Purpose
To develop an anomalous (non‐Gaussian) diffusion model for characterizing skeletal muscle perfusion using multi‐b‐value DWI.
Theory and methods
Fick’s first law was extended for describing ...tissue perfusion as anomalous superdiffusion, which is non‐Gaussian diffusion exhibiting greater particle spread than that of the Gaussian case. This was accomplished using a space‐fractional derivative that gives rise to a power‐law relationship between mean squared displacement and time, and produces a stretched exponential signal decay as a function of b‐value. Numerical simulations were used to estimate parameter errors under in vivo conditions, and examine the effect of limited SNR and residual fat signal. Stretched exponential DWI parameters, α and D, were measured in thigh muscles of 4 healthy volunteers at rest and following in‐magnet exercise. These parameters were related to a stable distribution of jump‐length probabilities and used to estimate microvascular volume fractions.
Results
Numerical simulations showed low dispersion in parameter estimates within 1.5% and 1%, and bias errors within 3% and 10%, for α and D, respectively. Superdiffusion was observed in resting muscle, and to a greater degree following exercise. Resting microvascular volume fraction was between 0.0067 and 0.0139 and increased between 2.2‐fold and 4.7‐fold following exercise.
Conclusions
This model captures superdiffusive molecular motions consistent with perfusion, using a parsimonious representation of the DWI signal, providing approximations of microvascular volume fraction comparable with histological estimates. This signal model demonstrates low parameter‐estimation errors, and therefore holds potential for a wide range of applications in skeletal muscle and elsewhere in the body.
Femtosecond laser‐induced photoexcitation of ferromagnet (FM)/heavy metal (HM) heterostructures has attracted attention by emitting broadband terahertz frequencies. The phenomenon relies on the ...formation of an ultrafast spin current, which is primarily attributed to the direct photoexcitation of the FM layer. However, during the process, the FM layer also experiences a secondary excitation led by the hot electrons from the HM layer that travel across the FM/HM interface and transfer additional energy in the FM. Thus, the generated secondary spins enhance the total spin current formation and lead to amplified spintronic terahertz emission. These results emphasize the significance of the secondary spin current, which even exceeds the primary spin currents when FM/HM heterostructures with thicker HM are used. An analytical model is developed to provide deeper insights into the microscopic processes within the individual layers, underlining the generalized ultrafast superdiffusive spin‐transport mechanism.
The presence of a secondary spin current (js') that significantly contributes to the amplification of terahertz emission in ferromagnet (FM)/heavy metal (HM) heterostructures is explored through precise control of the thickness of the HM layer.
Obtaining thermal parameters based in the analysis only on the amplitude or phase of the photoacoustic (PA) signal from photothermal measurements is useful and valid once classical theoretical ...expectations are that the same parameters are contained in the photoacoustic signal. This work studies the issue of disagreement between experimentally measured amplitude and phase for AISI 316 samples with the expected theoretical result from the classical model. The results of the thermal parameters obtained from individual amplitude analysis are inconsistent with phase analysis. This work aims to show a way to get a unique value of thermal parameters from simultaneous analysis of the amplitude and phase of the PA signal. Also, the fractional models were applied to improve the fit of experimental data and provided results closed with the expected thermal diffusivity value.
The process of burial and exhumation of bedload particles within a certain depth of the riverbed leads to vertical exchange of particles, which significantly affects the characteristics of streamwise ...bedload transport. In this paper, we revisit the classic active layer formulation and extend it by incorporating the burial and exhumation through conceptualizing the fluctuations of bed surface as the relative vertical movement of buried tracer particles in the substrate layer (i.e., we change the static reference system to the fluctuating riverbed surface). We theoretically demonstrate, for the first time, the emergence of the transient anomalous diffusion (both superdiffusion and subdiffusion) and power‐law advective slowdown at the intermediate timescales, which are induced by the nonequilibrium transport as characterized by the inhomogeneous vertical mixing of tracers due to particle burial and exhumation. Neglecting the ballistic regime at extremely short times, at small and large timescales, the transport regimes show normal diffusion. This result further implies that for the most typical fluvial riverbed with finite vertical exchange depth (i.e. nonaggrading or nondegrading bed), the subdiffusion of bedload tracers for large timescale transport may still be transient, which will eventually converge to the normal diffusion as time increases. Comparing the obtained analytical solutions with available numerical results as well as field observations, we show that the proposed formulation can capture well anomalous diffusion and the power‐law slowdown of the advective velocity of bedload tracers at intermediate timescales, and more importantly the transition from anomalous to normal diffusion at large timescales.
Key Points
Burial and exhumation of bedload tracers during streamwise transport are theoretically considered through bed surface elevation fluctuations
Transition of transport regimes from anomalous (both super‐ and sub‐) to normal diffusion at large timescales is analytically demonstrated
Analytical predictions are well supported by long‐term field data, revealing power‐law slowdown of virtual velocity eventually to a constant
Anomalous transport processes in porous media have become a central physical issue due to the increasing amount of processes and applications where it appears, ranging from contaminant transport in ...aquifers and oil recovery to anomalous diffusion in biological membranes. In all these cases, the existence of strong heterogeneities and anisotropies make proper physical and mathematical modelling a complicated problem, leading to simplified models where these spatial features and their implications for transport and diffusion are treated separately. In this work we propose a simple model for transport in porous media that includes anisotropy and strong heterogeneities. We show that depending on how strong the medium heterogeneities are, different regimes of superdiffusive transport emerge, going from superdiffusion due to long-range correlations to Lévy walks and ballistic diffusion.
•Anomalous diffusion in heterogeneous anisotropic porous media with preferential flow paths.•Complex dynamical behavior ranging from superdiffusion due to long-range correlations to Lévy walks.•Sub and superdiffusive transport along different spatial directions.•Lévy walks as a consequence of medium heterogeneity and anisotropy.
The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies of search processes often adopt a probabilistic framework, in which a searcher ...randomly explores a spatial domain for a randomly located target. There has been significant interest and controversy regarding optimal search strategies, especially for superdiffusive processes. The optimal search strategy is typically defined as the strategy that minimizes the time it takes a given single searcher to find a target, which is called a first hitting time (FHT). However, many systems involve multiple searchers, and the important timescale is the time it takes the fastest searcher to find a target, which is called an extreme FHT. In this paper, we study extreme FHTs for any stochastic process that is a random time change of Brownian motion by a Lévy subordinator. This class of stochastic processes includes superdiffusive Lévy flights in any space dimension, which are processes described by a Fokker–Planck equation with a fractional Laplacian. We find the short-time distribution of a single FHT for any Lévy subordinate Brownian motion and use this to find the full distribution and moments of extreme FHTs as the number of searchers grows. We illustrate these rigorous results in several examples and numerical simulations.
We investigate the dynamics of a SIRS epidemiological model taking into account cross-superdiffusion and delays in transmission, Beddington–DeAngelis incidence rate and Holling type II treatment. The ...superdiffusion is induced by inter-country and inter-urban exchange. The linear stability analysis for the steady-state solutions is performed, and the basic reproductive number is calculated. The sensitivity analysis of the basic reproductive number is presented, and we show that some parameters strongly influence the dynamics of the system. A bifurcation analysis to determine the direction and stability of the model is carried out using the normal form and center manifold theorem. The results reveal a proportionality between the transmission delay and the diffusion rate. The numerical results show the formation of patterns in the model, and their epidemiological implications are discussed.
1. Search processes play an important role in physical, chemical and biological systems. In animal foraging, the search strategy predators should use to search optimally for prey is an enduring ...question. Some models demonstrate that when prey is sparsely distributed, an optimal search pattern is a specialised random walk known as a Lévy flight, whereas when prey is abundant, simple Brownian motion is sufficiently efficient. These predictions form part of what has been termed the Lévy flight foraging hypothesis (LFF) which states that as Lévy flights optimise random searches, movements approximated by optimal Lévy flights may have naturally evolved in organisms to enhance encounters with targets (e.g. prey) when knowledge of their locations is incomplete. 2. Whether free-ranging predators exhibit the movement patterns predicted in the LFF hypothesis in response to known prey types and distributions, however, has not been determined. We tested this using vertical and horizontal movement data from electronic tagging of an apex predator, the great white shark Carcharodon carcharias, across widely differing habitats reflecting different prey types. 3. Individual white sharks exhibited movement patterns that predicted well the prey types expected under the LFF hypothesis. Shark movements were best approximated by Brownian motion when hunting near abundant, predictable sources of prey (e.g. seal colonies, fish aggregations), whereas movements approximating truncated Lévy flights were present when searching for sparsely distributed or potentially difficult-to-detect prey in oceanic or shelf environments, respectively. 4. That movement patterns approximated by truncated Lévy flights and Brownian behaviour were present in the predicted prey fields indicates search strategies adopted by white sharks appear to be the most efficient ones for encountering prey in the habitats where such patterns are observed. This suggests that C. carcharlas appears capable of exhibiting search patterns that are approximated as optimal in response to encountered changes in prey type and abundance, and across diverse marine habitats, from the surf zone to the deep ocean. 5. Our results provide some support for the LFF hypothesis. However, it is possible that the observed Lévy patterns of white sharks may not arise from an adaptive behaviour but could be an emergent property arising from simple, straight-line movements between complex (e.g. fractal) distributions of prey. Experimental studies are needed in vertebrates to test for the presence of Levy behaviour patterns in the absence of complex prey distributions.
Fronts in anomalous diffusion-reaction systems Volpert, V. A.; Nec, Y.; Nepomnyashchy, A. A.
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
01/2013, Letnik:
371, Številka:
1982
Journal Article
Recenzirano
Odprti dostop
A review of recent developments in the field of front dynamics in anomalous diffusion-reaction systems is presented. Both fronts between stable phases and those propagating into an unstable phase are ...considered. A number of models of anomalous diffusion with reaction are discussed, including models with Lévy flights, truncated Lévy flights, subdiffusion-limited reactions and models with intertwined subdiffusion and reaction operators.
PDF
