Biomedical subjects

Guenter Ahlers

Publications and source records attributed to Guenter Ahlers.

17 recordsLinked to original sources

PubMed2006

Onset of electroconvection of homeotropically aligned nematic liquid crystals.

We present experimental measurements near the onset of electroconvection (EC) of homeotropically aligned nematic liquid crystals Phase 5A and MBBA. A voltage of amplitude square root 2V0 and frequency f was applied. With increasing V0, EC occurred after the bend Freedericksz transition. We found supercritical bifurcations to EC that were either stationary bifurcations or Hopf bifurcations to traveling convection rolls, depending on the sample conductances. Results for the onset voltages Vc, the critical wave numbers kc, the obliqueness angles thetac, and the traveling-wave (Hopf) frequencies at onset omegac over a range of sample conductances and driving frequencies are presented and compared, to the extent possible, with theoretical predictions. For the most part good agreement was found. However, the experiment revealed some unusual results for the orientations of the convection rolls relative to the direction selected by the Freedericksz domain.

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PubMed2006

Spatiotemporal chaos in electroconvection of a homeotropically aligned nematic liquid crystal.

We present patterns of electroconvection (EC) for the homeotropically aligned nematic liquid crystal MBBA. A voltage V = square root of 2V0 sin(2pift) was applied. With increasing V0, the bend Freedericksz transition at VF was followed by the onset of EC at Vc > VF. We found four distinct pattern types. First, a primary supercritical Hopf bifurcation to traveling waves (TW's) of convection rolls occurred. The structure factor S(k) of this state reflected the azimuthal anisotropy of the underlying Freedericksz state. For f < fL approximately 75 Hz there was a superposition of two oblique-roll modes (pattern I). These patterns were chaotic in space and time. For larger f the patterns consisted of chaotic TW normal rolls (pattern II). Here the chaos was attributable to the motion of dislocations and domain walls between left- and right-traveling waves. A secondary bifurcation yielded pattern III; it had no dominant TW frequency but had broadband chaotic dynamics dominated by the motion of dislocations. This pattern type had been referred to by others as a "chevron pattern;" its structure factor still revealed azimuthal anisotropy. Finally, at somewhat larger identical with epsilon = V2/Vc2 -1 a highly disordered pattern IV with defect dynamics was found. This state had been studied before by Kai and co-workers and was referred to by them as "phase turbulence." It had a structure factor that was (within our resolution) invariant under rotation. For patterns I, II, and III, S(k) contained crescent-shaped peaks. The peak shape was qualitatively different from the case of planar EC where the structure factor has an elliptical cross section. We present measurements of the widths 1/xik and 1/xitheta in the radial (k) and the azimuthal (theta) directions. For small epsilon (patterns I and II) we found that xik was consistent with the usual Ginzburg-Landau scaling xik approximately epsilon(-nuk) with nuk approximately 1/2. However, for xitheta we found xitheta approximately epsilon(-nutheta) with nutheta approximately 3/4. Presumably this anomalous scaling of xitheta is associated with the Goldstone mode of homeotropic EC. We also show data for the height S0 of the structure factor that are consistent with S0 approximately epsilonbeta with beta approximately -0.5, implying that S0 diverges at onset. This differs from the case of domain chaos in rotating Rayleigh-Bénard convection where experiment is consistent with beta = 1/2 and thus with a vanishing S0. The difference between the shape of the structure-factor cross section and between the exponents, for the present case, for planar EC, and for domain chaos suggests that there are different universality classes for spatiotemporal chaos.

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PubMed2006

Effect of the centrifugal force on domain chaos in Rayleigh-Bénard convection.

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects the domain-chaos state observed in rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly stationary nearly radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency f approximately epsilon(mu) with mu approximately equal to 1 as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, mu and the domain size were consistent with experiment.

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PubMed2006

Domain chaos puzzle and the calculation of the structure factor and its half-width.

The disagreement of the scaling of the correlation length xi between experiment and the Ginzburg-Landau (GL) model for domain chaos was resolved. The Swift-Hohenberg (SH) domain chaos model was integrated numerically to acquire test images to study the effect of a finite image size on the extraction of from the structure factor (SF). The finite image size had a significant effect on the SF determined with the Fourier-transform (FT) method. The maximum entropy method (MEM) was able to overcome this finite image-size problem and produced fairly accurate SFs for the relatively small image sizes provided by experiments. Correlation lengths often have been determined from the second moment of the SF of chaotic patterns because the functional form of the SF is not known. Integration of several test functions provided analytic results indicating that this may not be a reliable method of extracting xi. For both a Gaussian and a squared SH form, the correlation length xi[triple bond]1/sigma, determined from the variance sigma2 of the SF, has the same dependence on the control parameter epsilon as the length xi contained explicitly in the functional forms. However, for the SH and the Lorentzian forms we find xi approximately xi (1/2). Results for xi determined from new experimental data by fitting the functional forms directly to the experimental SF yielded xi approximately epsilon(-v) with v approximately equal to 1/4 for all four functions in the case of the FT method, but v approximately equal to 1/2, in agreement with the GL prediction, in the case of the MEM. Over a wide range of epsilon and wave number k, the experimental SFs collapsed onto a unique curve when appropriately scaled by xi.

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PubMed2005

Reorientation of the large-scale circulation in turbulent Rayleigh-Bénard convection.

We present measurements of the orientation theta0(t) of the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in cylindrical cells of aspect ratio 1. Theta0(t) undergoes irregular reorientations. It contains reorientation events by rotation through angles delta theta with a monotonically decreasing probability distribution p(delta theta), and by cessations (where the LSC stops temporarily) with a uniform p(delta theta). Reorientations have Poissonian statistics in time. The amplitude of the LSC and the magnitude of the azimuthal rotation rate have a negative correlation.

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PubMed2005

Dynamics of fluctuations below a stationary bifurcation to electroconvection in the planar nematic liquid crystal N4.

We fitted C(k,tau,epsilon) proportional to exp([-sigma(k,epsilon)tau] to time-correlation functions C(k,tau,epsilon) of structure factors S(k,t,epsilon) of shadowgraph images of fluctuations below a supercritical bifurcation at V(0)=V(c) to electroconvection of a planar nematic liquid crystal in the presence of a voltage V=sqrt[2]V(0)cos((2pift) [k=(p,q) is the wave vector and epsilon identical with V(2)(0)/V(2)(c)-1]. There were stationary oblique (normal) rolls at small (large) f. Fits of a modified Swift-Hohenberg form to sigma(k,epsilon) gave f-dependent critical behavior for the minimum decay rates sigma(0)(epsilon) and the correlation lengths xi(p,q)(epsilon).

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PubMed2004

Wave-number selection by target patterns and sidewalls in Rayleigh-Bénard convection.

We present experimental results for patterns of Rayleigh-Bénard convection in a cylindrical container with static sidewall forcing. The fluid used was methanol, with a Prandlt number sigma=7.17 , and the aspect ratio was Gamma identical withR/d approximately 19 ( R is the radius and d the thickness of the fluid layer). In the presence of a small heat input along the sidewall, a sudden jump of the temperature difference DeltaT from below to slightly above a critical value Delta T(c) produced a stable pattern of concentric rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell. A quasistatic increase of epsilon identical withDeltaT/Delta T(c) -1 beyond epsilon(1,c) approximately 0.8 caused the umbilicus of the pattern to move off center. As observed by others, a further quasistatic increase of epsilon up to epsilon=15.6 caused a sequence of transitions at epsilon(i,b) ,i=1,...,8 , each associated with the loss of one convection roll at the umbilicus. Each loss of a roll was preceded by the displacement of the umbilicus away from the center of the cell. After each transition the umbilicus moved back toward but never quite reached the center. With decreasing epsilon new rolls formed at the umbilicus when epsilon was reduced below epsilon(i,a) < epsilon(i,b) . When decreasing epsilon , large umbilicus displacements did not occur. In addition to quantitative measurements of the umbilicus displacement, we determined and analyzed the entire wave-director field of each image. The wave numbers varied in the axial direction, with minima at the umbilicus and at the cell wall and a maximum at a radial position close to 2Gamma/3 . The wave numbers at the maximum showed hysteretic jumps at epsilon(i,b) and epsilon(i,a) , but on average agreed well with the theoretical predictions for the wave numbers selected in the far field of an infinitely extended target pattern. To our knowledge there is as yet no prediction for the wave number selected by the umbilicus itself, or by the cell wall of the finite experimental system.

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PubMed2004

Plume motion and large-scale circulation in a cylindrical Rayleigh-Bénard cell.

We used the time correlation of shadowgraph images to determine the angle Theta of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-Bénard cell of aspect ratio Gamma identical with D/L=1 (D is the diameter and L approximately 87 mm is the height) in the Rayleigh-number range 7 x 10(7)</=R</=3 x 10(9) for a Prandtl number sigma=6. We expect that Theta gives the direction of the large-scale circulation. It oscillates time periodically. Near the top and bottom plates Theta(t) has the same frequency but is anticorrelated.

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PubMed2004

Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection.

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-Bénard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.

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PubMed2003

Thermal-noise effect on the transition to Rayleigh-Bénard convection.

We report measurements of fluctuation and roll patterns near the transition to Rayleigh-Bénard convection which are consistent with a fluctuation-induced first-order transition, as predicted by Swift and Hohenberg. Above onset, we find convection rolls with noise-induced fluctuations, time-dependent amplitude modulation and roll undulation, and homogeneous dislocation nucleation.

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PubMed2003

Nusselt number measurements for turbulent Rayleigh-Bénard convection.

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for a cylindrical sample of water (Prandtl number sigma=4.4) of height L approximately equal to 50 cm and aspect ratio Gamma identical with D/L approximately equal to 1 (D is the diameter) for 3 x 10(9)< or =R< or =6 x 10(10). For R approximately 3 x 10(9) the data are consistent with existing results for acetone (sigma=4.0, R< or =3 x 10(9)). There the measurements are also consistent with a model by Grossmann and Lohse (GL). As R increases, the measurements fall below the GL prediction. Near R=6 x 10(10) the prediction is 8% above the data.

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PubMed2003

Finite-size scaling and universality of the thermal resistivity of liquid 4He near Tlambda.

We present measurements of the thermal resistivity rho(t,P,L) near the superfluid transition of 4He at saturated vapor pressure and confined in cylindrical geometries with radii L=0.5 and 1.0 microm [t identical with T/T(lambda)(P)-1]. For L=1.0 microm measurements at six pressures P are presented. At and above T(lambda) the data are consistent with a universal scaling function F(X)=(L/xi(0))(x/nu)(rho/rho(0)), X=(L/xi(0))(1/nu)t valid for all P (rho(0) and x are the pressure-dependent amplitude and effective exponent of the bulk resistivity rho, and xi=xi(0)t(-nu) is the correlation length). Indications of breakdown of scaling and universality are observed below T(lambda).

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PubMed2002

Rayleigh-Bénard convection in elliptic and stadium-shaped containers.

We report on defect formation in convection patterns of stadium-shaped and elliptical horizontal layers of fluid heated from below (Rayleigh-Bénard convection). The fluid was ethanol with a Prandtl number sigma=14.2. The outermost convection roll was forced to be parallel to the sidewall by a supplementary wall heater. The major- and minor-axis aspect ratios Gamma(i)=D(i)/2d, i=1, 2 (D(i) are the major and minor diameter and d the thickness) were 19.4 and 13.0, respectively. For the stadium shape, we found a stable pattern that was reflection-symmetric about the major diameter and had a downflow roll of length L(s) along a large part of this diameter. This roll terminated in two convex disclinations, as expected from theory. No other patterns with the outermost roll parallel to the sidewall were found. The wave numbers of the rolls in the curved sections and L(s) decreased with increasing epsilon identical with DeltaT/DeltaT(c)-1, consistent with a prediction for wave-number selection by curved rolls in an infinite system. At large epsilon, the roll adjacent to the sidewall became unstable due to the cross-roll instability. For the elliptical shape, wave-director frustration yielded a new defect structure predicted by Ercolani et al. Depending on the sample history, three different patterns with the outermost roll parallel to the wall were found. For one, the central downflow roll seen in the stadium was shortened to the point where it resembled a single convection cell. Along much of the major diameter there existed an upflow roll. The new defect structure occurred where the two downflow rolls surrounding the central upflow roll joined. This joint, instead of being smooth as in the stadium case, was angular and created a protuberance pointing outward along the major diameter. We also found a pattern with an upflow roll along the major diameter without the central downflow cell. A third pattern contained a downflow cell, but this cell was displaced by a roll width from the center along a minor diameter. As epsilon increased, the length L(e) between the two protuberances and the wave numbers along the outer parts of the major diameter decreased for all three patterns, analogous to what was found for the stadium. The upper stability limit of these patterns was also set by the cross-roll instability.

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PubMed2002

Rayleigh-Bénard convection with rotation at small Prandtl numbers.

We present experimental and theoretical results near the onset of the Rayleigh-Bénard convection with rotation about a vertical axis in a fluid with a Prandtl number sigma close to 0.18. In the experiment we used a H2-Xe gas mixture with a separation ratio Psi=0.22 and a Lewis number L=1.22 at various pressures and dimensionless rotation rates Omega up to 400. On the basis of a standard weakly nonlinear stability analysis, we found a supercritical, stationary bifurcation for Omega < than approximately 13, which became subcritical over the range 13 < than approximately Omega < or approximately 160. For Omega > than approximately 160 a supercritical Hopf bifurcation precedes the stationary instability of the uniform state. Following the unstable straight-roll fixed point in the subcritical regime by Galerkin methods we determined the location of the saddlenode and the stability of the nonlinear two-dimensional straight-roll state. The rolls were found to be unstable to three-dimensional Küppers-Lortz perturbations for 3.8 < than approximately Omega < than approximately 160. Theoretical results for a pure fluid with the same sigma were qualitatively similar. Measurements using shadowgraph flow visualization yielded a bifurcation line and an Omega range of subcriticality, which agreed with the stability analysis. In the subcritical range the experiment revealed a discontinuity of the pattern amplitude at onset, but was unable to find any hysteresis. Patterns at onset fluctuated irregularly between the ground state and the finite-amplitude state. In this parameter range the convection pattern further above onset was chaotically time dependent. Investigation of the Hopf bifurcation line was difficult because of a wall mode that, for large Omega, preceded the bulk instability. For Omega approximately equal to 400, patterns were found in the sample interior only when the expected Hopf bifurcation was exceeded by about 10%. This is consistent with the convective nature of the bifurcation. However, the observed structure, although time periodic, was spatially disordered and had a frequency that was considerably larger than the expected Hopf frequency. In a separate sample cell with a radial ramp in the spacing no structure was observed at all in the cell interior until the expected stationary instability was reached.

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PubMed2002

Temporal and spatial properties of fluctuations below a supercritical primary bifurcation to traveling oblique-roll electroconvection.

We present measurements of thermally-induced oblique-roll traveling-wave (TW) fluctuations below the supercritical primary bifurcation to electroconvection (EC) in the nematic liquid crystal 4-ethyl-2-fluoro-4'-[2-(trans-4-pentylcyclohexyl)ethyl]-biphenyl (I52). First we analyze time sequences of one-dimensional shadowgraph images taken parallel to the director to obtain the TW frequency omega and the fluctuation lifetime tau. Within our resolution we find that omega is independent of epsilon [triple bond] V/V(c)-1 (V is the applied voltage amplitude and V(c) its value at the onset of convection). Contrary to linear theory, the relaxation rate 1/tau remains finite at the bifurcation. Next we present the analysis of temporally uncorrelated two-dimensional shadowgraph images of the fluctuations for several values of the electrical conductivity sigma. We fitted an anisotropic two-dimensional Lorentzian function, corresponding to oblique-roll EC, to the time-averaged structure factors S(k) derived from the images. This yielded information about the components of the mean wave vector k(0) and about the correlation length xi as a function of sigma and epsilon. The angle of obliqueness theta of the roll patterns was independent of sigma but decreased anomalously as epsilon approached zero. The modulus k(0) of k(0) depended on sigma. It also showed an anomalous reduction close to onset. The anomalous epsilon dependence of k(0) and theta disagrees with linear theory, which predicts a smooth, essentially linear dependence on epsilon, and presumably is caused by nonlinear interactions between the fluctuations.

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PubMed2002

Traveling concentric-roll patterns in Rayleigh-Bénard convection with modulated rotation.

We present experimental results for pattern formation in Rayleigh-Bénard convection with modulated rotation about a vertical axis. The dimensionless rotation rate Omega was varied as Omega(m)=Omega[1+delta cos(phi Omega t)] (time is scaled by the vertical viscous diffusion time of the cell). We used a cylindrical cell of aspect ratio (radius/height) Gamma=11.8 and varied Omega, delta, phi, and epsilon identical with R/R(c)(Omega)-1 (R is the Rayleigh number). The fluid was water with a Prandtl number of 4.5. Sufficiently far above onset even a small delta greater than approximately 0.02 stabilized a concentric-roll (target) pattern. Multiarmed spirals were observed close to onset. The rolls of the target patterns traveled radially inward independent of the sense of rotation. The radial speed v was nearly independent of epsilon for fixed Omega, delta, and phi. However, v increased with any one of Omega, delta, and phi when all the other parameters were held fixed.

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PubMed2002

Singularity in the thermal boundary resistance between superfluid (4)He and a solid surface.

We report new measurements in four cells of the thermal boundary resistance R between copper and (4)He below but near the superfluid-transition temperature T(lambda). For 10(-7)< or =t identical to 1-T/T(lambda))< or =10(-4) fits of R = R(0)t(-x(b))+R(B) to the data yielded x(b) approximately equal to 0.18, whereas a fit to theoretical values based on the renormalization-group theory yielded x(b) = 0.23. Alternatively, a good fit of the theory to the data could be obtained if the amplitude of the prediction was reduced by a factor close to 2. The results raise the question whether the boundary conditions used in the theory should be modified.

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