Nonergodic Subdiffusion from Brownian Motion in an Inhomogeneous Medium

Abstract

Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random diffusivities. The particle is never trapped, but rather performs continuous Brownian motion with the local diffusion constant. Under simple assumptions on the distribution of the sizes and diffusivities, we find that the mean squared displacement displays subdiffusion due to non-ergodicity for both annealed and quenched disorder. The model is formulated as a walk continuous in both time and space, similar to the Lévy walk.

6 pages, 2 figures; removed spurious pi from (13), and k from inline eqn preceding (11). Fixed other typos

References in corpus (6)

• Anomalous transport in the crowded world of biological cells
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
• Mapping the energy and diffusion landscapes of membrane proteins at the cell surface using high-density single-molecule imaging and Bayesian inference: application to the multi-scale dynamics of glycine receptors in the neuronal membrane
• Multi-point Distribution Function for the Continuous Time Random Walk

Cited by in corpus (85)

• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• Machine learning method for single trajectory characterization
• Universal relation between instantaneous diffusivity and radius of gyration of proteins in aqueous solution
• Anomalous, non-Gaussian tracer diffusion in heterogeneously crowded environments
• First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time
• Non-universal tracer diffusion in crowded media of non-inert obstacles
• Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes
• Power spectral density of a single Brownian trajectory: What one can and cannot learn from it
• Bayesian deep learning for error estimation in the analysis of anomalous diffusion
• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers
• Fluctuation Analysis of Time-Averaged Mean-Square Displacement for Langevin Equation with Time-Dependent and Fluctuating Diffusivity
• Quantifying the non-ergodicity of scaled Brownian motion
• Langevin equation with fluctuating diffusivity: a two-state model
• Fractional kinetics emerging from ergodicity breaking in random media
• Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy
• Aging Scaled Brownian Motion
• Ageing underdamped scaled Brownian motion: ensemble and time averaged particle displacements, non-ergodicity, and the failure of the overdamping approximation
• Classification, inference and segmentation of anomalous diffusion with recurrent neural networks
• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
• Localization and universal fluctuations in ultraslow diffusion processes
• Characterization of anomalous diffusion classical statistics powered by deep learning (CONDOR)
• Learning physical properties of anomalous random walks using graph neural networks
• First passage statistics for aging diffusion in annealed and quenched disorder
• Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes
• Universal Fluctuations of Single-Particle Diffusivity in Quenched Environment
• Manifestations of Projection-Induced Memory: General Theory and the Tilted Single File
• Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• Boosting the performance of anomalous diffusion classifiers with the proper choice of features
• Anomalous diffusion in a quenched-trap model on fractal lattices
• Distributional Behaviors of Time-averaged Observables in Langevin Equation with Fluctuating Diffusivity: Normal Diffusion but Anomalous Fluctuations
• Relaxation Functions of Ornstein-Uhlenbeck Process with Fluctuating Diffusivity
• Inferring pointwise diffusion properties of single trajectories with deep learning
• Optimization and universality of Brownian search in quenched heterogeneous media
• Non-Gaussian diffusion of mixed origins
• Moses, Noah and Joseph Effects in Coupled Lévy Processes
• Characterization of anomalous diffusion through convolutional transformers
• Anomalous dispersion in correlated porous media: A coupled continuous time random walk approach
• Optimization of random search processes in the presence of an external bias
• Extreme Learning Machine for the Characterization of Anomalous Diffusion from Single Trajectories (AnDi-ELM)
• WaveNet-Based Deep Neural Networks for the Characterization of Anomalous Diffusion (WADNet)
• Unsupervised learning of anomalous diffusion data
• Semantic Segmentation of Anomalous Diffusion Using Deep Convolutional Networks
• Distributional Behavior of Diffusion Coefficients Obtained by Single Trajectories in Annealed Transit Time Model
• Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions
• Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor
• Gramian Angular Fields for leveraging pretrained computer vision models with anomalous diffusion trajectories
• Non-self-averaging behaviors and ergodicity in quenched trap model with finite system size
• Finite-range viscoelastic subdiffusion in disordered systems with inclusion of inertial effects
• Ergodic property of random diffusivity system with trapping events
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Superstatistical approach of the anomalous exponent for scaled Brownian motion
• Detection of Transition Times from Single-particle-tracking Trajectories
• A memory-induced diffusive-superdiffusive transition: ensemble and time-averaged observables
• Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity
• Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
• Control of anomalous diffusion of a Bose polaron
• Fractional Brownian motion with fluctuating diffusivities
• Nonergodic subdiffusion from transient interactions with heterogeneous partners
• Diffusion through a network of compartments separated by partially-transmitting boundaries
• Aging arcsine law in Brownian motion and its generalization
• Weak ergodicity breaking induced by global memory effects
• Machine Learning Analysis of Anomalous Diffusion
• Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
• Objective comparison of methods to decode anomalous diffusion
• Transient subdiffusion from an Ising environment
• A Coupled Time Domain Random Walk Approach for Transport in Media Characterized by Broadly-distributed Heterogeneity Length Scales
• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Transition from distributional to ergodic behavior in an inhomogeneous diffusion process: Method revealing an unknown surface diffusivity
• Large Deviations in Switching Diffusion: from Free Cumulants to Dynamical Transitions
• Time averages in continuous time random walks
• Subdiffusion with particle immobilization process described by differential equation with Riemann--Liouville type fractional time derivative
• Efficient recurrent neural network methods for anomalously diffusing single particle short and noisy trajectories
• Diffusion with a broad class of stochastic diffusion coefficients
• Normal and anomalous diffusion in a bouncing ball over an irregular surface
• Recovering discrete delayed fractional equations from trajectories
• Observation-Time-Induced Crossover from Fluctuating Diffusivity
• Bayesian inference of Lévy walks via hidden Markov models
• Improved mean squared displacement analysis for anomalous single particle trajectories
• Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion
• New insight into the diffusion of hydrogen and helium atoms in tungsten