Prolate Ellipsoids Research Articles

VOLUME CHANGES IN FLUID INCLUSIONS PRODUCED BY HEATING AND PRESSURIZATION: AN ASSESSMENT BY FINITE ELEMENT MODELING

Recent advances in using the hydrothermal diamond anvil cell (HDAC) to measure homogenization temperatures of inclusions trapped at high pressure have created a need to better understand changes in elastic volume of fluid inclusions experiencing high internal and external pressures. We have used finite element modeling to explore volume changes of fluid inclusions as a function of shape and distance from the free surface at a sample’s edge as an aid in understanding their behavior in HDAC studies. We have modeled a variety of oblate and prolate ellipsoids, as well as a disk that has the same cross-section as a negative crystal in quartz and two right cylinders. All of our models have an axisymmetric geometry and assume linear isotropic elasticity. We find that the percent change in volume of an inclusion is primarily a function of the aspect ratio of the inclusion. The presence or absence of corners and the sharpness of internal corners also affect the volume change, but to a lesser extent. Distance to a free surface is only significant for inclusions that are very close to the free surface. This effect is most pronounced for an oblate ellipsoid oriented with its long dimensions parallel to the free surface. For microthermometric studies of fluid inclusions at 1 atm, the changes in elastic volume due to increases in internal pressure are negligible. However, for HDAC studies, where the application of confining pressure allows more extreme conditions to be obtained, changes in elastic volume can be significant, but can be predicted using finite element models.

Electrophoretic mobility and primary electroviscous effect of dilute “hard” prolate ellipsoids

Electrophoretic mobilities and primary electroviscous coefficients are determined for “hard” prolate ellipsoids of axial ratio less than or equal to 4 in KCl, NaCl, and Tris–glycine salt solutions. Account is taken of the steady state distortion of the ion atmosphere around the ellipsoid by numerical solution of the coupled Poisson, low-Reynolds-number Navier–Stokes, and ion transport equations. This is accomplished by a boundary element procedure. Results are presented as ratios of mobilities and primary electroviscous coefficients of ellipsoids to those of corresponding spheres. It is shown that the electrophoretic mobility of an ellipsoid is very similar to that of a sphere under similar conditions of size, ionic strength, salt type, and zeta potential. Other factors being equal, shape has little effect on electrophoretic mobility. For the primary electroviscous coefficient, on the other hand, there is a substantial shape effect. It is argued that the complementary techniques of electrophoresis and viscosity together provide an effective means of studying the size, charge, and shape of macroions and colloidal particles.

Calculation of the electric-field enhancement at nanoparticles of arbitrary shape in close proximity to a metallic surface

An axis-symmetrical problem of light diffraction on a nanometer-sized particle placed in arbitrary distance close to a surface is solved based on Maxwell's equations. Complex dielectric functions for the particle and the surface are taken into account. By applying the Green function method, the initial Maxwell equations are reduced to an equivalent system of integral equations. The boundary element method permits one to transform these to a linear system of equations and to solve it by the Gaussian method. In this paper metallic spheres, prolate ellipsoids, and conical bodies of arbitrary size, placed in vacuum and near a metallic surface are considered. Enhancement factors of the electric field of these bodies consisting of Na, Ag, Au, and Cu are calculated surface averaged and at the poles. Large field enhancement factors (up to several hundred times) were indeed observed for these metals. It is shown that the presence of the metallic surface results in an additional field enhancement which is strongly dependent on the apex shape of the bodies.

Small-angle neutron scattering studies of nonionic surfactant: Effect of sugars

Micellar solution of nonionic surfactantn-dodecyloligo ethyleneoxide surfactant, decaoxyethylene monododecyl ether [CH3(CH2)11(OCH2CH2)10OH], C12E10 in D2O solution have been analysed by small-angle neutron scattering (SANS) at different temperatures (30, 45 and 60° C) both in the presence and absence of sugars. The structural parameters like micelle shape and size, aggregation number and micellar density have been determined. It is found that the micellar structure significantly depends on the temperature and concentration of sugars. The micelles are found to be prolate ellipsoids at 30° C and the axial ratio of the micelle increases with the increase in temperature. The presence of lower concentration of sugar reduces the size of micelles and it grows at higher concentration of sugar. The structure of micelles is almost independent of the different types of sugars used.

Investigation of the properties of decaoxyethylene n‐dodecyl ether, C12E10, in the aqueous sugar‐rich region

AbstractInterfacial, thermodynamic, and morphological properties of decaoxyethylene n‐dodecylether [CH3 (CH2)11(OCH2CH2)10OH](C12E10) in aqueous solution were analyzed by tensiometric, viscometric, proton nuclear magnetic resonance (NMR), and small‐angle neutron scattering (SANS) techniques. Dynamic and structural aspects at different temperatures in the absence and presence of sugars at different concentrations were measured. Critical micelle concentrations (CMC) were determined by surface tension measurements in the presence of ribose, glucose, and sucrose. The heat capacity (ΔCp.m.), transfer enthalpy (ΔHm.tr.), transfer heat capacities (ΔCp.m.tr.), micellization constant (Km), Setchenow constant (KSN), and partition coefficient (q) were determined and discussed as an extension of the usual thermodynamic quantities of micellization and adsorption at the air‐water interface. An enthalpy‐entropy compensation effect was observed with an isostructural temperature (Tc) of about 310 K for both micellization and interfacial adsorption. SANS measurements were taken to elucidate structural information, viz., aggregation number (Nagg), shape, size, and number density (Nm) on C12E10 micelles in D2O at different concentrations of sugars (0.05, 0.02, 0.3, and 0.5 M) and temperatures (30, 45, and 60°C). Intrinsic viscosity gave the hydrated micellar volume (Vh), volume of the hydrocarbon core (Vc), and volume of the palisade layer of the oxyethylene (OE) unit (VOE). SANS, as well as rheological data, supported the formation of nonspherical micelles with or without sugars. By SANS, we also observed that at the studied temperature intervals, oblate ellipsoid micelles changed into prolate ellipsoids and the number density of micelles decreased with an increase in temperature both in the presence and in the absence of sugars and also on increasing the concentration of sugars. Proton NMR showed a change in chemical shift of the OE group of micelles above the CMC. We also studied the phase separation of C12E10 by sugars in cloud point measurements.

Physical Structure of Planetary Nebulae. II. NGC 7662

We present a study of the structure and kinematics of the triple-shell planetary nebula NGC 7662 based on long-slit echelle spectroscopic observations and Hubble Space Telescope archival narrowband images. The structure of the main nebula consists of a central cavity surrounded by two concentric shells. The bright inner shell has a nonnegligible thickness and the highest density in the nebula. The outer shell is filled with nebular material whose density profile shows a ∝r-1 drop-off in the inner regions of the shell and flattens in the outermost regions. Both the inner and the outer shells can be described as prolate ellipsoids: the inner shell is more elongated, while the outermost layer of the outer shell expands faster. The physical structure of NGC 7662 is qualitatively consistent with the predictions of hydrodynamical simulations based on the interacting stellar wind models for planetary nebulae with a 0.605 M⊙ central star. Models with a higher asymptotic giant branch wind velocity are needed for detailed comparisons.

Unusually dense crystal packings of ellipsoids.

In this Letter, we report on the densest-known packings of congruent ellipsoids. The family of new packings consists of crystal arrangements of spheroids with a wide range of aspect ratios, and with density phi always surpassing that of the densest Bravais lattice packing phi approximately equal to 0.7405. A remarkable maximum density of phi approximately equal to 0.7707 is achieved for maximal aspect ratios larger than sqrt[3], when each ellipsoid has 14 touching neighbors. Our results are directly relevant to understanding the equilibrium behavior of systems of hard ellipsoids, and, in particular, the solid and glassy phases.

Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals.

We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation. The one-particle orientational distribution function rho((1)) (Omega) has a nontrivial dependence on the orientation Omega, in contrast to a liquid, and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations numerically for hard ellipsoids of revolution on a simple cubic lattice. Compared to molecular liquids, the orientational correlators in direct and reciprocal space exhibit less structure. However, depending on the lengths a and b of the rotation axis and the perpendicular axes of the ellipsoids, respectively, different behavior is found. For oblate and prolate ellipsoids with b greater, similar 0.35 (in units of the lattice constant), damped oscillations in distinct directions of direct space occur for some of the orientational correlators. They manifest themselves in some of the correlators in reciprocal space as a maximum at the Brillouin zone edge, accompanied by a maximum at the zone center for other correlators. The oscillations indicate alternating orientational fluctuations, while the maxima at the zone center originate from ferrorotational fluctuations. For a less, similar 2.5 and b less, similar 0.35, the oscillations are weaker, leading to no marked maxima at the Brillouin zone edge. For a greater, similar 3.0 and b less, similar 0.35, no oscillations occur any longer. For many of the orientational correlators in reciprocal space, an increase of a at fixed b or vice versa leads to a divergence at the zone center q=0, consistent with the formation of ferrorotational long-range fluctuations, and for some oblate and prolate systems with b less, similar 1.0 a simultaneous tendency to divergence of few other correlators at the zone edge is observed. Comparison of the orientational correlators with those from Monte Carlo simulations shows satisfactory agreement. From these simulations we also obtain a phase boundary in the a-b plane for order-disorder transitions.

Buoyancy measurements and vertical distribution of eggs of sardine (Sardina pilchardus) and anchovy (Engraulis encrasicolus)

Measurements were made of the density and settling velocity of eggs of sardine (Sardina pilchardus) and anchovy (Engraulis encrasicolus), using a density-gradient column. These results were related to observed vertical distributions of eggs obtained from stratified vertical distribution sampling in the Bay of Biscay. Eggs of both species had slightly positive buoyancy in local seawater throughout most of their development until near hatching, when there was a marked increase in density and they became negatively buoyant. The settling velocity of anchovy eggs, which are shaped as prolate ellipsoids, was close to predictions for spherical particles of equivalent volume. An improved model was developed for prediction of the settling velocity of sardine eggs, which are spherical with a relatively large perivitelline volume; this incorporated permeability of the chorion and adjustment of the density of the perivitelline fluid to ambient seawater. Eggs of both species were located mostly in the top 20 m of the water column, in increasing abundance towards the surface. A sub-surface peak of egg abundance was sometimes observed at the pycnocline, particularly where this was pronounced and associated with a low-salinity surface layer. There was a progressive deepening of the depth distributions for successive stages of egg development. Results from this study can be applied for improved plankton sampling of sardine and anchovy eggs and in modelling studies of their vertical distribution.

Characterization of recombinant soluble carcinoembryonic antigen cell adhesion molecule 1

Carcinoembryonic antigen cell adhesion molecule 1 (CEACAM1) is a type 1 transmembrane, homotypic cell adhesion protein expressed on epithelial and hematopoietic cells. CEACAM1 has four major isoforms with three or four immunoglobulin (Ig)-like ectodomains and either long or short cytoplasmic domains. In a 3D model of breast epithelial cell morphogenesis, CEACAM1 plays an essential role in lumen formation [J. Cell Sci. 112 (1999) 4193]. Two soluble ectodomain isoforms of CEACAM1 expressed in myeloma cells were immunologically active and highly glycosylated. The molecular weights of the 3-ecto- and 4-ectodomain isoforms were 90 and 110 kDa, respectively, and monomers by sedimentation equilibrium centrifugation. Both isoforms were prolate ellipsoids with axial ratios of 6 for the 3-ecto- and 8 for 4-ectodomain isoforms, respectively, by size exclusion chromatography and analytical ultracentrifugation. Both isoforms caused a significant reduction in lumen formation when tested in the 3D model culture system.

Recent Tectonic Deformations and Stresses in the Frontal Part of the Rif Cordillera and the Sa�ss Basin (Fes and Rabat Regions, Morocco)

Prerif Ridges are located at the frontal part of the Rif Cordillera, which develops at the Eurasian-African plate boundary. The ridges are formed by recent tectonic structures that also deform foreland basins (Saiss and Gharb basins) and the foreland (Moroccan Meseta). The position of the ridges is the consequence of inversion tectonics undergone in the area. The ENE-WSW trend of the northern edge of the Neogene Saiss basin is determined by the location of Mesozoic basins. Although Prerif ridges probably started to develop since the Early Miocene, the most active deformation phase affecting Pliocene rocks consisted of N-S to NW-SE oriented compression. Striated pebbles show that this compression has prolate stress ellipsoids. The deformation produces southwards vergent folds and NNW-SSE striae on reverse faults at the base of the ridges. The flexure of the Paleozoic basement by the emplacement of the Ridges produced extensional deformation and the development of the Saiss foreland basin. The extension in this basin is oblate and features a well determined NNE-SSW trend near the Ridges, whereas it becomes prolate and pluridirectional near the foreland edge represented by the Rabat region. This part of the Moroccan Meseta, commonly considered to be stable, is deformed by sets of orthogonal joints and faults with short slip that affect up to Quaternary sediments. Southwestward, the Meseta rocks are also deformed by transcurrent faults, which indicate NW-SE and N-S trends of compression. The NW-SE approximation of Eurasia and Africa determines a regional stress field with the same trend of compression. Regional stresses are notably disturbed by the development of the active structures in the Rif, which exhibit alternating trends of compression and extension. The clearest evidence of the relationship between the local deformation and the general plate motion is found at the deformation front of the Cordillera, that is, the Prerif Ridges.

The puzzle of axis-normal magnetic lineations in folded low-grade sediments (Bude Formation, SW England)

Abstract A single upright, open anticline from sub-greenschist facies sedimentary rocks of the Bude Formation (Cornwall, UK) was sampled in order to investigate the kinematic relationships between fold development and anisotropy of magnetic susceptibility (AMS). The mean magnetic susceptibility of these samples is 0.25 × 10 −3 SI, suggesting low concentrations of ferromagnetic phases. AMS ellipsoids have a mean corrected anisotropy degree of 1.03 and a mean shape parameter of −0.54 (prolate). K min and K int define a girdle distribution striking sub-parallel to the fold axial plane, with K min tending to cluster around the fold axis. K max axes from both limbs of the fold define a cluster with a mean azimuth perpendicular to the fold axis. This arrangement of K max and K min could represent an inverse magnetic fabric of composite primary/tectonic origin. This is discounted, however, on the basis of broad correlation between the orientation of AMS and AIRM (anisotropy of isothermal remanence) ellipsoids. The prolate shapes and axis-normal orientation of K max axes contrast markedly with the widely observed relationship of AMS ellipsoids in folds, which are typically oblate and have K max parallel to the fold axis. This relationship is interpreted to represent progressive overprinting of primary depositional/compactional fabrics ( K min perpendicular to bedding) by a tectonic fabric ( K min perpendicular to cleavage). Consistency of K max orientations irrespective of position within the fold clearly points to a fabric of tectonic origin. Prolate ellipsoids with long axes perpendicular to the fold hinge line are indicative of superimposed sub-horizontal stretching at a late stage or post-dating fold formation. Such a situation is not inconsistent with superimposed southward-directed thrusting simple shear that has been suggested in this area to account for variations in fold attitude on a regional scale. It is more likely, however, that the fabric reflects post-orogenic extension, with the fold occupying a position in the immediate hanging-wall of a major northward dipping normal fault. In either case, the AMS fabrics around the fold record only the last increments of deformation in this area, with earlier primary and fold-related fabrics being entirely obliterated.

The anisotropy of magnetic susceptibility (AMS) in low-grade, cleaved pelitic rocks: influence of cleavage/bedding angle and type and relative orientation of magnetic carriers

Abstract Cambrian and Silurian, low-grade, pelitic rocks of the single-phase deformed Brabant Massif consistently have a maximum magnetic susceptibility axis (K1) parallel to the cleavage/bedding intersection. In contrast, the minimum susceptibility axis (K3) either coincides with the bedding pole, with the cleavage pole or occupies an intermediate position. Anisotropy of anhysteretic remanence (AARM) and X-ray pole figure goniometry allow the distinguishing of the orientation distributions of the ferromagnetic and paramagnetic (white mica and chlorite) carriers, respectively. Mismatches between K3 and the poles to the macroscopic fabric elements (i.e. bedding and cleavage) are attributed to different orientations of the different magnetic ( s.l. ) carriers. A strong relationship exists between the cleavage/bedding angle and the shape parameter: low, respectively high angles leading to oblate, respectively prolate susceptibility ellipsoids. However, differences are observed between the Cambrian and Silurian samples in terms of the shape parameter and the behaviour of the degree of anisotropy with changing cleavage/bedding angle. This is tentatively attributed to differences in relative orientation and mineralogy of the magnetic ( s.l. ) carriers. These results demonstrate the influence of the relative orientation of the different carriers on AMS and suggest that, although being a petrofabric tool, AMS cannot be used as a strain gauge in the case of composite magnetic fabrics.

Characterizing Isoparaffin Transport Properties with Stokes−Einstein Relationships

We present extensive molecular dynamics simulation results for self-diffusion and viscosity for isoparaffins between C6 and C16 and examine the ability of several forms of Stokes−Einstein relationships to link the transport properties in a coherent framework. Based on a hydrodynamic model for drag past prolate ellipsoids in the slip limit, much of the variation between diffusion and viscosity can be explained as a function of molecular structure. For pure species, we demonstrate how one can exploit the linearity of the Stokes−Einstein relationship to make quantitative, extrapolative predictions of viscosity from computer simulations based on the self-diffusion coefficient and systematic characterization of the molecule's gyration ellipsoid.

Relationship between AMS and folding in an area of superimposed folding (Cotiella-Bóixols nappe, Southern Pyrenees)

We present the results of anisotropy of magnetic susceptibility (AMS) analysis carried out in weakly deformed, Upper Cretaceous marine marls from the Southern Pyrenees. The data refer to 23 sites distributed in the fine-grained intervals of the Vallcarga and Barbaruens formations, extending along the hangingwall and footwall of the Cotiella-Bóixols thrust. The observed magnetic fabrics are typical of early stages of deformation, and show oblate, triaxial and prolate magnetic ellipsoids. In most of the sites, a magnetic foliation parallel to bedding can be observed. A well-defined magnetic lineation, which is correlated with the main tectonic features of the studied region, can be recognised. We interpret the observed magnetic fabric as related to a tectonic overprint on an original, compaction, sedimentary fabric. The tectonic AMS fabric is related to the superimposition of two sequential, and non-coaxial fold-and-thrust events: N–S to NNW–SSE folding, related to oblique ramps of Late Cretaceous thrusts, and WNW–ESE folding, related to the main, Eocene Pyrenean thrusting stage.

Strain partitioning in transpressive shears zones in the southern branch of the Variscan Ibero-Armorican arc

The Torre de Moncorvo region (NE Portugal) is a key-sector of the Autochthon Domain of the Iberian Terrane. The region experienced Variscan deformation in the southern branch of the Ibero-Armorican Arc wherein the early structures (of Upper Devonian age—D 1) denotes the establishment of a heterogeneous sinistral transpressive regime. This regime was also responsible for the development of large-scale left-lateral shear zones whose direction is subparallel to major folds. Finite strains analyses were carried out in the Torre de Moncorvo region using the normalised Fry method on different strain markers: (1) distribution of detrital quartz grains in quartzite rocks of Arenigian–Lanvirnian age; (2) arrangement of oolites in discontinuous Ordovician–Silurian ironstone horizons; (3) the rotation experienced by Skolithos preserved in Lower Ordovician metasedimentary clastic rocks. The results obtained indicate the predominance of slightly prolate strain ellipsoids. Nevertheless, the variation of their orientation around mesoscopic folds emphasises the role of strain partitioning in a transpressive regime, suggesting that different folding mechanisms were active in the course of the same deformation phase. For the studied cases, tangential longitudinal strain and flexural shear combined with regional sinistral shear seem to be the most common mechanisms of folding. Some of these three-dimensional theoretical models for strain patterns in folds could be used in other regions, where a transpressive regime is inferred.

Vortical flow between rotating ellipsoids

Experimental results on incompressible viscous flows in the gap between rotating spheroids are presented. Oblate ellipsoids are discussed as a connecting link between a sphere and a disk, while a prolate ellipsoid represents the geometrical intermediate stage between a sphere and a cylinder. The axes ratios of the ellipsoids are A : B=2 : 1 and A : B=1 : 2, respectively. The basic flow field and the occurring instabilities in form of Taylor- and cross-flow vortices have been studied by flow visualization. The common properties and their differences regarding the various flow patterns of the disks, spheres, cylinders as well as of the oblate and prolate ellipsoids are treated. The location of the generation of the different vortex systems at the various rotating bodies is determined. A comparison of the friction torque for these bodies of rotation is given by diagrams. Finally, the theoretically derived curves for the friction torque of the disks, spheres and cylinders are compared with the experimentally obtained data for the oblate and prolate ellipsoids.

The Shape Parameter of Liposomes and DNA-Lipid Complexes Determined by Viscometry Utilizing Small Sample Volumes

A minicapillary viscometer utilizing <0.5 ml of sample at a volume fraction of <0.1% is described. The calculated a/b of DPPC/DPPG multilamellar liposome was 1.14 as prolate ellipsoids and a/ b of dioleoylpropyltrimethyl ammonium methylsulfate-DNA complex at a charge ratio of 4:1 (+/−) was 3.7 as prolate ellipsoids or 4.9 as oblate ellipsoids. The deviation of shape from perfect sphere is thus expressed quantitatively in more than two significant figures. In these measurement, the necessary amount of DNA is <0.5 mg.

Magnetic properties of regular arrays of non-spherical ferromagnetic nanogranules

Magnetic properties (ground state, magnetic phase diagram, phase transitions in a magnetic field) of two- and three-dimensional lattices of ferromagnetic granules with dipole intergranule interaction are studied. The basic attention is given to lattices of non-spherical granules (prolate and oblate ellipsoids of revolution) and their limiting shapes—rod-like and disk-like granules. The analysis shows that conclusions of the theory agree with results of a series of experiments.

Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow

A new boundary-integral algorithm for the motion of a particle between two parallel plane walls in Poiseuille flow at low Reynolds number was developed to study the translational and rotational velocities for a broad range of particle sizes and depths in the channel. Instead of the free-space Green’s function more commonly employed in boundary-integral equations, we used the Green’s function for the domain between two infinite plane walls [Liron and Mochon, J. Eng. Math. 10, 287 (1976)]. This formulation allows us to directly incorporate the effects of the wall interactions into the stress tensor, without discretizing the bounding walls, and use well-established iterative methods. Our results are in good agreement with previous computations [Ganatos et al., J. Fluid Mech. 99, 755 (1980)] and limiting cases, over their range of application, with additional results obtained for very small particle–wall separations of less than 1% of the particle radius. In addition to the boundary-integral solution in the mobility formulation, we used the resistance formulation to derive the near-field asymptotic forms for the translational and rotational velocities, extending the results to even smaller particle–wall separations. The decrease in translational velocity from the unperturbed fluid velocity increases with particle size and proximity of the particle to one or both of the walls. The rotational velocity exhibits a maximum magnitude between the centerline and either wall, due to the competing influences of wall retardation and the greater fluid velocity gradient near the walls. The average particle velocity for a uniform distribution of particles was generally found to exceed the average fluid velocity, due in large part to exclusion of the particle centers from the region of slowest fluid near the walls. The maximum average particle velocity is 18% greater than the average fluid velocity and occurs for particle diameters that are 42% of the channel height; particles with diameters greater than 82% of the channel height have smaller average velocities than does the fluid, due to the retarding effects of the nearby walls. Additionally, the translational and rotational velocities of oblate and prolate ellipsoids were calculated using the boundary-integral algorithm. The proximity of the walls to the ellipsoids was found to have a strong effect on particle velocity, so that a prolate spheroid aligned on the channel centerline moves faster than an oblate spheroid of the same volume, because the edge of the latter spheroid is closer to the channel walls. For off-centerline locations for a prolate spheroid with its major axis at an angle to the walls, a second translational velocity component normal to the walls is present. For each lower-wall gap examined, the maximum normal translational velocity occurs for smaller gaps from the upper wall (i.e., larger angle). The direction of this velocity component changes sign for mid-range angles studied, due to increased interactions with the lower wall that prevent the ellipsoid from rotating upward and, hence, yield a negative velocity perpendicular to the walls. The rotational velocity changes direction for particles at the smallest angles studied, due to the competition between the Poiseuille fluid velocity profile, which pushes the particle clockwise, and the lubrication forces, which impede this rotation.