Stationary Orientation Research Articles

Inertial effects on fibre motion in simple shear flow

The motion of a torque-free slender axisymmetric fibre in simple shear flow is examined theoretically for small but finite ${\textit{Re}}$, where ${\textit{Re}}$ is the Reynolds number based on the fibre length, and is a measure of the inertial forces in the fluid. In the limit of zero inertia, an axisymmetric particle in simple shear is known to rotate indefinitely in any of an infinite single-parameter family of periodic orbits, originally found by Jeffery (1922) – a degenerate situation wherein the particular choice of orbit is dictated by the initial orientation of the particle. We use a generalization of the well-known reciprocal theorem for Stokes flow to derive the orbit equations, to $O({\textit{Re}})$, for the slender fibre. The structure of the equations bears some resemblance to those previously derived by Leal (1975) for a neutrally buoyant fibre in a viscoelastic (second-order) fluid. It is thereby shown that fluid inertia, for small ${\textit{Re}}$, leads to a slow $O({\textit{Re}})$ drift of the rotating fibre toward the shearing plane, thereby eliminating the aforementioned degeneracy. For Reynolds numbers above a critical value, ${\textit{Re}}_c\,{=}\, ({15}/{4 \pi})(\ln \kappa/\beta \kappa)\sin^{-2}\theta$, the fibre ceases to rotate, however, instead drifting monotonically towards the shearing plane. The limiting stationary orientation in the flow–gradient plane makes an angle $\phi_f$ with the flow direction, where $\phi_f \,{=}\, 4\pi {\textit{Re}}/(15 \ln \kappa) + \{16 \pi {\textit{Re}}^2/(225(\ln \kappa)^2-1/(\beta^2\kappa^2) \}^{1/2}$ is an increasing function of ${\textit{Re}}$. Here, $\kappa$ is the fibre aspect ratio, $\theta$ is the angle made by the fibre with the vorticity axis, and $\beta$ is an $O(1)$ coefficient related to the Jeffery period of the rotating fibre.

Structure and orientation of the moving vortex lattice in clean type-II superconductors

The dynamics of the moving vortex lattice is considered in the framework of the time-dependent Ginzburg-Landau equation neglecting the effects of pinning. At high flux velocities the pinning dominated dynamics is expected to crossover into the interactions dominated dynamics for very clean materials recently studied experimentally. The stationary lattice structure and orientation depend on the flux flow velocity. For relatively velocities $V<{V}_{c}=\sqrt{8\ensuremath{\pi}B∕{\ensuremath{\Phi}}_{0}}∕\ensuremath{\gamma}$, where $\ensuremath{\gamma}$ is the inverse diffusion constant in the time-dependent Ginzburg-Landau equation, and the vortex lattice has a different orientation than for $V>{V}_{c}$. The two orientations can be desribed as motion ``in channels'' and motion of ``lines of vortices perpendicular to the direction of motion.'' Although we start from the lowest Landau level approximation, corrections to conductivity and the vortex lattice energy dissipation from higher Landau levels are systematically calculated and compared to a recent experiment.

Canal–Otolith Interactions After Off-Vertical Axis Rotations. II. Spatiotemporal Properties of Roll and Pitch Postrotatory Vestibuloocular Reflexes

We have examined the spatiotemporal characteristics of postrotatory eye velocity after roll and pitch off-vertical axis rotations (OVAR). Three rhesus monkeys were placed in one of 3 orientations on a 3-dimensional (3D) turntable: upright (90 degrees roll or pitch OVAR), 45 degrees nose-up (45 degrees roll OVAR), and 45 degrees left ear-down (45 degrees pitch OVAR). Subjects were then rotated at +/-60 degrees /s around the naso-occipital or interaural axis and stopped after 10 turns, in one of 7 final head orientations, each separated by 30 degrees . We found that postrotatory eye velocity showed horizontal-vertical components after roll OVAR and horizontal-torsional components after pitch OVAR that varied systematically as a function of final head orientation. The quantitative analysis suggests that, in contrast to the analogous yaw OVAR paradigm, a system of up to 3 real, gravity-dependent eigenvectors and eigenvalues determines the spatiotemporal characteristics of the residual eye velocities after roll and pitch OVAR. One of these eigenvectors closely aligned with gravity, whereas the other 2 determined the orientation of the earth horizontal plane. We propose that the spatial characteristics of eye velocity after roll and pitch OVAR follow the physical constraints of stationary orientation in a gravitational field and reflect the brain's best estimate of head-in-space orientation within an internal representation of 3D space.

Hydrodynamic formation of stable anisotropic structures in Couette flow of dilute suspension

The problem of rotary motion of rigid axially symmetric elongated particles in the Couette flow of dilute suspension with anisotropic carrier fluid is solved. It is shown that the stable stationary solutions of the dynamical set of ordinary differential equations describing the particles rotary motion are possible in the case of forming the stationary anisotropy in the carrier fluid of the suspension. It allows us to detect the stationary orientation of suspended particles and formation of stable anisotropic liquid-crystalline structures in the considered suspension under the action of hydrodynamic forces. The study of rheological properties of such a structured suspension shows that it behaves as a viscoelastic quasi-Newtonian anisotropic liquid medium. To cite this article: E.Yu. Taran et al., C. R. Mecanique 332 (2004).

Role of Light Polarization in the Optothermal Effect

It is shown that the highest optothermal effect in low-intensity irradiation is attained on chromophores of stationary orientation exposed to irradiation by a linearly polarized light. For chromophores with stochastization of orientation between the events of light absorption, the magnitude of the optothermal effect is independent of polarization and is three times lower than in stationary orientation. In anisotropic media, an optimally oriented linearly polarized light is more efficient.

Formation of composite materials in gradient flows of suspensions

The rheological constitutive equations for dilute suspension of rigid axisymmetric elongated particles immersed in the Ericksen anisotropic fluid are obtained within the framework of a structure–phenomenological approach. As a hydrodynamic model of suspended particles possessing zero buoyancy, a symmetric triaxial dumbbell is used. The effect of anisotropy of the suspension carrier fluid is investigated on the dynamics of suspended particles and on the rheological properties of the suspension in simple shear flow. A stationary orientation of the elongated suspended particles under the action of hydrodynamic forces is found. These results offer the possibility of formation of composite materials by friction forces arising in gradient flows of a dilute suspension of axisymmetric rigid particles with anisotropic carrier fluid.

Features of the Formation of Composite Materials in Anisotropic Liquid Systems with Elongated Suspended Particles

The equations of rotational motion of nondeformable spherical and axisymmetric elongated particles and a rheologic equation for stresses in arbitrary gradient flows of dilute suspensions of such particles in an anisotropic carrying fluid are obtained within the framework of a structural-phenomenological approach. As a rheologic model of the suspension-carrying fluid and a hydrodynamic model of the suspended particles, we use the Ericksen simple anisotropic fluid and a symmetric triaxial dumbbell, respectively. The constitutive equations obtained are used to study the effect of anisotropy of the carrying fluid on the dynamics of suspended particles and on the rheologic properties of suspensions in a simple shear flow. A stationary orientation of the elongated suspended particles under the action of hydrodynamic forces is discovered. The possibility of applying this phenomenon to the formation of composite materials is discussed.

Numerical Analysis of the Rheology of Polymeric Liquid Crystals. (2nd Report, Shear and Extensional Flow Behavior).

The Doi equations have been directly computed for shear and extensional flow without closure approximations. An extension is imposed on the shear flow plane. It is well-known that for simple shear flow there are three orientation regimes, depending on the magnitude of shear rate; rotational (tumbling), oscillatory (wagging), and stationary (aligning) orientation behaviors. When we add an extension to simple shear flow, the time period of tumbling is increased, while the order parameter in the regime is almost unchanged. In the wagging regime, however, both the time period and the order parameter are increased. Transitions from the tumbling and wagging regimes to the aligning regime are induced when more than a certain magnitude of extension is imposed on a system. An extension has also an effect to make the first normal stress difference positive. Furthermore, motion of individual molecules has been analyzed by integrating the Langevin equation. It is found that the aligning state in shear and extensional flow is due to an approximately stationary behavior of individual molecules, while the aligning state in simple shear flow is an apparently stationary behavior of a group of many rotational molecules.

Polarization sensitivity in crayfish lamina monopolar neurons

1. Polarization sensitivity (PS) was examined in photoreceptors and lamina monopolar cells (LMCs) in two species of crayfish, Procambarus clarkii and Pacifasticus leniusculus. The measurements were made with intracellular recordings and broad field illumination. 2. PS is about 40% greater in Pacifasticus than in Procambarus (Table 1). In both species the LMC stationary PS profiles (estimated with flashes) are similar to those of receptors (Figs. 1 and 2). Both receptor and LMC sensitivity profiles are well described by cos2θ functions (Fig. 3). PS was observed in all receptors and 78% of LMCs. 3. When stimulated with a rotating polarizer, receptors and LMCs exhibit membrane potential modulation with phase predicted by the stationary PS profile (Fig. 5). In photoreceptors, the polarization-elicited percent modulation falls off steeply as intensity increases. The LMC modulation is stronger than that in receptors and relatively insensitive to the mean intensity (Figs. 6 to 8). For low intensities the LMC modulation is 100%. The LMC dynamic behavior is consistent with either an opponency mechanism or strong but polarization-insensitive lateral inhibition. 4. Receptors and LMCs exhibit steady-state differential sensitivity to stationary e-vector orientation (Fig. 9). 5. About 10% of the LMC neurons exhibit PS maxima separated by 90°. These results imply a nonlinear summation of signals from orthogonal receptor channels (Fig. 10).

Lamellar phase under shear : SANS measurements

The static properties of lyotropic lamellar phases have been investigated for a long time. Recently, we studied the dynamic properties and more specifically the effect of shear on these phases. Using different techniques (conoscopy, light, neutron and X-ray scattering, microscopy and rheology), the different stationary orientation states of a lamellar phase (in a quaternary mixture water-SDS-pentanol-dodecane) have been analyzed; in this paper we describe the analysis of the oriented state of these lamellar phase at high shear rates; we consider a Gaussian distribution to define the mosaicity of this orientation where the normal of the membrane is parallel to the velocity gradient

X-ray and birefringence orientation measurements on uniaxially deformed polyethylene film

Characterization of the crystalline and amorphous orientation of a uniaxially deformed low-density polyethylene (LDPE) film has been accomplished by combining pole figure X-ray diffraction and birefringence measurements. Characterization of the crystalline regions of the extruded film reveals the existence of a row-nucleated morphology with the a axis preferentially oriented in the plane containing the machine (MD) and transverse (TD) directions and the b axis strongly oriented along the film normal. This morphology is embedded in an amorphous matrix, biaxially oriented in nature. Low uniaxial extension along the MD produces two major orientational states in the crystalline regions which seem independent of the corresponding amorphous orientation. The pole figure analysis clearly shows that the c axis weakly orients towards the MD. Upon further uniaxial extension, it begins to tilt progressively away from the stretching direction inducing a complementary orientational behaviour between the c and b crystallographic axes on account of the stationary a-axis orientation perpendicular to the stretching direction. At higher draw ratios, the c axis gradually realigns itself with the stretching direction and uniaxial orientational states in all regions of the microstructure are obtained, indicating the existence of a fibrillar-type morphology. Quantification of the induced orientation was carried out and compared in terms of Hermans, Nomura/Kawai and White/Spruiell orientation functions.

Atomic relaxation and dynamical generation of ordered and disordered chemical vapour infiltration (CVI) SiC polytypes

The coexistence of ordered and disordered polytypes in SiC deposits is discussed from the point of view of their formation under CVD/CVI conditions, i.e., far from equilibrium. Local deformations at layer n are considered to determine the orientation and the deformations of the ( n + 1)th layer. An analysis of this dependence is made by constructing a first return map of an atomic relaxation variable, based on the ab initio calculation data for some regular polytypes made by Cheng et al., J. Phys. (Condens. Matter) 2 (1990) 5115. Orientation sequences are linked to the local deformation parameter, and to 29Si and 13C NMR shifts. Iterations of this map are considered as a one-dimensional dynamical system simulating layer-by-layer growth. Depending on control parameter, the dynamical system exhibits stationary, periodic or chaotic orientation sequences, reproducing many experimentally obtained polytypes. The occurence of CVD- or CVI-grown one-dimensionally disordered polytypes can thus possibly arise from a deterministic process able to yield also regular structures for nearby values of control parameters.

Mating in the reef white-tip shark Triaenodon obesus

Mating reef white-tip sharks, Triaenodon obesus, were observed and photographed in shallow waters of the Hawaiian Islands. The sharks copulated in a stationary parallel orientation with their heads on the bottom and bodies angled upwards approximately 45° into the water column. Pair contact during copulation was maintained by the male's left clasper anchored in the female's vent and by his tight oral grasp of the female's left pectoral fin. Results show that reposed sedentary modes of copulation are not limited to small species. In a reproductive context, biting behavior by male sharks functions as a premating releaser for female cooperation and for pair-contact maintenance during copulation.

Two bilateral sources of the late AEP as identified by a spatio-temporal dipole model

A new spatio-temporal dipole model is presented, which enables prediction and analysis of scalp potential wave forms due to spatio-temporal overlap of multiple generators. Each generator is thought to represent a local neural subset, the electric activity of which can be modelled by an equivalent dipole with stationary location and orientation closely related to the spatial organization of the neural subset. The temporal course of dipole magnitude is assumed to depict the external far field due to the compound discharge processes of the generator. Simulations of uni- and bilateral dipoles within the temporal lobe, oriented vertically and horizontally, demonstrate how spatiotemporal overlap mag bring about the ‘vertex response’ of the late AEP and the wave form changes observed over temporal sites. Analyses of late AEPs reported for a coronal chain of electrodes by Peronnet et al. (1974) and Vaughan et al. (1980) revealed that the wave forms in the 60–250 msec range could be perfectly matched at all electrodes by model wave forms due to 2 bilateral sources within the temporal lobe. Their locations, orientations and their latency difference of about 30 msec suggest consistently that the sequential activation of primary and secondary auditory cortices is the predominant source to the late AEPs.

Two-dimensional approach to the motion of a red blood cell in a plane couette flow of plasma

In relation to microrheology of blood, a theoretical approach to the motion of a red blood cell in a plane Couette flow between two parallel plates is made with emphasis on effects of wall. The red blood cell is assumed to be an elliptic cylindrical particle with a thin, inextensible membrane moving like a tank-tread along its perimeter and to contain a Newtonian fluid inside. Fluid motions are analysed numerically both inside and outside the particle on the basis of the Stokes equations, using the finite element method. A quasi-static equilibrium condition leads to the solution for the motion of the particle. It is shown that two types of motion exist (a stationary orientation motion and a flipping motion), depending on the viscosity ratio of inner to outer fluid, the axis ratio of the elliptic cylinder and the ratio of particle size to channel width. The results are applied to capillary blood flow.

Influence of an electric field on the rheological behavior of a dilute suspension of dipolar dumbbells in a viscoelastic oldroyd liquid

1. Rheological equations of state of a dilute suspension of dipolar dumbbels in a viscoelastic Oldroyd liquid have been obtained for a stationary orientation of suspended particles in steady flows and electric fields.

A theory of the pattern induced flight orientation of the fly Musca domestica II.

In a preceding paper, Poggio and Reichardt (1973a), a phenomenological theory describing the visual orientation behaviour of fixed flying flies (Musca domestica) towards elementary patterns was presented. Some of the problems raised in this first paper are treated here in more detail. The mapping between the position dependent torque distribution -- D(?) characteristics -- associated with a given pattern and the stationary orientation distribution p(?), is studied taking into account that the fluctuation process (generated by the fly) is coloured gaussian noise. Under certain critical conditions this may lead to an "early symmetry breaking" in the mean values of the p(?) distribution. The validity of the "superposition principle" has also been examined. Although shift and superposition give the main qualitative features of the "attractiveness profile" D(?), associated with a 2-stripe pattern, superposition does not hold quantitatively for stripe separations up to about 80°. Evidence is presented suggesting that such an effect is due to inhibitory interactions between input channels of the fly's eye. Implications of this finding with respect to the problem of spontaneous pattern preference are also discussed.

Visual control of locomotion in the walking fruitflyDrosophila

To investigate the optomotor leg responses ofDrosophila melanogaster the free walking fly is kept in stationary orientation and position on top of a ball. The stimulus consists of continuous pattern movement in the equatorial zone of the visual field. The rotatory and translatory responses are derived from the signals of a servo-system which maintains the stationary state of the walking fly by appropriate rotations of the ball.

On Solving Nonlinear Equations with a One-Parameter Operator Imbedding

One parameter operator imbedding to modify Newton method for solution of nonlinear equations

On the motion perception of the mealworm Tenebrio molitor

The locomotory turns of the beetle Tenebrio molitor were recorded from free walking animals which were held in stationary position and orientation by means of a tread compensator. Striped patterns revolved around an animal elicit optomotor responses which undergo an inversion at smaller stripe widths. The position of the inversion point characterizes the resolving power of the motion detectors, and corresponds to a 6.5° average angle between the optical axes of interacting elements in the motion detecting device. This indirectly determined value is consistent with the anatomically measured 7° average angle between the axes of neighbouring ommatidia in the Tenebrio compound eye.