Oblate Ones Research Articles

Effect of slip-induced fluid inertial torque on the angular dynamics of spheroids in a linear shear flow

The angular dynamics of tiny spheroidal particles in shear flows have been widely investigated, but most of the studies mainly focus on the effect of strong shear, while the combined effect of both shear and slip velocity at the center of the particle has been less considered. Actually, the fluid inertial torque induced by the slip velocity between particle and fluid plays a significant role in spheroid angular dynamics. However, it is difficult to investigate these dynamics theoretically until the analytical expression of the fluid inertial torque at a small Reynolds number was derived by Dabade et al. [J. Fluid Mech. 778, 133–188 (2015)]. In this study, the effect of the fluid inertial torque on the particle rotations is considered in a linear shear flow with a small streamwise slip velocity at the center of the particle. We find that as the fluid inertial torque dominates, the prolate spheroids tend to logroll while oblate ones have a tendency to tumble or align to a direction with a relative angle to the streamwise direction. These results are opposite to the earlier results in the absence of the fluid inertial torque. Different ultimate rotation modes of spheroids are dependent on the relative importance between the fluid inertial torque and the particle inertia, as well as the initial orientations. This reflects a non-trivial effect of fluid inertial torque on the angular dynamics of inertial spheroidal particles.

Influence of Block form on the Shear Behaviour of Soft Soil–Rock Mixtures by 3D Block Modelling Approaches

The influence of block forms on the shear behaviour of soil–rock mixtures with soft blocks (soft S–RMs) can be efficiently investigated by the discrete element method (DEM) on the basis of accurate 3D models accounting for the block breakage. This paper proposes a novel modelling approach, based on the spherical harmonics series, for the generation of 3D block geometries with different forms but same convexity and angularity. An already existing non-overlapping modelling approach was improved, characterized by a reduced computational cost, for the set-up of 3D block DEM models accounting for the block breakage. A number of soft S–RM DEM samples, subjected to numerical direct shear tests, were generated to analyze the influence of block forms and volumetric block proportion VBP on the mesoscopic and macroscopic behaviours. The results showed that the breakage degree is maximum for the spheroidal blocks, followed by the oblate, prolate and blade ones, due to the combined influence of the block frictional sliding and rotation. The shear strength of soft S–RMs is mainly controlled by the block interlocking and breakage, being maximum in the case of spheroidal block samples when the applied normal stress is low and in the case of prolate and blade ones for a high normal stress. It was found that a nonlinear Mohr–Coulomb criterion can provide a good description of the shear strength envelope of soft S–RMs. Soft S–RMs are characterized by a higher friction angle if composed by spheroidal and prolate blocks when the VBP is 40%, due to their elevated block interlocking, and in the case of prolate and blade blocks when the VBP is 60% at the higher normal stress, due to their lower block breakage degree.

Rotation of anisotropic particles in Rayleigh–Bénard turbulence

Abstract

Numerical investigation on the mutual interaction between heat transfer and non-spherical particle dynamics in the blast furnace raceway

In this paper, the coupled computational fluid dynamics (CFD) and discrete element method (DEM) scheme is used to investigate the microstructure and heat transfer characteristics in a blast furnace (BF) raceway. The impact of gas velocity and particle shape on raceway evolution, microstructure characteristics, and particle temperature and voidage distributions is comprehensively explored based on the voidage change caused by the consumption of coke particles. Numerical results show that the oblate ellipsoidal particle system possesses higher average voidage in the original packing state and implements the faster burden descending rate than the prolate one under the same inlet velocity. For the non-spherical particle systems, larger contact forces exist in the oblate ellipsoidal particle system while the contact forces in the prolate ellipsoidal particle system are smaller. More uniform temperature distribution and higher average voidage can be caused by higher inlet gas velocities. Meanwhile, more prolate ellipsoidal particles are consumed than oblate ones under the same inlet velocity. These findings could be beneficial for understanding the kinetic and thermodynamic behaviors of particulate system within a BF raceway.

Settling tracer spheroids in vertical turbulent channel flows

The motion of particles settling in turbulence is an intriguing problem, which is relevant to an in-depth understanding of planktons in marine flows or the design of photobioreactors. This work studies the motion, orientation and distribution of inertia-less spheroidal particles settling in vertical channel flows by direct numerical simulations. We show that, compared to spherical tracers, the settling velocity of spheroidal tracers is enhanced due to preferential orientation and local clustering (not due to particle inertia, in the present case). Prolate spheroids tend to align their symmetry axes in the direction of gravity while oblate ones align perpendicular to it. Both kinds of particles attain a larger slip velocity in the direction of gravity and, therefore, settle faster. We also show that particles sample preferentially regions of high fluid velocity in downward flow and regions of low fluid velocity in upward flow. Such preferential sampling, which also contributes to the enhancement of settling, is the result of clustering. Besides, tracer particles are observed to accumulate in the channel center in downward flow and near the wall in upward flow: We show that tracer transport in the wall-normal direction is controlled by the particle-to-fluid slip velocity and by clustering. The slip velocity dominates the transport initially, but tracers increasingly cluster in regions with opposite flow direction as they accumulate either in the channel center or near the wall. Clustering appears to be associate with the coherent structures that characterize wall turbulence, and tracer distribution in the wall-normal direction is found to reach a steady state when the two qualitatively different mechanisms balance each other.

Spin states of electrons in quantum dots upon heating. Simulation by the Feynman path integral method. Magnetic properties

Temperature dependences of spin states and spin paramagnetic susceptibility in ellipsoidal quantum dots (QDs) containing two or three electrons are numerically simulated using ab initio calculations based on the Feynman path integral method. Limits of the thermal stability of spin states are estimated. Upon cooling, the pairing of spins of an electron pair is most intense in spherical QDs; notably, prolate QDs hinder the pairing more strongly than the oblate ones. When the spherical shape of a QD is distorted, a characteristic peak in the temperature dependence of the electron-pair magnetic susceptibility shifts to lower temperatures. A spin of the system of three electrons may either increase or decrease upon cooling, depending on the QD shape. In the case of three electrons, strong spatial anisotropy of the electron-confining field causes a relative decrease in the energy of states with large spin values.

Anisotropy of spin–spin and spin–lattice relaxation times in liquids entrapped in nanocavities: Application to MRI study of biological systems

Spin–spin and spin–lattice relaxations in liquid or gas entrapped in nanosized ellipsoidal cavities with different orientation ordering are theoretically investigated. The model is flexible in order to be applied to explain experimental results in cavities with various forms, from very prolate up to oblate ones, and different degree of ordering of nanocavities.In the framework of the considered model, the dipole–dipole interaction is determined by a single coupling constant, which depends on the form, size, and orientation of the cavity and number of nuclear spins in the cavity. It was shown that the transverse and longitudinal relaxation rates differently depend on the angle between the external magnetic field and cavity main axis.The calculation results for the local dipolar field, transverse and longitudinal relaxation times explain the angular dependencies observed in MRI experiments with biological objects: cartilage and tendon. Microstructure of these tissues can be characterized by the standard deviation of the Gaussian distribution of fibril orientations. The comparison of the theoretical and experimental results shows that the value of the standard deviation obtained at the matching of the calculation to experimental results can be used as a parameter characterizing the disorder in the biological sample.

Effect of orientational restriction on monolayers of hard ellipsoids.

The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using the Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross section areas of the particles with the plane. In the lack of out-of-plane orientational freedom the monolayer of prolate particles is identical to a two-dimensional hard ellipse system, which undergoes an isotropic-nematic ordering transition with increasing density. With gradually switching on the out-of-plane orientational freedom the prolate particles lean out from the confining plane and destabilisation of the in-plane isotropic-nematic phase transition is observed. The system of oblate particles behaves oppositely to that of prolates. It corresponds to a two-dimensional system of hard disks in the lack of out-of-plane freedom, while it behaves similar to that of hard ellipses in the freely rotating case. Solid phases can be realised by lower surface coverage due to the out-of-plane orientation freedom for both oblate and prolate shapes.

Nilsson-SU3 self-consistency in heavy N=Z nuclei

It is argued that there exist natural shell model spaces optimally adapted to the operation of two variants of Elliott' SU3 symmetry that provide accurate predictions of quadrupole moments of deformed states. A selfconsistent Nilsson-like calculation describes the competition between the realistic quadrupole force and the central field, indicating a {\em remarkable stability of the quadruplole moments}---which remain close to their quasi and pseudo SU3 values---as the single particle splittings increase. A detailed study of the $N=Z$ even nuclei from $^{56}$Ni to $^{96}$Cd reveals that the region of prolate deformation is bounded by a pair of transitional nuclei $^{72}$Kr and $^{84}$Mo in which prolate ground state bands are predicted to dominate, though coexisting with oblate ones,

Influence of aggregate shapes on drying and carbonation phenomena in 3D concrete numerical samples

This study aims at generating numerical 3D samples of concrete so as to study the effects of the granular inclusions shape on the macroscopic kinetics of reactive transport phenomena. Two types of mesostructure configurations are considered: the first one is composed of a matrix of mortar in which are randomly distributed inclusions corresponding to the concrete coarse aggregates, and the second one also includes a steel rebar. The choice of a mesoscopic modeling for the mortar matrix is based on the need to obtain numerical structures of reasonable size. In particular, the Interfacial Transition Zones (ITZs) are assumed to be incorporated into the homogenized mortar properties. This study is applied to the case of drying and atmospheric carbonation by using simplified models solved by the finite element code Cast3M. The purpose is to quantify the influence of the aggregate shape on the kinetics of macroscopic transfer and the isovalue lines for some physical variables representative of the reactive transport problems: saturation degree for drying, and porosity, calcite and portlandite concentrations for carbonation. Basic aggregates shapes are studied (spheres, cubes), as well as more complex ones (Voronoi particles) which are supposed to be more representative of real aggregates. The effects of ‘non-isotropic’ shapes (oblate and prolate ones) are also investigated. It is shown that the influence of the aggregate shapes appears negligibly small on macroscopic indicators, except for oblate shapes with aspect ratios of 3. This latter case also exhibits substantial local delayed effects and a more important variability, which may have some importance for a precise description and estimation of degradation processes related to steel rebar corrosion.

Effect of tumor shape and size on drug delivery to solid tumors

Tumor shape and size effect on drug delivery to solid tumors are studied, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for predefined tumor geometries. The governing equations are solved using a numerical method, the element-based finite volume method. Interstitial fluid pressure and velocity are used to show the details of drug delivery in a solid tumor, under an assumption that drug particles flow with the interstitial fluid. Drug delivery problems have been most extensively researched in spherical tumors, which have been the simplest to examine with the analytical methods. With our numerical method, however, more complex shapes of the tumor can be studied. The numerical model of fluid flow in solid tumors previously introduced by our group is further developed to incorporate and investigate non-spherical tumors such as prolate and oblate ones. Also the effects of the surface area per unit volume of the tissue, vascular and interstitial hydraulic conductivity on drug delivery are investigated.

Assessment of hollow spheroid models for ductile failure prediction by limit analysis and conic programming

Abstract Several extensions of the Gurson model have been proposed such as to account for void shape effects (e.g. Gologanu, M., Leblond, J., 1993. Approximate models for ductile metals containing non-spherical voids – case of axisymmetric prolate ellipsoidal cavities. Journal of the Mechanics and Physics of Solids 41 (11), 1723–1754; Gologanu, M., Leblond, J., Perrin, G., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids – case of axisymmetric oblate ellipsoidal cavities. Journal of Engineering Materials and Technology 116, 290–297; Gologanu, M., Leblond, J., Perrin, G., Devaux, J., 1997. Recent extensions of Gurson's model for porous ductile metals. In: Suquet, P. (Ed.), Continuum Micromechanics, Springer Verlag; Garajeu, M., Suquet, P., 1997. Effective properties of porous ideally plastic or viscoplastic materials containing rigid particles. Journal of the Mechanics and Physics of Solids 45, 873–902 and more recently by Monchiet, V., Charkaluk, E., Kondo, D., 2007. An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields. Comptes Rendus Mecanique 335, 32–41). The main goal of this study is to assess the latter models by establishing relevant numerical LA-type lower and upper bounds to the exact solutions for 3D stress and strain conditions. Numerical limit analysis techniques are extended to the case of spheroid cavities under various 3D loading conditions. First numerical tests for the hollow sphere (Gurson) model were performed to verify the computational efficiency of the new codes. A second series of tests, performed for uniform strain rate boundary conditions and axisymmetric loadings, allowed to assess the criteria proposed by Gologanu et al. in the case of prolate voids as well as oblate ones. It is shown that the 1997-Gologanu et al. criterion appears to be very accurate for the above boundary conditions. For the assessment of a recent criterion derived by Monchiet et al. (2007), we performed other computations corresponding to uniform stress boundary conditions for both oblate and prolate cavities. It is shown that the Monchiet et al. (2007) criterion appears to be an estimate which may be improved. However, this criterion is very accurate when compared to the numerical results with strain rate boundary conditions. Finally a first attempt with 3D-loadings seems to confirm the above conclusions.

Dynamics of particles around a pseudo-Newtonian Kerr black hole with halos

The regular and chaotic dynamics of test particles in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is detailed. In particular, the dependence of dynamics on the quadrupolar parameter of the halos and the spin angular momentum of the rotating black hole is studied. It is found that the small quadrupolar moment, in contrast with the spin angular momentum, does not have a great effect on the stability and radii of the innermost stable circular orbits of these test particles. In addition, chaos mainly occurs for small absolute values of the rotating parameters, and does not exist for the maximum counter-rotating case under some certain initial conditions and parameters. This means that the rotating parameters of the black hole weaken the chaotic properties. It is also found that the counter-rotating system is more unstable than the co-rotating one. Furthermore, chaos is absent for small absolute values of the quadrupoles, and the onset of chaos is easier for the prolate halos than for the oblate ones.

GENERATING ANISOTROPIC FLUIDS FROM VACUUM ERNST EQUATIONS

Starting with any stationary axisymmetric vacuum metric, we build anisotropic fluids. With the help of the Ernst method, the basic equations are derived together with the expression for the energy–momentum tensor and with the equation of state compatible with the field equations. The method is presented by using different coordinate systems: the cylindrical coordinates ρ, z and the oblate spheroidal ones. A class of interior solutions matching with stationary axisymmetric asymptotically flat vacuum solutions is found in oblate spheroidal coordinates. The solutions presented satisfy the three energy conditions.

Shape-factor effect on melting in an elliptic capsule

An approximate mathematical model of contact melting of an unfixed material in an elliptical capsule is developed. The main characteristic scales and non-dimensional parameters which describe the principal features of the melting process are found. Choosing a special heat flux distribution on the wall of the capsule allows us to derive a closed-form evolution equation for the motion of the solid accounting for the energy convection in the liquid, expressed through the non-linearity of the temperature distribution across the molten layer. It is shown that the melting rate of the solid depends on the shape of the capsule. Generally, elliptical capsules show higher rate of melting than circular ones. Elongated capsules provide more effective melting than oblate ones, even though they have the same aspect ratios and vertical cross-sectional areas. This phenomenon is caused by the fact, that the pressure necessary to support the solid is larger for the elongated capsules than that for oblate ones, which leads to thinning of the molten layer along with the increase of the heat flux across it. The time required for complete melting can be achieved by the right choice of the shape of the capsule, which is specified by the value of the aspect ratio. The found influence of the capsule shape on the melting rate can be used for design and optimization of practical latent-heat–thermal-energy systems.

Power series expansions for spheroidal wave functions with small arguments

Power series expansions for the angular spheroidal wave functions of the first kind S mn ( c, η), with small arguments c, are derived for general integer values of m and n. The various evaluated expansion coefficients can also be used in the calculation of the corresponding angular functions of the second kind, as well as for the radial functions of any kind. Only the prolate functions are considered explicitly, but corresponding formulas for the oblate ones are obtained immediately.

Prolate dominance of nuclear shape caused by a strong interference between the effects of spin-orbit andl2terms of the Nilsson potential

The origin of the dominance of prolate shapes over oblate ones of the ground states of atomic nuclei is investigated with the Nilsson-Strutinsky method. The number of prolate nuclei among all the deformed even-even nuclei is calculated as a function of the strengths of the spin-orbit and the ${l}^{2}$ terms of the Nilsson potential. The latter simulates a square-well-like radial profile of the mean potential. The proportion of prolate nuclei is 86% with the standard strengths corresponding to the actual atomic nuclei. By weakening the spin-orbit potential, the proportion oscillates strongly, having a local minimum value of 42% with about half of the standard strength and a local maximum value of 79% without the spin-orbit potential.

Classically dynamical behaviour of a nucleon in heavy nuclei

Within the framework of the two-center shell model the classically dynamical behaviour of a nucleon in heavy nuclei is investigated systematically with the change of nuclear shape parameters for the first time. It is found that as long as the nucleonic energy is appreciably higher than the height of the potential barrier there is a good quantum-classical correspondence of nucleonic regular (chaotic) motion. Thus, Bohigas, Giannoni and Schmit conjecture is confirmed once again. We find that the difference between the potential barrier for prolate nuclei and that for oblate ones is reponsible for the energy-dependence difference between the nucleonic chaotic dynamics for prolate nuclei and that for oblate ones. In addition, it is suggested that nuclear dissipation is shape-dependent, and strong nuclear dissipation can be expected for medium or large separations in the presence of a considerable neck deformation built on a pronounced octupole-like deformation, which provides us a dynamical understanding of nuclear shape dependence of nuclear dissipation.

Relative population of oblate and prolate structures in189Au

High spin states of189Au were populated via the174Yb (19F, 4n reaction at 86, 90, 95 and 100 MeV beam energies. The study of the relative population of oblate and prolate structures shows a striking disappearance of the prolate band relative to the oblate ones as the beam energy goes from 86 to 100 MeV.

Band-edge absorption and luminescence of nonspherical nanometer-size crystals.

The effect of nonspherical shape on the optical properties of semiconductor microcrystals with a degenerate valence band has been theoretically studied. The asymmetry of microcrystals leads to a splitting of the fourfold-degenerate ground hole state into two twofold-degenerate ones. The value of this splitting is proportional to the deviation from sphericity and inversely proportional to the square of the microcrystal size, and is the function of the ratio of light- to heavy-hole effective masses (\ensuremath{\beta}). This splitting could lead to the formation of long-lived electron-hole pairs in the prolate microcrystals of semiconductors with small \ensuremath{\beta} and in the oblate ones with \ensuremath{\beta}>0.14.