Anisotropy of the oscillation dynamics of a breather on a trap in the electroconvective twist structure of a nematic

The oscillation dynamics of dislocations with a dissociated nucleus in the electroconvective twist structure of a nematic liquid crystal has been studied. The initial state of the roll twist structure is unstable. One of the origins of this is the helical flows of the nematic in the neighboring rolls with the antiparallel axial velocity components. As a result, oscillating or “breathing” defects are formed, which have the properties of breathers and are described by the sine-Gordon equation. It has been demonstrated that the space-time anisotropy of the character of motion of the dislocations in opposite directions orthogonal to the roll structure takes place in such a nonstationary system.     

Effect of viscoelasticity on dynamics and stability in roll coatings

Flow behaviors and coating windows of Newtonian and viscoelastic liquids in forward and reverse roll coating processes have been examined. Viscoelastic liquids considered in this study, as a Boger fluid, have different elastic or extensional properties but almost same shear viscosity as Newtonian case. Coating thickness in both flows strongly depends on the viscoelasticity in polymer solutions as well as operating conditions such as capillary number and gap size between two rolls. Also, uniform coating windows are drastically reduced for the viscoelastic liquids. These results evidently support that a small amount of polymer in coating liquids play an indispensable role in altering dynamics and stability of coating processes.     

WAVENUMBER SELECTION IN RAYLEIGH -BENARD CONVECTION: EXPERIMENTAL EVIDENCE FOR THE EXISTENCE OF AN INHERENT OPTIMAL SCALE

Abstract

The selection of wavenumbers in roll convection has been studied experimentally. Roll flow of a given initial wavenumber, artificially induced in the middle of a chamber, is evolved freely in contact with a less ordered flow on both sides of the induction zpne. The induced rolls adjust their wavenumber to a physically optimal ( referred) value determined by the Rayleigh number. This process is mainly two-dimensional, nondiffusive and independent of the side walls. The preferred wavenumber seems to coincide with the mean wavenumber of steady roll flow observed in experiments with random initial disturbances, being apparently an inherent characteristic of cellular convection     

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.     

Chaotic travelling rolls in Rayleigh-Bénard convection

In this paper we investigate two-dimensional (2D) Rayleigh-Bénard convection using direct numerical simulation in Boussinesq fluids with Prandtl number P = 6.8 confined between thermally conducting plates. We show through the simulation that in a small range of reduced Rayleigh number r (770 < r < 890) the 2D rolls move chaotically in a direction normal to the roll axis. The lateral shift of the rolls may lead to a global flow reversal of the convective motion. The chaotic travelling rolls are observed in simulations with free-slip as well as no-slip boundary conditions on the velocity field. We show that the travelling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes.     

Heteroclinic behavior in rotating Rayleigh-Bénard convection

We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle. Received 10 June 1999     

Polymer cover induced self-excited vibrations of nipped rolls

As a result of increased speeds, the dynamic instability of rotatory machines including polymer-covered nipped rolls has grown. The instability originates from the viscoelastic behavior of the covers and leads to strong barring vibrations, which limit the operating speed of many machines. In this work, the self-excited vibrations of a nipped two-roll system with a polymer cover on the other roll are investigated using an analytical model developed for the roll system. The viscoelastic properties of the cover are accounted for by the standard linear solid (SLS) model. The numerical results display wave-like roll cover deformation patterns, separate instability regions of the system and moving wave patterns near the resonances. The roll system is unstable when the excitation frequency of the polygonal cover deformation lies in the vicinity of the higher eigenfrequency of the system. By using a speed-up ramp, it is shown that at high speeds the instability regions may become too wide and unstable to be crossed in industrial machines. An experiment was carried out, and a good agreement is found between the numerical and experimental results.     

Instabilities in a liquid-fluidized bed of gas bubbles

Gas bubbles in an aqueous foam can be unjammed, or fluidized, by introducing a forced flow of the continuous liquid phase at a sufficiently high rate. We observe that the resulting bubble dynamics are spatially inhomogeneous, exhibiting a sequence of instabilities vs increasing flow rate. First irregular swirls appear, then a single convective roll, and finally a series of stratified convection rolls each with a different average bubble size.     

Breathers in the one-dimensional roll structure of twisted nematics

The dynamics of nonsingular defects has been studied experimentally and theoretically in the periodic roll structures arising at electroconvection in nematic liquid crystals twisted by π/2. The presence of an axial component of the velocity of the hydrodynamic flow with the opposite direction in the neighboring rolls is characteristic of roll structures in twisted nematics. The quantitative estimates of the critical frequency of the oscillations of structural defects have been obtained on the basis of the nonlinear equation of motion for the roll displacement. It has been found that the periodic creation and annihilation of a pair of edge dislocations with the topological indices +1 and −1 occur in the process of oscillations of a defect with a nonsingular nucleus. It has been demonstrated that oscillating defects with zero topological indices correspond to the solution of the sine-Gordon equation in the form of standing breathers.     

Dynamics of zero-Prandtl number convection near onset

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Be?nard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.     

Breatherlike defects and their dynamics in the one-dimensional roll structure of twisted nematics

The dynamics of the nonsingular defects in the periodic structures of the rolls that appear in π/2-twisted nematic liquid crystals during electroconvection is studied experimentally and theoretically. The roll structures in twisted nematics are characterized by the presence of an axial component of the hydrodynamic flow velocity with opposite directions in neighboring rolls. The critical oscillation frequency of structural defects is quantitatively estimated using a nonlinear equation of motion for roll displacements. It is found that a pair of edge dislocations with topological charges of +1 and–1 nucleates and annihilates periodically during the oscillations of a defect with a nonsingular core. Oscillating defects with a zero topological charge is shown to correspond to the solution of the sine-Gordon equation in the form of standing breathers. Asymmetry is detected in the full oscillation cycle of a breather defect, and it is related to the twist symmetry of a twist nematic. This asymmetry is taken into account as effective anisotropic friction. The behavior of a breather on a trap, namely, a classical defect (dislocation), is investigated. Dislocation motion is shown to be anisotropic in the oscillation cycle: in one direction, a dislocation moves regularly; in the second phase, the transition into the initial state proceeds via the decay of the breather into a dipole pair of dislocations of opposite signs followed by their annihilation.     

Transitions in convection driven by a horizontal temperature gradient

We report the first detailed experimental study of transitions in the convection of a low Prandtl number fluid driven by a horizontal temperature gradient. The observed states, from time independent to one frequency with noise, to pure noise, to two frequencies with noise, can be related to the two secondary flows predicted for a cavity with large lateral extent, transverse stationary and longitudinal oscillatory rolls. Measured wavelengths and frequencies for the longitudinal rolls are in agreement with theoretical values, while the critical Grashof number is much higher than expected. Our results call for a new theoretical approach which takes both instability mechanisms into account.     

Convection in highly fluidized three-dimensional granular beds

Free, buoyancy-driven convection has been observed experimentally in three-dimensional highly fluidized granular flows for the first time. Positron emission particle tracking was used to determine the position of a tracer grain in a vibrofluidized bed, from which packing fraction distributions as well as the velocity fields could be determined. The convection rolls, although small compared to the magnitude of velocity fluctuations (<5%), were consistently observed for a range of grain numbers and shaker amplitudes. Density variations are a signature of free convection and, with negative temperature gradients also present, were interpreted as the mechanism by which the convection rolls were initiated.     

Nonlinear analysis of spatial structures in two-dimensional anisotropic pattern forming systems

Motivated in particular by recent experiments on convective instabilities in nematic liquid crystals we examine the possible stationary patterns in anisotropic quasi-two-dimensional systems. The generalized SH-model we use exhibits the typical Lifshitz point, which separates the regions of normal and of oblique rolls at threshold. Above threshold the two-dimensional wavenumber regions of stable roll solutions take on interesting shapes in the vicinity of the Lifshitz point. Undulated (wavy) rolls also exist metastably in a narrow parameter range. We derive envelope equations which show that this scenario is general near threshold. Our results suggest experimental investigation, especially in the neighborhood of the Lifshitz point.Dedicated to Prof. Dr. L. Tewordt in honour of his 60th birthday     

Flexoelectric origin of oblique rolls with helical flow in electroconvective nematics under DC excitation

We present a 3-dimensional, linear analysis of electrohydrodynamic (EHD) roll instability in a nematic liquid crystal under DC excitation. It is shown that the flexoelectric effect leads to a new symmetry of the flow pattern, viz. ahelical flow inoblique rolls. Our experimental observations agree with the theoretical predictions.     

热连轧粗轧调宽轧制过程边角部金属流动三维数值模拟

以梅山钢铁股份有限公司热轧机组的粗轧板坯边部出现“黑线”为背景,对孔型立辊的5道次可逆立-平轧制过程进行了数值模拟.模拟结果表明：孔型立辊轧制能更有效地纠正双鼓变形,避免产生边部夹层;轧件的边角部金属在轧制过程中逐渐流动到轧件的上下表面;在相同轧制工艺条件下,随着孔型内倒角半径的增加翻平量逐渐增大;轧制过程中,低温、高应力应变状态的金属在轧件边部的累积最终可能导致轧件边部沿长度方向产生“黑线”缺陷;合理地设计立辊的形状和优化立轧压下制度可以避免边部夹层的产生,并减少“黑线”缺陷甚至消除该缺陷. 关键词： 热连轧 数值模拟 “黑线”缺陷     

Hydrodynamic vector potentials

Solving the Navier-Stokes equation for incompressible fluids is greatly simplified by the solution of the vorticity equation. To accomplish this for three-dimensional flows requires vector potentials. These potentials are not only useful to take care of the incompressibility. Their modes are suitable also as test functions since the familiar Galerkin procedure does not work. The new method is checked by examples with known results and its relation to the classical approach with the stream function is clarified. The principle demonstration, however, concerns the transition to turbulence in plane shear flows. A simple layer of long rolls with axes parallel to the basic flow incites the transition. Received 20 August 2001     

Spatiotemporal antiphase dynamics in coupled extended optical media

Experimental evidence of spatiotemporal antiphase dynamics is given for an extended system made of two liquid crystal slices that are optically coupled by two equal amplitude counterpropagating pumping beams. Theory and experiments carried out in a transverse one-dimensional configuration show that roll patterns are generated in each slice. These rolls are spatially in-phase or antiphase for a focusing or a defocusing nonlinearity type, respectively. These in-phase or antiphase dynamics remain robust even for complex spatiotemporal regimes such as dislocation regimes.     

Integrable systems and invariant curve flows in centro-equiaffine symplectic geometry

In this paper, the theory for curves in centro-equiaffine symplectic geometry is established. Integrable systems satisfied by the curvatures of curves under inextensible motions in centro-equiaffine symplectic geometry are identified. It is shown that certain non-stretching invariant curve flows in centro-equiaffine symplectic geometry are closely related to the matrix KdV equations and their extension.     

From fractional Chern insulators to a fractional quantum spin hall effect

Horizontal rolls, generated in convective flow above a partially heated bottom in a rectangular box are studied experimentally for a wide range of the Prandtl number (7 ≤ P _r ≤ 1020), the Rayleigh number (300 ≤ R _a ≤ 2.8 × 10⁷) and the aspect ratio (0.08 ≤ a ≤ 0.7). Experimental studies are supported by direct numerical simulations, which made possible the examination of the regimes inaccessible in the experiment, and also to investigate in detail the heat transfer in the convective flow. A variety of regimes with longitudinal helical rolls, with transverse rolls and with mixed structures has been observed. The structure of secondary flows is defined by the level of convective supercriticality in the boundary layer (Rayleigh number) and the intensity of the throughflow, defined by the Reynolds number, which depends itself on the heating and size, i.e. on the Rayleigh number. Most of the studied regimes were characterized by the appearance of longitudinal rolls. The transverse rolls appear in the flow only under the conditions of the large vertical drop in the temperature and weak large-scale flow (that is possible only at large values of the Prandtl number). Both longitudinal and transverse rolls lead to remarkable heat transfer enhancement. The formation and characteristics of horizontal rolls are described in details.