Helicity within the vortex filament model

Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle to that of classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments

Tightening slip knots in raw and degummed silk to increase toughness without losing strength

NMP is supported by the European Research Council (ERC StG Ideas 2011 BIHSNAM n. 279985 on “Bio-Inspired hierarchical super-nanomaterials”, ERC PoC 2013-1 REPLICA2 n. 619448 on “Large-area replication of biological anti-adhesive nanosurfaces”, ERC PoC 2013-2 KNOTOUGH n. 632277 on “Super-tough knotted fibres”), by the European Commission under the Graphene Flagship (WP10 “Nanocomposites”, n. 604391) and by the Provincia Autonoma di Trento (“Graphene Nanocomposites”, n. S116/2012-242637 and reg.delib. n. 2266)

Zigzag line defects and manipulation of colloids in a nematic liquid crystal in microwrinkle grooves

Spatially confined liquid crystals exhibit non-uniform alignment, often accompanied by self-organised topological defects of non-trivial shape in response to imposed boundary conditions and geometry. Here we show that a nematic liquid crystal, when confined in a sinusoidal microwrinkle groove, exhibits a new periodic arrangement of twist deformations and a zigzag line defect. This periodic ordering results from the inherent liquid crystal elastic anisotropy and the antagonistic boundary conditions at the flat liquid crystal–air and the curved liquid crystal–groove interfaces. The periodic structure can be tuned by controlling the groove geometry and the molecular chirality, which demonstrates the importance of boundary conditions and introduced asymmetry for the engineering of topological defects. Moreover, the kinks in the zigzag defects can trap small particles, which may afford a new method for manipulation of colloids. Our system, which uses easily fabricated microwrinkle grooves, provides a new microfabrication method based on the arrangement of controllable defects

Physical Links: Defining and detecting inter-chain entanglement

Fluctuating filaments, from densely-packed biopolymers to defect lines in structured fluids, are prone to become interlaced and form intricate architectures. Understanding the ensuing mechanical and relaxation properties depends critically on being able to capture such entanglement in quantitative terms. So far, this has been an elusive challenge. Here we introduce the first general characterization of non-ephemeral forms of entanglement in linear curves by introducing novel descriptors that extend topological measures of linking from close to open curves. We thus establish the concept of physical links. This general method is applied to diverse contexts: equilibrated ring polymers, mechanically-stretched links and concentrated solutions of linear chains. The abundance, complexity and space distribution of their physical links gives access to a whole new layer of understanding of such systems and open new perspectives for others, such as reconnection events and topological simplification in dissipative fields and defect lines

Učinak bakra na toksičnost i genotoksičnost kadmija u vodenoj leći (Lemna minor L.)

We investigated interactions between copper (in the concentrations of 2.5 μmol L-1 and 5 μmol L-1) and cadmium (5 μmol L-1) in common duckweed (Lemna minor L.) by exposing it to either metal or to their combinations for four or seven days. Their uptake increased with time, but it was lower in plants treated with combinations of metals than in plants treated with either metal given alone. In separate treatments, either metal increased malondialdehyde (MDA) level and catalase and peroxidase activity. Both induced DNA damage, but copper did it only after 7 days of treatment. On day 4, the combination of cadmium and 5 μmol L-1 copper additionally increased MDA as well as catalase and peroxidase activity. In contrast, on day 7, MDA dropped in plants treated with combinations of metals, and especially with 2.5 μmol L-1 copper plus cadmium. In these plants, catalase activity was higher than in copper treated plants. Peroxidase activity increased after treatment with cadmium and 2.5 μmol L-1 copper but decreased in plants treated with cadmium and 5 μmol L-1 copper. Compared to copper alone, combinations of metals enhanced DNA damage after 4 days of treatment but it dropped on day 7. In conclusion, either metal given alone was toxic/genotoxic and caused oxidative stress. On day 4 of combined treatment, the higher copper concentration was more toxic than either metal alone. In contrast, on day 7 of combined treatment, the lower copper concentration showed lower oxidative and DNA damage. These complex interactions can not be explained by simple antagonism and/or synergism. Further studies should go in that direction.U svrhu istraživanja interakcija između bakra kao esencijalnog elementa te kadmija kao neesencijalnog i toksičnog metala, vodenu leću Lemna minor L. uzgajali smo na podlogama s kadmijem (5 μmol L-1) odnosno s bakrom (2,5 μmol L-1 i 5 μmol L-1) te s njihovim kombinacijama. Unos metala u biljke povećavao se s trajanjem pokusa, a kod kombinacije metala u biljkama je izmjerena niža količina kadmija nego u onima uzgajanima samo na kadmiju. U biljkama tretiranim pojedinačnim metalom došlo je do povećanja sadržaja malondialdehida (MDA) te aktivnosti katalaze i peroksidaze u odnosu na kontrolne biljke. Također, primijećeno je oštećenje DNA iako kod bakra tek sedmog dana tretmana. Količina MDA i aktivnost obaju enzima dodatno se povećala na tretmanu kombinacijom kadmija i bakra (5 μmol L-1) nakon četvrtog dana pokusa, dok se količina MDA smanjila nakon sedmog dana kod kombinacije kadmija i 2,5 μmol L-1 bakra. U tim biljkama primijećena je i veća aktivnost katalaze, dok je aktivnost peroksidaze porasla na tretmanu kadmijem i 2,5 μmol L-1 bakrom, ali se smanjila na tretmanu kadmijem i 5 μmol L-1 bakrom. Oštećenje DNA koje je bilo veće kod kombinacije metala nakon četvrtog dana, osobito u usporedbi sa samim bakrom, smanjilo se nakon sedmog dana pokusa. Iz ovih rezultata može se zaključiti da su oba metala u istraživanim koncentracijama toksična i genotoksična za vodenu leću i da uzrokuju oksidacijski stres. Kadmij u kombinaciji s bakrom više koncentracije bio je toksičniji od pojedinačnih metala nakon četvrtog dana pokusa, dok su u biljaka tretiranih kombinacijom kadmija i bakra niže koncentracije toksični učinci bili manji. Budući da su primijećene interakcije vrlo kompleksne i ne uključuju samo antagonizam odnosno sinergizam potrebna su daljnja istraživanja

Mechanical Bonds and Topological Effects in Radical Dimer Stabilization

While mechanical bonding stabilizes tetrathiafulvalene (TTF) radical dimers, the question arises: what role does topology play in catenanes containing TTF units? Here, we report how topology, together with mechanical bonding, in isomeric [3]- and doubly interlocked [2]catenanes controls the formation of TTF radical dimers within their structural frameworks, including a ring-in-ring complex (formed between an organoplatinum square and a {2+2} macrocyclic polyether containing two 1,5-dioxynaphthalene (DNP) and two TTF units) that is topologically isomeric with the doubly interlocked [2]catenane. The separate TTF units in the two {1+1} macrocycles (each containing also one DNP unit) of the isomeric [3]catenane exhibit slightly different redox properties compared with those in the {2+2} macrocycle present in the [2]catenane, while comparison with its topological isomer reveals substantially different redox behavior. Although the stabilities of the mixed-valence (TTF2)^(•+) dimers are similar in the two catenanes, the radical cationic (TTF^(•+))_2 dimer in the [2]catenane occurs only fleetingly compared with its prominent existence in the [3]catenane, while both dimers are absent altogether in the ring-in-ring complex. The electrochemical behavior of these three radically configurable isomers demonstrates that a fundamental relationship exists between topology and redox properties

Transport and crystallization of colloidal particles in a thin nematic cell

In a thin planar nematic cell, the application of an AC electric field induces a macroscopic transport of micrometer-sized colloidal particles along the nematic director. We have analyzed the dependence of particle velocities on the electric-field amplitude and frequency and found that it decreases exponentially with increasing frequency. Using specially designed electrodes we have observed that colloidal particles could be pumped and accelerated across the field-no-field interface, and measured the structural force and the corresponding potential, which is of the order of 10000 kBT for 4μm particles. We demonstrate that spatially periodic close-packed crystalline colloidal structures can be obtained, which are thermodinamically metastable for many days after turning off the electric field and slowly decay into linear chains. Above the nematic-isotropic phase transition, such crystalline structures are non-stable and decay in few minutes

Vortexlike topological defects in nematic colloids: chiral colloidal dimers and 2D crystals.

We show that chiral ordering of the underlying complex fluid strongly influences defect formation and colloidal interactions. Nonsingular defect loops with a topological charge -2 are observed, with a cross section identical to hyperbolic vortices in magnetic systems. These loops are binding spontaneously formed pairs of colloidal particles and dimers, which are chiral objects. Chiral dimer-dimer interaction weakly depends on the chirality of dimers and leads to the assembly of 2D nematic colloidal crystals of pure or "mixed" chirality, intercalated with a lattice of nonsingular vortexlike defects