Avoiding Patterns in the Abelian Sense

We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some properties of ω-words avoiding these patterns.Research of both authors supported by NSERC Operating Grants.https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/avoiding-patterns-in-the-abelian-sense/42148B0781A38A6618A537AAD7D39B8

Phase separation and rotor self-assembly in active particle suspensions

Adding a non-adsorbing polymer to passive colloids induces an attraction between the particles via the `depletion' mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory and simulations to demonstrate that using active colloids (such as motile bacteria) dramatically changes the physics of such mixtures. First, significantly stronger inter-particle attraction is needed to cause phase separation. Secondly, the finite size aggregates formed at lower inter-particle attraction show unidirectional rotation. These micro-rotors demonstrate the self assembly of functional structures using active particles. The angular speed of the rotating clusters scales approximately as the inverse of their size, which may be understood theoretically by assuming that the torques exerted by the outermost bacteria in a cluster add up randomly. Our simulations suggest that both the suppression of phase separation and the self assembly of rotors are generic features of aggregating swimmers, and should therefore occur in a variety of biological and synthetic active particle systems.Comment: Main text: 6 pages, 5 figures. Supplementary information: 5 pages, 4 figures. Supplementary movies available from httP://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1116334109/-/DCSupplementa

When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation

Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis ${\bf u}$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant \u until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density $\rho$ but not on ${\bf u}$, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing $v(\rho)$ causes phase separation in dimensions $d=2,3$, even when no attractive forces act between the particles. This points to a generic role for motility-induced phase separation in active matter. However, we show that the ABP/RTP equivalence does not automatically extend to the more general case of \u-dependent motilities

Differential Dynamic Microscopy of Bacterial Motility

We demonstrate 'differential dynamic microscopy' (DDM) for the fast, high throughput characterization of the dynamics of active particles. Specifically, we characterize the swimming speed distribution and the fraction of motile cells in suspensions of Escherichia coli bacteria. By averaging over ~10^4 cells, our results are highly accurate compared to conventional tracking. The diffusivity of non-motile cells is enhanced by an amount proportional to the concentration of motile cells.Comment: 4 pages, 4 figures. In this updated version we have added simulations to support our interpretation, and changed the model for the swimming speed probability distribution from log-normal to a Schulz distribution. Neither modification significantly changes our conclusion

Enhanced gas-liquid mass transfer of an oscillatory constricted-tubular reactor

The mass transfer performance has been tested for gas-liquid flow in a new tubular reactor system, the oscillating mesotube (OMT), which features the oscillatory movement of fluid across a series of smooth constrictions located periodically along the vertical 4.4 mm internal diameter tube. The effect of the fluid oscillations (frequency,f, and center-to-peak amplitude, x(0), in the range of 0-20 s(-1) and 0-3 mm, respectively) on the overall volumetric mass transfer coefficient (k(L)a) has been tested by measuring the oxygen saturation levels with a fiber-optical microprobe (oxygen micro-optrode), and a mathematical model has been produced to describe the oxygen mass transport in the OMT. The oxygen mass transfer rates were about I order of magnitude higher (k(L)a values up to 0.16 s(-1)) than those values reported for gas-liquid contacting in a 50 mm internal diameter oscillatory flow reactor (OFR), for the same peak fluid oscillatory velocity, i.e., 2 pi fx(0). This represents remarkable oxygen transfer efficiencies, especially when considering the very low mean superficial gas velocity involved in this work (0.37 mm s(-1)). The narrower constrictions helped to increase the gas fraction (holdup) by reducing the rise velocity of the bubbles. However, the extent of radial mixing and the detachment of vortex rings from the surface of the periodic constrictions are actually the main causes of bubbles retention and effective gas-liquid contacting and are, thus, responsible for the enhancement of k(L)a in the OMT.N.R. thanks the Portuguese Foundation for Science and Technology (FCT) for financial support of his work (SFRH/BD/6954/2001)

Transport and Noise Properties of sub-100-nm Planar Nb Josephson Junctions with Metallic Hf-Ti Barriers for nano-SQUID Applications

We analyze electric transport and noise properties at 4.2 K of self-shunted superconductor-normal metal-superconductor (SNS) sandwich-type Josephson junctions, comprising Nb as the superconductor and Hf-Ti as the normal conducting material, with lateral dimensions down to approximately 80 nm. The junctions are fabricated with an optimized multilayer Nb technology based on nanopatterning by electron-beam lithography and chemical-mechanical polishing. The dependence of transport properties on the junction geometry (lateral size and barrier thickness d(Hf-Ti)) is studied, yielding a characteristic voltage V-c up to approximately 100 mu V for the smallest d(Hf-Ti) = 17 nm. The observed small hysteresis in the current-voltage curves of devices with high V-c and large size can be attributed to self-heating of the junctions and fitted with an extended version of the resistively shunted junction model. Measurements of voltage noise of single junctions are consistent with the model including self-heating effects. The potential of our technology for further miniaturization of nanoscale superconducting quantum interference devices and for the improvement of their performance is discussed

YBa2Cu3O7 and Nb NanoSQUIDs for the Investigation of Magnetization Reversal of Individual Magnetic Nanoparticles

We report on the fabrication, performance and application of sensitive YBa2Cu3O7 (YBCO) and Nb nanoSQUIDs to magnetization reversal measurements of individual magnetic nanoparticles. The YBCO SQUIDs are based on grain boundary Josephson junctions and are patterned in a single layer of epitaxially grown YBCO films by Ga focused ion beam milling. The Nb SQUIDs contain sandwich-type Josephson junctions with normal conducting HfTi barriers; they are fabricated with a multilayer technology that includes patterning by e-beam lithography and a combination of milling techniques and chemical-mechanical polishing. Due to the small inductance of the SQUID loops, ultralow white flux noise at 4.2 K can be achieved, which yields spin sensitivities of down to a few Bohr magnetons per unit bandwidth for a magnetic nanoparticle placed at 10 nm distance to the SQUID loop