Random Walk Simulations Research Articles

Attempts at the Characterization of In-Cell Biophysical Processes Non-Invasively-Quantitative NMR Diffusometry of a Model Cellular System.

In the literature, diffusion studies of cell systems are usually limited to two water pools that are associated with the extracellular space and the entire interior of the cell. Therefore, the time-dependent diffusion coefficient contains information about the geometry of these two water regions and the water exchange through their boundary. This approach is due to the fact that most of these studies use pulse techniques and relatively low gradients, which prevents the achievement of high b-values. As a consequence, it is not possible to register the signal coming from proton populations with a very low bulk or apparent self-diffusion coefficient, such as cell organelles. The purpose of this work was to obtain information on the geometry and dynamics of water at a level lower than the cell size, i.e., in cellular structures, using the time-dependent diffusion coefficient method. The model of the cell system was made of baker’s yeast (Saccharomyces cerevisiae) since that is commonly available and well-characterized. We measured characteristic fresh yeast properties with the application of a compact Nuclear Magnetic Resonance (NMR)-Magritek Mobile Universal Surface Explorer (MoUSE) device with a very high, constant gradient (~24 T/m), which enabled us to obtain a sufficient stimulated echo attenuation even for very short diffusion times (0.2–40 ms) and to apply very short diffusion encoding times. In this work, due to a very large diffusion weighting (b-values), splitting the signal into three components was possible, among which one was associated only with cellular structures. Time-dependent diffusion coefficient analysis allowed us to determine the self-diffusion coefficients of extracellular fluid, cytoplasm and cellular organelles, as well as compartment sizes. Cellular organelles contributing to each compartment were identified based on the random walk simulations and approximate volumes of water pools calculated using theoretical sizes or molar fractions. Information about different cell structures is contained in different compartments depending on the diffusion regime, which is inherent in studies applying extremely high gradients.

Random-walk simulation of non-conservative pollutant transport in shallow water flows

The random-walk method is inherently simple and numerically stable. However, when used in hydro-environmental analyses, most of the existing random-walk methods ignore the influence of the non-uniform water depth and only consider the transport of inert materials, hence the inability of modelling biochemical reactions. In addition, the existing applications mainly focus on instantaneous-release problems, where a fixed number of particles move in the computational domain. This paper first presents examples to showcase the capability of a newly-developed random-walk model in simulating the continuous sources of non-conservative substances. Then, the method is applied to examine the BOD-DO balance along a hypothetical river. The predictions agree well with analytical solutions. Finally, the developed model is used to study the pollutant transport in the Thames Estuary. The current model is illustrated to be able to accurately predict the interaction between multiple pollutants in real-world situations with uneven bathymetry and extensive intertidal floodplains.

Quantitative analysis of dispersion state for nearly two-dimensional systems

Many researchers attempted to quantify dispersion states of microstructures. Several algorithms to analyze micrographs are proposed to evaluate indicators reflecting the dispersion states. However, the values of these indicators can correlate several performances of a given system, to some degree. This paper proposes a new indicator, the degree of dispersion (DoD), that assesses the dispersion state by a random walk simulation and a cloud overlap estimation. The novelty of the proposed method is summarized as follows: firstly, the DoD possesses various features such as stability, effectivity, and flexibility; secondly, the DoD considers inter- and intra-cluster dispersions naturally; and finally, the DoD has an adjustable parameter that reflects different contexts of various applications. The computation time takes about 1–3 min for 600 by 600 pixels images. We believe that the DoD can be used in various industrial applications such as films, batteries, colloids, and nanocomposites.

Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains.

Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a one-dimensional domain that is evolving. The model equations, which have been derived from generalized continuous time random walks, can incorporate complexities such as subdiffusive transport and inhomogeneous domain stretching and shrinking. Inhomogeneously growing domains are frequently encountered in biological phenomena involving stochastic transport, such as tumor growth and morphogen gradient formation. A method for constructing analytic expressions for short-time moments of the position of the particles is developed and moments calculated from this approach are shown to compare favorably with results from random walk simulations and numerical integration of the reaction transport equation. The results show the important role played by the initial condition. In particular, it strongly affects the time dependence of the moments in the short-time regime by introducing additional drift and diffusion terms. We also discuss how our reaction transport equation could be applied to study the spreading of a population on an evolving interface. From a more general perspective, our findings help to mitigate the scarcity of analytic results for reaction-diffusion problems in geometries displaying nonuniform growth. They are also expected to pave the way for further results, including the treatment of first-passage problems associated with encounter-controlled reactions in such domains.

Statistics of adatom diffusion in a model of thin film growth.

We study the statistics of the number of executed hops of adatoms at the surface of films grown with the Clarke-Vvedensky (CV) model in simple cubic lattices. The distributions of this number N are determined in films with average thicknesses close to 50 and 100 monolayers for a broad range of values of the diffusion-to-deposition ratio R and of the probability ε that lowers the diffusion coefficient for each lateral neighbor. The mobility of subsurface atoms and the energy barriers for crossing step edges are neglected. Simulations show that the adatoms execute uncorrelated diffusion during the time in which they move on the film surface. In a low temperature regime, typically with Rε≲1, the attachment to lateral neighbors is almost irreversible, the average number of hops scales as 〈N〉∼R^{0.38±0.01}, and the distribution of that number decays approximately as exp[-(N/〈N〉)^{0.80±0.07}]. Similar decay is observed in simulations of random walks in a plane with randomly distributed absorbing traps and the estimated relation between 〈N〉 and the density of terrace steps is similar to that observed in the trapping problem, which provides a conceptual explanation of that regime. As the temperature increases, 〈N〉 crosses over to another regime when Rε^{3.0±0.3}∼1, which indicates high mobility of all adatoms at terrace borders. The distributions P(N) change to simple exponential decays, due to the constant probability for an adatom to become immobile after being covered by a new deposited layer. At higher temperatures, the surfaces become very smooth and 〈N〉∼Rε^{1.85±0.15}, which is explained by an analogy with submonolayer growth. Thus, the statistics of adatom hops on growing film surfaces is related to universal and nonuniversal features of the growth model and with properties of trapping models if the hopping time is limited by the landscape and not by the deposition of other layers.

Stochastic collision electrochemistry of single silver nanoparticles

Abstract The electrochemical oxidation of single colloidal Ag nanoparticles (NPs) at an electrode surface has previously been studied as an in situ particle-sizing methodology. However, the discovery of multipeak amperometric behavior in 2017 sparked new interest toward understanding the precise physical mechanism of the manner in which a freely diffusing Ag NP interacts with the electrode surface. Random walk simulations, unique electrochemical experiments, and correlated optical/spectroscopic techniques have revealed exciting new results regarding the physical and chemical processes occurring on single NP collision.

Entropy and Random Walk Trails Water Confinement and Non-Thermal Equilibrium in Photon-Induced Nanocavities.

Molecules near surfaces are regularly trapped in small cavitations. Molecular confinement, especially water confinement, shows intriguing and unexpected behavior including surface entropy adjustment; nevertheless, observations of entropic variation during molecular confinement are scarce. An experimental assessment of the correlation between surface strain and entropy during molecular confinement in tiny crevices is difficult because strain variances fall in the nanometer scale. In this work, entropic variations during water confinement in 2D nano/micro cavitations were observed. Experimental results and random walk simulations of water molecules inside different size nanocavitations show that the mean escaping time of molecular water from nanocavities largely deviates from the mean collision time of water molecules near surfaces, crafted by 157 nm vacuum ultraviolet laser light on polyacrylamide matrixes. The mean escape time distribution of a few molecules indicates a non-thermal equilibrium state inside the cavity. The time differentiation inside and outside nanocavities reveals an additional state of ordered arrangements between nanocavities and molecular water ensembles of fixed molecular length near the surface. The configured number of microstates correctly counts for the experimental surface entropy deviation during molecular water confinement. The methodology has the potential to identify confined water molecules in nanocavities with life science importance.

Construction of one-dimensional random walk lattices using DNA algorithmic self-assembly

Algorithmic DNA lattices are constructed using pre-defined rules such as COPY, NOT, and XOR, where patterns are predicted based on initial values. However, the experimental implementation of an unpredictable random walk pattern (which is the implementation of a random rule, i.e., equally probable to move toward either the left or right in 1D systems) in DNA has not been reported yet. Here, we construct DNA lattices with DNA rule tiles implemented using the random rule. Patterns are visualized by atomic force microscopy. Finally, we discussed the average displacement, mean-square displacement, and number of displacement occurrences of experimental as well as simulated 1D random walk. The encoded information in sticky ends of DNA rule tiles demonstrates the feasibility of universal computation through DNA algorithmic self-assembly, which could be extremely beneficial in future computations.

An interaction mechanism for the maintenance of fission-fusion dynamics under different individual densities.

Animals often show high consistency in their social organisation despite facing changing environmental conditions. Especially in shoaling fish, fission–fusion dynamics that describe for which periods individuals are solitary or social have been found to remain unaltered even when density changed. This compensatory ability is assumed to be an adaptation towards constant predation pressure, but the mechanism through which individuals can actively compensate for density changes is yet unknown. The aim of the current study is to identify behavioural patterns that enable this active compensation. We compared the fission–fusion dynamics of two populations of the live-bearing Atlantic molly (Poecilia mexicana) that live in adjacent habitats with very different predator regimes: cave mollies that inhabit a low-predation environment inside a sulfidic cave with a low density of predatory water bugs (Belostoma sp.), and mollies that live directly outside the cave (henceforth called “surface” mollies) in a high-predation environment. We analysed their fission–fusion dynamics under two different fish densities of 12 and 6 fish per 0.36 m2. As expected, surface mollies spent more time being social than cave mollies, and this difference in social time was a result of surface mollies being less likely to discontinue social contact (once they had a social partner) and being more likely to resume social contact (once alone) than cave mollies. Interestingly, surface mollies were also less likely to switch among social partners than cave mollies. A random walk simulation predicted each population to show reduced social encounters in the low density treatment. While cave mollies largely followed this prediction, surface mollies maintained their interaction probabilities even at low density. Surface mollies achieved this by a reduction in the size of a convex polygon formed by the group as density decreased. This may allow them to largely maintain their fission–fusion dynamics while still being able to visit large parts of the available area as a group. A slight reduction (21%) in the area visited at low densities was also observed but insufficient to explain how the fish maintained their fission–fusion dynamics. Finally, we discuss potential movement rules that could account for the reduction of polygon size and test their performance.

(Invited) Surface Photovoltage Analysis of Photocatalytic Materials

A brief review of surface photovoltage (SPV) techniques and their application to photocatalytic materials is given. SPV is defined by the light-induced change of the contact potential difference (∆CPD) between two electrodes, i.e. SPV signals can be obtained whenever photogenerated charge carriers are separated in space [1]. SPV signals depend on processes of light absorption, photogeneration, directed charge transfer, charge transport and recombination. Therefore, SPV techniques can be well applied to the analysis of electronic, transport and recombination properties of photoactive materials [2].Basics of SPV are introduced including the relaxation of a disturbed space charge, the center of charge approach and mechanisms of charge separation. Principles of SPV measurements will be given and illustrated with applications. Depending whether fixed capacitors, Kelvin probes, electron beams or photoelectrons are applied (see also figure 1), SPV signals can be measured at crystals, layers or powders of photocatalysts with high sensitivity over wide ranges in time or high resolution in space and in different ambient (gases, vacuum, electrolytes). In-operando SPV measurements are realized.For measurements with fixed capacitors, SPV signals are coupled out directly with a high-impedance buffer. Due to the discharge of the measurement capacitor via a very large measurement resistance, the application of fixed capacitors is limited to transient [3] and modulated [4] SPV measurements. With fixed capacitors, the widest range in time ((sub)ns...ms...h, transient, example: nano-composite of TiO2/In2S3 [5]) and the highest sensitivity (10...100 nV, modulated, see [6] for defect analysis in (FA0.85MA0.1Cs0.05)PbBr3) are reached whereas no additional interactions are involved. Attention will be paid to the application of transient SPV spectroscopy [7] at constant photon flux for the investigation of defect states and charge transfer across interfaces [8] (c-Si(n++)/TiO2). Furthermore, principles of random walk simulations for the modeling of transient [9] and modulated [10] SPV signals in small systems will be discussed [2].With Kelvin probes, the ac current between a sample and a vibrating electrode (vibrating electrode [11], most applied technique, see, for example [12]) or the electrostatic force between the sample surface and a vibrating tip electrode (Kelvin probe force microscopy [13] [14], KPFM) are nulled by applying an external bias potential. The highest resolution in space is reached for SPV measurements with KPFM (tens of nm). Examples will be shown for SPV measurements with vibrating electrodes for TiO2 [15] and KPFM for Cu2O [16] and BiVO4 with co-catalysts [17].In SPV measurements with electron beams [18, 19], a low electron current is kept constant with a compensating bias potential. In photoelectron spectroscopy, core levels shift with regard to ∆CPD. Additional interactions of the sample with electrons and/or x-rays are possible. The application of synchrotron radiation allows for SPV measurements at extremely short times [20, 21]. Further opportunities opened for SPV measurements by ambient pressure photoelectron emission spectroscopy [22].[1] review of L. Kronik, Y. Shapira, Surf. Sci. Rep. 37 (1999) 1.[2] Th. Dittrich, S. Fengler, Surface photovoltage analysis of photoactive materials, World Scientific (2019), ISBN: 978-1-78634-765-7.[3] E. O. Johnson, J. Appl. Phys. 28 (1957) 1349.[4] V. Duzhko, et al., Phys. Rev. B 64 (2001) 075204.[5] Th. Dittrich, et al., Rev. Sci. Instrum. 88 (2017) 053904 and 90 (2019) 026102.[6] I. Levine, et al., ACS Energy Lett. 4 (2019) 1150.[7] Th. Dittrich, et al., Appl. Phys. Lett. 110 (2017) 023901.[8] S. Fengler, et al., submitted.[9] S. Fengler, et al., J. Phys. Chem. C 117 (2013) 6462.[10] S. Fengler, Th. Dittrich, J. Phys. Chem. C 120 (2016) 17777.[11] K. Besocke, S. Berger, Rev. Sci. Instrum. 47 (1976) 840.[12] M. A. Melo et al., Nano Lett. 18 (2018) 805.[13] M. Nonnenmacher, et al., Appl. Phys. Lett. 58 (1991) 2921.[14] T. Glatzel, S. Sadewasser (edts.) Kelvin probe force microscopy – from single charge detection to device characterization, Springer, Cham. (2018).[15] M. K. Nowotny, et al., Mater. Lett. 64 (2010) 928.[16] R. Chen, et al., Nano Lett. 19 (2019) 426.[17] J. Zhu, et al., Nano Lett. 17 (2017) 6735; R. Chen, et al., Chem. Soc. Rev. 47 (2018) 8238.[18] F. Steinrisser, R. E. Hatrick, Rev. Sci. Instrum. 42 (1971) 3014.[19] J. Clabes, M. Henzler, Phys. Rev. B 21 (1980) 625.[20] W. Widdra, et al., Surf. Sci. 543 (2003) 87.[21] S. Yamamoto, I. Matsuda, J. Phys. Soc. Jpn. 82 (2013) 021003.[22] J. R. Harwell et al., Phys. Chem. Chem. Phys. 18 (2016) 19738. Figure 1

In Vivo Confocal Imaging of Fluorescently Labeled Microbubbles: Implications for Ultrasound Localization Microscopy.

We report the time kinetics of fluorescently labeled microbubbles (MBs) in capillary-level microvasculature as measured via confocal microscopy and compare these results to ultrasound localization microscopy (ULM). The observed 19.4 ± 4.2 MBs per confocal field-of-view ( [Formula: see text]) are in excellent agreement with the expected count of 19.1 MBs per frame. The estimated time to fully perfuse this capillary network was 193 s, which corroborates the values reported in the literature. We then modeled the capillary network as an empirically determined discrete-time Markov chain with adjustable MB transition probabilities though individual capillaries. The Monte Carlo random walk simulations found perfusion times ranging from 24.5 s for unbiased Markov chains up to 182 s for heterogeneous flow distributions. This pilot study confirms a probability-derived explanation for the long acquisition times required for super-resolution ULM.

Evidence of absorption dominating over scattering in light attenuation by nanodiamonds

We show an experimental evidence of the domination of absorption over scattering in absorbance spectra of detonation nanodiamonds. We perform the absorbance measurements on the UV-Vis spectrophotometer equipped with integrating sphere and compare them with conventional absorbance spectra. Additionally, we measure the scattering light intensity at the cuvette side wall (scattering at 90 degrees angle). The obtained experimental data were interpreted using the simulations of photon random walk in turbid media and Kubelka-Munk approach. The scattering cross sections and indicatrices were obtained by Mie theory. We discover that despite being very close to $\lambda^{-4}$ power law (like Rayleigh scattering) the light extinction by the primary 4 nm diamond crystallites is due to absorption only and scattering can be neglected. That is the reason why previously absorption and scattering contributions were confused. The scattering is governed only by the agglomerates of 100 nm and larger in size remaining in the hydrosols and their fraction can be effectively controlled by centrifugation. Only Mie theory reproduces correctly the close to $\lambda^{-2}$ scattering by the agglomerates accounting for the weird interplay between their size, fractal dimension, and dielectric properties. Finally, using the obtained absorbance spectra we estimate the fraction of non diamond phase in nanodiamonds and their agglomerates.

Characterization of the Structure and Transport Properties of Alginate/Chitosan Microparticle Membranes Utilized in the Pervaporative Dehydration of Ethanol.

The structure and transport properties of alginate/chitosan microparticle membranes used in ethanol dehydration processes were investigated. The membranes were characterized based on images obtained from high-resolution microscopy. The following parameters were determined: the observed total amount of void space, the average size of the void domains, their length and diameter, the fractal dimension, and the generalized stochastic fractal parameters. The total amount of void space was determined to be between 54% and 64%. The average size of the void domains is smaller for alginate membranes containing neat (CS) and phosphorylated (CS-P) chitosan particles when compared to those membranes filled with glycidol-modified (CS-G) and glutaraldehyde crosslinked (CS-GA) chitosan particles. Furthermore, the transport of ethanol and water particles through the studied membranes was modelled using a random walk framework. It was observed that the results from the theoretical and experimental studies are directly correlated. The smallest values of water to ethanol diffusion coefficient ratios (i.e., 14) were obtained for Alg (sodium alginate) membranes loaded with the CS and CS-P particles, respectively. Significantly larger values (27 and 19) were noted for membranes filled with CS-G and CS-GA particles, respectively. The simulation results show that the size of channels which develop in the alginate matrix is less suited for ethanol molecules compared to water molecules because of their larger size. Such a situation facilitates the separation of water from ethanol. The comparison of the structural analysis of the membranes and random walk simulations allows one to understand the factors that influence the transport phenomena, in the studied membranes, and comment on the effect of the length, diameter, number of channels, and variations in the pore diameters on these transport parameters.

Semi In-Situ Observation on Void Formation in Electromigrated Sn-Ag Film and its Prediction by Random-Walk Simulation

In this study a thin metallic film composed of Sn-3.5Ag (wt.%) was subjected to a current density of 7.77×104 A/cm2 at room temperature, in order to test the ability of existing models of electromigration (EM) to predict the nucleation and evolution of voids generated by the resulting atomic migration. The computer simulation used to compute the coupled current distribution, thermal distribution and atomic migration problems relied on a Random Walk (RW) method that has not previously been applied to this problem but is particularly well suited to modelling a domain which is undergoing changes due to the formation of voids. Comparison of the experimental results and computer simulations provide proof of concept that the RW method can be successfully applied to this class of problem, but also that imperfections in the film can lead to deviations from the predicted patterns.

The effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk

In the optical quantum random walk system, phase fluctuation and beam splitter fluctuation are two unavoidable decoherence factors. These two factors degrade the performance of quantum random walk by destroying coherence, and even degrade it into a classical one. We propose a scheme for the simulation of quantum random walk using phase shifters, tunable beam splitters, and photodetectors. This proposed scheme enables us to analyze the effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk. Furthermore, it is helpful to guide the control of phase fluctuation and beam splitter fluctuation in the experiment.

Predicting quantum advantage by quantum walk with convolutional neural networks

Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from classical random walks analogs, in particular, they walk faster than classical ones on certain graphs, enabling in these cases quantum algorithmic applications and quantum-enhanced energy transfer. However, little is known about the possible advantages on arbitrary graphs not having explicit symmetries. For these graphs one would need to perform simulations of classical and quantum walk dynamics to check if the speedup occurs, which could take a long computational time. Here we present a new approach for the solution of the quantum speedup problem, which is based on a machine learning algorithm that predicts the quantum advantage by just ‘looking’ at a graph. The convolutional neural network, which we designed specifically to learn from graphs, observes simulated examples and learns complex features of graphs that lead to a quantum advantage, allowing to identify graphs that exhibit quantum advantage without performing any quantum walk or random walk simulations. The performance of our approach is evaluated for line and random graphs, where classification was always better than random guess even for the most challenging cases. Our findings pave the way to an automated elaboration of novel large-scale quantum circuits utilizing quantum walk based algorithms, and to simulating high-efficiency energy transfer in biophotonics and material science.

Analytical Solution of Advection‐Dispersion Boundary Value Processes in Environmental Flows

AbstractThe one‐dimensional advection‐dispersion equation with streamwise boundaries has been used to model a wide range of real‐world processes including groundwater contaminant transport, atmospheric plume deposition, and the movement of planktonic organisms and migratory animals through riverine systems. Imposing boundary conditions at upstream and downstream locations complicates the analysis of this equation, and processes that require such boundary conditions are, therefore, typically modeled using approximations that are valid only under certain conditions. Approximations typically involve a simplification of the mass influx into the system, require a large separation between source and boundary, or work only in either strongly advection‐ or strongly dispersion‐dominated systems. Here, we circumvent these limitations by providing an analytical solution to a class of advection‐dispersion equations that are broadly applicable to the processes described above as well as many other physical and biological problems. Our solution makes it possible to relax the assumptions required under previous analytic approximations, making it a more flexible approach for modeling advection‐dispersion processes under realistic field conditions. We show that the solution is in good agreement with random walk simulations. To illustrate the broad utility of the method, we also apply it to an empirical data set from a population of migratory fish moving through a river system in the California Central Valley and demonstrate that it describes the data more accurately than do existing methods.

Accumulation-Driven Unified Spatiotemporal Synthesis and Structuring of Immiscible Metallic Nanoalloys

Summary Accumulation-mediated chemical reactions are a ubiquitous phenomenon in nature. Here, we explore microbubble-induced accumulation of precursor ions to achieve surfactant-free synthesis of immiscible metallic nanoalloys and simultaneously pattern the nanoalloys into targeted architectures for their enhanced catalytic applications. Our unified spatiotemporal synthesis and structuring (US3) strategy, whereby millisecond-scale accumulation of the ions takes place in a highly confined laser-mediated microbubble trap (MBT), drives ultrafast alloy synthesis in sync with the structuring process. As a case in point, we employ the US3 strategy for the in situ surfactant-free synthesis and patterning of traditionally immiscible rhodium-gold (RhAu) nanoalloys. Stochastic random walk simulations justify the millisecond-scale accumulation process, leading to a 3-order reduction in synthesis time. The catalytic activity and structure-property relationship were evaluated using the reduction of p-nitrophenol with NaBH4. Our in situ synthesis and structuring strategy can be translated for high-throughput production and screening of multimetallic systems with tailored catalytic, optoelectronic, and magnetic functions.

Mechanical Interaction between Cells Facilitates Molecular Transport.

In vivo, eukaryotic cells are embedded in a matrix environment, where they grow and develop. Generally, this extracellular matrix (ECM) is an anisotropic fibrous structure, through which macromolecules and biochemical signaling molecules at the nanometer scale diffuse. The ECM is continuously remodeled by cells, via mechanical interactions, which lead to a potential link between biomechanical and biochemical cell-cell interactions. Here, it is studied how cell-induced forces applied on the ECM impact the biochemical transport of molecules between distant cells. It is experimentally observed that cells remodel the ECM by increasing fiber alignment and density of the matrix between them over time. Using random walk simulations on a 3D lattice, elongated fixed obstacles are implemented that mimic the fibrous ECM structure. Both diffusion of a tracer molecule and the mean first-passage time a molecule secreted from one cell takes to reach another cell are measured. The model predicts that cell-induced remodeling can lead to a dramatic speedup in the transport of molecules between cells. Fiber alignment and densification cause reduction of the transport dimensionality from a 3D to a much more rapid 1D process. Thus, a novel mechanism of mechano-biochemical feedback in the regulation of long-range cell-cell communication is suggested.

Transport through random bimodal and multimodal fiber structures

Random walk simulation results are reported for the transport and structural properties of random bimodal fibrous media for a range of values of the porosity, relative fiber size, and relative fiber density. Analytical expressions are derived for the mean intercept length of random bimodal and multimodal fiber structures, and are validated through simulations. A fiber dispersity factor emerges from the derivations, accounting for the deviation of the mean intercept length of such structures from that of unimodal fiber beds of the same porosity. Tortuosity factors in all diffusion regimes for in-plane and transverse flow through bimodal fibrous media of moderate or high porosity are practically independent of the relative fiber size and density and equal to those reported earlier for beds of unimodal fibers. The same holds for the formation factor of such structures, accounting for the dimensionless effective bulk diffusivity, thermal and electrical conductivity, magnetic permeability, dielectric constant and refractive index. The dimensionless viscous permeability of bimodal and multimodal fiber structures of moderate or high porosity may be obtained from that of unimodal fiber structures through simple multiplication by the square of the dispersity factor. This result is in line with a multitude of experimental data of the literature.