Magnetic Flux Braiding: Force-Free Equilibria and Current Sheets

We use a numerical nonlinear multigrid magnetic relaxation technique to investigate the generation of current sheets in three-dimensional magnetic flux braiding experiments. We are able to catalogue the relaxed nonlinear force-free equilibria resulting from the application of deformations to an initially undisturbed region of plasma containing a uniform, vertical magnetic field. The deformations are manifested by imposing motions on the bounding planes to which the magnetic field is anchored. Once imposed the new distribution of magnetic footpoints are then taken to be fixed, so that the rest of the plasma must then relax to a new equilibrium configuration. For the class of footpoint motions we have examined, we find that singular and nonsingular equilibria can be generated. By singular we mean that within the limits imposed by numerical resolution we find that there is no convergence to a well-defined equilibrium as the number of grid points in the numerical domain is increased. These singular equilibria contain current "sheets" of ever-increasing current intensity and decreasing width; they occur when the footpoint motions exceed a certain threshold, and must include both twist and shear to be effective. On the basis of these results we contend that flux braiding will indeed result in significant current generation. We discuss the implications of our results for coronal heating.Comment: 13 pages, 12 figure

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

The use of imaging systems to monitor shoreline dynamics

The development of imaging systems is nowadays established as one of the most powerful and reliable tools for monitoring beach morphodynamics. Two different techniques for shoreline detection are presented here and, in one case, applied to the study of beach width oscillations on a sandy beach (Pauanui Beach, New Zealand). Results indicate that images can provide datasets whose length and sample interval are accurate enough to resolve inter-annual and seasonal oscillations, and long-term trends. Similarly, imaging systems can be extremely useful in determining the statistics of rip current occurrence. Further improvements in accuracy and reliability are expected with the recent introduction of digital systems

S ‐Aryl‐ l ‐cysteine sulphoxides and related organosulphur compounds alter oral biofilm development and AI ‐2‐based cell–cell communication

Aims To design and synthesize a library of structurally related, small molecules related to homologues of compounds produced by the plant Petiveria alliacea and determine their ability to interfere with AI ‐2 cell–cell communication and biofilm formation by oral bacteria. Many human diseases are associated with persistent bacterial biofilms. Oral biofilms (dental plaque) are problematic as they are often associated with tooth decay, periodontal disease and systemic disorders such as heart disease and diabetes. Methods and Results Using a microplate‐based approach, a bio‐inspired small molecule library was screened for anti‐biofilm activity against the oral species Streptococcus mutans UA 159 , Streptococcus sanguis 10556 and Actinomyces oris MG 1. To complement the static screen, a flow‐based BioFlux microfluidic system screen was also performed under conditions representative of the human oral cavity. Several compounds were found to display biofilm inhibitory activity in all three of the oral bacteria tested. These compounds were also shown to inhibit bioluminescence by Vibrio harveyi and were thus inferred to be quorum sensing ( QS ) inhibitors. Conclusion Due to the structural similarity of these compounds to each other, and to key molecules in AI ‐2 biosynthetic pathways, we propose that these molecules potentially reduce biofilm formation via antagonism of QS or QS ‐related pathways. Significance and Impact of the Study This study highlights the potential for a non‐antimicrobial‐based strategy, focused on AI ‐2 cell–cell signalling, to control the development of dental plaque. Considering that many bacterial species use AI ‐2 cell–cell signalling, as well as the increased concern of the use of antimicrobials in healthcare products, such an anti‐biofilm approach could also be used to control biofilms in environments beyond the human oral cavity.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109321/1/jam12616.pd

On Berenstein-Douglas-Seiberg Duality

I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the requirements. Then I explicitly show that a pair of toric dual quivers is also dual according to their proposal. All these computations go beyond tilting modules, and really work in the derived category. I introduce all necessary mathematics where needed.Comment: 22 pages, LaTe

Atomic Scale Depth Profile of Space Weathering in an Itokawa Olivine Grain

No abstract available

Generalised models for torsional spine and fan magnetic reconnection

Three-dimensional null points are present in abundance in the solar corona, and the same is likely to be true in other astrophysical environments. Recent studies suggest that reconnection at such 3D nulls may play an important role in the coronal dynamics. In this paper the properties of the torsional spine and torsional fan modes of magnetic reconnection at 3D nulls are investigated. New analytical models are developed, which for the first time include a current layer that is spatially localised around the null, extending along either the spine or the fan of the null. These are complemented with numerical simulations. The principal aim is to investigate the effect of varying the degree of asymmetry of the null point magnetic field on the resulting reconnection process - where previous studies always considered a non-generic radially symmetric null. The geometry of the current layers within which torsional spine and torsional fan reconnection occur is found to be strongly dependent on the symmetry of the magnetic field. Torsional spine reconnection still occurs in a narrow tube around the spine, but with elliptical cross-section when the fan eigenvalues are different, and with the short axis of the ellipse being along the strong field direction. The spatiotemporal peak current, and the peak reconnection rate attained, are found not to depend strongly on the degree of asymmetry. For torsional fan reconnection, the reconnection occurs in a planar disk in the fan surface, which is again elliptical when the symmetry of the magnetic field is broken. The short axis of the ellipse is along the weak field direction, with the current being peaked in these weak field regions. The peak current and peak reconnection rate in this case are clearly dependent on the asymmetry, with the peak current increasing but the reconnection rate decreasing as the degree of asymmetry is increased

Cellular Models of Aggregation-Dependent Template-Directed Proteolysis to Characterize Tau Aggregation Inhibitors for Treatment of Alzheimer's Disease

Copyright © 2015, The American Society for Biochemistry and Molecular Biology. Acknowledgements-We thank Drs Timo Rager and Rolf Hilfiker (Solvias, Switzerland) for polymorph analyses.Peer reviewedPublisher PD

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure