W. van Saarloos

Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation

The dynamical behavior of a large one-dimensional system obeying the cubic complex Ginzburg-Landau equation is studied numerically as a function of parameters near a supercritical bifurcation. Two types of chaotic behavior can be distinguished beyond the Benjamin-Feir instability, a phase turbulence regime with a conserved phase winding number and no phase dislocations (space-time defects), and a defect regime with a nonzero density of defects. The transition between the two can either be continuous or discontinuous (hysteretic), depending on parameters. The spatial decay of the phase correlation function is inferred to be exponential in both regimes, with a sharp decrease of the correlation length upon entering the defect phase. The temporal decay of correlations is exponential in the defect regime.

A giant atomic slide-puzzle

Atoms in close-packed surfaces of metal crystals move around at surprisingly high rates, even though each atom is locked in tightly by its neighbours. Here we use a low density of indium atoms, embedded in the outermost atomic layer of a copper surface, as tracer particles for scanning tunnelling microscopy to reveal the high vacancy-assisted mobility of atoms in this surface. We believe that most close-packed surfaces of metals and other materials will exhibit a similar vacancy-assisted motion at room temperature, with such surfaces behaving like a gigantic atomic slide-puzzle.

Location of zeros in the complex temperature plane: absence of Lee-Yang theorem

In the Yang-Lee theory (1952) the occurrence of a phase transition at real (physical) values of the magnetic field is related to the behaviour of the density of zeros of the partition function in the complex magnetic field plane. As shown by Lee and Yang, these zeros fall on lines for a wide class of ferromagnetic models. In extensions of the Yang-Lee theory to the complex temperature plane, it has often been assumed that the zeros of the partition function would again fall on lines rather than in areas. Though this happens to be true for the isotropic Ising model, the authors point out that there is in general no basis for this assumption. They discuss the location of the zeros of the partition function of the anisotropic Ising model in the complex temperature plane and show that they indeed always fall in areas.

Aging and solidification of supercooled glycerol.

We experimentally investigate the solidification of supercooled glycerol during aging that has recently been observed by Zondervan et al. We find that a slow cooling at 5 K/h prior to the aging is required for solidification to take place. Furthermore, we show that the time of onset depends strongly on the aging temperature which we varied between 220 and 240 K. The nature of the solid phase remains unclear. The experiments show that upon heating the solid glycerol melts at the crystal melting point. However, rheology experiments in the plate-plate geometry revealed the growth of a soft, slushlike phase that is distinct from a crystal grown by seeding at the same aging temperature. The slushlike glycerol grows from a nucleation point at almost the same speed as a seeded crystal quenched to the same temperature, but its shear modulus is almost 2 orders of magnitude lower than the crystal phase, which we measure independently. While solidification was reproducible in the Couette geometry, it was not in the plate-plate geometry.

Layer Formation of Dilute Colloidal Suspensions As a Result of a Concentration-Dependent Sedimentation Velocity: Some Simple Considerations and Suggestions for Further Experiments

In a number of experiments on sedimentation in colloidal suspensions, the formation of a vertically layered structure in the concentration profile has been observed. We argue that this may be interpreted as the formation of shock fronts in the concentration profile due to the concentration dependence of the sedimentation velocity, a mechanism first identified by Kynch. We propose several experiments to test this suggestion, and draw attention to the possibility of observing anomalous diffusion in a sedimenting suspension with reversible aggregation.

Phase VS. Defect Turbulence in the 1D Complex Ginzburg-Landau Equation

The understanding of the dynamical properties of spatially extended systems remains a major challenge, in spite of some recent progress. In this paper, we will restrict ourselves to the very rich variety of cellular instabilities observed in hydrodynamic systems, such as the Taylor-Couette flow at moderate Taylor numbers, as discussed in this book. This is only one of many possible situations where the space-time dynamics leads to non trivial properties1.

The Formation and Propagation of Fronts at the Electric Field Induced Bend Freedericksz Transition

The electric field induced bend Freedericksz transition in 5CB is first order. At the threshold value of the applied voltage, the deformed and undeformed states can coexist in equilibrium. The width of the front separating the two states gives a measure of the abruptness of the transition. If the applied voltage differs from its threshold value, the stable state invades the metastable one, and the front separating the two states moves. We present data for the velocity of front propagation in 5CB, and compare results with the predictions of theory.

Comment on "a Generalized Langevin Equation for 1/ƒ Noise"

Abstract We point out that in a recent generalized Langevin equation approach to 1 ƒ noise, the frequency dependent transport coefficient violates the Kramers-Kronig causality relations. An investigation of the possibility of using a generalized Langevin equation that does not violate causality leads to the conclusion that this idea is not a viable approach to the problem of 1 ƒ noise.