Biomedical subjects
Publications and source records attributed to B Eckhardt.
In experiments on dilute polymers between rotating cylinders Groisman and Steinberg [Phys. Rev. Lett. 78, 1460 (1997)] observed the formation of vortices that were not equidistantly spaced but rather paired up in what they called "diwhirls." We calculate these states within an Oldroyd-B model with parameters adapted to the experiment and find good agreement with the observed characteristics of the diwhirls.
We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible nor incompressible but strongly influenced by the 3D flow underneath the surface. The velocity correlation functions in the 2D surface and in the 3D volume scale with the same exponents. In the viscous subrange the amplitudes are the same, but in the inertial subrange the 2D one is reduced to 2/3 of the 3D amplitude. The surface flow is more strongly intermittent than the 3D volume flow. Geometric scaling theory is used to derive a relation between the scaling of the velocity field and the density fluctuations of a passive scalar advected on the surface.
We report an experimental and numerical study of turbulent fluid motion in a free surface. The flow is realized experimentally on the surface of a tank filled with water stirred by a vertically oscillating grid positioned well below the surface. The effect of surface waves appears to be negligible so that the flow can numerically be realized with a flat surface and stress-free boundary conditions. The surface flow is unconventional in that it is not incompressible and neither energy nor enstrophy are conserved. Nevertheless, according to both experiment and numerical simulation, the second order structure function S2(R) scales essentially as for a three-dimensional system. However, the surface flow seems to be more intermittent.
The evolution of turbulent spots in a parallel shear flow is studied by means of full three-dimensional numerical simulations. The flow is bounded by free surfaces and driven by a volume force. Three regions in the spanwise spot cross section can be identified: a turbulent interior, an interface layer with prominent streamwise streaks and vortices, and a laminar exterior region with a large scale flow induced by the presence of the spot. The lift-up of streamwise streaks that is caused by non-normal amplification is clearly detected in the region adjacent to the spot interface. The spot can be characterized by an exponentially decaying front that moves with a speed different from that of the cross-stream outflow or the spanwise phase velocity of the streamwise roll pattern. Growth of the spots seems to be intimately connected to the large scale outside flow, for a turbulent ribbon extending across the box in the downstream direction does not show the large scale flow and does not grow. Quantitatively, the large scale flow induces a linear instability in the neighborhood of the spot, but the associated front velocity is too small to explain the spot spreading.
We discuss the flow between concentric rotating cylinders in the limit of large radii where the system approaches plane Couette flow. We discuss how in this limit the linear instability that leads to the formation of Taylor vortices is lost and how the character of the transition approaches that of planar shear flows. In particular, a parameter regime is identified where fractal distributions of lifetimes and spatiotemporal intermittency occur. Experiments in this regime should allow us to study the characteristics of shear flow turbulence in a closed flow geometry.
We analyze the phase-space structure of a model for thermoreceptors in fish and mammals. As a function of the temperature we identify a period doubling scenario at low temperatures, a regime where an unstable stationary fixed point collides with the attractor and blocks the thermoreceptor, and a transition from period n+1 to period n as the temperature is further increased. The period reduction phenomenon is due to an autoresonance between fast and slow ion channels and shows the features typical for mode locking.
We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.
We consider distributions of diagonal matrix elements for smooth observables in systems whose classical phase space has a mixture of chaotic and nearly integrable regions. The quantum distributions agree very well with distributions obtained from classical trajectory segments whose length is the Heisenberg time. Non-Gaussian wings in the distributions can be linked to classical trapping in certain parts of phase space, sometimes connected to islands, but also to regions separated by other barriers to transport. Thus classical deviations from ergodicity are quantitatively reflected in quantum matrix elements. The relation to scars is discussed.
The structure function of a scalar theta(x,t), passively advected in a two-dimensional turbulent flow u(x,t), is discussed by means of the fractal dimension delta1g of the passive-scalar graph. A relation between delta1g, the scaling exponent zeta(theta)(1) of the scalar structure function D1(theta)r, and the structure function D2(r) of the underlying flow field is derived. Different from the three-dimensional (3D) case, the 2D structure function also depends on an additional parameter, characteristic of the driving of the passive scalar. In the enstrophy inertial subrange a mean-field approximation for the velocity structure function gives a scaling of the passive scalar graph with delta1g<2 for intermediate and large values of the Prandtl number Pr. In the energy inertial subrange a model for the energy spectrum and thus D2(r) gives a passive-scalar graph scaling with exponent delta1g=5/3. Finally, we discuss an application to recent observations of scalar dispersion in nonuniversal 2D flows.
We analyze the properties of a 19-dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations shows a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition scenario in shear flows.
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Adhesion of the scleral flap is one of the postoperative complications in glaucoma surgery, especially in cases with trabeculectomy. From July 1989 to February 1990 a trabeculectomy was done in 102 patients with chronic open-angle glaucoma. To prevent adhesion of the scleral flap in the early postoperative period, a 9-0 nylon suture loop was fixed at the scleral flap and led through the conjunctiva. If in the early postoperative phase the intraocular pressure rose due to adhesion of the scleral flap, the flap was opened by pulling the suture loop and thereby releasing the scleral flap. The success of this method is indicated by the drop in intraocular pressure and the filling of the filtering bleb. In 31 of 102 patients an adhesion was observed. Twenty-four of these 31 patients recompensated after one or more pulls at the suture loop, causing the intraocular pressure to remain at a normal level.
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