Monoidal Hom-Hopf algebras

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras and Lie algebras.Comment: 25 pages; extended version: compared to the version that appeared in Comm. Algebra, the Section Preliminary Results and Remarks 5.1 and 6.1 have been adde

Effective Edwards-Wilkinson equation for single-file diffusion

In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles. The effective equation gives a description of single-file diffusion using the global roughness of the system of particles, which presents three characteristic regimes, namely normal diffusion, subdiffusion and saturation, separated by two crossover times. We show how these regimes scale with the parameters of the original system. Additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms. Finally, we show that the roughness distribution can be well characterized by the Edwards-Wilkinson universal form for the different single-file diffusion processes studied here.Comment: 9 pages, 9 figure

On U_q(SU(2))-symmetric Driven Diffusion

We study analytically a model where particles with a hard-core repulsion diffuse on a finite one-dimensional lattice with space-dependent, asymmetric hopping rates. The system dynamics are given by the \mbox{U$_{q}$[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic Heisenberg antiferromagnet. Exploiting this symmetry we derive exact expressions for various correlation functions. We discuss the density profile and the two-point function and compute the correlation length $\xi_s$ as well as the correlation time $\xi_t$. The dynamics of the density and the correlations are shown to be governed by the energy gaps of a one-particle system. For large systems $\xi_s$ and $\xi_t$ depend only on the asymmetry. For small asymmetry one finds $\xi_t \sim \xi_s^2$ indicating a dynamical exponent $z=2$ as for symmetric diffusion.Comment: 10 pages, LATE

Classification of graph C*-algebras with no more than four primitive ideals

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less

Discovery of a wandering radio jet base after a large X-ray flare in the blazar Markarian 421

We investigate the location of the radio jet bases ("radio cores") of blazars in radio images, and their stationarity by means of dense very long baseline interferometry (VLBI) observations. In order to measure the position of a radio core, we conducted 12 epoch astrometric observation of the blazar Markarian 421 with the VLBI Exploration of Radio Astrometry at 22 GHz immediately after a large X-ray flare, which occurred in the middle of 2011 September. For the first time, we find that the radio core is not stationary but rather changes its location toward 0.5 mas downstream. This angular scale corresponds to the de-projected length of a scale of $10^5$ Schwarzschild radii (Rs) at the distance of Markarian~421. This radio-core wandering may be a new type of manifestation associated with the phenomena of large X-ray flares.Comment: 6 pages, 4 figures, 1 table, has been published in ApJ Letter

Hydrodynamic synchronisation of non-linear oscillators at low Reynolds number

We introduce a generic model of weakly non-linear self-sustained oscillator as a simplified tool to study synchronisation in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of hydrodynamic interactions on the slow dynamics of two oscillators and show that they can lead to synchronisation. Furthermore, we find that synchronisation is strongly enhanced when the oscillators are non-isochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Non-isochronity is determined by a nonlinear coupling $\alpha$ being non-zero. We find that its ($\alpha$) sign determines if they synchronise in- or anti-phase. We then study an infinite array of oscillators in the long wavelength limit, in presence of noise. For $\alpha > 0$, hydrodynamic interactions can lead to a homogeneous synchronised state. Numerical simulations for a finite number of oscillators confirm this and, when $\alpha <0$, show the propagation of waves, reminiscent of metachronal coordination.Comment: 4 pages, 2 figure

Turbulent Drag Reduction by Flexible and Rodlike Polymers: Crossover Effects at Small Concentrations

Drag reduction by polymers is bounded between two universal asymptotes, the von-K\'arm\'an log-law of the law and the Maximum Drag Reduction (MDR) asymptote. It is theoretically understood why the MDR asymptote is universal, independent of whether the polymers are flexible or rodlike. The cross-over behavior from the Newtonian von-K\'arm\'an log-law to the MDR is however not universal, showing different characteristics for flexible and rodlike polymers. In this paper we provide a theory for this cross-over phenomenology.Comment: 5 pages, 4 figures, submitted to Physical Review

Slow plasmon modes in polymeric salt solutions

The dynamics of polymeric salt solutions are presented. The salt consists of chains $\rm A$ and $\rm B$, which are chemically different and interact with a Flory-interaction parameter $\chi$, the $\rm A$ chain ends carry a positive charge whereas the $\rm B$ chain ends are modified by negative charges. The static structure factor shows a peak corresponding to a micro phase separation. At low momentum transfer, the interdiffusion mode is driven by electrostatics and is of the plasmon-type, but with an unusually low frequency, easily accessible by experiments. This is due to the polymer connectivity that introduces high friction and amplifies the charge scattering thus allowing for low charge densities. The interdiffusion mode shows a minimum (critical slowing down) at finite $k$ when the interaction parameter increases we find then a low $k$ frequency quasi-plateau.Comment: accepted in Europhys. Let

Conformational transformations induced by the charge-curvature interaction at finite temperature

The role of thermal fluctuations on the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to polygonal shape. The transition occurs both in the case of hardening and softening charge-bending interaction. In the former case the charge and curvature are smoothly distributed along the chain while in the latter spontaneous kink formation is initiated. The transition to a non-circular conformation is analogous to the phase transition of the second kind.Comment: 23 pages (Latex), 10 figures (Postscript), 2 biblio file (bib-file and bbl-file