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At least 163 records · Page 9

Experimental Observation of Magnetic Island Heteroclinic Bifurcation in Tokamaks

We report empirical observations of magnetic island heteroclinic bifurcation for the first time. This behavior is observed in interacting coupled 2/1 tearing modes in the core of a DIII-D tokamak plasma. Poincaré maps constrained by measured magnetic amplitudes and phasing show bifurcation from heteroclinic to homoclinic topology in the 2/1 island as the 4/2 relative amplitude (R 4/2 ) decreases. Initially, the local electron temperature peak in the 2/1 island splits, consistent with two O points. As R 4/2 decreases a single peak forms, consistent with one O point. Lastly, these call for developing tearing stability theory and control solutions for heteroclinic islands in tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Utilizing bifurcated halogen-bonding interactions with the uranyl oxo group in the assembly of a UO 2 –3-bromo-5-iodobenzoic acid coordination polymer

The synthesis and crystal structure of a new uranyl coordination polymer featuring 3-bromo-5-iodobenzoic acid is described and the luminescent and vibrational properties of the material have been explored. Compound (1), [UO 2 (C 7 H 3 BrIO 2 ) 2 ] n , features dimeric uranyl units chelated and then linked by 3-bromo-5-iodobenzoic acid ligands to form a one-dimensional coordination polymer that is subsequently assembled via bifurcated halogen-bonding interactions with uranyl oxo atoms to form a supramolecular three-dimensional network. The asymmetric, bifurcated halogen-bonding interaction in (1) is notable as it represents the first observation of this synthon in a uranyl hybrid material. Raman and IR spectroscopy showed that halogen-bonding interactions with the uranyl oxo atoms result in small shifts in υ 1 and υ 3 frequencies, whereas luminescence spectra collected at an excitation wavelength of 420 nm reveal partially resolved uranyl emission.

Chemistry↗

Bifurcation and collapse analysis of stringer and ring-stringer stiffened cylindrical shells with cutouts

Results for cylindrical configurations using the STAGS computer program were presented. Discontinuities were imposed upon the shell's skin by incorporating symmetrical cutout openings. In addition, the surface is stiffened with both stringer and ring-stringer arrangements. The cutout problem has been shown to be highly nonlinear for smooth surface shells, but it was found that bifurcation and collapse loads are close when one is considering stiffened skin configurations. In order to arrive at this conclusion, it was necessary to evaluate the following: (1) comparison between smeared and discrete stiffener theory for linear solutions, (2) numerical finite difference convergence as directed toward buckling determination, (3) collapse load results with the various skin stiffeners. A linear bifurcation study relating to stiffening effects around cutout areas present within stringer and ring-stringer shell surfaces was included. Comparisons were made between a variety of geometric positions considering cutout frame and thickened skin additions.

Palazotto, A. N.↗

Hydroelastic effects in the aorta bifurcation zone

The mechanical behavior of the vessels and blood is mathematically analyzed at the point of aortic bifurcation using a homogeneous single layer channel as a model of the aorta. Allowance is made for the fact that the aortic intima is considerably less rigid than the other layers. For analysis of blood flow in the major arteries, the blood is treated as a viscous Newtonian fluid whose movements are described by Navier-Stokes equations and a continuity equation. Blood flow dynamics at the aortic bifurcation are discussed on the basis of the results.

Volmir, A. S.↗

Hopf bifurcation in the presence of symmetry

Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.

Golubitsky, M.↗

A numerical study of bifurcations in a barotropic shear flow

In the last few years, more and more evidence has emerged suggesting that transition to turbulence may be viewed as a succession of bifurcations to deterministic chaos. Most experimental and numerical observations have been restricted to Rayleigh-Benard convection and Taylor-Couette flow between concentric cylinders. An attempt is made to accurately describe the bifurcation sequence leading to chaos in a 2-D temporal free shear layer on the beta-plane. The beta-plane is a locally Cartesian reduction of the equations describing the dynamicss of a shallow layer of fluid on a rotating spherical planet. It is a valid model for large scale flows of interest in meteorology and oceanography.

Huerre, P.↗

The route to chaos in thermal convection at infinite Prandtl number. I - Some trajectories and bifurcations

The question of whether or not thermal convection in the earth's mantle is chaotic is addressed. It is suggested that the high Prandtl number/high Raleigh number thermal convection associated with mantle convection is chaotic. To test this hypothesis, the route to chaos in a fluid with infinite Prandtl number is examined, using the Saltzman (1962) equations and the Lorenz (1963) equations. It is concluded that thermal convection at infinite Prandtl number becomes chaotic by means of symmetry-breaking pitchfork bifurcations and the appearance of Hopf bifurcations which produce unstable periodic orbits.

Stewart, Cheryl A.↗

Bifurcating families of periodic traveling waves in rarefied plasmas

A necessary condition for the existence of undamped spatially periodic traveling waves near spatially uniform equilibria is derived. When the necessary condition is satisfied, a bifurcation analysis of Berstein-Greene-Kruskal modes is used to construct branches of such waves with wavelength equal to the fundamental wavelength. Expansions of the bifurcating potential for these waves are derived, and the reconstruction of the distribution function is discussed.

Holloway, James Paul↗

Intraseasonal oscillations in the extratropics - Hopf bifurcation and topographic instabilities

A potential vorticity model in a beta-channel is used to analyze the resonant response of equivalent-barotropic flow to topography in the presence of a forced zonal jet with arbitrary meridional structure. The nonlinear dynamics near different resonances is studied considering both wave-wave and wave-zonal flow interactions. It is shown that Hopf bifurcations from stationary to periodic flows are possible due to the nonlinear instability of nonzonal, topographically forced flow. Low-frequency, finite-amplitude oscillations arise due to a combination of two factors: (1) nonlinear wave-wave interactions, which tend to reduce the Rossby wave frequency; and (2) wave-zonal flow interactions, which reflect the importance of wave momentum transport in shifting the westerly jet and of the topographic form drag. The physical mechanism of atmospherically realistic Hopf bifurcations depends crucially on the meridional profile of the mean zonal flow giving rise to a dipole-shaped resonance.

Jin, F.-F.↗

Equilibria, stability and bifurcations of rotating columns of fluid subjected to planar disturbances

Long gyrostatically rotating drops bonded by surface tension are amenable to conventional bifurcation analysis and newer, computer-aided analytical methods, and therefore are useful prototypes of three-dimensional drops. A study is conducted by setting aside instability to Rayleigh's axisymmetric mode and investigating the effects of translationally symmetric (planar) disturbances. The disadvantage of employing single-coordinate representation of drop shapes close to break-up is brought out. It is shown that a family of symmetric two-lobed shapes bifurcates from the main family of perfectly cylindrical shapes when the rotation rate reaches a critical value, in accord with the linearized hydrodynamic analysis of Hocking.

Benner, R. E., Jr.↗

Cellular instability in rapid directional solidification - Bifurcation theory

Merchant and Davis performed a linear stability analysis on a model for the directional solidification of a dilute binary alloy valid for all speeds. The analysis revealed that nonequilibrium segregation effects modify the Mullins and Sekerka cellular mode, whereas attachment kinetics has no effect on these cells. In this paper, the nonlinear stability of the steady cellular mode is analyzed. A Landau equation is obtained that determines the amplitude of the cells. The Landau coefficient here depends on both nonequilibrium segregation effects and attachment kinetics. This equation gives the ranges of parameters for subcritical bifurcation (jump transition) or supercritical bifurcation (smooth transition) to cells.

Braun, R. J.↗

Some Aspects of Bifurcation Structure of Laminar Flow in Curved Ducts

A bifurcation study is made of laminar flow in curved ducts. The problem is formulated in a curvilinear coordinate system, and the governing equations, after orthogonal mapping is applied, are solved numerically by an iterative finite-difference method. Many computer runs were made with various duct cross-sections ranging from a circle to a square, to learn the transition of bifurcation structure with this change in cross-section and to reconcile the differences between them. In addition, a simpler technique is proposed to generate symmetric four-cell solutions in a circular pipe and a means is put forward to stabilize four-vortex structures in a complete cross-section.

Kao, Hsiao C.↗

Bifurcating optical pattern recognition in photorefractive crystals

A new concept and experimental demonstration of a bifurcating optical pattern recognizer that uses a nonlinear gain saturation memory medium such as a high-gain photorefractive crystal are presented. A barium titanate crystal is used as a typical example of the nonlinear medium for the demonstration of the bifurcating optical pattern recognizer.

Liu, Hua-Kuang↗

Local and Global Bifurcations of Flow Fields During Physical Vapor Transport: Application to a Microgravity Experiment

The local bifurcation of the flow field, during physical vapor transport for a parametric range of experimental interest, shows that its dynamical state ranges from steady to aperiodic. Comparison of computationally predicted velocity profiles with laser doppler velocimetry measurements shows reasonable agreement in both magnitude and planform. Correlation of experimentally measured crystal quality with the predicted dynamical state of the flow field shows a degradation of quality with an increase in Rayleigh number. The global bifurcation of the flow field corresponding to low crystal quality indicates the presence of a traveling wave for Ra = 1.09 x 10(exp 5). For this Rayleigh number threshold a chaotic transport state occurs. However, a microgravity environment for this case effectively stabilizes the flow to diffusive-advective and provides the setting to grow crystals with optimal quality.

Duval, W. M. B.↗

Bifurcation and Hysteresis of the Magnetospheric Structure with a varying Southward IMF: Field Topology and Global Three-dimensional Full Particle Simulations

Using a three-dimensional full electromagnetic particle model (EMPM), we have performed global simulations of the interaction between the solar wind and the terrestrial magnetosphere, and have investigated its asymptotic stability. The distance between the dayside magnetopause subsolar point and the Earth center, R(sub mp) is measured, as the intensity of southward IMF |B(sub z)| is slowly varying. Based on the field topology theory, one analyzes the variation of R(sub mp) as a reference index of the dynamics of this interaction, when IMF |B(sub z)| successively increases and decreases to its original value. Two striking results are observed. First, as the IMF |B(sub z)| increases above a critical value, the variation of R(sub mp) suddenly changes (so called 'bifurcation' process in field topology). Above this critical value, the overall magnetic field topology changes drastically and is identified as being the signature of magnetic reconnection at the subsolar point on the magnetopause. Second, this subsolar point recovers its original location R(sub mp) by following different paths as the IMF |B(sub z)| value increases (from zero to a maximum fixed value) and decreases (from this maximum to zero) passing through some critical values. These different paths are the signature of 'hysteresis' effect, and are characteristic of the so-called 'subcritical-type' bifurcation. This hysteresis signature indicates that dissipation processes take place via an energy transfer from the solar wind to the magnetosphere by some irreversible way, which leads to a drastic change in the magnetospheric field topology. This hysteresis is interpreted herein as a consequence of the magnetic reconnection taking place at the dayside magnetopause. The field topology reveals to be a very powerful tool to analyze the signatures of three-dimensional magnetic reconnection without the obligation for determining the mechanisms responsible for, and the consequences of the reconnection on the overall magnetospheric dynamics.

Cai, DongSheng↗

On the Crack Bifurcation and Fanning of Crack Growth Data

Crack growth data obtained from ASTM load shedding method for different R values show some fanning especially for aluminum alloys. It is believed by the authors and it has been shown before that the observed fanning is due to the crack bifurcation occurs in the near threshold region which is a function of intrinsic properties of the alloy. Therefore, validity of the ASTM load shedding test procedure and results is confirmed. However, this position has been argued by some experimentalists who believe the fanning is an artifact of the test procedure and thus the obtained results are invalid. It has been shown that using a special test procedure such as using compressively pre-cracked specimens will eliminate the fanning effect. Since not using the fanned data fit can result in a significantly lower calculated cyclic life, design of a component, particularly for rotorcraft and propeller systems will considerably be impacted and therefore this study is of paramount importance. In this effort both test procedures i.e. ASTM load shedding and the proposed compressive pre-cracking have been used to study the fatigue crack growth behavior of compact tension specimens made of aluminum alloy 2524-T3. Fatigue crack growth paths have been closely observed using SEM machines to investigate the effects of compression pre-cracking on the crack bifurcation behavior. The results of this study will shed a light on resolving the existing argument by better understanding of near threshold fatigue crack growth behavior.

Forman, Royce G.↗

Stability and bifurcation analysis of Japanese encephalitis model with/without effects of some control parameters

In this paper, a mathematical model on transmission of Japanese Encephalitis disease has been developed considering some control parameters and time-dependent environmental-carrying capacity. Here, the total vector population is divided into two subpopulations such as susceptible mosquito and infected mosquito. Here also, total reservoir population (i.e., the population in which the encephalitis virus grows) such as pig, horse, etc., has been considered which is divided into three subpopulations such as susceptible reservoir, infected reservoir and recovered reservoir. Total human population is also divided into three subpopulations such as susceptible human, infected human and recovered human. The dynamical behaviors of the system have been investigated. Here, the basic reproduction number associated with the system has been analyzed with respect to control parameters both theoretically and numerically. The biological feasible equilibria and their stability properties have been discussed and the existence condition of the disease has been illustrated numerically. For a certain set of parametric values, effectiveness of control parameters of our proposed model has been checked numerically. At last, Hopf bifurcations have been made numerically without considering control parameters for the case of constant environmental-carrying capacity of mosquito.

97 MATHEMATICS AND COMPUTING↗

New approach for stability and bifurcation analysis on predator–prey harvesting model for interval biological parameters with time delays

This paper presents a prey–predator harvesting model with time delay for bifurcation analysis. We consider the parameters of the proposed model with imprecise data as form of interval in nature, due to the lack of precise numerical information of the biological parameters such as prey population growth rate and predator population decay rate. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey under impreciseness of the biological parameters. Parametric functional form of interval number with two parameters is introduced. This study reveals that not only delay and harvesting effort play a significant role on the stability on the system but also interval parameters play a crucial role on the stability of the system. Computer simulations of numerical examples are given to explain our proposed imprecise model. We also address critically the biological implications of our analytical findings with proper numerical example.

97 MATHEMATICS AND COMPUTING↗