Small Characteristic Length Research Articles

Signatures of microstructure in gradient-echo andspin-echo signals.

To determine whether the spatial scale and magnetic susceptibility of microstructure can be evaluated robustly from the decay of gradient-echo and spin-echo signals. Gradient-echo and spin-echo images were acquired from suspensions of spherical polystyrene microbeads of 10, 20, and 40 μm nominal diameter. The sizes of the beads and their magnetic susceptibility relative to the medium were estimated from the signal decay curves, using a lookup table generated from Monte Carlo simulations and an analytic model based on the Gaussian phase approximation. Fitting Monte Carlo predictions to spin-echo data yielded acceptable estimates of microstructural parameters for the 20 and 40 μm microbeads. Using gradient-echo data, the Monte Carlo lookup table provided satisfactory parameter estimates for the 20 μm beads but unstable results for the diameter of the largest beads. Neither spin-echo nor gradient-echo data allowed accurate parameter estimation for the smallest beads. The analytic model performed poorly over all bead sizes. Microstructural sources of magnetic susceptibility produce distinctive non-exponential signatures in the decay of gradient-echo and spin-echo signals. However, inverting the problem to extract microstructural parameters from the signals is nontrivial and, in certain regimes, ill-conditioned. For microstructure with small characteristic length scales, parameter estimation is hampered by the difficulty of acquiring accurate data at very short echo times. For microstructure with large characteristic lengths, the gradient-echo signal approaches the static-dephasing regime, where it becomes insensitive to size. Applicability of the analytic model was further limited by failure of the Gaussian phase approximation for all but the smallest beads.

Nonlocal antiplane shear interfacial waves

In this paper, non-local shear interfacial waves between two non-local elastic half-spaces in perfect contact along a common boundary are investigated. For the sake of simplicity, an anti-plane problem formulated through the framework of Eringen’s theory is considered. The non-locality is taken only in the transverse coordinate making the analysis of the problem easier than that of non-local problems of 2D. Effective boundary conditions are obtained, with the help of a small internal characteristic length scale, along the interface utilizing an asymptotic approach enabling one to write the non-local stresses through their local counterparts. Antiplane non-local shear interfacial waves are analysed by the derived formulation. Numerical results are presented for certain characteristic values of the problem parameters.

Influence of structural length-scale sensitivities on Hermite–Gaussian rectangular vortex beam propagation in biological tissues

A modified power spectrum of biological tissues involving upper length-scale and bottom length-scale was introduced. In addition, the analytical expression of Hermite–Gaussian rectangular vortex beam with the parameter () in free space was derived. By this modified power spectrum, we established the normalized probability model of orbital angular momentum (OAM) states for Hermite–Gaussian rectangular vortex beams propagation in biological tissues. The results revealed that Hermite–Gaussian rectangular vortex beam exhibits a better anti-interference performance than Laguerre–Gaussian beam under the same conditions. The Hermite–Gaussian rectangular vortex beam propagates through a biological tissue with large bottom length-scale, small upper length-scale, small characteristic length of heterogeneity, low the fractal dimensions, and weak fluctuation strength, which produces a large normalized probability of signal OAM states. These results are fundamental to improving light propagation in tissue and provide a quantitative guidance for medical imaging and diagnosis.

The Effect of Non-Uniform Magnetic Field on the Efficiency of Mixing in Droplet-Based Microfluidics: A Numerical Investigation.

Achieving high efficiency and throughput in droplet-based mixing over a small characteristic length, such as microfluidic channels, is one of the crucial parameters in Lab-on-a-Chip (LOC) applications. One solution to achieve efficient mixing is to use active mixers in which an external power source is utilized to mix two fluids. One of these active methods is magnetic micromixers using ferrofluid. In this technique, magnetic nanoparticles are used to make one phase responsive to magnetic force, and then by applying a magnetic field, two fluid phases, one of which is magneto-responsive, will sufficiently mix. In this study, we investigated the effect of the magnetic field’s characteristics on the efficiency of the mixing process inside droplets. When different concentrations of ferrofluids are affected by a constant magnetic field, there is no significant change in mixing efficiency. As the magnetic field intensifies, the magnetic force makes the circulation flow inside the droplet asymmetric, leading to chaotic advection, which creates a flow that increases the mixing efficiency. The results show that the use of magnetic fields is an effective method to enhance the mixing efficiency within droplets, and the efficiency of mixing increases from 65.4 to 86.1% by increasing the magnetic field intensity from 0 to 90 mT. Besides that, the effect of ferrofluid’s concentration on the mixing efficiency is studied. It is shown that when the concentration of the ferrofluid changes from 0 to 0.6 mol/m3, the mixing efficiency increases considerably. It is also shown that by changing the intensity of the magnetic field, the mixing efficiency increases by about 11%.

Ultrafine nanoporous intermetallic catalysts by high-temperature liquid metal dealloying for electrochemical hydrogen production

Intermetallic compounds formed from non-precious transition metals are promising cost-effective and robust catalysts for electrochemical hydrogen production. However, the development of monolithic nanoporous intermetallics, with ample active sites and sufficient electrocatalytic activity, remains a challenge. Here we report the fabrication of nanoporous Co7Mo6 and Fe7Mo6 intermetallic compounds via liquid metal dealloying. Along with the development of three-dimensional bicontinuous open porosity, high-temperature dealloying overcomes the kinetic energy barrier, enabling the direct formation of chemically ordered intermetallic phases. Unprecedented small characteristic lengths are observed for the nanoporous intermetallic compounds, resulting from an intermetallic effect whereby the chemical ordering during nanopore formation lowers surface diffusivity and significantly suppresses the thermal coarsening of dealloyed nanostructure. The resulting ultrafine nanoporous Co7Mo6 exhibits high catalytic activity and durability in electrochemical hydrogen evolution reactions. This study sheds light on the previously unexplored intermetallic effect in dealloying and facilitates the development of advanced intermetallic catalysts for energy applications.

Finite-size and temperature effects up to all orders : effective scalar models

We discuss some general behaviors up to all orders in a perturbative expansion investigating a parametric representation of the model under interest. To consider finite-size and temperature effects we build two extensions of the usual Schwinger parametric representation: one suited for small characteristic lengths (and high temperatures) and another suited for large lengths (and low temperatures). As a first step, we consider scalar fields with periodic boundary conditions in the spatial directions and discuss both the asymptotic limits of very small lengths (and very high temperatures) and the asymptotic limit of very large lengths (and zero temperature).

Designing a Large Scale Autonomous Observing Network: A Set Theory Approach

A well designed observing network is vital to improve our understanding of the oceans and to obtain better predictions of the future. As autonomous marine technology develops, the potential for deploying large autonomous observing systems becomes feasible. Though there are many design considerations to take into account (according to the target data use cases), a fundamental requirement is to take observations that capture the variability at the appropriate length scales. In doing so, a balance must be struck between the limited observation resources available and how well they are able to represent different areas of the ocean. In this paper we present and evaluate a new method to aid decision makers in designing near-optimal observing networks. The method uses ideas from set theory to recommend an irregular network of observations which provides a guaranteed level of representation (correlation) across a domain. We show that our method places more observations in areas with smaller characteristic length scales and vice versa, as desired. We compare the method to two other grid types: regular and randomly allocated observation locations. Our new method is able to provide comparable average representation of data across the domain, whilst efficiently targeting resource to regions with shorter length scale and thereby elevating the minimum skill baseline, compared to the other two grid types. The method is also able to provide a network that represents up to 15% more of the domain area. Assessing error metrics such as Root Mean Square Error and correlation shows that our method is able to reconstruct data more consistently across all length scales, especially at smaller scales where we see RMSE 2-3 times lower and correlations of over 0.2 higher. We provide an additional discussion on the variability inherent in such methods as well as practical advice for the user. We show that considerations must be made based on time filtering, seasonality, depth and horizontal resolution.

Growth of vortical disturbances entrained in the entrance region of a circular pipe

The development and growth of unsteady three-dimensional vortical disturbances entrained in the entry region of a circular pipe is investigated by asymptotic and numerical methods for Reynolds numbers between $1000$ and $10\,000$ , based on the pipe radius and the bulk velocity. Near the pipe mouth, composite asymptotic solutions describe the dynamics of the oncoming disturbances, revealing how these disturbances are altered by the viscous layer attached to the pipe wall. The perturbation velocity profiles near the pipe mouth are employed as rigorous initial conditions for the boundary-region equations, which describe the flow in the limit of low frequency and large Reynolds number. The disturbance flow is initially primarily present within the base-flow boundary layer in the form of streamwise-elongated vortical structures, i.e. the streamwise velocity component displays an intense algebraic growth, while the cross-flow velocity components decay. Farther downstream the disturbance flow occupies the whole pipe, although the base flow is mostly inviscid in the core. The transient growth and subsequent viscous decay are confined in the entrance region, i.e. where the base flow has not reached the fully developed Poiseuille profile. Increasing the Reynolds number and decreasing the frequency causes more intense perturbations, whereas small azimuthal wavelengths and radial characteristic length scales intensify the viscous dissipation of the disturbance. The azimuthal wavelength that causes the maximum growth is found. The velocity profiles are compared successfully with available experimental data and the theoretical results are helpful to interpret the only direct numerical dataset of a disturbed pipe-entry flow.

An analytical solution for aerosol penetration in the slip flow regime

The classical theory for the diffusional loss of aerosol particles in a fully developed laminar flow through a circular tube derived by Gormley and Kennedy (1949) did not consider the slip-flow condition. However, the non-slip condition for the gas velocity boundary condition may not be appropriate for the gas flow in microgeometries such as microchannels and microtubes. This paper extends the work of Gormley and Kennedy (GK) to include the effect of slip-flow, which often occurs in the gas flow at low pressure or with a small characteristic length scale. In the present solution, the separation of variables was applied to solve the convection-diffusion equation, then confluent hypergeometric function was used to solve for the number concentration as a function of radial distance analytically. Eigenvalues were evaluated for Knudsen numbers ranging from 0.001 to 0.1. Finally, a simple power series correlation was developed to describe aerosol penetration in the slip flow regime as a function of the dimensionless deposition factor and Knudsen number (Kn). In the slip flow regime, the penetration decreases with increasing Kn. The correlation is reduced to GK’s solution when Kn = 0. The present solution of aerosol penetration calculated at Kn = 0 shows good agreement with GK’s solution and validates the applicable range of the approximate solution by Alonso et al. (2016).

Asymptotic analysis of pore crack initiation near a free edge

The matched asymptotic (MA) approach of the coupled criterion (CC) enables studying crack initiation at a pore located near a free edge, which leads to a competition between three possible crack initiation mechanisms, namely crack initiation in the ligament, at the pore side opposite to the free edge or simultaneously at both pore sides. The mechanism that is the most likely to occur depends on both the pore-to-free edge ligament size and the material characteristic length to pore diameter ratio. Simultaneous crack initiations at both pore sides occur for large enough ligament size. For smaller ligament sizes, unilateral pore crack initiation is more likely to occur, within the ligament for small characteristic length to pore diameter ratios and at the pore side opposite to the free edge otherwise. The CC MA approach enables estimating the initiation remote imposed stress as well as the initiation crack length.

Laboratory Verification of Electron‐Scale Reconnection Regions Modulated by a Three‐Dimensional Instability

AbstractDuring magnetic reconnection in collisionless space plasma, the electron fluid decouples from the magnetic field within narrow current layers, and theoretical models for this process can be distinguished in terms of their predicted current layer widths. From theory, the off‐diagonal stress in the electron pressure tensor is related to the thermal noncircular orbit motion of electrons around the magnetic field lines. This stress becomes significant when the width of the reconnecting current layer approaches the small characteristic length scale of the electron motion. To aid in situ spacecraft and numerical investigations of reconnection, the structure of the electron diffusion region is here investigated using the Terrestrial Reconnection Experiment. In agreement with the closely matched kinetic simulations, laboratory observations reveal the presence of electron‐scale current layer widths. Although the layers are modulated by a current‐driven instability, three‐dimensional simulations demonstrate that it is the off‐diagonal stress that is responsible for breaking the frozen‐in condition of the electron fluid.

Modulation of Dirac electrons in epitaxial Bi2Se3 ultrathin films on van der Waals ferromagnet Cr2Si2Te6

We investigated the Dirac-cone state and its modulation when an ultrathin film of topological insulator Bi2Se3 was epitaxially grown on a van-der-Waals ferromagnet Cr2Si2Te6 (CST) by angle-resolved photoemission spectroscopy. We observed a gapless Dirac-cone surface state in 6 quintuple-layer (QL) Bi2Se3 on CST, whereas the Dirac cone exhibits a gap of 0.37 eV in 2QL counterpart. Intriguingly, this gap is much larger than those for Bi2Se3 films on Si(111). We also revealed no discernible change in the gap magnitude across the ferromagnetic transition of CST, suggesting the very small characteristic length and energy scale of the magnetic proximity effect. The present results suggest a crucial role of interfacial coupling for modulating Dirac electrons in topological-insulator hybrids.

Graph Theoretic Analysis of Brain Connectomics in Multiple Sclerosis: Reliability and Relationship with Cognition.

Research suggests that disruption of brain networks might explain cognitive deficits in multiple sclerosis (MS). The reliability and effectiveness of graph theoretic network metrics as measures of cognitive performance were tested in 37 people with MS and 23 controls. Specifically, relationships with cognitive performance (linear regression against the paced auditory serial addition test-3 seconds [PASAT-3], symbol digit modalities test [SDMT], and attention network test) and 1-month reliability (using the intraclass correlation coefficient [ICC]) of network metrics were measured using both resting-state functional and diffusion magnetic resonance imaging data. Cognitive impairment was directly related to measures of brain network segregation and inversely related to network integration (prediction of PASAT-3 by small worldness, modularity, characteristic path length, R2 = 0.55; prediction of SDMT by small worldness, global efficiency, and characteristic path length, R2 = 0.60). Reliability of the measures for 1 month in a subset of nine participants was mostly rated as good (ICC >0.6) for both controls and MS patients in both functional and diffusion data, but was highly dependent on the chosen parcellation and graph density, with the 0.2–0.5 density range being the most reliable. This suggests that disrupted network organization predicts cognitive impairment in MS and its measurement is reliable for a 1-month period. These new findings support the hypothesis of network disruption as a major determinant of cognitive deficits in MS and the future possibility of the application of derived metrics as surrogate outcomes in trials of therapies for cognitive impairment.

Size effects in the martensitic transformation hysteresis in Ni–Mn–Sn Heusler alloy films

Understanding the effect of small characteristic length scales on phase transformations requires microscopic observations to identify mechanisms which may influence the progression of the transformation. Here, we report thickness-dependent hysteresis in electrochemically deposited Ni–Mn–Sn Heusler alloy films, as observed by optical microscopy. This approach allows for analyzing size dependent phase transformation behavior within individual grains from films with decreasing thickness. Hysteresis is not correlated with grain size, but increases with decreasing film thickness following a power law relationship. This behavior is attributable to internal friction-induced energy dissipation at the film/substrate interface in microscale alloy films.

An Analytical Model of the Small World Effect in D2D Wireless Networks

Small-world networks are characterized by large clustering coefficients and small characteristic path lengths. These properties are induced by replacing a small fraction of short-range local scale links of a geometric/Euclidean graph with long-range global scale links. Advances in wireless networks allow for cost-efficient addition of secondary long-range wireless interfaces in devices. We derive analytical mean-field solutions for 1) clustering coefficient and 2) characteristic path length of peer-to-peer D2D wireless networks with topologies mimicking small-world networks. In graph-theoretic terms these topologies correspond to geometric graphs of randomly deployed nodes in two-dimensions with range limited shortcuts. The models show that in spite of the fact that links used to create shortcuts are range limited, the network still retains the essential phase difference between characteristic path length and clustering coefficient that is the hallmark of small-world networks when a small fraction of all nodes, as little as 1%–5%, have range limited shortcut links. We also demonstrate the utility of these models as design tools for determining deployment parameters of small-world wireless sensor networks.

Influence of Passivation Layers on Positive Gate Bias-Stress Stability of Amorphous InGaZnO Thin-Film Transistors.

Passivation (PV) layers could effectively improve the positive gate bias-stress (PGBS) stability of amorphous InGaZnO (a-IGZO) thin-film transistors (TFTs), whereas the related physical mechanism remains unclear. In this study, SiO2 or Al2O3 films with different thicknesses were used to passivate the a-IGZO TFTs, making the devices more stable during PGBS tests. With the increase in PV layer thickness, the PGBS stability of a-IGZO TFTs improved due to the stronger barrier effect of the PV layers. When the PV layer thickness was larger than the characteristic length, nearly no threshold voltage shift occurred, indicating that the ambient atmosphere effect rather than the charge trapping dominated the PGBS instability of a-IGZO TFTs in this study. The SiO2 PV layers showed a better improvement effect than the Al2O3 because the former had a smaller characteristic length (~5 nm) than that of the Al2O3 PV layers (~10 nm).

Beam spreading and wander of partially coherent Lommel–Gaussian beam in turbulent biological tissue

Aiming at the partially coherent Lommel–Gaussian beam, we investigate its propagation in turbulent biological tissue. By use of Wigner distribution function, a theoretical model is constructed to describe turbulence induced beam wander and long-term spreading. We analyze the effects of tissue parameters including the fractal dimension D, strength coefficient S of refractive-index fluctuation, small length-scale factor l0 and characteristic length lc of heterogeneity. We find that beam suffers less turbulence interference in tissue with smaller D, S, lc and larger l0. As for beam optimization, Lommel–Gaussian beam with low-order vortex and moderate waist width is preferable. The beam symmetry can be arbitrary, but incoherent beam with long wavelength is undesirable. The theoretical model and results give useful references for investigations of light propagation in tissue and biomedical applications of vortex beam.

Galloping oscillation of a circular cylinder firmly combined with different shaped fairing devices

The galloping oscillation of a circular cylinder combined with different fairing devices is numerically studied. The fairing devices are integrated with a circular cylinder that is supported by a spring and a damper. An unsteady Reynolds-averaged Navier–Stokes (URANS) model corrected with the arbitrary Lagrange Euler (ALE) method is used as the governing model of the fluid flow while the governing equations are solved with a total variation diminishing (TVD) finite volume method (FVM). The SST turbulence model is used. The fluid–structure-interaction (FSI) simulations are performed under the reduced velocities ranging from 3 to 25. The simulation results are validated with the available experimental and numerical results with a short-tail fairing device. The influences of the shapes and the characteristic lengths of the fairing devices on the galloping oscillation are discussed. The shape of the fairing devices are found to influence the vortex shedding patterns in the wake of the flow field while the characteristic length decides the galloping behavior of the cylinder at different reduced velocities. The fairing devices with the smallest characteristic length have the best vibration suppression performance in the present study.

A game-theoretic approach to optimize ad hoc networks inspired by small-world network topology

Nodes in ad hoc networks are connected in a self-organized manner. Limited communication radius makes information transmit in multi-hop mode, and each forwarding needs to consume the energy of nodes. Insufficient communication radius or exhaustion of energy may cause the absence of some relay nodes and links, further breaking network connectivity. On the other hand, nodes in the network may refuse to cooperate due to objective faulty or personal selfish, hindering regular communication in the network. This paper proposes a model called Repeated Game in Small World Networks (RGSWN). In this model, we first construct ad hoc networks with small-world feature by forming “communication shortcuts” between multiple-radio nodes. Small characteristic path length reduces average forwarding times in networks; meanwhile high clustering coefficient enhances network robustness. Such networks still maintain relative low global power consumption, which is beneficial to extend the network survival time. Then we use MTTFT strategy (Mend-Tolerance Tit-for-Tat) for repeated game as a rule for the interactions between neighbors in the small-world networks. Compared with other five strategies of repeated game, this strategy not only punishes the nodes’ selfishness more reasonably, but also has the best tolerance to the network failure. This work is insightful for designing an efficient and robust ad hoc network.

Direct Numerical Simulation of the Microscale Fluid Flow and Heat Transfer in the Three-Phase Contact Line Region During Evaporation

The heat and mass transfer close to the apparent three-phase contact line is of tremendous importance in many evaporation processes. Despite the extremely small dimensions of this region referred to as the microregion compared to the macroscopic length scale of a boiling process, a considerable fraction of heat can be transferred in this region. Due to its small characteristic length scale, physical phenomena are relevant in the microregion, which are completely negligible on the macroscopic scale, including the action of adhesion forces and the interfacial heat resistance. In the past, models have been developed taking these effects into account. However, so far these models are based on the assumption of one-dimensional (1D) heat conduction, and the flow within the thin liquid film forming the microregion near the apparent three-phase contact line is modeled utilizing the lubrication approximation. Hence, the application of existing models is restricted to small apparent contact angles. Moreover, the effects of surface structures or roughness are not included in these lubrication models. To overcome these limitations, a direct numerical simulation (DNS) of the liquid flow and heat transfer within the microregion is presented in this paper. The DNS is employed for validation of the existing lubrication model and for investigation of the influence of surface nanostructures on the apparent contact angle and in particular on the heat transfer within the microregion.