Oblate Ellipsoids Research Articles

Deposition of general ellipsoidal particles

We present a systematic overview of granular deposits composed of ellipsoidal particles with different particle shapes and size polydispersities. We study the density and anisotropy of such deposits as functions of small to moderate size polydispersity and two shape parameters that fully describe the shape of a general ellipsoid. Our results show that, while shape influences significantly the macroscopic properties of the deposits, polydispersity in the studied range plays apparently a secondary role. The density attains a maximum for a particular family of nonsymmetrical ellipsoids, larger than the density observed for prolate or oblate ellipsoids. As for anisotropy measures, the contact forces are increasingly preferred along the vertical direction as the shape of the particles deviates from a sphere. The deposits are constructed by means of a molecular dynamics method, where the contact forces are efficiently and accurately computed. The main results are discussed in the light of applications for porous media models and sedimentation processes.

Synthesis of colloidal solutions of SrFe12O19 plate-like nanoparticles featuring extraordinary magnetic-field-dependent optical transmission

Hard-magnetic plate-like nanoparticles of SrFe12O19 were synthesised hydrothermally. The particles, fixed in a polymer, exhibited a coercivity in the range 0.9–1.8 kOe, and the saturation magnetization values reached 64 emu g−1. Electrostatically stabilized aqueous colloidal solutions of the plate-like particles with average thickness of 5–8 nm and average diameter of 30–80 nm were prepared. The nanoparticles readily oriented when applying a weak magnetic field as low as a few Oe, and due to the linear dichroism phenomena a strong change in the optical transmittance of the solution took place. The extinction coefficient ratio for the perpendicular and the parallel light's electric field vector relative to the magnetic field direction was found to be up to 4.5. The experimental results were compared with a theoretical model, in which the optical absorption of the nanoparticles was calculated from the polarizability of oblate ellipsoids.

Analysis of superposed strain: A case study from Barr Conglomerate in the South Delhi Fold Belt, Rajasthan, India

The structural geometry in the Barr conglomerate and the neighboring rocks in the western flank of the Meso- to Neoproterozoic South Delhi Fold Belt indicate superposed deformation, with structures developed by horizontal dextral simple shear deformation superimposed on earlier structures formed during approximately ESE-WNW compression and subvertical maximum elongation. The first deformation produced NNE-SSW trending subvertical schistosity, and associated steeply plunging isoclinal folds, mineral lineation and pebble elongation lineation having almost downdip alignment on the schistosity surface. The second deformation produced dextral folds both on bedding and schistosity surfaces and modified the shape of the pebbles already deformed by the first deformation. On vertical sections perpendicular to the schistosity trace the pebbles show sub-ellipsoidal shape with their mean elongation direction parallel to the schistosity trace. On the horizontal section the pebbles often show asymmetrical shape and asymmetrical deflection of the schistosity surface around the pebbles. The mean elongation direction makes a small angle (2°–8°) in the counter-clockwise sense with the schistosity surface. This obliquity is due to modification of post-first-deformation sub-ellipsoidal shape by later horizontal simple shear using the schistosity surface as the movement plane. Analytical expressions are derived for the modification of an original ellipse by simple shear parallel to the long axis of the ellipse. A family of curves has been generated to depict the change in axial ratio and orientation of long axis for different initial axial ratios, and for different values of shear strain ( γ). Using these curves it has been possible to factorize the total strain into two components representing the earlier compression and the later simple shear. It is noted that the computed earlier shortening strain ellipsoids are consistently in the flattening field close to the line of pure oblate ellipsoids in the Flinn plot. There is no systematic spatial control on the variation in the values of shear strain ( γ), strain ellipsoid shape parameter ( k), and intensity of distortion ( d) as one proceeds south to north along the strike of the conglomerate.

Hard ellipsoids: Analytically approaching the exact overlap distance

Following previous work [G. Odriozola and F. de J. Guevara-Rodríguez, J. Chem. Phys. 134, 201103 (2011)], the replica exchange Monte Carlo technique is used to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. Here, in addition to the analytical approximation of the overlap distance given by Berne and Pechukas (BP) and the exact numerical solution of Perram and Wertheim, we tested a simple modification of the original BP approximation (MBP) which corrects the known T-shape mismatch of BP for all aspect ratios. We found that the MBP equation of state shows a very good quantitative agreement with the exact solution. The MBP analytical expression allowed us to study size effects on the previously reported results. For the thermodynamic limit, we estimated the exact 1:5 hard ellipsoid isotropic-nematic transition at the volume fraction 0.343 ± 0.003, and the nematic-solid transition in the volume fraction interval (0.592 ± 0.006)-(0.634 ± 0.008).

Bubble Collapse Structure: A Microstructural Record of Fluids, Bubble Formation and Collapse, and Mineralization in Pseudotachylyte

AbstractA complex microstructural feature has been discovered within centimeter-scale pseudotachylyte veins and is here termed “bubble collapse structure” (BCS). Three first-order features of BCSs are (1) a central quartz–dominated monocrystal or polycrystal, (2) a light-colored reaction halo, and (3) a generally radial but commonly curving pattern of opaque seams and/or elliptical quartz amygdules. Two populations of bubbles were principally responsible for forming BCSs. One was a population of millimeter-scale bubbles, and the second involved much more numerous small bubbles (mean diameter, μm). The first population likely formed from liquid water interstitial to the precursory cataclasite or from melting of hydrous minerals, whereas the second population formed by diffusional growth. BCSs began forming as the pseudotachylyte melt cooled and the pressure inside the bubbles decreased. As the large bubbles flattened into oblate ellipsoids parallel to the vein margins, melt flowed toward each collapsing bu...

Anisotropic domain growth and complex coacervation in nanoclay-polyelectrolyte solutions

In this review, the generalized domain growth in a coacervating solution is discussed. Associative electrostatic interaction between nanoclay (Laponite) and gelatin-A (a polyelectrolyte) is shown to drive complex coacervation at room temperature (25 °C). Phase separation kinetics, leading to spontaneous coacervation transition occurring below spinodal temperature (315 K) was studied by depolarized dynamic light scattering. Depolarization and axial ratio data clearly revealed that the domains formed of soluble complexes undergo time-dependent anisotropic growth during the initial period of phase separation (t < 500 s). The equatorial axis of these domains was observed to grow following a power-law behavior: a( t) ~ t β and β = 0.25 ± 0.04 independent of quench depth that was not deep. In contrast, the polar axis shrunk with time following: b( t) ~ t − δ and δ = 0.15 ± 0.05 independent of quench depth. These domains preferentially grew as oblate ellipsoids during this time. Effect of gravity on domain growth was not observed in our experiments. These results answer the basic issue of binding between discotic colloidal particles and polyelectrolytes in dispersion phase and the resultant phase separation kinetics.

Communication: Equation of state of hard oblate ellipsoids by replica exchange Monte Carlo

We implemented the replica exchange Monte Carlo technique to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. For this purpose, we considered the analytical approximation of the overlap distance given by Bern and Pechukas and the exact numerical solution given by Perram and Wertheim. For both cases we capture the expected isotropic-nematic transition at low densities and a nematic-crystal transition at larger densities. For the exact case, these transitions occur at the volume fraction 0.341, and in the interval 0.584-0.605, respectively.

Solubilization of Indomethacin by Polysorbate 80 in Mixed Water-Sorbitol Solvents

The effect of indomethacin on the micellar properties of the non-ionic surfactant, polysorbate 80, in water-sorbitol mixtures containing up to 25% w/v sorbitol has been investigated by light scattering, photon correlation spectroscopy and viscometric techniques. The molecular weight of polysorbate 80 micelles containing solubilized indomethacin increased linearly with increase of sorbitol concentration. Solubilization of indomethacin resulted in an increase of micellar weight due not only to the incorporation of solubilizate but also to an increase in the number of polysorbate molecules per micelle. The micelles in all systems were most satisfactorily represented as oblate ellipsoids, the asymmetry and hydration of which increased with increase of sorbitol concentration. Indomethacin solubilization caused a restructuring of the micelle to produce a more symmetrical micelle of increased hydration.

Mechanical and damage analysis along a flat-rolled wire cold forming schedule

Numerical simulation is used to study patented high-C steel flat-rolled wire cold forming processes. An elasto-plastic power law, identified from mechanical tests, is used into Forge2005® finite element (FEM) package in order to describe the material behaviour during wire drawing followed by cold rolling. A through-process approach has been favoured, transferring residual wire-drawing stresses and strain into the flat-rolling preform. This mechanical analysis, associated with a triaxiality study, points to dangerous areas where fracture may initiate due to high tensile stresses. Lemaitre’s isotropic damage criterion, including crack closure effect, a -1/3 cut-off value of stress triaxiality, and tension/compression damage asymmetry, has been used and has confirmed the previous analysis. A number of non-coalesced voids nucleated on inclusions have been observed in the Scanning Electron Microscopy (SEM), especially in high-deformation zones (“blacksmith’s cross”). Their evolution has been simulated in the FEM model using spherical numerical markers, which deform into oblate or prolate ellipsoids. The deformation-induced morphological evolution of voids observed in the SEM compares well with the geometrical evolution of the markers, which suggests that the morphologies observed do not result from micro-crack propagation, but from material transport of the nucleated voids.

A Design Equation for the Stress Concentration Factor of an Oblate Ellipsoidal Cavity

The stress concentration factor (SCF) of an oblate ellipsoidal cavity in an isotropic material subjected to a uniform normal stress at infinity perpendicular to the equator of the cavity is determined by the equivalent inclusion method. Numerical results are obtained for general cases; particularly, explicit and exact results are obtained for cases of strongly oblate cavities. To extend the range of validity for these cases, a two-dimensional model is developed for finding the correction terms and a simple equation for the SCF of an oblate ellipsoidal cavity is thus obtained. The accuracy of the equation is probed and it is shown that the proposed formula is sufficiently accurate for design purposes.

The shape distribution of splash-form tektites predicted by numerical simulations of rotating fluid drops

Splash-form tektites are glassy rocks ranging in size from roughly 1 to 100 mm that are believed to have formed from the splash of silicate liquid after a large terrestrial impact from which they are strewn over thousands of kilometres. They are found in an array of shapes including spheres, oblate ellipsoids, dumbbells, rods and possibly fragments of tori. It has recently become appreciated that surface tension and centrifugal forces associated with the rotation of fluid droplets are the main factors determining the shapes of these tektites. In this contribution, we compare the shape distribution of 1163 measured splash-form tektites with the results of the time evolution of a 3D numerical model of a rotating fluid drop with surface tension. We demonstrate that many aspects of the measured shape distribution can be explained by the results of the dynamical model.

Role of the shape of various bacteria in their separation by Microthermal Field-Flow Fractionation

The steady-state movement of the spherical and non-spherical particles, such as prolate or oblate rotational ellipsoids, cylinders, or parallelepipeds, suspended in a liquid and exposed to a unidirectional temperature gradient, is analyzed theoretically. The differences in the ratios of the rotational to translational diffusion coefficients of the non-spherical to spherical particles, the heterogeneity of thermal conductivity of the particle body, and the heterogeneity in surface chemical nature make possible to separate the particles according to differences in shape. Preliminary experimental separations of Gram-positive and Gram-negative, nearly spherical and rod-shaped bacteria performed by Microthermal Field-Flow Fractionation confirmed that the fractionation of the cells according to differences in shape is possible.

Charge Ordering Induces a Smectic Phase in Oblate Ionic Liquid Crystals

We report a computer simulation study of an electroneutral mixture of oppositely charged oblate ellipsoids of revolution with aspect ratio A=1/3. In contrast with hard or soft repulsive ellipsoids, which are purely nematic, this system exhibits a smectic-A phase in which charges of equal sign are counterintuitively packed in layers perpendicular to the nematic director.

Dynamical description of vesicle growth and shape change

We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity of this prediction is examined in the light of the various assumptions made in its derivation.

Crystallization of Deformable Spherical Colloids

We introduce and characterize a first-order model for a generic class of colloidal particles that have a preferred spherical shape but can undergo deformations while always maintaining hard-body interactions. The model consists of hard spheres that can continuously change shape at fixed volume into prolate or oblate ellipsoids of revolution, subject to an energetic penalty. The severity of this penalty is specified by a single parameter that determines the flexibility of the particles. The deformable hard spheres crystallize at higher packing fractions than rigid hard spheres, have a narrower solid-fluid coexistence region and can reach high densities by a second transition to an orientationally ordered crystal.

Dynamics of a nonmagnetic drop suspended in a magnetic fluid in a rotating magnetic field

The behavior of a nonmagnetic drop suspended in a magnetic fluid and subjected to the action of a rotating magnetic field is studied experimentally. The configurations of the drop in the form of prolate and oblate ellipsoids of revolution in the rotating field are investigated, and disintegration of the drop in the rotating field and the development of comb instability of its surface under certain conditions are observed.

Three-dimensional analysis of ferrite allotrimorphs nucleated on grain boundary faces, edges and corners

The ferrite allotriomorphs nucleated on austenite grain boundary faces exhibit complex morphologies. Most of them are of oblate ellipsoids in shape and some of them are plate-like or pyramid-like. Ferrite allotriomorphs nucleated on austenite grain boundary edges take the form of triangular pyramids or triangular bi-pyramids. Ferrite allotriomorphs nucleated on austenite grain boundary corners are of irregular shapes.

Phonons in InAs quantum dot structures

AbstractWe present a Raman study of the phonon spectra of periodical structures with (In,Ga)As QDs in (Al,Ga)As matrix as well as AlAs QDs embedded in InAs grown by molecular beam epitaxy. Raman scattering by optical, interface and acoustic phonons was observed in the QD structures. TO and LO phonons in the QDs are strongly affected by both strain and confinement. The Raman study reveals a two‐mode behavior of optical phonons in the whole composition range for both InGaAs QDs and the AlGaAs matrix. Raman scattering by InAs‐ and GaAs‐like LO phonons in InGaAs QDs shows a size‐selective resonant behaviour. Interface phonons were investigated in InGaAs QDs and the AlGaAs matrix. Their frequency positions were analyzed as a function of the alloy content within the dielectric continuum model. The positions of IF phonons in the QD structures observed in the experiment agree well with calculated ones assuming that the QDs have the shape of oblate ellipsoids. Multiple phonon Raman scattering involving both pure overtones of the first‐order InAs, GaAs and AlAs optical and interface phonons and combination of phonons from the materials is observed in the vicinity with E0 resonance in QDs. Possible mechanisms of these processes are discussed. Low frequency resonant Raman scattering by acoustic phonons was observed in the QD structures. The periodic oscillations seen in the Raman spectra are well described by the elastic continuum model. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Pan-African strike–slip tectonics in eastern Cameroon—Magnetic fabrics (AMS) and structure in the Lom basin and its gneissic basement

Field, microstructural, and anisotropy of magnetic susceptibility (AMS) or magnetic fabric studies were applied to identify the sequence and character of the Pan-African structures in the basement of Eastern Cameroon at both sides of the regional scale Bétaré-Oya Shear Zone (BOSZ). The NE-SW trending BOSZ separates older gneisses and migmatites towards SE (domain I) from the younger rocks of the Lom meta-volcano-sedimentary basin towards NW (domain II). In domain I, early, ductile compressional deformation occurred in two events, D1 and D2, under relatively high T conditions. During subsequent cooling, strain partitioned between the competent basement gneisses with only mild compression and the bordering shear zone (BOSZ) with intense simple shear-wrenching (D3). Strain in the less competent rocks of domain II is dominated by simple shear, strike-slip wrenching (D3), with an earlier stage of compressional deformation preserved only in some low strain pods. Magnetic fabrics (AMS) document a progressive change from oblate ellipsoids towards prolate ellipsoids in domain I, when proceeding from the south towards the BOSZ. Foliations are mostly steep but define a girdle with a pole plunging gently towards WSW. The magnetic lineations also plunge mostly towards WSW at shallow angles. These fabrics indicate a compression approximately normal to the BOSZ, which is also the SE margin of the Lom Basin. In the Lom metasediments (domain II), AMS ellipsoids are typically oblate. Foliations trend NE-SW with mostly steep dips. Magnetic lineations plunge gently NE or SW. This fabric with foliations mostly steep and subparallel with the major BOSZ, combined with generally subhorizontal lineations implies the BOSZ as a Pan-African strike–slip shear zone with a subordinate component of compression. At a larger scale, the area is part of a continent-scale shear zone, separating external Pan-African domains of compression along the northern margin of the Congo craton from internal domains dominated by high-angle strike–slip and transpressional deformation. Together with published data, the present study thus demonstrates that transpression is a regional phenomenon in the Pan-African orogen of central and eastern Cameroon.

Computational fluid dynamics of aggregating red blood cells in postcapillary venules

Aggregate formation of red blood cells (RBCs) in a postcapillary venular bifurcation is investigated with three-dimensional computer simulations using the Chimera grid method. Interaction energy between the RBCs is modelled by a depletion interaction theory; RBCs are modelled as rigid oblate ellipsoids. The cell–cell interactions of RBCs are strongly dependent on vessel geometry and shear rates. The experimental data on vessel geometry, pseudoshear rates, and Dextran concentration obtained in our previous in vivo RBC aggregation study in postcapillary venules of the rat spinotrapezius muscle were used to simulate RBC aggregation. The computational results were compared to the experimental results from the in vivo study. The results show that cells have a larger tendency to form an aggregate under reduced flows. Aggregate formation also depends on the angle and location of the cells before they enter the bifurcation region. Comparisons with experimental data are discussed.