cannot account for the anomalous coupling between translation and rotation observed in experiments, as was recently proposed. Finally, we study the probability distributions (PDFs) of translational and rotational displacements. In accordance with experimental observations, for short observation times we observe strongly non-Gaussian PDFs that collapse when rescaled with their variance, which we attribute to the ballistic nature of tracer motion at short times.

A data-driven flight schedule optimization model considering the uncertainty of operational displacement

The slot allocation mechanism aims to match flight demand and airport resources from a strategic perspective. However, current research mainly focused on airlines' interests, ignoring the influencing factors that lead to primary delays, which makes the temporal and spatial distribution of flight schedules unreasonable. This paper proposes a data-driven approach to reduce operational delays at a strategic level by considering operational efficiency and airline interests. The displacement probability distribution between the actual execution time and the scheduled time is first mined from the historical operation data. We then develop a model with the ultimate objective of improving the punctuality rate and reducing the actual operational delays by minimizing the total operational displacement. In addition to considering the basic operational restrictions of airports, the model also introduces the corridor capacity of the terminal airspace surrounding an airport, reducing the delay caused by the corridor flow control to a certain extent. The proposed model is applied to Hangzhou Xiaoshan International Airport in China. The experimental results suggest that the optimized flight schedule can significantly reduce flight delay, conforms to airport operational restrictions, and maintains flight connectivity.

Trapped active toy robots: theory and experiment

We characterise the diffusion, mean-square speed, mean-square angular displacement, radial and speed probability distributions of toy robots called ‘hexbugs-nano’ that move on a dish antenna (with added surface roughness) simulating a harmonic well. It is observed that a model considering the system’s translational inertia but neglecting its moment of inertia, together with the inclusion of a constant external torque in the orientational motion, suffices to describe the robots’ dynamics. Langevin dynamics simulation are also performed and a good agreement between theory, simulations and experiments is observed.

Pulsed field gradient NMR diffusion measurement in nanoporous materials

Labeling in diffusion measurements by pulsed field gradient (PFG) NMR is based on the observation of the phase of nuclear spins acquired in a constant magnetic field with purposefully superimposed field gradients. This labeling does in no way affect microdynamics and provides information about the probability distribution of molecular displacements as a function of time. An introduction of the measuring principle is followed by a detailed description of the ranges of measurements and their limitation. Particular emphasis is given to an explanation of possible pitfalls in the measurements and the ways to circumvent them. Showcases presented for illustrating the wealth of information provided by PFG NMR include a survey on the various patterns of concentration dependence of intra-particle diffusion and examples of transport inhibition by additional transport resistances within the nanoporous particles and on their external surface. The latter information is attained by combination with the outcome of tracer exchange experiments, which are shown to become possible via a special formalism of PFG NMR data analysis. Further evidence provided by PFG NMR concerns diffusion enhancement in pore hierarchies, diffusion anisotropy and the impact of diffusion on chemical conversion in porous catalysts. A compilation of the specifics of PFG NMR and of the parallels with other measurement techniques concludes the paper.

A continuous time random walk method to predict dissolution in porous media based on validation of experimental NMR data

We develop a reactive transport model for dissolution of porous materials using a Continuous Time Random Walk (CTRW) formulation with first-order kinetics. Our model is validated with a dataset for a Ketton carbonate rock sample undergoing dissolution on injection of an acid, monitored using Nuclear Magnetic Resonance (NMR). The experimental data includes the 3D porosity distribution at the beginning and end of the experiment, 1D porosity profiles along the direction of flow during dissolution, as well as the molecular fluid displacement probability distributions (propagators). With the calibration of only a single parameter, we successfully predict the porosity changes and the propagators as a signature of flow heterogeneity evolution in the dissolution experiment.We also demonstrate that heterogeneity in the flow field leads to an effective reaction rate, limited by transport of reactants, that is almost three orders of magnitude lower than measured under batch reaction conditions. The effective reaction rate predicted by the model is in good agreement with the experimentally measured rate. Furthermore, as dissolution proceeds, the formation of channels in the rock focused the flow in a few fast-flowing regions. The predicted dissolution patterns are similar to those observed experimentally. This study establishes a workflow to calibrate and validate the CTRW reactive transport model with NMR experiments.

Ab initio molecular dynamics study of isotope effects in lithium-ion conductors

We investigate isotope effects of lithium-ion diffusion in Lithium-ion conductors using ab initio computational methods in light of recently proposed novel lithium isotope separation technology based on ionic conductors. Using ab initio molecular dynamics simulations, we compute the diffusion coefficients D6(7) of 6Li+ (7Li+) in tetragonal Li7La3Zr2O12 and Li10GeP2S12 as a slow Li+-ion conductor and a fast Li+-ion conductor, respectively. We note that careful uncertainty estimations in the molecular dynamics simulations would be necessary to extract many-body effects on the diffusion coefficient ratio D6/D7 beyond the canonical value given by the transition-state theory. Numerical results for Li10GeP2S12 indicate that the isotope effect depends on the migration path. Specifically, the faster diffusion path along the c−axis exhibits a stronger isotope effect that is also temperature dependent, whereas the diffusion on the ab−plane shows a relatively weaker and temperature-independent effect. We introduce the probability distribution of the ionic displacement to reveal distinct differences in the ion-diffusion mechanism.