Random Resistor Network Model Research Articles

Cooperation in bioluminescence: understanding the role of autoinducers by a stochastic random resistor model

Quorum sensing is a communication mechanism adopted by different bacterial strains for the regulation of gene transcription. It takes place through the exchange of molecules called autoinducers. Bioluminescence is an emergent threshold phenomenon shown by some bacteria strains. Its precise relationship to quorum sensing is a debated topic, particularly regarding the role of the different autoinducers used by bacteria. In this paper, assuming a direct relationship between bioluminescence and quorum sensing, we investigate the role of multiple autoinducers in the bioluminescence response of Vibrio harveyi, considered as a model bioluminescent strain, due to its quorum sensing circuitry involving an array of three different autoinducers. Experiments on mutants of this bacterium, obtained by suppression of one or more autoinducers, reveal their relative non-trivial relevance and cooperative interaction patterns. The proposed analysis is implemented on a regular lattice, whose nodes represent microbial entities equipped with charges, which represent the ability to up/down regulate the gene expression. Quorum sensing results from a Coulomb-type field, produced by the charges. In analogy with random resistor network models, the lattice is permeated by an effective current which accounts for the amount and distribution of the charges. We propose that the presence of different autoinducers correspond to a different up/down regulation of gene expression, i.e., to a different way to account for the charges. Then, by introducing a modulation of the charge dependence into the current flowing within the network, we show that it is able to describe the bioluminescence exhibited by V. harveyi mutants. Furthermore, modulation of the charge dependence allows the interactions between the different autoinducers to be taken into account, providing a prediction regarding the data obtainable under specific growth conditions.Graphical abstract

Percolation threshold and electrical conductivity of conductive polymer composites filled with curved fibers in two-dimensional space.

Quantifying the influence of fiber curvature on the percolation behavior of flexible conductive fiber and further on the electrical conductivity of conductive polymer composites (CPCs) is crucial for the design of CPCs. This study considers CPCs as a random packing of soft curved discorectangles (CDCRs) in a polymer matrix. The geometry of CDCR is developed, and an inter-CDCR contact detection algorithm is used to generate a random packing structure of CDCRs. The effects of aspect ratio α and bending central angles θ of CDCR on the percolation threshold ϕc of the overlapped CDCR system in a two-dimensional plane are then investigated using the finite-size scaling method. The result reveals that ϕc decreases monotonically as α grows and increases monotonically as θ rises. A shape-independent power law formula, denoted as ϕc = 2.2015 A-0.8172dex is developed to quantify the relationship between the Adex and ϕc. A comparison of our numerical simulations, published data, and predictions verifies the reliability and universality of the fitting model. Subsequently, a resistor network searching algorithm (RNSA) is proposed to construct the random resistor network model (RRNM). A power law model, denoted as is developed to evaluate the effects of the normalized reduced density (η - ηc)/ηc on the effective conductivity σeff of CPC. Comparing our predictions with data from the literature and our simulation verifies the reliability of our RNSA and the fitting model. This paper's methodology and findings may provide a theoretical hint for the CPC's design.

Quantifying the influence of graphene film nanostructure on the macroscopic electrical conductivity

Graphene films have emerged as a promising nanostructured material class to exploit graphene's outstanding nanoscopic properties on the macroscale. Their potential applications include solar cells (Eda et al 2008 Appl. Phys. Lett. 92, 233305; Müllen et al 2008 Nano Lett. 8, 323–7), antennas (Zhang et al 2018 Electronics 7, 285; Song et al 2018 Carbon 130, 164–9), or electromagnetic interference shielding (Zhou et al 2017 Nanoscale 9, 18613–8; Wan et al 2017 Carbon 122, 74–81; Wang et al 2018 Small 14, 1704332), all of which require a high electrical conductivity. While an outstanding electrical conductivity is a key feature of pristine graphene monolayers, the transfer to the macroscale is challenging. Here, we combined theory and experiment to quantify the impact of specific structural graphene film properties. We synthesized graphene films with systematically varied flake sizes, studied their electrical conductivities, and found excellent agreement to simulations with a three-dimensional random resistor network model. In a further percolation-type study, we computed the critical share of non-conductive elements in a graphene film θ c = 10% where a substantial loss of electrical conductivity occurs. We prepared mixed films from graphene and graphene oxide to validate the threshold experimentally. In combination, experiments and simulations provide a coherent picture of how the graphene film microstructure is related to the macroscopic electrical conductivity (Rizzi et al 2018 ACS Appl. Mater. Interfaces 10 43088–94; Rizzi et al 2019 Comput. Mater. Sci. 161, 364–70). Our findings provide valuable insights for the production of highly conductive graphene-based macro-materials.

Current-Resistance Effects Inducing Nonlinear Fluctuation Mechanisms in Granular Aluminum Oxide Nanowires.

The unusual superconducting properties of granular aluminum oxide have been recently investigated for application in quantum circuits. However, the intrinsic irregular structure of this material requires a good understanding of the transport mechanisms and, in particular, the effect of disorder, especially when patterned at the nanoscale level. In view of these aspects, electric transport and voltage fluctuations have been investigated on thin-film based granular aluminum oxide nanowires, in the normal state and at temperatures between 8 and 300 K. The nonlinear resistivity and two-level tunneling fluctuators have been observed. Regarding the nature of the noise processes, the experimental findings give a clear indication in favor of a dynamic random resistor network model, rather than the possible existence of a local ordering of magnetic origin. The identification of the charge carrier fluctuations in the normal state of granular aluminum oxide nanowires is very useful for improving the fabrication process and, therefore, reducing the possible sources of decoherence in the superconducting state, where quantum technologies that are based on these nanostructures should work.

Charge Transport in Mixed Semiconducting SWCNT Networks with Tailored Diameter Distributions

The recent availability of purely semiconducting single-walled carbon nanotubes (SWCNTs) and the ability to prepare dense and uniform SWCNT networks from dispersion has led to promising applications in optoelectronics, e.g. in field-effect transistors (FETs), light-emitting diodes, notch filters and solar cells. Further optimization and controlled tuning of nanotube networks is desirable to establish them as competitive semiconducting materials. The impact of the SWCNT network composition on the overall charge transport was demonstrated recently [1]. The uneven energy landscape of networks with a broad tube diameter and thus bandgap distribution results in inferior transport properties. Contrary to common belief, the charge transport in networks is not solely determined by tube-tube junctions but intra-nanotube transport also has a significant impact on the overall network mobility. Here, we examine this hypothesis in a detailed charge transport study of FETs with SWCNT networks consisting of polymer-sorted small diameter (6,5) SWCNTs (0.76 nm) and large diameter plasma torch SWCNTs (1.2-1.5 nm) with different but controlled mixing ratios. All FETs showed balanced ambipolar transport with low off-currents and negligible hysteresis. The extracted mobilities varied characteristically with network composition. The obtained experimental data are compared to results from numerically simulated networks with analogous SWCNT compositions. The employed random resistor network model was recently shown to adequately describe the carrier density-dependent mobility in SWCNT networks [2]. [1] M Brohmann et al., J. Phys Chem. C 122, 19886-19896 (2018) [2] S. P. Schießl et al., Phys. Rev. Mater. 1, 046003 (2017) Figure 1

Equivalence of effective medium and random resistor network models for disorder-induced unsaturating linear magnetoresistance

A linear unsaturating magnetoresistance at high perpendicular magnetic fields, together with a quadratic positive magnetoresistance at low fields, has been seen in many different experimental materials, ranging from silver chalcogenides and thin films of InSb to topological materials like graphene and Dirac semimetals. In the literature, two very different theoretical approaches have been used to explain this classical magnetoresistance as a consequence of sample disorder. The phenomenological random resistor network model constructs a grid of four terminal resistors, each with a varying random resistance. The effective medium theory model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. Here, we demonstrate numerically that both models belong to the same universality class and that a restricted class of the random resistor network is actually equivalent to the effective medium theory. Both models are also in good agreement with experiments on a diverse range of materials. Moreover, we show that in both cases, a single parameter, i.e., the ratio of the fluctuations in the carrier density to the average carrier density, completely determines the magnetoresistance profile.

Gradient-driven diffusion and pattern formation in crowded mixtures.

Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion affects microstructure, which in turn affects diffusivity; a key question is how this complex coupling controls both transport and pattern formation. To examine these mechanisms, we study a two-dimensional multicomponent lattice gas model, where "tracer" molecules diffuse between a source and a sink separated by a solution of sticky "crowder" molecules that cluster to form dynamically evolving obstacles. In the high-temperature limit, crowders and tracers are miscible, and transport may be predicted analytically. At intermediate temperatures, crowders phase separate into clusters that drift toward the tracer sink. As a result, steady-state tracer diffusivity depends nonmonotonically on both temperature and crowder density, and we observe a variety of complex microstructures. In the low-temperature limit, crowders rapidly aggregate to form obstacles that are kinetically arrested; if crowder density is near the percolation threshold, resulting tracer diffusivity shows scaling behavior with the same scaling exponent as the random resistor network model. Though highly idealized, this simple model reveals fundamental mechanisms governing coupled gradient-driven diffusion, phase separation, and microstructural evolution in crowded mixtures.

Linear magnetoresistance in compensated graphene bilayer

We report a nonsaturating linear magnetoresistance in charge-compensated bilayer graphene in a temperature range from 1.5 to 150 K. The observed linear magnetoresistance disappears away from charge neutrality ruling out the traditional explanation of the effect in terms of the classical random resistor network model. We show that experimental results qualitatively agree with a phenomenological two-fluid model taking into account electron-hole recombination and finite-size sample geometry.

Relating permeability and electrical resistivity in fractures using random resistor network models

AbstractWe use random resistor network models to explore the relationship between electrical resistivity and permeability in a fracture filled with an electrically conductive fluid. Fluid flow and current are controlled by both the distribution and the volume of pore space. Therefore, the aperture distribution of fractures must be accurately modeled in order to realistically represent their hydraulic and electrical properties. We have constructed fracture surface pairs based on characteristics measured on rock samples. We use these to construct resistor networks with variable hydraulic and electrical resistance in order to investigate the changes in both properties as a fault is opened. At small apertures, electrical conductivity and permeability increase moderately with aperture until the fault reaches its percolation threshold. Above this point, the permeability increases by 4 orders of magnitude over a change in mean aperture of less than 0.1 mm, while the resistivity decreases by up to a factor of 10 over this aperture change. Because permeability increases at a greater rate than matrix to fracture resistivity ratio, the percolation threshold can also be defined in terms of the matrix to fracture resistivity ratio, M. The value of M at the percolation threshold, MPT, varies with the ratio of rock to fluid resistivity, the fault spacing, and the fault offset. However, MPT is almost always less than 10. Greater M values are associated with fractures above their percolation threshold. Therefore, if such M values are observed over fluid‐filled fractures, it is likely that they are open for fluid flow.

Slow dynamics in a two-dimensional Anderson-Hubbard model

We study the real-time dynamics of a two-dimensional Anderson-Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small clusters, we demonstrate that for strong disorder this technique approaches the exact result on all available timescales, while for intermediate disorder, in the vicinity of the many-body localization transition, it produces quantitatively accurate results up to nontrivial times. Our method allows for the treatment of system sizes inaccessible by any numerically exact method and for the complete elimination of finite-size effects for the times considered. We show that for a sufficiently strong disorder the system becomes nonergodic, while for intermediate disorder strengths and for all accessible timescales transport in the system is strictly subdiffusive. We argue that these results are incompatible with a simple percolation picture, but are consistent with the heuristic random resistor network model where subdiffusion may be observed for long times until a crossover to diffusion occurs. The prediction of slow finite-time dynamics in a two-dimensional interacting and disordered system can be directly verified in future cold-atoms experiments.

Gate-modulated thermopower of disordered nanowires: II. Variable-range hopping regime

We study the thermopower of a disordered nanowire in the field effect transistor configuration. After a first paper devoted to the elastic coherent regime (Bosisio, Fleury and Pichard 2014 New J. Phys. 16 035004), we consider here the inelastic activated regime taking place at higher temperatures. In the case where the charge transport is thermally assisted by phonons (Mott Variable Range Hopping regime), we use the Miller–Abrahams random resistor network model as recently adapted by Jiang et al for thermoelectric transport. This approach, previously used to study the bulk of the nanowire impurity band, is extended for studying its edges. In this limit, we show that the typical thermopower is largely enhanced, attaining values larger than and exhibiting a non-trivial behaviour as a function of the temperature. A percolation theory by Zvyagin extended to disordered nanowires allows us to account for the main observed edge behaviours of the thermopower.

Application of a random resistor network model of space–time to various physical phenomena

Application of a random resistor network model of space–time to various physical phenomena

Nonlinear current-voltage characteristics of conductive polyethylene composites with carbon black filled pet microfibrils

Current-voltage electrical behavior of in situ microfibrillar carbon black (CB)/poly(ethylene terephthalate) (PET)/polyethylene (PE) (m-CB/PET/PE) composites with various CB concentrations at ambient temperatures was studied under a direct-current electric field. The current-voltage (I-V) curves exhibited nonlinearity beyond a critical value of voltage. The dynamic random resistor network (DRRN) model was adopted to semi-qualitatively explain the nonlinear conduction behavior of m-CB/PET/PE composites. Macroscopic nonlinearity originated from the interfacial interactions between CB/PET micro fibrils and additional conduction channels. Combined with the special conductive networks, an illustration was proposed to interpret the nonlinear I-V characteristics by a field emission or tunneling mechanism between CB particles in the CB/PET microfibers intersections.

Modelling a nanowire grid for light-sensing applications

Nanostructures hold promise as building blocks for a new generation of sensing devices because they could enhance detection and conversion of nonelectrical phenomena into electrical signals. In this paper, we discuss the possible use of a semiconductor (GaAs) nanowire grid as a light sensor. Based on the previously measured electrical properties of a single GaAs nanowire, we propose a model to determine the resistance of a structure consisting of many nanowires forming a grid with metallic contacts. Due to the fact that the proposed geometry is partially disordered, the total resistance of the structure is determined implementing the random resistor network (RRN) methodology in our simulation model. In order to reduce the error caused by condition number and the machine epsilon, the RRN model is improved by introducing additional conditions for solving the transfer matrix formulation precisely. The proposed complex nanowire geometry is analysed for different grid sizes varying the number of nanowires and contacts. According to the nanowire doping profile, we have defined the fraction of active segments (FoS) that is light-sensitive. Simulation results have shown that light sensitivity of a nanowire grid is enhanced with increasing number of active segments while a relative change in the active segment resistance has only a minor influence on the resistance of the complete structure. Finally, we have optimized nanowire grid dimensions with respect to the simulation results and practical limitations.

Linear magnetoresistance due to multiple-electron scattering by low-mobility islands in an inhomogeneous conductor

Linear transverse magnetoresistance is commonly observed in many material systems including semimetals, narrow band-gap semiconductors, multi-layer graphene and topological insulators. It can originate in an inhomogeneous conductor from distortions in the current paths induced by macroscopic spatial fluctuations in the carrier mobility and it has been explained using a phenomenological semiclassical random resistor network model. However, the link between the linear magnetoresistance and the microscopic nature of the electron dynamics remains unknown. Here we demonstrate how the linear magnetoresistance arises from the stochastic behaviour of the electronic cycloidal trajectories around low-mobility islands in high-mobility inhomogeneous conductors and that this process is only weakly affected by the applied electric field strength. Also, we establish a quantitative link between the island morphology and the strength of linear magnetoresistance of relevance for future applications.

Three-dimensional random resistor-network model for solid oxide fuel cell composite electrodes

Abstract A three-dimensional reconstruction of solid oxide fuel cell (SOFC) composite electrodes was developed to evaluate the performance and further investigate the effect of microstructure on the performance of SOFC electrodes. Porosity of the electrode is controlled by adding pore former particles (spheres) to the electrode and ignoring them in analysis step. To enhance connectivity between particles and increase the length of triple-phase boundary (TPB), sintering process is mimicked by enlarging particles to certain degree after settling them inside the packing. Geometrical characteristics such as length of TBP and active contact area as well as porosity can easily be calculated using the current model. Electrochemical process is simulated using resistor-network model and complete Butler–Volmer equation is used to deal with charge transfer process on TBP. The model shows that TPBs are not uniformly distributed across the electrode and location of TPBs as well as amount of electrochemical reaction is not uniform. Effects of electrode thickness, particle size ratio, electron and ion conductor conductivities and rate of electrochemical reaction on overall electrochemical performance of electrode are investigated.

Possible origins for paramagnetic-ferromagnetic and insulator-metal transitions as well as colossal magnetoresistance in manganites

Systematical investigations of zero-field resistivity, magnetoresistance and magnetization were performed for a typical manganese compound La2/3Ca1/3MnO3. It is argued that the common origin for insulator-metal and paramagenetic ferromagnetic-transitions as well as colossal magnetoresistance is due to the formation of ferromagnetic clusters in the paramagnetic background. The transition to metallic state is resulted from percolation of ferromagnetic metallic clusters, while the colossal magnetoresistance is due to the application of magnetic field, which accelerates the growth of ferromagnetic metallic clusters and causes the shift of the onset temperature for the metallic percolation to higher temperature. Based on the random resistor network model, the zero-field resistivity versus temperature dependence is simulated by using experimental parameters, and experimental data well agree with those in whole temperature range, giving a strong support to our approach.

Strain effects on percolation conduction in conductive particle filled composites

The effect of uniaxial and multiaxial mechanical strain on the electrical conductivity of particle filled polymer composites is investigated in the framework of concentration-driven percolation. For composites consisting of low aspect ratio, rigid conductive particles in a compliant polymer matrix, a simple argument leads to the conclusion that the effective volume fraction of conductive particles (the ratio of total particle volume to the total volume of the deformed composite) plays a dominant role, with conductivity remaining isotropic despite the directional bias of the strain state. As such, conductivity is expected to exhibit classical power, law-dependence on concentration, which in this case takes the form of a strain-dependent effective volume fraction. Consideration of deformation effects on particle agglomerates suggest, however, that particle-to-particle network connections are likely to be affected most significantly along directions experiencing the most severe strains, introducing a directional bias in network connectivity at a higher length scale. To assess the importance of this possible directional bias, random resistor network models are used to study the conductivity of uniaxially strained composites. For conservative assumptions on the severity of the bias in bond probabilities, network conductivities exhibit approximately isotropic, concentration-driven behavior for moderate strains, supporting the predictive utility of the simple percolation conduction-effective volume fraction approach. Further corroboration is provided by experiments in the literature on silicone-graphite composites subjected to uniaxial compressive strain, where good agreement is obtained through moderate strains for the theoretically correct value of the conduction exponent in concentration-driven percolation.

Random Resistor Network Model of Minimal Conductivity in Graphene

Transport in undoped graphene is related to percolating current patterns in the networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.

Nonsaturating magnetoresistance of inhomogeneous conductors: Comparison of experiment and simulation

The silver chalcogenides provide a striking example of the benefits of imperfection. Nanothreads of excess silver cause distortions in the current flow that yield a linear and nonsaturating transverse magnetoresistance (MR). Associated with the large and positive MR is a negative longitudinal MR. The longitudinal MR only occurs in the three-dimensional limit and thereby permits the determination of a characteristic length scale set by the spatial inhomogeneity. We find that this fundamental inhomogeneity length can be as large as 10μm. Systematic measurements of the diagonal and off-diagonal components of the resistivity tensor in various sample geometries show clear evidence of the distorted current paths posited in theoretical simulations. We use a random-resistor network model to fit the linear MR, and expand it from two to three dimensions to depict current distortions in the third (thickness) dimension. When compared directly to experiments on Ag_(2±δ)Se and Ag_(2±δ)Te, in magnetic fields up to 55T, the model identifies conductivity fluctuations due to macroscopic inhomogeneities as the underlying physical mechanism. It also accounts reasonably quantitatively for the various components of the resistivity tensor observed in the experiments.