Analytical investigation of magnetic field distributions around superconducting strips on ferromagnetic substrates

The complex-field approach is developed to derive analytical expressions of the magnetic field distributions around superconducting strips on ferromagnetic substrates (SC/FM strips). We consider the ferromagnetic substrates as ideal soft magnets with an infinite magnetic permeability, neglecting the ferromagnetic hysteresis. On the basis of the critical state model for a superconducting strip, the ac susceptibility $\chi_1'+i\chi_1''$ of a SC/FM strip exposed to a perpendicular ac magnetic field is theoretically investigated, and the results are compared with those for superconducting strips on nonmagnetic substrates (SC/NM strips). The real part $\chi_1'$ for $H_0/j_cd_s\to 0$ (where $H_0$ is the amplitude of the ac magnetic field, $j_c$ is the critical current density, and $d_s$ is the thickness of the superconducting strip) of a SC/FM strip is 3/4 of that of a SC/NM strip. The imaginary part $\chi_1''$ (or ac loss $Q$) for $H_0/j_cd_s<0.14$ of a SC/FM strip is larger than that of a SC/NM strip, even when the ferromagnetic hysteresis is neglected, and this enhancement of $\chi_1''$ (or $Q$) is due to the edge effect of the ferromagnetic substrate.Comment: 8 pages, 6 figures, submitted to Phys. Rev.

Force-extension relation of cross-linked anisotropic polymer networks

Cross-linked polymer networks with orientational order constitute a wide class of soft materials and are relevant to biological systems (e.g., F-actin bundles). We analytically study the nonlinear force-extension relation of an array of parallel-aligned, strongly stretched semiflexible polymers with random cross-links. In the strong stretching limit, the effect of the cross-links is purely entropic, independent of the bending rigidity of the chains. Cross-links enhance the differential stretching stiffness of the bundle. For hard cross-links, the cross-link contribution to the force-extension relation scales inversely proportional to the force. Its dependence on the cross-link density, close to the gelation transition, is the same as that of the shear modulus. The qualitative behavior is captured by a toy model of two chains with a single cross-link in the middle.Comment: 7 pages, 4 figure

SEQUENTIAL LOCALIZATION OF SENSOR NETWORKS

The sensor network localization problem with distance information is to determine the positions of all sensors in a network, given the positions of some of the sensors and the distances between some pairs of sensors. A definition is given for a sensor network in the plane to be "sequentially localizable." It is shown that the graph of a sequentially localizable network must have a "bilateration ordering," and a polynomial time algorithm is given for deciding whether or not a network's graph has such an ordering. A provably correct algorithm is given which consists of solving a sequence of quadratic equations, and it is shown that the algorithm can localize any localizable network in the plane whose graph has a bilateration ordering.

Inadequacies in the conventional treatment of the radiation field of moving sources

There is a fundamental difference between the classical expression for the retarded electromagnetic potential and the corresponding retarded solution of the wave equation that governs the electromagnetic field. While the boundary contribution to the retarded solution for the {\em potential} can always be rendered equal to zero by means of a gauge transformation that preserves the Lorenz condition, the boundary contribution to the retarded solution of the wave equation governing the {\em field} may be neglected only if it diminishes with distance faster than the contribution of the source density in the far zone. In the case of a source whose distribution pattern both rotates and travels faster than light {\em in vacuo}, as realized in recent experiments, the boundary term in the retarded solution governing the field is by a factor of the order of $R^{1/2}$ {\em larger} than the source term of this solution in the limit that the distance $R$ of the boundary from the source tends to infinity. This result is consistent with the prediction of the retarded potential that part of the radiation field generated by a rotating superluminal source decays as $R^{-1/2}$, instead of $R^{-1}$, a prediction that is confirmed experimentally. More importantly, it pinpoints the reason why an argument based on a solution of the wave equation governing the field in which the boundary term is neglected (such as appears in the published literature) misses the nonspherical decay of the field

Phase transitions on the surface of a carbon nanotube

A suspended carbon nanotube can act as a nanoscale resonator with remarkable electromechanical properties and the ability to detect adsorption on its surface at the level of single atoms. Understanding adsorption on nanotubes and other graphitic materials is key to many sensing and storage applications. Here we show that nanotube resonators offer a powerful new means of investigating fundamental aspects of adsorption on carbon, including the collective behaviour of adsorbed matter and its coupling to the substrate electrons. By monitoring the vibrational resonance frequency in the presence of noble gases, we observe the formation of monolayers on the cylindrical surface and phase transitions within these monolayers, and simultaneous modification of the electrical conductance. The monolayer observations also demonstrate the possibility of studying the fundamental behaviour of matter in cylindrical geometry.Comment: Unpublished; 7 pages with 4 figures plus 3 pages of supplementary materia

Dissipative dynamics of topological defects in frustrated Heisenberg spin systems

We study the dynamics of topological defects of a frustrated spin system displaying spiral order. As a starting point we consider the SO(3) nonlinear sigma model to describe long-wavelength fluctuations around the noncollinear spiral state. Besides the usual spin-wave magnetic excitations, the model allows for topologically non-trivial static solutions of the equations of motion, associated with the change of chirality (clockwise or counterclockwise) of the spiral. We consider two types of these topological defects, single vortices and vortex-antivortex pairs, and quantize the corresponding solutions by generalizing the semiclassical approach to a non-Abelian field theory. The use of the collective coordinates allows us to represent the defect as a particle coupled to a bath of harmonic oscillators, which can be integrated out employing the Feynman-Vernon path-integral formalism. The resulting effective action for the defect indicates that its motion is damped due to the scattering by the magnons. We derive a general expression for the damping coefficient of the defect, and evaluate its temperature dependence in both cases, for a single vortex and for a vortex-antivortex pair. Finally, we consider an application of the model for cuprates, where a spiral state has been argued to be realized in the spin-glass regime. By assuming that the defect motion contributes to the dissipative dynamics of the charges, we can compare our results with the measured inverse mobility in a wide range of temperature. The relatively good agreement between our calculations and the experiments confirms the possible relevance of an incommensurate spiral order for lightly doped cuprates.Comment: 22 pages, 7 figures, final published versio

Discriminating cool-water from warm-water carbonates and their diagenetic environments using element geochemistry: the Oligocene Tikorangi Formation (Taranaki Basin) and the dolomite effect

Fields portrayed within bivariate element plots have been used to distinguish between carbonates formed in warm- (tropical) water and cool- (temperate) water depositional settings. Here, element concentrations (Ca, Mg, Sr, Na, Fe, and Mn) have been determined for the carbonate fraction of bulk samples from the late Oligocene Tikorangi Formation, a subsurface, mixed dolomite-calcite, cool-water limestone sequence in Taranaki Basin, New Zealand. While the occurrence of dolomite is rare in New Zealand Cenozoic carbonates, and in cool-water carbonates more generally, the dolomite in the Tikorangi carbonates is shown to have a dramatic effect on the "traditional" positioning of cool-water limestone fields within bivariate element plots. Rare undolomitised, wholly calcitic carbonate samples in the Tikorangi Formation have the following average composition: Mg 2800 ppm; Ca 319 100 ppm; Na 800 ppm; Fe 6300 ppm; Sr 2400 ppm; and Mn 300 ppm. Tikorangi Formation dolomite-rich samples (>15% dolomite) have average values of: Mg 53 400 ppm; Ca 290 400 ppm; Na 4700 ppm; Fe 28 100 ppm; Sr 5400 ppm; and Mn 500 ppm. Element-element plots for dolomite-bearing samples show elevated Mg, Na, and Sr values compared with most other low-Mg calcite New Zealand Cenozoic limestones. The increased trace element contents are directly attributable to the trace element-enriched nature of the burial-derived dolomites, termed here the "dolomite effect". Fe levels in the Tikorangi Formation carbonates far exceed both modern and ancient cool-water and warm-water analogues, while Sr values are also higher than those in modern Tasmanian cool-water carbonates, and approach modern Bahaman warm-water carbonate values. Trace element data used in conjunction with more traditional petrographic data have aided in the diagenetic interpretation of the carbonate-dominated Tikorangi sequence. The geochemical results have been particularly useful for providing more definitive evidence for deep burial dolomitisation of the deposits under the influence of marine-modified pore fluids

How to be causal: time, spacetime, and spectra

I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers Kronig relations. The specification of causality in terms of temporal differential eqations then shows us the way to write down dynamical models so that their causal nature /in the sense used here/ should be obvious to all. To extend existing treatments of causality that work only in the frequency domain, I derive a reformulation of the long-standing Kramers Kronig relations applicable not only to just temporal causality, but also to spacetime "light-cone" causality based on signals carried by waves. I also apply this causal reasoning to Maxwell's equations, which is an instructive example since their casual properties are sometimes debated.Comment: v4 - add Appdx A, "discrete" picture (not in EJP); v5 - add Appdx B, cause classification/frames (not in EJP); v7 - unusual model case; v8 add reference

Scientific rationale of a Saturn probe mission

We describe the main scientific goals to be addressed by future in situ exploration of Saturn