Large Characteristic Length Research Articles

Dynamics of magmatic intrusions in the upper crust: Theory and applications to laccoliths on Earth and the Moon

[1] To understand the dynamics of shallow magmatic intrusions, I propose a theoretical model of magma spreading laterally below an elastic crust. Nondimensionalization of the flow equation leads to the identification of characteristic scales for the intrusion: while the characteristic intrusion length is controlled by the elastic response of the crust, its characteristic thickness primarily depends on magma properties and injection rate. Three spreading regimes are identified and characterized by different morphologies as well as by scaling laws for thickness versus length and thickness versus time. The first spreading regime is controlled by the elastic response of the crust and the shape of the flow is self-similar. When the time, length, and thickness become larger than an elastic time, length, and thickness scale, the edges of the flow become steeper and the system transitions to a gravity current regime. When the intrusion is thick enough to accommodate the pressure head, the flow enters a regime of lateral propagation and keeps a constant thickness. The intrusion shape in the elastic regime fits the observed shape of terrestrial laccoliths. The elastic scaling law for intrusion thickness versus length fits observations of laccoliths at Elba Island, Italy, and provides for a physical explanation for the observed relationship between length and thickness on terrestrial laccoliths. Laccoliths are predicted to form over short time scales, depending on magma viscosity, that vary between approximately a month to several years for felsic magmas on Earth. On the Moon, several elongated low-slope domes have recently been identified as possibly formed by laccolith intrusions at depth, although they are much larger than terrestrial laccoliths. Because the Moon has a smaller gravity than on the Earth, a deeper magma source, and a more mafic magma composition than for terrestrial laccoliths (implying smaller pressure gradient and dike width), lunar intrusions have a larger characteristic length and a smaller characteristic thickness. After nondimensionalization, the morphologies (length versus thickness) of terrestrial and inferred lunar laccoliths follow the same curve and are well fitted by the elastic scaling law. This model thus explains the size discrepancy between terrestrial laccoliths and lunar low-slope domes. Therefore, low-slope domes identified on the Moon are good candidates for laccolith-type intrusions at depth.

Two‐fluid model with interface sharpening

AbstractTwo‐fluid models are applicable for simulations of all types of two‐phase flows ranging from separated flows with large characteristic interfacial length scales to highly dispersed flows with very small characteristic interfacial length scales. The main drawback of the two‐fluid model, when used for simulations of stratified flows, is the numerical diffusion of the interface. Stratified flows can be easily and more accurately solved with interface tracking methods; however, these methods are limited to the flows, that do not develop into dispersed types of flows. The present paper describes a new approach, where the advantage of the two‐fluid model is combined with the conservative level set method for interface tracking. The advection step of the volume fraction transport equation is followed by the interface sharpening, which preserves the thickness of the interface during the simulation. The proposed two‐fluid model with interface sharpening was found to be more accurate than the existing two‐fluid models. The mixed flow with both: stratified and dispersed flow, is simulated with the coupled model in this paper. In the coupled model, the dispersed two‐fluid model and two‐fluid model with interface sharpening are used locally, depending on the parameter which recognizes the flow regime. Copyright © 2010 John Wiley & Sons, Ltd.

Mechanisms of magnetic and temperature hysteresis in ErFeO3 and TmFeO3 single crystals

Magnetic hysteresis is studied in the orthoferrites ErFeO3 and TmFeO3 using the single crystal samples of millimeter dimensions. It is shown that in both materials one observes a temperature transition manifesting itself through the temperature hysteresis of the magnetic moment and a peculiar temperature evolution of the field hysteresis loop shapes near this transition. Experiments rule out the hypothesis that the ordering of the orthoferrite’s rare-earth magnetic moments plays an important role in these phenomena. The hysteresis curves can be explained by a few-domain magnetic state of the samples that results from the weak ferromagnetism of the orthoferrites. The phenomenon is generic for weak ferromagnets with temperature dependent magnetization. A large characteristic magnetic length makes the behavior of the relatively big samples analogous to that observed in the nanosize samples of strong ferromagnets.

Monochromatic waves induced by large-scale parametric forcing

We study the formation and stability of monochromatic waves induced by large-scale modulations in the framework of the complex Ginzburg-Landau equation with parametric nonresonant forcing dependent on the spatial coordinate. In the limiting case of forcing with very large characteristic length scale, analytical solutions for the equation are found and conditions of their existence are outlined. Stability analysis indicates that the interval of existence of a monochromatic wave can contain a subinterval where the wave is stable. We discuss potential applications of the model in rheology, fluid dynamics, and optics.

Effect of steady flow and Newton's cooling on the propagation and damping of small-amplitude prominence plasma oscillations

AbstractWe study the propagation and damping of small-amplitude prominence oscillations invoking steady flow and radiative losses due to Newton's cooling with constant relaxation time. We find that the strength of steady flow has a large influence on the propagation (e.g. period, phase velocity) of wave modes. In the presence of steady flow, the thermal mode is a propagating wave and hence it can be observed in solar prominences. The thermal mode contributes to the non-thermal line broadening in the solar atmosphere. The steady flow does not affect the damping time of the wave modes. The damping of slow and thermal modes is highly dependent on the radiative relaxation time. The thermal perturbation, in the presence of steady flow, is found to be larger in the case of the thermal mode than in the slow and fast modes. The energy flux (~300 W m−2) associated with the thermal mode is sufficient to heat the quiet regions of the Sun. The slow mode contribution to non-thermal broadening has been estimated. The non-thermal broadening is found to be large in the case of the prominence with large characteristic length. The steady flow, in the presence of Newton's cooling, breaks the symmetry between the forward and backward propagating modes. No modes with negative energy have been found. For strong flows (above 10 km s−1), the canonical backward wave propagates in the forward direction, which can play an important role in wave detection and prominence seismology.

Separated flow structures around a cylindrical obstacle in a narrow channel

A detailed experimental study is performed on the separated flow structures around a low aspect-ratio circular cylinder (pin-fin) in a practical configuration of liquid cooling channel. Distinctive features of the present arrangement are the confinement of the cylinder at both ends, water flow at low Reynolds numbers ( Re = 800, 1800, 2800), very high core flow turbulence and undeveloped boundary layers at the position of the obstacle. The horseshoe vortex system at the junctions between the cylinder and the confining walls and the near wake region behind the obstacle are deeply investigated by means of Particle Image Velocimetry (PIV). Upstream of the cylinder, the horseshoe vortex system turns out to be perturbed by vorticity bursts from the incoming boundary layers, leading to aperiodical vortex oscillations at Re = 800 or to break-away and secondary vorticity eruptions at the higher Reynolds numbers. The flow structures in the near wake show a complex three-dimensional behaviour associated with a peculiar mechanism of spanwise mass transport. High levels of free-stream turbulence trigger an early instabilization of the shear layers and strong Bloor–Gerrard vortices are observed even at Re = 800. Coalescence of these vortices and intense spanwise flow inhibit the alternate primary vortex shedding for time periods whose length and frequency increase as the Reynolds number is reduced. The inhibition of alternate vortex shedding for long time periods is finally related to the very large wake characteristic lengths and to the low velocity fluctuations observed especially at the lowest Reynolds number.

Analytical power series solution for contaminant transport with hyperbolic asymptotic distance-dependent dispersivity

Summary A hyperbolic asymptotic function, which characterizes that the dispersivity initially increases with travel distance and eventually reaches an asymptotic value at long travel distance, is adopted and incorporated into the general advection–dispersion equation for describing scale-dependent solute transport in porous media in this study. An analytical technique for solving advection–dispersion equation with hyperbolic asymptotic distance-dependent dispersivity is presented. The analytical solution is derived by applying the extended power series method coupling with the Laplace transform. The developed analytical solution is compared with the corresponding numerical solution to evaluate its accuracy. Results demonstrate that the breakthrough curves at different locations obtained from the derived power series solution agree closely with those from the numerical solution. Moreover, breakthrough curves obtained from the hyperbolic asymptotic dispersivity model are compared with those obtained from the constant dispersivity model to scrutinize the relationship of the transport parameters derived by Mishra and Parker [Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc. 4(1), 45–47]. The result reveals that the relationship postulated by Mishra and Parker [Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc. 4(1), 45–47] is only valid under conditions with small dimensionless asymptotic dispersivity (aa) and large dimensionless characteristic half length (b).

Theoretical study of the three-phase contact line and its tension in adsorbed colloid-polymer mixtures

We perform a theoretical study of the three-phase contact line and the line tension in an adsorbed colloid-polymer mixture near a first-order wetting transition, employing an interface displacement model. We use a simple free-energy functional to describe a colloid-polymer mixture near a hard wall. The bulk phase behavior and the substrate-adsorbate interaction are modeled by the free-volume theory for ideal polymers. The large size of the colloidal particles and the suppression of the van der Waals interaction by optical matching of colloid and solvent justify the planar hard wall model for the substrate. Following the Fisher-Jin scheme, we derive from the free-energy functional an interface potential V(l) for these mixtures. For a particle diameter of 10-100 nm, the calculations indicate a line tension tau approximately 10(-12)-10(-13) N at room temperature. In view of the ultralow interfacial tension in colloid-polymer mixtures, gamma approximately 10(-7) Nm, this leads to a rather large characteristic length scale taugamma in the micrometer range for the three-phase contact zone width. In contrast with molecular fluids, this zone could be studied directly with optical techniques such as confocal scanning laser microscopy.

Revealing Long-Range Density Fluctuations in Dialkylimidazolium Chloride Ionic Liquids by Dynamic Light Scattering

In this study, the structures and dynamics of ionic liquids of 1-allyl-3-methylimidazolium chloride ([AMIM][Cl]) and 1-n-butyl-3-methylimidazolium chloride ([BMIM][Cl]) were studied by dynamic light scattering with polarized and depolarized geometries in the temperature range from 300 to 400 K. The temperature range covered supercooled and liquid states for [BMIM][Cl] and covered the liquid state for [AMIM][Cl]. The results show that for these ionic liquids at all chosen temperatures only one ultraslow relaxation is observed in the polarized component of dynamic light scattering, however, the ultraslow relaxation is not observed in the depolarized component. The ultraslow relaxation exhibited several typical features of the "cluster" mode generally found in glass-forming liquids and polymer melts, such as diffusive, strongly scattering-vector-dependent, and nearly exponential characters, which thus corresponded to long-range density fluctuations. The physical origin for long-range density fluctuations was the existence of heterogeneities with large characteristic length scales in these ionic liquids. It was further considered that molecules of these ionic liquids not only tended to aggregate to form dynamic clusters but also possibly formed dynamic networks in the supercooled state and the heterogeneities could exist even at temperatures higher than the melting points.

Defect propagation at a circular interface

In this paper a nonlinear, nonuniform cohesive zone is employed to study the detailed features of quasi-static defect evolution in a simple, planar elastic system consisting of a circular inclusion embedded in an unbounded matrix subject to different remote loading configurations. The inclusion–matrix interface is assumed to be described by Needleman-type force-separation relations characterized by an interface strength, a characteristic force length and a shear stiffness parameter. Interface defects are modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body inclusion displacement, are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. For equibiaxial tension, quasi-static defect initiation and propagation occur under increasing remote load. For decreasing characteristic force length, a transition occurs from more or less uniform decohesion along the bond line to propagation of a crack-like defect. In the later case a critical failure load is well defined and interface failure is shown to be defect dominated (brittle decohesion). For interfaces with large characteristic force length, the matrix “lifts off” the inclusion accompanied by a delay in defect propagation (ductile decohesion). The decohesion modes ultimately give rise to a cavity with the inclusion situated within it on the side opposite to the original defect. Results for small characteristic force length show consistency with England’s results for the sharp arc crack on a circular interface (England AH (1966) ASME J Appl Mech 33:637–640) Stress oscillation and contact at the tip of the defect are observed primarily for small characteristic force lengths under extremely small loading. Results for remote tension, compression and pure shear loading are discussed as well. In the final section of the paper the results obtained in the first part are utilized to estimate the plane effective bulk response of a composite containing a dilute distribution of inclusions with randomly oriented interface defects.

Size Effect on Strength of Quasibrittle Structures with Reentrant Corners Symmetrically Loaded in Tension

The effect of V-notches (or reentrant corners) on fracture propagation has been analyzed for brittle materials, but not for quasibrittle materials such as concrete, marked by a large material characteristic length producing a strong size effect transitional between plasticity and linear elastic fracture mechanics. A simple size effect law for the nominal strength of quasibrittle structures with symmetrically loaded notches, incorporating the effect of notch angle, is derived by asymptotic matching of the following five limit cases: (1) Bažant’s size effect law for quasibrittle structures with large cracks for notch angle approaching zero; (2) absence of size effect for vanishing structure size; (3) absence of size effect for notch angle approaching π ; (4) plasticity-based notch angle effect for vanishing size; and (5) the notch angle effect on crack initiation in brittle structures, which represents the large-size limit of quasibrittle structures. Accuracy for the brittle large-size limit, with notch ang...

Measuring characteristic length scales of eigenfunctions of Sturm–Liouville equations in one and two dimensions

The spatial resolution of eigenfunctions of Sturm–Liouville equations in one-dimension is frequently measured by examining the minimum distance between their roots. For example, it is well known that the roots of polynomials on finite domains cluster like O(1/N 2) near the boundaries. This technique works well in one dimension, and in higher dimensions that are tensor products of one-dimensional eigenfunctions. However, for non-tensor-product eigenfunctions, finding good interpolation points is much more complicated than finding the roots of eigenfunctions. In fact, in some cases, even quasi-optimal interpolation points are unknown. In this work an alternative measure, l, is proposed for estimating the characteristic length scale of eigenfunctions of Sturm–Liouville equations that does not rely on knowledge of the roots. It is first shown that l is a reasonable measure for evaluating the eigenfunctions since in one dimension it recovers known results. Then results are presented in higher dimensions. It is shown that for tensor products of one-dimensional eigenfunctions in the square the results reduce trivially to the one-dimensional result. For the non-tensor product Proriol polynomials, there are quasi-optimal interpolation points (Fekete points). Comparing the minimum distance between Fekete points to l shows that l is a reasonably good measure of the characteristic length scale in two dimensions as well. The measure is finally applied to the non-tensor product generalized eigenfunctions in the triangle proposed by Taylor MA, Wingate BA [(2006) J Engng Math, accepted] where optimal interpolation points are unknown. While some of the eigenfunctions have larger characteristic length scales than the Proriol polynomials, others show little improvement.

Fabrication and characterization of metal-semiconductor field-effect-transistor-type quantum devices

Quantum dot transistors and nanowire transistors are fabricated from a metal-semiconductor field-effect-transistor-type wafer and are characterized at low temperatures. Clear single-electron tunneling and various quantum effects, such as transport through excited states and negative differential resistance, are observed in our wire device. Our data suggest that the potential fluctuation of the heavily doped GaAs layer has a much larger characteristic length than interimpurity spacing, and that this is due to the low ionization rate (approximately 10%) of the dopant atoms at 4.2 K.

Effect of relative stress on post-peak uniaxial compression fracture energy of concrete

Fracture energy in strain softening regime was investigated analytically by considering microstructures interaction and interplay. Based on gradient-dependent plasticity, the thickness of localized band was determined completely and strictly by characteristic length in relation to average grain diameter. After obtaining the plastic shear displacement of the band, the formula on axial response of concrete was proposed and the analytical post-peak fracture energy was deduced. A comparison between present theoretical results and earlier experimental results was carried out and the analytical result is reasonable and has a plausible foundation as considering the localized failure theoretically. Decreasing the relative stress leads to increasing the fracture energy non-linearly. The large the shear elastic modulus and shear softening modulus, the lower the post-peak fracture energy. A larger fracture energy is caused by a larger thickness of shear band or a larger characteristic length of concrete material. If the inclination angle of the shear band and the compressive strength are not concerned with structural size of specimen, the post-peak fracture energy is size independent.

Thermal model of thin film anemometer

This work presents a thermal model for thin film anemometers and shows the importance of the characteristic length of the heater in convection phenomena. The techniques of silicon micro-machining were used to manufacture an anemometer with low electric consumption and great sensitivity. A thermal model of the sensor is described and then confronted with experimental results. The calculation of thermal conductance due to convection, radiation and conduction is presented. The coefficient of convection was deducted and it was found very high in comparison with the one of a macroscopic structure: 200Wm−2K−1 typically for free convection. The response of the sensor in the airflow is also presented as a function of the coefficient of convection or a function of the flow velocity and it shows that the coefficient of convection does not follow the macroscopic laws. Then, a new sensor with a larger characteristic length was manufactured and its response and coefficient of convection are compared to the smaller sensor ones.

Compression Loading Applied to Round Double Beam Fracture Specimens. I: Application to Materials with Large Characteristic Lengths

The round double beam loaded in tension, RDB(T), or wedging, RDB(W), is part of standard test methods for measuring the fracture toughness of aluminum (ASTM E 1307), cemented carbides (ASTM B 644), and rock. When the combination RDB(T) or RDB(W) is used with materials with a relatively large characteristic length, which is defined as the square of the ratio of fracture toughness to tensile strength, the crack tends to depart from the intended fracture plane rendering the data unusable. Loading the RDB in eccentric compression, RDB(B), has been investigated as an acceptable loading alternative in such cases. Tests of over 100 RDB(B) specimens made from different concrete mixtures using three specimen sizes all produced usable data. In addition, the fracture toughness values obtained from RDB(B) tests are consistent with values obtained from RDB(W) tests. The test equipment, test procedures, and data reduction method are all described in detail for the RDB(B).

Compression Loading Applied to Round Double Beam Fracture Specimens. II: Derivation of Geometry Factor

The round double beam loaded in eccentric compression has been shown to produce usable data when determining the fracture properties of materials with a relatively large characteristic length. In order to reduce these data, the geometry calibration factor must be known for the combination of specimen geometry and loading technique. Numerical simulations using the boundary element method have been used to determine the geometry calibration factor for a round double beam with a length to diameter ratio of 2:1 loaded in eccentric compression. The factor was determined by compliance calibration and direct calculation of stress intensities. Recognizing that laboratory test specimens will not have exactly the same geometry as the simulated specimen, geometry calibration factors have been determined for variations in the base geometry as well.

Syntheses of Silica/Polystyrene-block-Poly(ethylene oxide) Films with Regular and Reverse Mesostructures of Large Characteristic Length Scales by Solvent Evaporation-Induced Self-Assembly

Silica/diblock films with various mesostructures of large characteristic length scales were synthesized through evaporation-induced self-assembly (EISA). The structure-directing agents used were amphiphilic polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymers of high molecular weights. The synthesis process began with a dilute homogeneous solution of a silica precursor and the diblock copolymer in a mixture of tetrahydrofuran (THF) and water. After this dilute solution was cast, THF preferentially evaporated; accordingly, the species in the depositing film increasingly concentrated and the solvent quality for the diblock progressively decreased. At some critical point, cooperative self-assembly of both the PS-b-PEO diblock and the silicate started. Subsequently, liquid-crystalline mesophases were obtained. The present study indicates that silica/diblock films with different mesostructures can be synthesized by using one identical diblock; as the volume ratio of the diblock to silica increa...

Formation Mechanism of Silica/Diblock Mesophases by Solvent Evaporation-Induced Self-Assembly

ABSTRACTIntermediate structures were trapped during the mesophase transition from lamellae to higher curvature structures in a sol-gel matrix. The target structures included normal hexagonally arranged cylinders and/or normal spheres in a cubic array distributed in a hydrophilic matrix. The present system is believed to be the first to trap these intermediates. Through solvent evaporation-induced self-assembly (EISA), mesostructured silica/diblock films with large characteristic length scales were prepared. The structure-directing agents were polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymers with high molecular weight, which are water insoluble and alcohol insoluble. We believe that no micellization took place in the present system; a disorder-to-order transition occurred due to the cooperative self- assembly of the diblock and silicates as the solvent preferentially evaporated from a film cast from a dilute homogeneous solution. During further preferential evaporation, the morphogenic effect of the increase of species concentration facilitates the mesophase development in the direction of a normal cubic to hexagonal to lamellar pathway. However, the morphogenic effects of both the decrease of the PS coil dimension and the siloxane condensation drive the mesophase development in opposite directions. The decrease of the PS coil dimension plays an important role in the present self-assembly process. Trapping of the intermediates and coexisting multiple mesophases are related to the facts that PS has high Tg and high hydrophobicity in particular, as well as to the fact that polymers have relatively low mobility in general.

Molecular beam epitaxial growth of Sb/GaSb multilayer structures: potential application as a narrow bandgap system

We have performed an investigation into the synthesis of Sb/GaSb heterojunctions and multilayered structures grown by molecular beam epitaxy. The study has been motivated by the potential of the system as an indirect narrow-gap superlattice, where spacial quantization effects are proposed to induce a positive valence-conduction band energy gap in the Sb semimetal layers, and the potential to exploit the large characteristic lengths in the Sb layers for the study of size quantization effects. The GaSb/Sb system presents a number of unique features with regard to synthesis of the epitaxial semimetal/semiconductor system. On the (111) plane of the rhombohedral crystal structure of Sb, both the hexagonal symmetry and in-plane lattice parameter allow near perfect registry to the Sb atoms on the (111) plane of the zincblende structure of GaSb. We show that Sb can be grown epitaxially on GaSb on both (111)A and (111)B orientations for growth temperature T s <240° C and that GaSb can subsequently be grown on the Sb epilayers. The successful growth of GaSb at temperatures less than 240°C has been achieved using migration enhanced epitaxy. Epilayer growth of Sb and Sb/GaSb heterojunction structures have been characterized by in situ reflection high energy electron diffraction, X-ray diffraction and X-ray photoelectron spectroscopy.