Additional Length Scale Research Articles

Evaluating duplex microstructures in polycrystalline steel with diffuse ultrasonic backscatter

The performance of metallic components is governed in large part by the microstructure of the base material from which the component is manufactured. In this presentation, diffuse ultrasonic backscatter techniques are discussed with respect to their use for monitoring the microstructure of polycrystalline steel as a result of the manufacturing process. To improve the mechanical properties, the surface of polycrystalline steel is quenched, a process which transforms the initial phase to a pearlite phase within grains. A diffuse ultrasonic backscatter model is developed that includes the duplex microstructure through the addition of an additional length scale in the two-point spatial correlation function. This function defines the probability that two randomly chosen points will fall into the same grain and/or same crystallite. The model clearly shows the dependence of the diffuse ultrasonic backscatter signal with respect to frequency, average grain size and lamellar spacing of the crystallites. Experimental results are used to show how the two length scales can be extracted from the measurements. The spatial variation of the microstructure with respect to depth from the quench surface is also examined. These diffuse ultrasonic techniques are shown to have the sensitivity to deduce the duplex microstructure throughout the sample.

Nucleate boiling from smooth and rough surfaces – Part 2: Analysis of surface roughness effects on nucleate boiling

The effect of surface roughness on nucleate boiling heat transfer is not clearly understood. This study is devised to conduct detailed heat transfer and bubble measurements during boiling on a heater surface with controlled roughness. This second of two companion papers presents an analysis of heat transfer and bubble ebullition in nucleate boiling with new measures of surface roughness: area ratio, surface mean normal angle, and maximum idealized surface curvature. An additional length scale of importance, the maximum base diameter of an emergent bubble, is identified. Measurements of bubble departure diameters, growth periods, ebullition periods, and void fraction above the surface are obtained from high-speed videographic visualizations by an automated procedure. Correlations of heat transfer coefficient and bubble ebullition characteristics with different measures of surface roughness are compared in terms of relative uncertainty. The data set of results for pool boiling in the perfluorinated dielectric liquid, FC-72, are found to correlate best with a length-scale filtered value of average roughness Ra, filt. Over a larger database with three different data sets including FC-72, FC-77, and water at atmospheric pressure, the most reliable correlations were obtained with the appropriately filtered area ratio. FC-72 bubble growth curves are well correlated for all test conditions with the normalized relationship D*∼(t*)1/3. Finally, the maximum void fraction in the region above the surface is correlated with normalized heat flux for these data and for water as the two-thirds power of heat flux.

Architectured materials: Expanding materials space

The objective of this introduction to the viewpoint set on architectured materials is to illustrate the paradigm shift which occurs by introducing additional length scales into a material in addition to those provided by the microstructure. This provides new opportunities both to relate the processing of materials directly to design needs and to develop a variety of multifunctional materials in which both the microstructure and the overall architecture of the material are optimized.

Double-exponential decay of orientational correlations in semiflexible polyelectrolytes

In this paper we revisited the problem of persistence length of polyelectrolytes. We performed a series of Molecular Dynamics simulations using the Debye-Hückel approximation for electrostatics to test several equations which go beyond the classical description of Odijk, Skolnick and Fixman (OSF). The data confirm earlier observations that in the limit of large contour separations the decay of orientational correlations can be described by a single-exponential function and the decay length can be described by the OSF relation. However, at short countour separations the behaviour is more complex. Recent equations which introduce more complicated expressions and an additional length scale could describe the results very well on both the short and the long length scale. The equation of Manghi and Netz when used without adjustable parameters could capture the qualitative trend but deviated in a quantitative comparison. Better quantitative agreement within the estimated error could be obtained using three equations with one adjustable parameter: 1) the equation of Manghi and Netz; 2) the equation proposed by us in this paper; 3) the equation proposed by Cannavacciuolo and Pedersen. Two characteristic length scales can be identified in the data: the intrinsic or bare persistence length and the electrostatic persistence length. All three equations use a single parameter to describe a smooth crossover from the short-range behaviour dominated by the intrinsic stiffness of the chain to the long-range OSF-like behaviour.

A Method for Increasing the Turbulent Kinetic Energy in the Mellor–Yamada–Janjić Boundary-Layer Parametrization

A method for enhancing the calculation of turbulent kinetic energy in the Mellor–Yamada–Janjic planetary boundary-layer parametrization in the Weather Research and Forecasting numerical model is presented. This requires some unconventional selections for the closure constants and an additional stability dependent surface length scale. Single column model and three-dimensional model simulations are presented showing a similar performance with the existing boundary-layer parametrization, but with a more realistic magnitude of turbulence intensity closer to the surface with respect to observations. The intended application is an enhanced calculation of turbulence intensity for the purposes of a more accurate wind-energy forecast.

Holographic studies of entanglement entropy in superconductors

We present the results of our studies of the entanglement entropy of a super- conducting system described holographically as a fully back-reacted gravity system, with a stable ground state. We use the holographic prescription for the entanglement entropy. We uncover the behavior of the entropy across the superconducting phase transition, showing the reorganization of the degrees of freedom of the system. We exhibit the behaviour of the entanglement entropy from the superconducting transition all the way down to the ground state at T = 0. In some cases, we also observe a novel transition in the entanglement entropy at intermediate temperatures, resulting from the detection of an additional length scale.

Gradient Elastic Stress Analysis for Anisotropic Bimaterial Interface with Arbitrarily Oriented Crack

Singularities occurring at a crack tip are a well known phenomenon; gradient elasticity has been proven to have the ability to remove singularities through additional length scale parameters which at the same time provides extra microstructural information of the material. This study uses gradient elasticity to simulate singularity-free stresses at bi-material bone-implant interfaces and outlines the relationship between the fracture orientation and maximum stresses at crack tip depicted by this model.

Drag force on a sphere moving toward an anisotropic superhydrophobic plane

We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured superhydrophobic plane that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and φ2 (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and H (local separation). The effect of effective slip is predicted to decrease the force as compared with what is expected for two hydrophilic surfaces and described by the Taylor equation. The presence of additional length scales, L, b1, and b2, implies that a film drainage can be much richer than in the case of a sphere moving toward a hydrophilic plane. For a large (compared to L) gap the reduction of the force is small, and for all textures the force is similar to expected when a sphere is moving toward a smooth hydrophilic plane that is shifted down from the superhydrophobic wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing striped superhydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap. We show that at a thinner gap the force reduction becomes more pronounced, and that it depends strongly on the fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent force measurements in the presence of a superhydrophobic surface.

Turbulent diffusion in tall tubes. II. Confinement by stratification

Rayleigh-Taylor instability between two initially homogeneous layers has been shown to evolve in a self similar manner in high-aspect-ratio domains, and in Part I, we demonstrated close agreement between experimental measurements and a range of modelling approaches. However, changing the initial conditions such that one layer is linearly stably stratified in density introduces an additional length scale to the problem and breaks the global self-similarity seen in the case of homogeneous layers. Here, in Part II, we explore the development of this modified instability. We again compare experimental measurements with a range of modelling approaches, achieving excellent agreement assuming a one-dimensional nonlinear turbulent diffusion, and demonstrating that implicit large eddy simulations are able to capture the detailed development despite limitations in the manner in which both mass and momentum are redistributed by numerical rather than molecular diffusion.

Molecular dynamics simulations of shear-driven gas flows in nano-channels

Using the recently developed smart wall molecular dynamics algorithm, shear-driven gas flows in nano-scale channels are investigated to reveal the surface–gas interaction effects for flows in the transition and free molecular flow regimes. For the specified surface properties and gas–surface pair interactions, density and stress profiles exhibit a universal behavior inside the wall force penetration region at different flow conditions. Shear stress results are utilized to calculate the tangential momentum accommodation coefficient (TMAC) between argon gas and FCC walls. The TMAC value is shown to be independent of the flow properties and Knudsen number in all simulations. Velocity profiles show distinct deviations from the kinetic theory based solutions inside the wall force penetration depth, while they match the linearized Boltzmann equation solution outside these zones. Results indicate emergence of the wall force field penetration depth as an additional length scale for gas flows in nano-channels, breaking the dynamic similarity between rarefied and nano-scale gas flows solely based on the Knudsen and Mach numbers.

Mottness collapse and T -linear resistivity in cuprate superconductors

Central to the normal state of cuprate high-temperature superconductors is the collapse of the pseudo-gap, briefly reviewed here, at a critical point and the subsequent onset of the strange metal characterized by a resistivity that scales linearly with temperature. A possible clue to the resolution of this problem is the inter-relation between two facts: (i) a robust theory of T-linear resistivity resulting from quantum criticality requires an additional length scale outside the standard one-parameter scaling scenario and (ii) breaking the Landau correspondence between the Fermi gas and an interacting system with short-range repulsions requires non-fermionic degrees. We show that a low-energy theory of the Hubbard model that correctly incorporates dynamical spectral weight transfer has the extra degrees of freedom needed to describe this physics. The degrees of freedom that mix into the lower band as a result of dynamical spectral weight transfer are shown to either decouple beyond a critical doping, thereby signalling Mottness collapse, or unbind above a critical temperature, yielding strange metal behaviour characterized by T-linear resistivity.

Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model

An exact solution is found for the problem of the center-of-band ($E=0$) anomaly in the one-dimensional (1D) Anderson model of localization. By deriving and solving an equation for the generating function $\Phi(u,\phi)$ we obtained an exact expression in quadratures for statistical moments $I_{q}=\langle |\psi_{E}({\bf r})|^{2q}\rangle$ of normalized wavefunctions $\psi_{E}({\bf r})$ which show violation of one-parameter scaling and emergence of an additional length scale at $E\approx 0$.

Effect of the Coulomb interaction on the gap in monolayer and bilayer graphene

We study effects of a repulsive Coulomb interaction on the spectral gap in monolayer and bilayer graphene in the vicinity of the charge neutrality point by employing the functional renormalization-group technique. In both cases Coulomb interaction supports the gap once it is open. For monolayer graphene we correctly reproduce results obtained previously by several authors, e.g., an apparent logarithmic divergence of the Fermi velocity and the gap as well as a fixed point corresponding to a quantum phase transition at infinitely large Coulomb interaction. On the other hand, we show that the gap introduces an additional length scale at which renormalization flow of diverging quantities saturates. An analogous analysis is also performed for bilayer graphene with similar results. We find an additional fixed point in the gapless regime with linear spectrum corresponding to the vanishing electronic band mass. This fixed point is unstable with respect to gap fluctuations and can not be reached as soon as the gap is opened. This preserves the quadratic scaling of the spectrum and finite electronic band mass.

Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory

Using the results of recent numerical simulations, we extend an existing kinetic theory for dense flows of identical, nearly elastic, frictionless spheres to identical, very dissipative, frictional spheres. The existing theory incorporates an additional length scale in the expression for the collisional rate of dissipation; this length scale is identified with the size of a cluster of correlated particles. Parameters of the theory for very dissipative, frictional spheres are set using the results of physical experiments on inclined flows of spheres over a rigid, bumpy base in the absence of sidewalls. The resulting theory is then tested against the results of physical experiments on flows of the same material over the surface of an erodible heap when frictional sidewalls are present.

Self-Assembly of Supramolecular Triblock Copolymer Complexes

Four different poly(tert-butoxystyrene)-b-polystyrene-b-poly(4-vinylpyridine) (PtBOS-b-PS-b-P4VP) linear triblock copolymers, with the P4VP weight fraction varying from 0.08 to 0.39, were synthesized via sequential anionic polymerization. The values of the unknown interaction parameters between styrene and tert-butoxystyrene and between tert-butoxystyrene and 4-vinylpyridine were determined from random copolymer blend miscibility studies and found to satisfy 0.031 < χS,tBOS < 0.034 and 0.39 < χ4VP,tBOS <0.43, the latter being slightly larger than the known 0.30 < χS,4VP ≤ 0.35 value range. All triblock copolymers synthesized adopted a P4VP/PS core/shell cylindrical self-assembled morphology. From these four triblock copolymers supramolecular complexes were prepared by hydrogen bonding a stoichiometric amount of pentadecylphenol (PDP) to the P4VP blocks. Three of these complexes formed a triple lamellar ordered state with additional short length scale ordering inside the P4VP(PDP) layers. The self-assembled state of the supramolecular complex based on the triblock copolymer with the largest fraction of P4VP consisted of alternating layers of PtBOS and P4VP(PDP) layers with PS cylinders inside the latter layers. The difference in morphology between the triblock copolymers and the supramolecular complexes is due to two effects: (i) a change in effective composition and, (ii) a reduction in interfacial tension between the PS and P4VP containing domains. The small angle X-ray scattering patterns of the supramolecules systems are very temperature sensitive. A striking feature is the disappearance of the first order scattering peak of the triple lamellar state in certain temperature intervals, while the higher order peaks (including the third order) remain. This is argued to be due to the thermal sensitivity of the hydrogen bonding and thus directly related to the very nature of these systems.

Analysis of Thermoelectric Properties of Scaled Silicon Nanowires Using an Atomistic Tight-Binding Model

Low-dimensional materials provide the possibility of improved thermoelectric performance due to the additional length scale degree of freedom for engineering their electronic and thermal properties. As a result of suppressed phonon conduction, large improvements in the thermoelectric figure of merit, ZT, have recently been reported in nanostructures, compared to the raw materials. In addition, low dimensionality can improve a device’s power factor, offering an additional enhancement in ZT. In this work the atomistic sp3d5s* spin-orbit-coupled tight-binding model is used to calculate the electronic structure of silicon nanowires (NWs). The Landauer formalism is applied to calculate an upper limit for the electrical conductivity, the Seebeck coefficient, and the power factor. We examine n-type and p-type nanowires with diameters from 3 nm to 12 nm, in [100], [110], and [111] transport orientations, at different doping concentrations. Using experimental values for the lattice thermal conductivity in nanowires, an upper limit for ZT is computed. We find that at room temperature, scaling the diameter below 7 nm can at most double the power factor and enhance ZT. In some cases, however, scaling does not enhance the performance at all. Orientations, geometries, and subband engineering techniques for optimized designs are discussed.

Equilibrium charge density on a thin curved wire

We address the electrostatic problem of a thin, curved, and cylindrical conductor (a conducting filament) and show that the corresponding linear charge density slowly tends to uniformity as the inverse of the logarithm of a characteristic parameter, which is the ratio of the diameter to the smaller of the length and minimum radius of curvature of the filament. An alternative derivation of this result based on energy minimization is given. These results follow from a general asymptotic analysis of the electric field components and potential near a charged filament in the limit of vanishing diameter. It is found that the divergent parts of the radial and azimuthal electric field components are determined by the local charge density, while the axial component is determined by the local dipole density. For a straight filament our results reduce to those known for conducting needles. For curved filaments, the configuration of charges and fields is no longer azimuthally symmetric, and there is an additional length scale arising from the finite radius of curvature of the filament. The basic uniformity result survives the added complications, which include an azimuthal variation in the surface charge density of the filament. As with the variations in linear charge density along the filament, the azimuthal variations vanish with the characteristic parameter, only more rapidly. These findings allow us to derive an asymptotic formula for the capacitance of a curved filament that generalizes a result first obtained by Maxwell. The examples of a straight filament with uniform and linearly varying charge densities and a circular filament with a uniform charge distribution are treated analytically and found to agree with the general analysis. Numerical calculations illustrating the slow convergence of linear charge distribution to uniformity for an elliptical filament are presented. An interactive computer program implementing and animating the numerical calculations is available.

Depth of Rock Damage from Strong Seismic Ground Motions near the 2004 Parkfield Mainshock

Changes in the S - P delay of repeating earthquakes near Parkfield, California, after strong shaking in the 2004 mainshock, occur at surface stations but not at borehole stations. This result indicates that rock damage occurs mainly in the upper few tens of meters in fractured rock with a low seismic velocity. In addition, changes in coda-primary delay are comparable to changes in S - P delay. This observation along with the lack of S - P delay changes at borehole stations yields a simple model for the coda. Direct waves pass through the shallow damaged layer once. Coda waves scatter or refract in the deep undamaged subsurface and hence also pass through the subsurface just once. The coda, however, contains some brief reverberations within the shallow subsurface where the additional path length scales to the thickness of the shallow layer. The coda-primary delay measured by correlation includes both the zero delay change of direct coda and the increased delay of reverberating coda. Published changes in Rayleigh-wave group velocity before and after the Parkfield mainshock are compatible with their main cause being from the shallow velocity changes inferred from repeating earthquakes but have little spatial resolution. Stacking of earthquake seismograms resolved surface reflections at one shallow (63 m deep) borehole station GHIB. A change in P -wave travel-time body of ∼8 msec was marginally resolved and is compatible with the repeating earthquake S - P delay changes. Autocorrelation passive seismology resolved ∼32 msec P -wave reverberation delay change above the 251 m deep borehole station CCRB.

The concept of comparative information yield curves and its application to risk‐based site characterization

Defining rational and effective hydrogeological data acquisition strategies is of crucial importance as such efforts are always resource limited. Usually, strategies are developed with the goal of reducing uncertainty, but less often they are developed in the context of their impacts on uncertainty. This paper presents an approach for determining site characterization needs on the basis of human health risk. The main challenge is in striking a balance between reduction in uncertainty in hydrogeological, behavioral, and physiological parameters. Striking this balance can provide clear guidance on setting priorities for data acquisition and for better estimating adverse health effects in humans. This paper addresses this challenge through theoretical developments and numerical simulation. A wide range of factors that affect site characterization needs are investigated, including the dimensions of the contaminant plume and additional length scales that characterize the transport problem, as well as the model of human health risk. The concept of comparative information yield curves is used for investigating the relative impact of hydrogeological and physiological parameters in risk. Results show that characterization needs are dependent on the ratios between flow and transport scales within a risk‐driven approach. Additionally, the results indicate that human health risk becomes less sensitive to hydrogeological measurements for large plumes. This indicates that under near‐ergodic conditions, uncertainty reduction in human health risk may benefit from better understanding of the physiological component as opposed to a more detailed hydrogeological characterization.

Dynamics of confined suspensions of swimming particles

Low Reynolds number direct simulations of large populations of hydrodynamicallyinteracting swimming particles confined between planar walls are performed. The results ofsimulations are compared with a theory that describes dilute suspensions of swimmers. Thetheory yields scalings with concentration for diffusivities and velocity fluctuations as well asa prediction of the fluid velocity spatial autocorrelation function. Even for uncorrelatedswimmers, the theory predicts anticorrelations between nearby fluid elements thatcorrespond to vortex-like swirling motions in the fluid with length scale set by the size of aswimmer and the slit height. Very similar results arise from the full simulationsindicating either that correlated motion of the swimmers is not significant at theconcentrations considered or that the fluid phase autocorrelation is not a sensitivemeasure of the correlated motion. This result is in stark contrast with resultsfrom unconfined systems, for which the fluid autocorrelation captures large-scalecollective fluid structures. The additional length scale (screening length) introducedby the confinement seems to prevent these large-scale structures from forming.