The evaluation of directionally writhing polymers

We discuss the appropriate techniques for modelling the geometry of open ended elastic polymer molecules. The molecule is assumed to have fixed endpoints on a boundary surface. In particular we discuss the concept of the winding number, a directional measure of the linking of two curves, which can be shown to be invariant to the set of continuous deformations vanishing at the polymer's end-point and which forbid it from passing through itself. This measure is shown to be the appropriate constraint required to evaluate the geometrical properties of a constrained DNA molecule. Using the net winding measure we define a model of an open ended constrained DNA molecule which combines the necessary constraint of self-avoidance with being analytically tractable. This model builds upon the local models of Bouchiat and Mezard (2000). In particular, we present a new derivation of the polar writhe expression, which detects both the local winding of the curve and non local winding between different sections of the curve. We then show that this expression correctly tracks the net twisting of a DNA molecule subject to rotation at the endpoints, unlike other definitions used in the literature

Helicity, linking, and writhe in a spherical geometry

Open Access journalLinking numbers, helicity integrals, twist, and writhe all describe the topology and geometry of curves and vector fields. The topology of the space the curves and fields live in, however, can affect the behaviour of these quantities. Here we examine curves and fields living in regions exterior to a sphere or in spherical shells. The winding of two curves need not be conserved because of the topology of a spherical shell. Avoiding the presence of magnetic monopoles inside the sphere is very important if magnetic helicity is to be a conserved quantity. Considerations of parallel transport are important in determining the transfer of helicity through the foot of a magnetic flux tube when it is in motion

Photospheric flux density of magnetic helicity

Copyright © 2005 EDP Sciences. This article appeared in Astronomy & Astrophysics 439 (2005) and may be found at http://www.aanda.org/index.php?option=article&access=doi&doi=10.1051/0004-6361:20052663Several recent studies have developed the measurement of magnetic helicity flux from the time evolution of photospheric magnetograms. The total flux is computed by summing the flux density over the analyzed region. All previous analyses used the density GA (=−2(A•u)Bn) which involves the vector potential A of the magnetic field. In all the studied active regions, the density GA has strong polarities of both signs with comparable magnitude. Unfortunately, the density GA can exhibit spurious signals which do not provide a true helicity flux density. The main objective of this study is to resolve the above problem by defining the flux of magnetic helicity per unit surface. In a first step, we define a new density, Gθ, which reduces the fake polarities by more than an order of magnitude in most cases (using the same photospheric data as GA). In a second step, we show that the coronal linkage needs to be provided in order to define the true helicity flux density. It represents how all the elementary flux tubes move relatively to a given elementary flux tube, and the helicity flux density is defined per elementary flux tube. From this we define a helicity flux per unit surface, GΦ. We show that it is a field-weighted average of Gθ at both photospheric feet of coronal connections. We compare these three densities (GA, Gθ, GΦ) using theoretical examples representing the main cases found in magnetograms (moving magnetic polarities, separating polarities, one polarity rotating around another one and emergence of a twisted flux tube). We conclude that Gθ is a much better proxy of the magnetic helicity flux density than GA because most fake polarities are removed. Indeed Gθ gives results close to GΦ and should be used to monitor the photospheric injection of helicity (when coronal linkages are not well known). These results are applicable to the results of any method determining the photospheric velocities. They can provide separately the flux density coming from shearing and advection motions if plasma motions are known

Self-organized braiding in solar coronal loops

In this paper, we investigate the evolution of braided solar coronal loops. We assume that coronal loops consist of several internal strands which twist and braid about each other. Reconnection between the strands leads to small flares and heating of the loop to X-ray temperatures. Using a method of generating and releasing braid structure similar to a forest fire model, we show that the reconnected field lines evolve to a self-organised critical state. In this state, the frequency distributions of coherent braid sequences as well as flare energies follow power law distributions. We demonstrate how the presence of net helicity in the loop alters the distribution laws.Leverhulme TrustAI

On the Relationship Between Photospheric Footpoint Motions and Coronal Heating in Solar Active Regions

PublishedArticleCoronal heating theories can be classified as either direct current (DC) or alternating current (AC) mechanisms, depending on whether the coronal magnetic field responds quasi-statically or dynamically to the photospheric footpoint motions. In this paper we investigate whether photospheric footpoint motions with velocities of 1-2 km s–1 can heat the corona in active regions, and whether the corona responds quasi-statically or dynamically to such motions (DC versus AC heating). We construct three-dimensional magnetohydrodynamic models for the Alfvén waves and quasi-static perturbations generated within a coronal loop. We find that in models where the effects of the lower atmosphere are neglected, the corona responds quasi-statically to the footpoint motions (DC heating), but the energy flux into the corona is too low compared to observational requirements. In more realistic models that include the lower atmosphere, the corona responds more dynamically to the footpoint motions (AC heating) and the predicted heating rates due to Alfvén wave turbulence are sufficient to explain the observed hot loops. The higher heating rates are due to the amplification of Alfvén waves in the lower atmosphere. We conclude that magnetic braiding is a highly dynamic process

On the effective strain tensor in heterogeneous materials

ArticleThis is the author's accepted manuscript. The final published version of record is available at https://dx.doi.org/10.1177/1081286514521092This paper considers effective strain tensors within the context of linear elastic equilibrium theory. The elastic properties of structured materials are often averaged over subvolumes of various scales inside the material. For subvolumes smaller than a representative volume element, simple volume-averaging of the stress and strain may not preserve the elastic energy. We introduce an averaging process which preserves the energy for all boundary conditions. This averaging process emphasizes the parts of the material which carry the most stress. Here the effective strain is weighted by the local stress, and can be interpreted as an average strain over all paths taken by loads and forces through the volume. This alternative effective strain may be especially appropriate for materials with voids, such as foams and granular matter, as the averaging only involves the material itself. For uniform boundary conditions the weighted strain matches the volume-averaged strain. This paper investigates the properties of this weighted strain tensor. First, for each path taken by loads and forces through the volume we can measure a net length as well as a net extension due to the linear deformation. The weighted effective strain equals the ratio of average length to average extension, where the averaging is over all possible force paths. Thus this method provides a connection to load path analysis. Secondly, even when the average rotation within the subvolume is zero, there may be local fluctuations in the rotation field. These rotations can act like a mechanism, transferring elastic energy between boundaries or degrees of freedom. The effective strain defined here highlights this mechanism effect

The pomeron-pomeron interaction in the perturbative QCD

The pomeron-pomeron interaction is studied in the perturbative approach of BFKL-Bartels. The total pomeron-pomeron cross-section is proportional to $\alpha_{s}^{4}s^{\Delta}/\sqrt {t_{1}t_{2}}$ where $\sqrt{s}$ is the c.m. energy and $t_{1,2}$ are the virtualities of the colliding pomerons. Upon calculating the coefficient the cross-section is found to be of the order 2.2 mb at $\sqrt{s}= 6$ TeV and $\sqrt{-t_{1}}\sim\sqrt{-t_{2}}\sim 1$ GeV/c.Comment: 12 pages in LaTeX plus 2 postscript file

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give suficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.Comment: 16 page

Closing the window on the axigluon mass using top quark production data

The contribution of axigluons (the massive color-octet gauge bosons in all chiral color models) to top quark pair production in hadronic collisions is considered. The agreement between the experimental values of the ttbar production cross-section at the TEVATRON and recent QCD predictions is used to discuss limits on the axigluon mass. Specifically,intermediate mass axigluons, those in the mass range 50 GeV < M_A < 120 GeV which has not already been excluded, would increase the tree-level qqbar -> ttbar cross-section by a factor of >= 2, thereby increasing the theoretical predictions for sigma_{ttbar} by Delta sigma_{ttbar} = 3.2-3.7 pb (2.7-3.1 pb) using leading-order (next-to-leading order) parton distributions over this mass range, independent of the axigluon decay width. Such an increase is roughly 1.3-1.6 (0.9-1.2) standard deviations larger than that suggested by the apparent good agreement between combined experimental results and recent theoretical calculations and so is not ruled out, but is definitely disfavored. Future high-statistics top-quark production runs will likely make a more definitive statement. The forward-backward asymmetry in ttbar production induced by axigluons in this mass window is also discussed and found to be quite large and so could provide another constraint.Comment: 9 pages, LaTeX, 2 separate postscript file