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Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
Statistical Mechanics · Submitted 24 Sep 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristic even for short time series.
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The abstract, sentence by sentence
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristic even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytucal expressions for the velocity correlation functions. Knowledge of the results presented here are expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | The resulting time series are usually evaluated in terms of time averages. | background 0.97 | 0.07 | 0.02 | asserted 0.97 |
| s2 | Often anomalous diffusion is connected with non-ergodic behaviour. | background 1.00 | 0.04 | 0.03 | asserted 0.56 |
| s3 | In such cases the time averages remain random variables and hence irreproducible. | background 0.98 | 0.06 | 0.04 | asserted 1.00 |
| s4 | Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. | contribution 1.00 | 0.93 | 0.07 | asserted 0.95 |
| s5 | We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. | contribution 0.89 | 0.78 | 0.05 | asserted 0.91 |
| s6 | We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristic even for short time series. | result 0.94 | 0.93 | 0.25 | asserted 1.00 |
| s7 | Recently, velocity correlation functions were suggested to distinguish between these processes. | background 0.98 | 0.04 | 0.03 | hedged possibility 0.65 |
| s8 | We here present analytucal expressions for the velocity correlation functions. | contribution 0.81 | 0.92 | 0.05 | asserted 0.98 |
| s9 | Knowledge of the results presented here are expected to be relevant for the correct interpretation of single particle trajectory data in complex systems. | interpretation 0.98 | 0.10 | 0.18 | hedged possibility 0.96 |
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Original abstract
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristic even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytucal expressions for the velocity correlation functions. Knowledge of the results presented here are expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.
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