Asymmetric Perturbations Research Articles

Quantification of lumbar motion in response to asymmetric platform perturbations

Quantification of lumbar motion in response to asymmetric platform perturbations

An experimental and numerical study of the Dean problem: flow development towards two-dimensional multiple solutions

An experimental and numerical study investigating the flow development and fully developed flows of an incompressible Newtonian fluid in a curved duct of square cross section with a curvature ratio of 15.1 is presented. Numerical simulations of flow development from a specified inlet profile were performed using a parabolized form of the steady three-dimensional Navier-Stokes equations. No symmetry conditions were imposed. In general there was good agreement between the numerical predictions of the developing axial velocity profiles and LDV measurements. In addition, for computational expediency, the two-dimensional solution structure was calculated by imposing fully developed conditions together with symmetry conditions along the horizontal duct centreline.Laser-Doppler measurements of axial velocity and flow visualization at Dean number Dn = 125, 137 and 150, revealed a steady and symmetric two-vortex flow at Dn = 125, and a steady and symmetric four-vortex flow at both Dn = 137 and 150 (Dn = Re/(R/a)½, where Re is the Reynolds number, R is the radius of curvature of the duct and a is the duct dimension). Axial velocity measurements showed that the four-vortex flow at Dn = 150 developed to the solution predicted by the two-dimensional numerical simulation. However, the four-vortex flow at Dn = 137 was still developing when the flow had reached the end of the 240° axial length of the duct. A numerical investigation for Dean numbers in the range of 50 to 175 revealed that at the limit point of the two-cell to four-cell transition the development length appeared to be infinite, and thereafter decreased for increasing Dean numbers. The behaviour of decreasing development length of the four-vortex flow with increasing Dean number has not been reported previously.Using a symmetrically positioned pin at θ = 5° to induce the four-cell flows, the two-dimensional solution structure for Dn [les ] 150 was experimentally observed for the first time. Experiments were consistent with the prediction by Winters (1987) that four-vortex flows are stable to symmetric perturbations, but unstable to asymmetric perturbations. Experimental and numerical investigations suggested that, when perturbed asymmetrically, the four-vortex flow might evolve to flows with sustained spatial oscillations farther downstream.

Stability of dark solitary waves trapped in media with gain and loss.

The stability of dark solitary waves trapped in self-defocusing media that include gain and two-photon absorption is investigated. The stationary propagation of the dark solitary waves is found to be stable to a symmetric perturbation but unstable to an asymmetric perturbation. This contrasts with their bright counterparts, which are unstable to all perturbations.

Further characterization of reversal of signs of induced cotton effects of dicumarol derivatives-α 1-acid glycoprotein systems by protriptyline

The interaction of dicumarol derivatives and protriptyline with respect to the binding to α 1-acid glycoprotein (AGP) has been investigated by circular dichroism (CD), equilibrium dialysis and ultrafiltration. Investigation of the induced CD spectra of dicumarol derivatives bound to AGP indicated that the conformations of these compounds were different when bound to AGP. Though all the dicumarol derivatives, protriptyline and AGP formed a ternary complex, interaction modes were different, depending upon the substituent groups at position 3 of the dicumarol molecule. On the basis of the protriptyline effect on the CD spectra of all dicumarol derivatives bound to AGP, the compounds were classified in the following way: (1) Dicumarol, ethylidenebis 4-hydroxycoumarin and propylidenebis 4-hydroxycoumarin caused reversal of the sign of ellipticity. This interaction was explained by cooperative binding. (2) Butylidenebis 4-hydroxycoumarin and pentylidenebis 4-hydroxycoumarin generated new band and disappeared ellipticity of the original Cotton effect. This interaction was also explained by the cooperative binding mode. (3) Ethylbiscoumacetate which generated the CD band similar to that of dicumarol in the absence of protriptyline, reversed the sign of the CD spectrum only at 325 nm. The interaction was anticooperative in nature. (4) Benzylidenebis 4-hydroxycoumarin represented type four which had no change in the CD spectrum by the addition of protriptyline. This interaction was explained by the two-state model accompanying the conformational change of AGP. These results suggested that all compounds, except for benzylidenebis 4-hydroxycoumarin, induced negative Cotton effects at 325 nm by taking the same asymmetrical perturbation by the addition of protriptyline and the interaction was carried out according to model 2. An attempt to study the interaction mechanism of two or more drugs with regard to the binding to protein using these models is thought to help in understanding drug-protein interactions.

Hemifacial microsomia: developmental consequence of perturbation of the auriculofacial cartilage model?

The cause of hemifacial microsomia (HFM) is currently the subject of much investigation. Despite a large body of clinical and experimental data, little is certain other than the heterogeneity of this malformation complex. Here we suggest that some of the cases previously designated as being multifactorial in origin may be interpreted instead as resulting from a single-gene mutation, by applying a stochastic single-gene model. A variety of models of the pathogenesis of HFM have been described, including the proposal that local embryonic haemorrhage is a causal mechanism. More recently, it has been suggested that an interference in chondrogenesis is primarily responsible for the HFM phenotype. In this paper direct experimental evidence, based on surgical interference of mandibular development in the chick embryo, is applied in favour of the latter concept. In particular, asymmetrical perturbation of Meckel's cartilage has been shown to result in asymmetry of the mandible, and it is proposed that, irrespective of cause, the skeletal pathogenesis of HFM primarily involves the auriculofacial cartilage model.

Magnetohydrodynamic oscillation of a gas jet of zero inertia dispersed in a resistive liquid with energy conservation

The dynamical oscillation and instability of a gas cylinder of zero inertia immersed in a resistive liquid has been developed for symmetric perturbations. In the absence of the magnetic field we have used the conservation of energy to study such problem for all symmetric and asymmetric perturbations. In the latter it is found that the temporal amplification is much lower than that of the full fluid jet. The model is capillary stable for all short and long wavelengths in the asymmetric perturbation while in the symmetric disturbances it is stabilizing or not according the perturbed wavelength is shorter than the gas cylinder circumference or not. The resistivity is stabilizing or destabilizing according to restrictions. The electromagnetic body force is stabilizing for all wavelengths in the rotationally-symmetric disturbances. The Lorentz body force, for high magnetic field intensity, could be suppressing the destabilizing character of the present model. This may be due to the fact that the acting magnetic field is uniform and that the fluid is considered to be incompressible.

Collapse of asymmetric perturbations in a stratified fluid

A solution of the problem of laminar collapse, i.e., a solution of the initial-value problem with small initial density perturbations and motions, is given within the framework of the linear description. In contrast to other publications, special attention is paid to the analysis of the role of the horizontal asymmetry of the perturbations. This anisotropy may be caused by the horizontal vorticity of the initial mixing, the nonsymmetry of the density “traumas” of the medium, and external shear flows. These factors are taken into account indirectly in assigning the initial vorticity and the “skewness” of the density perturbations.

A point vortex dipole model of an isolated modon

A point vortex dipole model for an isolated modon governed by the Charney–Hasegawa–Mima (CHM) equation is developed, building on the point vortex formulation of Zabusky and McWilliams [Phys. Fluids 25, 2175 (1982)]. The model dipole is compared to the exact modon solution in order to determine parameter values for which the model dipole matches the modon’s speed and far-field behavior. The model allows one to study nonuniform motions analytically. It predicts that right-moving modons in uniform motion should be stable in the sense that their paths exhibit small-amplitude oscillations in response to small perturbations of their initial orientation. It also predicts that left-moving modons in uniform motion should be unstable, being pushed into finite-amplitude motions by arbitrarily small perturbations. These predictions are confirmed by direct numerical simulation of modons evolving under the CHM equation. It is noted that although the distribution of vorticity within modons may be Lyapunov stable in nearly uniform motions, the paths of modons may be unstable to asymmetric perturbations.

Investigation of asymmetric perturbations of nickel(II) octaethylporphyrin in dichloromethane by Raman dispersion spectroscopy

Investigation of asymmetric perturbations of nickel(II) octaethylporphyrin in dichloromethane by Raman dispersion spectroscopy

A bifurcation study of mixed-convection heat transfer in horizontal ducts

The bifurcation structure of two-dimensional, pressure-driven flows through a horizontal, rectangular duet that is heated with a uniform flux in the axial direction and a uniform temperature around the periphery is examined. The solution structure of the flow in a square duct is determined for Grashof numbers (Gr) in the range of 0 to 106using an arclength continuation scheme. The structure is much more complicated than reported earlier by Nandakumar, Masliyah & Law (1985). The primary branch with two limit points and a hysteresis behaviour between the two-and four-cell flow structure that was computed by Nandakumaret al.is confirmed. An additional symmetric solution branch, which is disconnected from the primary branch (or rather connected via an asymmetric solution branch), is found. This has a two-cell flow structure at one end, a four-cell flow structure at the other, and three limit points are located on the path. Two asymmetric solution branches emanating from symmetry-breaking bifurcation points are also found for a square duct. Thus a much richer solution structure is found with up to five solutions over certain ranges of Or. A determination of linear stability indicates that all two-dimensional solutions develop some form of unstable mode by the time Gr is increased to about 220000. In particular, the four-cell becomes unstable to asymmetric perturbations. The paths of the singular points are tracked with respect to variation in the aspect ratio using the fold-following algorithm. Transcritical points are found at aspect ratios of 1.408 and 1.456 respectively for Prandtl numbersPr= 0.73 and 5. Above these aspect ratios the four-cell solution is no longer on the primary branch. Some of the fold curves are connected in such a way as to form a tilted cusp. When the channel cross-section is tilted even slightly (1°) with respect to the gravity vector, the bifurcation points unfold and the two-cell solution evolves smoothly as the Grashof number is increased. The four-cell solutions then become genuinely disconnected from the primary branch. The uniqueness range in Grashof number increases with increasing tilt, decreasing aspect ratio and decreasing Prandtl number.

Flow through rotating rectangular ducts

The bifurcation structure of two-dimensional, pressure-driven flows through a rectangular duct that is rotating about an axis perpendicular to its own is examined at a fixed Ekman number (Ek=ν/b2Ω) of 0.01. The solution structure for flow through a square duct (aspect ratio γ=1) is determined for Rossby numbers (Ro=U/bΩ) in the range of 0–5 using a computational scheme based on the arclength continuation method. The structure is much more complicated than reported earlier by Kheshgi and Scriven [Phys. Fluids 28, 2968 (1985)]. The primary branch with two limit points in Rossby number and a hysteresis behavior between the two- and four-cell flow structure that was computed by Kheshgi and Scriven is confirmed. An additional symmetric solution branch, which is disconnected from the primary branch (or rather connected via an asymmetric solution branch), is found. This has a two-cell flow structure at one end, a four-cell flow structure at the other and three limit points are located on the path. Two asymmetric solution branches emanating from symmetry breaking bifurcation points are also found for a square duct. Thus even within a Rossby number range of 0–5 a much richer solutions structure is found with up to five solutions at Ro=5. An eigenvalue calculation indicates that all two-dimensional solutions develop some form of unstable mode by the time Ro is increased to 5.0. In particular, the four-cell solution becomes unstable to asymmetric perturbations as found in a related problem of flow through a curved duct. The paths of the singular points are tracked with respect to variation in the aspect ratio using the fold following algorithm. A transcritical point is found at an aspect ratio of 0.815 and below which the four-cell solution is no longer on the primary branch. When the channel cross section is tilted even slightly (1°) with respect to the axis of rotation, the bifurcation points unfold and the two-cell solution evolves smoothly as Rossby number is increased. The four-cell solutions then become genuinely disconnected from the primary branch. The uniqueness range in Rossby number increases with increasing tilt.

Linear Normal Modes of a Moving, Shallow-Water Barotropic Vortex

Calculations with a linear semispectral model of a moving tropical-cyclone-like barotropic vortex (Willoughby 1988) show that a vortex with cyclonic circulation throughout exhibits unphysically fast poleward motion on a beta plane, but a vortex with enough anticyclonic circulation at its periphery to make the total relative angular momentum (LR) small moves slowly. The high poleward speed arises because the vortex has a linear normal mode at zero frequency, where the beta effect forces asymmetric perturbations. Advection of planetary vorticity by the axisymmetric circulation forces this normal mode at a rate proportional to LR. Because the governing equations are third-order in time, as many as three wavenumber-one normal modes are possible. A completely cyclonic vortex has three repeated stable normal modes at zero frequency, whereas one with small LR has a single stable mode at zero frequency and a conjugate pair of barotropically unstable modes. The frequency of the unstable modes lies at the most anticyclonic rotation frequency of the axisymmetric circulation, and the growth rate is slow; the e-folding time is typically 75 days. If the fluid is made very shallow, the stable normal mode moves away from zero frequency. In this situation, the beta effect fails to force the resonance, and the vortex propagates westward much as a planetary Rossby wave does. In this model, meridional motion of vortices with LR ≠ 0 always acts to adjust LR toward zero through conservation of absolute angular momentum. Since the asymmetric perturbations are Rossby waves that propagate upon the radial gradient of mean relative vorticity, the mode at zero frequency experiences critical-radius absorption where the mean swirling wind is zero—at the boundary between cyclonic and anticyclonic mean circulation and at the edge of the vortex. Regardless of the sign of LR, the wave momentum convergence is concentrated at these critical radii and weakens the circulation while expanding it spatially. When LR = 0, waves emanating from the cyclonic and anticyclonic circulations interfere destructively, so that the vortex radiates no angular momentum to its environment.

The transition to chaos in an asymmetric perturbation of the Lorenz system

Simple mathematical models of physical systems with complicated dynamics may possess a symmetry which is not shared by the real-life system itself. If the chaos is predicted to persist for asymmetric models (as for the Lorenz system), then the size of the asymmetry allowed decides the usefulness of the symmetric model.

The effect of initial perturbation shape and symmetry on fold development

Single-layer fold experiments were carried out to study the influence of initial perturbation symmetry on the symmetry of folds developed using paraffin wax as a rock analogue. Under experimental conditions, both matrix and layer have a power-law rheology, with an initial effective viscosity contrast of ca 17:1. The matrix flows in steady state with n = 2.7 and the layer work softens with n eff = 10. Folds developed from an initially symmetric perturbation remain symmetric, reflecting the pure shear-plane strain boundary conditions. Folds developed from an initially asymmetric perturbation, however, show a progressive exaggeration of this asymmetry, such that the introduced 3.5° difference in limb dip increases to 65° at 23% bulk shortening. These experiments indicate that, for low competence contrast between layer and matrix, the geometry of initial perturbations of finite amplitude (e.g. ripple marks, channels, half-graben structures) may be an important factor in determining the geometry and distribution of folds.

Chirality of polyvinyl compounds. 10. Asymmetric perturbation of side-chain chromophores caused by the main-chain configuration of optically active vinyl polymers

Etude du dichroisme circulaire et du pouvoir rotatoire des copolymeres obtenus par copolymerisation du o-cyclohexylidene-3,4 D-mannitol 1,2:5,6 bis-o[(vinyl-4 phenyl)] boronate avec des comonomeres a chromophore aromatique (benzene, stilbene, biphenyle, benzene) situe a distances variables du groupe polymerisable, suivie de l'elimination du D-mannitol

Barotropic Vortex Stability to Perturbations from Axisymmetry

Abstract Tropical cyclones and dynamically similar model vortices robustly maintain a near-axisymmetric horizontal structure where the vortex flow is strongly nonlinear in spite of persistent asymmetric forcing represented by horizontal variations in the environmental winds and the Coriolis parameter. Since tropical cyclone motion relative to environmental “steering” has been associated with vortex asymmetries in even the simplest numerical models, identification of a barotropic mechanism that stabilizes vortices to dispersive influences is important. A nondivergent, barotropic analytical model is used to identify the asymmetry-damping influence of symmetric angular windshear as the mechanism by which a barotropic vortex resists asymmetric forcing. Solutions are obtained for the evolution of linear asymmetric perturbations imposed as initial conditions on a steady, Rankine vortical flow. Perturbations combining various radial and azimuthal structures that might be expected from environmental and convectiv...

Optical fiber up-tapers with index perturbations-performance analysis

The performance of step index up-tapers subjected to certain index perturbations in investigated by computer simulation. Concentric symmetric and asymmetric index profile perturbations as well as localized spherical, called regions bubbles, having a different index are studied. It is found that some low-valued perturbations of small scale size (less than a wavelength) do not alter the optical fiber performance. However, the amount of beam expansion in the up-taper may be ultimately limited by such perturbations. Excessive magnification in the presence of perturbations can cause a distortion of the quasi-Gaussian shape and symmetry of the pure step-index fundamental mode as well as increase the excess loss and degrade the lateral and axial displacement tolerance improvements of the up-tapers. For example, an index variation of Delta n approximately=10/sup -5/ in conjunction with a perturbation scale size of 40 mu m can be detrimental. Bubble-type perturbations could also cause similar problems. A single 12.8- mu m-diameter bubble with a relative index of -0.02, embedded in a 128- mu m-diameter step index core with relative index of 0.5%, produced a 0.3-dB excess loss. >

The influence of structural variations in the F- and FG-helix of the beta-subunit modified oxyHb-NES on the heme structure detected by resonance Raman spectroscopy.

The dispersion of the depolarization ratio of two prominent Raman lines (1,375 cm-1 and 1,638 cm-1) of oxyhemoglobin-N-ethyl succinimide have been examined for pH values between pH = 6.0 and 8.5. Both exhibit a significant pH dependence. Calculation of the Raman tensor in terms of a fifth-order time dependent theory provides information about the pH-dependence of parameters reflecting symmetry classified distortions of the prosthetic heme group. To correlate these distortions with the functional properties of the molecule the following protocol was used: 1) An allosteric model suggested by Herzfeld and Stanley (1974) has been applied to O2-binding curves measured at different pH values between 6.5 and 9.0. From this calculation one obtains both, the energy differences between different molecular conformations and the equilibrium constants of oxygen and proton binding. 2) A titration model was formulated relating each conformation of a molecule to a distinct set of distortion parameters of the heme group. 3) The distortion parameters resulting from the analysis of our Raman data were assigned as an effective value due to incoherent superposition of the distortion parameters related to the different titration states. The application of this procedure yields an excellent reproduction of the pH-dependent effective distortion parameters of both Raman lines investigated. It is shown that the protonation of two tertiary effector groups located in the beta-subunits affect the symmetry of the heme in a contrary manner: the protonation of a His-residue (pK = 8.2, probably His(FG4) beta) causes a symmetric position of the proximal imidazole thus lowering the perturbations of the heme core. Further it influences the interaction between amino acid residues of the heme cavity and pyrrole side chains (probably Val(FG5) beta-vinyl (pyrrole 3) thus causing a decrease of the distortions related to the peripheral part of the heme. In contrast, the protonation of Lys (EF6) beta causes a tilt position of the proximal imidazole and an increase of asymmetric perturbations of the heme core, whereas the interaction between the pyrrole side chains and the heme cavity is weakened. Our results are consistent with stereochemical predictions of Moffat (1971) concerning the existence of a H-bond between His(FG4) beta and Cys(F9) beta.

Detection of the heme perturbations caused by the quaternary R----T transition in oxyhemoglobin trout IV by resonance Raman scattering

The depolarization ratio dispersion and the respective excitation profiles of two structural sensitive Raman lines of oxyhemoglobin-trout IV (1,375 and 1,638 cm-1) have been measured at pH-values between 6.5 and 8.5. They were analyzed by employing a fifth order time dependent perturbation theory to calculate the polarizability tensor. This provides information about the pH-dependence of parameters reflecting symmetry classified distortions of the prosthetic heme groups. In order to correlate these distortions with functional properties of the molecule the following protocol has been employed: (a) a titration model was formulated relating each conformation of the molecule to a distinct set of distortion parameters the incoherent superposition of which provides the respective distortion parameter obtained from our Raman data. (b) The thermodynamic constants determining the equilibrium between these molecular conformations (i.e., the quaternary T and R-states, the low affinity t and the high affinity r-states of the distinct subunits, the pK-values of the Root- and Bohr groups) were obtained from a set of O2-binding curves that were analyzed in terms of an allosteric model suggested by Herzfeld and Stanley 1974. J. Mol. Biol. 82:231. The application of this procedure yields excellent reproduction of the pH-dependent effective distortion parameters of both Raman lines investigated. Thus established correlation between hemoglobin function (O2-binding) and structure (asymmetric perturbation of the hemegroup) provides some interesting insights into the molecular basis of the allosteric Root effect.

Symmetric and asymmetric perturbations of the index of refraction in three-waveguide optical planar couplers

A study is presented on the behavior of modes propagating in three coupled, dielectric slab waveguides with a perturbation to the index of refraction. In an electro-optic crystal, an applied electric field changes the index of refraction. A voltage applied to a given electrode configuration generates the electric field. For various initial excitations of the three guides, the optical power in each waveguide is calculated as a function of the voltage applied to the electrodes. The amount of optical power coupled from one outside waveguide to the other is calculated as a function of the applied voltage. The calculation is done for both asymmetric and symmetric perturbations to the index of refraction. For an initial excitation of the center waveguide, the optical power coupled to the two outside waveguides is calculated as a function of the applied voltage. It is calculated for both asymmetric and symmetric perturbations of the index of refraction. It is shown that, in general, the applied voltage that is necessary to transfer optical power from one outside waveguide to the other is lower for an asymmetric perturbation of the index of refraction. However, for transfer of optical power from the center waveguide to the two outside waveguides, the necessary applied voltage is lower for a symmetric perturbation.