Depinning of a vortex chain in a disordered flow channel

We study depinning of vortex chains in channels formed by static, disordered vortex arrays. Depinning is governed either by the barrier for defect nucleation or for defect motion, depending on whether the chain periodicity is commensurate or incommensurate with the surrounding arrays. We analyze the reduction of the gap between these barriers as function of disorder. At large disorder, commensurability becomes irrelevant and the pinning force is reduced to a small fraction of the ideal shear strength of ordered channels. Implications for experiments on channel devices are discussed.Comment: 5 pages, 4 figures. Accepted for publication in Europhysics Letter

Stability analysis in continuous and discrete time, using the Cayley transform

For semigroups and for bounded operators we introduce the new notion of Bergman distance. Systems with a finite Bergman distance share the same stability properties, and the Bergman distance is preserved under the Cayley transform. This way, we get stability results in continuous and discrete time. As an example, we show that bounded perturbations lead to pairs of semigroups with finite Bergman distance. This is extended to a class of Desch–Schappacher perturbations

Methods to calibrate and scale axial distances in confocal microscopy as a function of refractive index

Accurate distance measurement in 3D confocal microscopy is important for quantitative analysis, volume visualization and image restoration. However, axial distances can be distorted by both the point spread function and by a refractive-index mismatch between the sample and immersion liquid, which are difficult to separate. Additionally, accurate calibration of the axial distances in confocal microscopy remains cumbersome, although several high-end methods exist. In this paper we present two methods to calibrate axial distances in 3D confocal microscopy that are both accurate and easily implemented. With these methods, we measured axial scaling factors as a function of refractive-index mismatch for high-aperture confocal microscopy imaging. We found that our scaling factors are almost completely linearly dependent on refractive index and that they were in good agreement with theoretical predictions that take the full vectorial properties of light into account. There was however a strong deviation with the theoretical predictions using (high-angle) geometrical optics, which predict much lower scaling factors. As an illustration, we measured the point-spread-function of a point-scanning confocal microscope and showed that an index-matched, micron-sized spherical object is still significantly elongated due to this PSF, which confirms that single micron-sized spheres are not well suited to determine accurate axial calibration nor axial scaling.Comment: 8 pages, 5 figure

Depinning and dynamics of vortices confined in mesoscopic flow channels

We study the behavior of vortex matter in artificial flow channels confined by pinned vortices in the channel edges (CE's). The critical current $J_s$ is governed by the interaction with static vortices in the CE's. We study structural changes associated with (in)commensurability between the channel width $w$ and the natural row spacing $b_0$, and their effect on $J_s$. The behavior depends crucially on the presence of disorder in the CE arrays. For ordered CE's, maxima in $J_s$ occur at matching $w=nb_0$ ($n$ integer), while for $w\neq nb_0$ defects along the CE's cause a vanishing $J_s$. For weak CE disorder, the sharp peaks in $J_s$ at $w=nb_0$ become smeared via nucleation and pinning of defects. The corresponding quasi-1D $n$ row configurations can be described by a (disordered)sine-Gordon model. For larger disorder and $w\simeq nb_0$, $J_s$ levels at $\sim 30$ of the ideal lattice strength $J_s^0$. Around 'half filling' ($w/b_0 \simeq n\pm 1/2$), disorder causes new features, namely {\it misaligned} defects and coexistence of $n$ and $n \pm 1$ rows in the channel. This causes a {\it maximum} in $J_s$ around mismatch, while $J_s$ smoothly decreases towards matching due to annealing of the misaligned regions. We study the evolution of static and dynamic structures on changing $w/b_0$, the relation between modulations of $J_s$ and transverse fluctuations and dynamic ordering of the arrays. The numerical results at strong disorder show good qualitative agreement with recent mode-locking experiments.Comment: 29 pages, 32 figure

Phase behavior of flowerlike micelles in a SCF cell model

We study the interactions between flowerlike micelles, self-assembled from telechelic associative polymers, using a molecular self-consistent field (SCF) theory and discuss the corresponding phase behavior. In these calculations we do not impose properties such as aggregation number, micellar structure and number of bridging chains. Adopting a SCF cell model, we calculate the free energy of interaction between a central micelle surrounded by others. Based on these results, we predict the binodal for coexistence of dilute and dense liquid phases, as a function of the length of the hydrophobic and hydrophilic blocks. In the same cell model we compute the number of bridges between micelles, allowing us to predict the network transition. Several quantitative trends obtained from the numerical results can be rationalized in terms of transparent scaling argument

Brownian particles in transient polymer networks

We discuss the thermal motion of colloidal particles in transient polymer networks. For particles that are physically bound to the surrounding chains, light-scattering experiments reveal that the submillisecond dynamics changes from diffusive to Rouse-like upon crossing the network formation threshold. Particles that are not bound do not show such a transition. At longer time scales the mean-square displacement (MSD) exhibits a caging plateau and, ultimately, a slow diffusive motion. The slow diffusion at longer time scales can be related to the macroscopic viscosity of the polymer solutions. Expressions that relate the caging plateau to the macroscopic network elasticity are found to fail for the cases presented here. The typical Rouse scaling of the MSD with the square root of time, as found in experiments at short time scales, is explained by developing a bead-spring model of a large colloidal particle connected to several polymer chains. The resulting analytical expressions for the MSD of the colloidal particle are shown to be consistent with experimental findings

Dynamic melting of confined vortex matter

We study {\em dynamic} melting of confined vortex matter moving in disordered, mesoscopic channels by mode-locking experiments. The dynamic melting transition, characterized by a collapse of the mode-locking effect, strongly depends on the frequency, i.e. on the average velocity of the vortices. The associated dynamic ordering velocity diverges upon approaching the equilibrium melting line $T_{m,e}(B)$ as $v_c \sim (T_{m,e}-T)^{-1}$. The data provide the first direct evidence for velocity dependent melting and show that the phenomenon also takes place in a system under disordered confinement. \pacs{74.25.Qt,83.50.Ha,64.70.Dv,64.60.Ht}Comment: Some small changes have been made. 4 pages, 4 figures included. Accepted for publication in Phys. Rev. Let

Dynamical fluctuations in mode locking experiments on vortices moving through mesoscopic channels

We have studied the flow properties of vortices driven through easy flow mesoscopic channels by means of the mode locking (ML) technique. We observe a ML jump with large voltage broadening in the real part of the rf-impedance. Upon approaching the pure dc flow by reducing the rf amplitude, the ML jump is smeared out via a divergence of the voltage width. This indicates a large spread in internal frequencies and lack of temporal coherence in the dc-driven state.Comment: 2 pages, 2 figures, contribution to M2S-HTSC 2003, Ri