Analysis Of Anomalous Diffusion Research Articles

Bayesian deep learning for error estimation in the analysis of anomalous diffusion

Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusion model and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a well-calibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.

Efficient analytical approach to solve system of BVPs associated with fractional obstacle problem

The general obstacle framework has found applications in steady state fluid interaction, thin-plate fluid dynamics, study of minimal surfaces, control theory, elasto-statics, etc. The obstacle problem involving the fractional operator indeed appears in many contexts, such as in the analysis of anomalous diffusion, in the quasi-geostrophic flow problem, and in pricing of American options regulated by assets evolving in relation to jump processes; these notable applications in financial mathematics and physics made the obstacle problem very important in recent times. In this work, we present a fractional contact problem in which derivative of fractional order in the sense of Caputo is involved. Using the penalty function method, we degenerate it into a system of fractional boundary value problems with known obstacle. We apply the variational iteration method (VIM) for finding the series solution of these fractional BVPs. In order to ensure the accuracy and convergence of solution, residual errors of the solutions for various values of fractional parameters are plotted. The quite accurate results show that variational iteration method is one of the highly potential and robust method for solving fractional BVPs.

Analysis of anomalous diffusion of molecules in a crowded environment with actin filaments

Analysis of anomalous diffusion of molecules in a crowded environment with actin filaments

Quantifying non-ergodicity of anomalous diffusion with higher order moments

Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.

Neutron radiography study of water absorption in porous building materials: anomalous diffusion analysis

Dynamic neutron radiography was applied to obtain the experimental data concerning the kinetics of the wetting process in two different types (fired-clay and siliceous brick) of porous construction materials. The technique provides accurate experimental data concerning the first instants as well as the advanced stages of the imbibing process. A significant difference in water absorption parameters, contrasting the materials studied, is found. Both the advance of the wetting front and the time evolution of water content distribution within the sample are analysed. It is shown that for both materials the time dependence of the wetting front position d deviates from the classical square root of time t behaviour. The deviation is analysed in terms of the intercept b in the approximation and the exponent n in the power law d ∼ tn/2. Both materials differ in the sign of the intercept parameter: b > 0 for siliceous brick and b < 0 for fired-clay brick. Two stages of the process with different values of the power law exponent were observed. The advanced period exponents are different for each type of brick: n < 1 for siliceous brick and n > 1 for fired-clay brick. At the initial stages (t < 1000 s) the exponents are substantially less than 1 and smaller than those describing the advanced process. The initial stage exponents are lower for the siliceous brick samples. It is shown that the experimental water content profiles collapse to a single curve when plotted against the variable xt−n/2. The evolution of the distribution of liquid in the porous medium was analysed in terms of the anomalous diffusion equation of Küntz and Lavallée (2001 Experimental evidence and theoretical analysis of anomalous diffusion during water infiltration in porous building materials J. Phys. D: Appl. Phys. 34 2547–54) based on the non-linear generalization of the Fick's law. This approach makes a detailed analysis of the generalized hydraulic diffusivity in the low water content region possible. Successful fitting of experimental data with the diffusivity vanishing at null water content proved the importance of the hypodiffusive component of the process.

Diffusion in a random medium with long-range correlations

A renormalisation group analysis of anomalous diffusion in a random medium with constrained long-range correlations is carried out to two-loop order. The crossover between the long-range correlated model and its short-range correlated counterpart is investigated and the dynamic exponent z is shown to be continuous at the crossover.