Scale invariance in anomalous diffusion

Intrinsic mode functions locate implicit turbulent attractors in time in frontal lobe MEG recordings

In seeking evidence for the presence and characteristic range of coupled time scale(s) of putative implicit turbulent attractors of dorsal frontal lobe magnetic fields, the recorded nonstationary, nonlinear MEG signals were non-orthogonally decomposed using Huang's Empirical Mode Decomposition, EMD, (Huang and Attoh-Okine, 2005) into 16 Intrinsic Mode Functions, EMD→IMFi, i=1…16. Measures known to be invariant in non-uniformly hyperbolic (turbulent) dynamical systems, topological entropy, hT, metric entropy, hM, non-uniform entropy, hU and power spectral scaling exponent, α, were imposed on each of the IMFi which evidenced most clearly an invariant temporal scale zone of IMFi, i=6…11, for hT, which we have found to be the most robust of invariant measures of MEG's magnetic field turbulent attractors (Mandell et al., 2011a,b; Mandell, 2013). The ergodic theory of dynamical systems (Walters, 1982; Pollicott and Yuri, 1998) allows the inference that an implicit attractor with consistently hT>0 will also evidence at least one positive Lyapounov exponent indicating the presence of a turbulent attractor with exponential separation of nearby initial conditions, exponential convergence of distant points and disordering, mixing, of orbital sequences. It appears that this approach permits the inference of the presence of chaotic, turbulent attractor and its characteristic time scales without the invocation of arbitrary n-dimensional embedding, phase space reconstructions or (inappropriate) orthogonal decompositions.

Crowding effects in vehicular traffic

While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of crowding due to car density and driving fluctuations on the transport of vehicles. Using a microscopic model for traffic, we found that crowding can push car movement from a superballistic down to a subdiffusive state. The transition is also associated with a change in the shape of the probability distribution of positions from a negatively-skewed normal to an exponential distribution. Moreover, crowding broadens the distribution of cars’ trap times and cluster sizes. At steady state, the subdiffusive state persists only when there is a large variability in car speeds. We further relate our work to prior findings from random walk models of transport in cellular systems.

Chaotic advection and the emergence of tori in the Küppers-Lortz state

Motivated by the roll-switching behavior observed in rotating Rayleigh-Benard convection, we define a Küppers-Lortz (K-L) state as a volume-preserving flow with periodic roll switching. For an individual roll state, the Lagrangian particle trajectories are periodic. In a system with roll-switching, the particles can exhibit three-dimensional, chaotic motion. We study a simple phenomenological map that models the Lagrangian dynamics in a K-L state. When the roll axes differ by 120 degrees in the plane of rotation, we show that the phase space is dominated by invariant tori if the ratio of switching time to roll turnover time is small. When this parameter approaches zero these tori limit onto the classical hexagonal convection patterns, and, as it gets large, the dynamics becomes fully chaotic and well mixed. For intermediate values, there are interlinked toroidal and poloidal structures separated by chaotic regions. We also compute the exit time distributions and show that the unbounded chaotic orbits are normally diffusive. Although the map presumes instantaneous switching between roll states, we show that the qualitative features of the flow persist when the model has smooth, overlapping time-dependence for the roll amplitudes (the Busse-Heikes model).

Propagator representation of anomalous diffusion: the orientational structure factor formalism in NMR

The radial Fourier transform for the isotropic space with a fractal dimension is discussed. The moments of diffusive displacements with non-Gaussian propagators arising as solutions of fractional diffusion equations are calculated. The Fourier propagator is applied to NMR correlation and spectral density functions in context with the orientational structure factor formalism. It is shown that the low-frequency molecular fluctuations of liquids in porous media with strong or forced adsorption at surfaces are due to reorientations mediated by translational displacements caused by surface diffusion of the adsorbate molecules. In terms of this formalism, field-cycling NMR experiments provide information on the static and dynamic fractal dimensions related to surface diffusion. The experimental results for liquids in porous silica glass can be explained by a surface fractal dimension df=2.5, where the mean squared displacement scales as <r(2)(t)> proportional, variantt(2/dw) with dw=1 (ballistic transport), if the surface population can exchange with the bulklike phase in the pores, and with dw=2, if the bulklike phase is frozen. The former dynamics is interpreted in terms of bulk-mediated surface diffusion.

Anomalous diffusion of major histocompatibility complex class I molecules on HeLa cells determined by single particle tracking

Single-particle tracking (SPT) was used to determine the mobility characteristics of MHC (major histocompatibility complex) class I molecules at the surface of HeLa cells at 22 degrees C and on different time scales. MHC class I was labeled using the Fab fragment of a monoclonal antibody (W6/32), covalently bound to either R-phycoerythrin or fluorescent microspheres, and the particles were tracked using high-sensitivity fluorescence imaging. Analysis of the data for a fixed time interval suggests a reasonable fit to a random diffusion model. The best fit values of the diffusion coefficient D decreased markedly, however, with increasing time interval, demonstrating the existence of anomalous diffusion. Further analysis of the data shows that the diffusion is anomalous over the complete time range investigated, 4-300 s. Fitting the results obtained with the R-phycoerythrin probe to D = D0talpha-1, where Do is a constant and t is the time, gave D0 = (6.7 +/- 4.5) x 10(-11) cm2 s-1 and alpha = 0.49 +/- 0.16. Experiments with fluorescent microspheres were less reproducible and gave slower anomalous diffusion. The R-phycoerythrin probe is considered more reliable for fluorescent SPT because it is small (11 x 8 nm) and monovalent. The type of motion exhibited by the class I molecules will greatly affect their ability to migrate in the plane of the membrane. Anomalous diffusion, in particular, greatly reduces the distance a class I molecule can travel on the time scale of minutes. The present data are discussed in relation to the possible role of diffusion and clustering in T-cell activation.

Surface fractals probed by adsorbate spin-lattice relaxation dispersion

Spin-lattice relaxation of strong adsorbates confined in disordered structures such as porous silica glass is treated on the basis of a relaxation mechanism due to "reorientation mediated by translational displacements." In such a situation the low-frequency spin-lattice relaxation dispersion beyond the regime where local reorientations dominate reflects molecular dynamics as well as the surface geometry on a length scale longer than 1 nm. It is shown that the power law frequently observed for the spin-lattice relaxation dispersion in porous media can be traced back to surface fractality. The fractal properties of rough surfaces and the statistics governing surface displacements enter explicitly in the expression for the dipolar correlation function. The surface fractal dimension can thus be evaluated from the low-frequency spin-lattice relaxation dispersion accessible by field-cycling NMR relaxometry.