Skyrmions and Bags in the 2D-O(3) model

Localized static solutions of the 2D-O(3) model are investigated in a representation with the 3-vector field $\vec Phi$ split into the unit vector $\hat Phi$ and the modulus $\Phi$. As in the nonlinear version of the model this allows for the definition of a topological winding number $B$, and for the separation of the complete configuration space into distinct $B$-sectors. For small values of the $\Phi^4$-coupling strength the stable energy minima in these sectors are characterized by bag formation in the modulus field which in the standard cartesian representation of the linear O(3) model would be unstable towards decay into the trivial B=0 vacuum. Stabilized by $B$-conservation they exhibit a surprising variety of very appealing features for multiply charged systems. With the total charge bound into one common deep bag opposite ways of distributing the topological charge density inside the bag can be realized: Pointlike structures which retain the individuality of single constituents (or doubly charged pairs), or a deconfined charge density spread uniformly throughout the interior of the bag. It is suggested that this extension supplies a crucial link to overcome the unsatisfactory existing mismatch between multiskyrmion configurations and nuclear structure.Comment: 13 pages, 15 figure

A model of fasciculation and sorting in mixed populations of axons

We extend a recently proposed model (Chaudhuri et al., EPL 87, 20003 (2009)) aiming to describe the formation of fascicles of axons during neural development. The growing axons are represented as paths of interacting directed random walkers in two spatial dimensions. To mimic turnover of axons, whole paths are removed and new walkers are injected with specified rates. In the simplest version of the model, we use strongly adhesive short-range inter-axon interactions that are identical for all pairs of axons. We generalize the model to adhesive interactions of finite strengths and to multiple types of axons with type-specific interactions. The dynamic steady state is characterized by the position-dependent distribution of fascicle sizes. With distance in the direction of axon growth, the mean fascicle size and emergent time scales grow monotonically, while the degree of sorting of fascicles by axon type has a maximum at a finite distance. To understand the emergence of slow time scales, we develop an analytical framework to analyze the interaction between neighboring fascicles.Comment: 19 pages, 13 figures; version accepted for publication in Phys Rev

First integrals of Ginzburg-Landau equations and stability criteria for vortex-free state in unconventional superconductors

The first integrals of the Ginzburg-Landau equations for a vortex-free state of superconductors with different mixed symmetries of the order parameter are found. The general boundary conditions for the order parameter at the ideal interface between the superconductor and vacuum are derived. Based on these integrals and boundary conditions, we analyze the stability criteria for vortex-free state in unconventional superconductors. The threshold field above which the Abrikosov vortices can enter the superconductor is found to be higher or equal to the thermodynamic critical field for all states under study.Comment: 8 pages, pdf file, no figure

Physiology of spontaneous [Ca2+]i oscillations in the isolated vasopressin and oxytocin neurones of the rat supraoptic nucleus

AbstractThe magnocellular vasopressin (AVP) and oxytocin (OT) neurones exhibit specific electrophysiological behaviour, synthesise AVP and OT peptides and secrete them into the neurohypophysial system in response to various physiological stimulations. The activity of these neurones is regulated by the very same peptides released either somato-dendritically or when applied to supraoptic nucleus (SON) preparations in vitro. The AVP and OT, secreted somato-dendritically (i.e. in the SON proper) act through specific autoreceptors, induce distinct Ca2+ signals and regulate cellular events. Here, we demonstrate that about 70% of freshly isolated individual SON neurones from the adult non-transgenic or transgenic rats bearing AVP (AVP-eGFP) or OT (OT-mRFP1) markers, produce distinct spontaneous [Ca2+]i oscillations. In the neurones identified (through specific fluorescence), about 80% of AVP neurones and about 60% of OT neurones exhibited these oscillations. Exposure to AVP triggered [Ca2+]i oscillations in silent AVP neurones, or modified the oscillatory pattern in spontaneously active cells. Hyper- and hypo-osmotic stimuli (325 or 275 mOsmol/l) respectively intensified or inhibited spontaneous [Ca2+]i dynamics. In rats dehydrated for 3 or 5days almost 90% of neurones displayed spontaneous [Ca2+]i oscillations. More than 80% of OT-mRFP1 neurones from 3 to 6-day-lactating rats were oscillatory vs. about 44% (OT-mRFP1 neurones) in virgins. Together, these results unveil for the first time that both AVP and OT neurones maintain, via Ca2+ signals, their remarkable intrinsic in vivo physiological properties in an isolated condition

Dynamics of path aggregation in the presence of turnover

We investigate the slow time scales that arise from aging of the paths during the process of path aggregation. This is studied using Monte-Carlo simulations of a model aiming to describe the formation of fascicles of axons mediated by contact axon-axon interactions. The growing axons are represented as interacting directed random walks in two spatial dimensions. To mimic axonal turnover, random walkers are injected and whole paths of individual walkers are removed at specified rates. We identify several distinct time scales that emerge from the system dynamics and can exceed the average axonal lifetime by orders of magnitude. In the dynamical steady state, the position-dependent distribution of fascicle sizes obeys a scaling law. We discuss our findings in terms of an analytically tractable, effective model of fascicle dynamics.Comment: 6 pages, 5 figures; changed the order of presentation, rewritten the abstract and introduction, changed the title, expanded discussions; the main results remain the sam

Field dynamics and kink-antikink production in rapidly expanding systems

Field dynamics in a rapidly expanding system is investigated by transforming from space-time to the rapidity - proper-time frame. The proper-time dependence of different contributions to the total energy is established. For systems characterized by a finite momentum cut-off, a freeze-out time can be defined after which the field propagation in rapidity space ends and the system decays into decoupled solitons, antisolitons and local vacuum fluctuations. Numerical simulations of field evolutions on a lattice for the (1+1)-dimensional $\Phi^4$ model illustrate the general results and show that the freeze-out time and average multiplicities of kinks (plus antikinks) produced in this 'phase transition' can be obtained from simple averages over the initial ensemble of field configurations. An extension to explicitly include additional dissipation is discussed. The validity of an adiabatic approximation for the case of an overdamped system is investigated. The (3+1)-dimensional generalization may serve as model for baryon-antibaryon production after heavy-ion collisions.Comment: 18 pages, 7 figures. Two references added. New subsection III.E added. Final version accepted for publication in PR

Ordering kinetics of stripe patterns

We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure factor of the order parameter, and a finite size scaling analysis of the grain boundary perimeter, suggest that the linear scale of the structure grows as a power law of time with a craracteristic exponent z=3. We interpret theoretically the exponent z=3 from the law of grain boundary motion.Comment: 4 pages, 4 figure

Dynamical Induction of s-wave Component in d-wave Superconductor Driven by Thermal Fluctuations

We investigated the mutual induction effects between the d-wave and the s-wave components of order parameters due to superconducting fluctuation above the critical temperatures and calculated its contributions to paraconductivity and excess Hall conductivity based on the two-component stochastic TDGL equation. It is shown that the coupling of two components increases paraconductivity while it decreases excess Hall conductivity compared to the cases when each component fluctuates independently. We also found the singular behavior in the paraconductivity and the excess Hall conductivity dependence on the coupling parameter which is consistent with the natural restriction among the coefficients of gradient terms.Comment: 10 pages, 4 figures included, submitted to J.Phys.Soc.Jp

Induction of non-d-wave order-parameter components by currents in d-wave superconductors

It is shown, within the framework of the Ginzburg-Landau theory for a superconductor with d_{x^2-y^2} symmetry, that the passing of a supercurrent through the sample results, in general, in the induction of order-parameter components of distinct symmetry. The induction of s-wave and d_{xy(x^2-y^2)-wave components are considered in detail. It is shown that in both cases the order parameter remains gapless; however, the structure of the lines of nodes and the lobes of the order parameter are modified in distinct ways, and the magnitudes of these modifications differ in their dependence on the (a-b plane) current direction. The magnitude of the induced s-wave component is estimated using the results of the calculations of Ren et al. [Phys. Rev. Lett. 74, 3680 (1995)], which are based on a microscopic approach.Comment: 15 pages, includes 2 figures. To appear in Phys. Rev.