Kink Dynamics in a Topological Phi^4 Lattice

It was recently proposed a novel discretization for nonlinear Klein-Gordon field theories in which the resulting lattice preserves the topological (Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no Peierls-Nabarro barrier even for large spatial discretizations (h~1.0). It was then suggested that these ``topological discrete systems'' are a natural choice for the numerical study of continuum kink dynamics. Giving particular emphasis to the phi^4 theory, we numerically investigate kink-antikink scattering and breather formation in these topological lattices. Our results indicate that, even though these systems are quite accurate for studying free kinks in coarse lattices, for legitimate dynamical kink problems the accuracy is rather restricted to fine lattices (h~0.1). We suggest that this fact is related to the breaking of the Bogomol'nyi bound during the kink-antikink interaction, where the field profile loses its static property as required by the Bogomol'nyi argument. We conclude, therefore, that these lattices are not suitable for the study of more general kink dynamics, since a standard discretization is simpler and has effectively the same accuracy for such resolutions.Comment: RevTeX, 4 pages, 4 figures; Revised version, accepted to Physical Review E (Brief Reports

Slow Schroedinger dynamics of gauged vortices

Multivortex dynamics in Manton's Schroedinger--Chern--Simons variant of the Landau-Ginzburg model of thin superconductors is studied within a moduli space approximation. It is shown that the reduced flow on M_N, the N vortex moduli space, is hamiltonian with respect to \omega_{L^2}, the L^2 Kaehler form on \M_N. A purely hamiltonian discussion of the conserved momenta associated with the euclidean symmetry of the model is given, and it is shown that the euclidean action on (M_N,\omega_{L^2}) is not hamiltonian. It is argued that the N=3 flow is integrable in the sense of Liouville. Asymptotic formulae for \omega_{L^2} and the reduced Hamiltonian for large intervortex separation are conjectured. Using these, a qualitative analysis of internal 3-vortex dynamics is given and a spectral stability analysis of certain rotating vortex polygons is performed. Comparison is made with the dynamics of classical fluid point vortices and geostrophic vortices.Comment: 22 pages, 2 figure

Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Travelling kinks in discrete phi^4 models

In recent years, three exceptional discretizations of the phi^4 theory have been discovered [J.M. Speight and R.S. Ward, Nonlinearity 7, 475 (1994); C.M. Bender and A. Tovbis, J. Math. Phys. 38, 3700 (1997); P.G. Kevrekidis, Physica D 183, 68 (2003)] which support translationally invariant kinks, i.e. families of stationary kinks centred at arbitrary points between the lattice sites. It has been suggested that the translationally invariant stationary kinks may persist as 'sliding kinks', i.e. discrete kinks travelling at nonzero velocities without experiencing any radiation damping. The purpose of this study is to check whether this is indeed the case. By computing the Stokes constants in beyond-all-order asymptotic expansions, we prove that the three exceptional discretizations do not support sliding kinks for most values of the velocity - just like the standard, one-site, discretization. There are, however, isolated values of velocity for which radiationless kink propagation becomes possible. There is one such value for the discretization of Speight and Ward and three 'sliding velocities' for the model of Kevrekedis.Comment: To be published in Nonlinearity. 22 pages, 5 figures. Extensive clarifications to the text have been mad

Evaluating the repeatability and set-up sensitivity of a large field of view distortion phantom and software for magnetic resonance-only radiotherapy

Background and purpose: Magnetic Resonance (MR)-only radiotherapy requires geometrically accurate MR images over the full scanner Field of View (FoV). This study aimed to investigate the repeatability of distortion measurements made using a commercial large FoV phantom and analysis software and the sensitivity of these measurements to small set-up errors. Materials and methods: Geometric distortion was measured using a commercial phantom and software with 2D and 3D acquisition sequences on three different MR scanners. Two sets of repeatability measurements were made: three scans acquired without moving the phantom between scans (single set-up) and five scans acquired with the phantom re-set up in between each scan (repeated set-up). The set-up sensitivity was assessed by scanning the phantom with an intentional 1 mm lateral offset and independently an intentional 1° rotation. Results: The mean standard deviation of distortion for all phantom markers for the repeated set-up scans was for all scanners and sequences. For the lateral offset scan of the markers agreed within two standard deviations of the mean of the repeated set-up scan (median of all scanners and sequences, range 78%–93%). For the 1° rotation scan, 80% of markers agreed within two standard deviations of the mean (range 69%–93%). Conclusions: Geometric distortion measurements using a commercial phantom and associated software appear repeatable, although with some sensitivity to set-up errors. This suggests the phantom and software are appropriate for commissioning a MR-only radiotherapy workflow

Interaction between vortices in models with two order parameters

The interaction energy and force between widely separated strings is analyzed in a field theory having applications to superconducting cosmic strings, the SO(5) model of high-temperature superconductivity, and solitons in nonlinear optics. The field theory has two order parameters, one of which is broken in the vacuum (giving rise to strings), the other of which is unbroken in the vacuum but which could nonetheless be broken in the core of the string. If this does occur, there is an effect on the energetics of widely separated strings. This effect is important if the length scale of this second order parameter is longer than that of the other fields in the problem.Comment: 11 pages, 3 figures. Minor changes in the text. Accepted for publication in Phys. Rev.

NS5-Branes, T-Duality and Worldsheet Instantons

The equivalence of NS5-branes and ALF spaces under T-duality is well known. However, a naive application of T-duality transforms the ALF space into a smeared NS5-brane, de-localized on the dual, transverse, circle. In this paper we re-examine this duality, starting from a two-dimensional N=(4,4) gauged linear sigma model describing Taub-NUT space. After dualizing the circle fiber, we find that the smeared NS5-brane target space metric receives corrections from multi-worldsheet instantons. These instantons are identified as Nielsen-Olesen vortices. We show that their effect is to break the isometry of the target space, localizing the NS5-brane at a point. The contribution from the k-instanton sector is shown to be proportional to the weighted integral of the Euler form over the k-vortex moduli space. The duality also predicts the, previously unknown, asymptotic exponential decay coefficient of the BPS vortex solution.Comment: 26 pages. v2: Fourier modes of multi-vortex fermion zero mode corrected. Reference added. v3: typo correcte

DNA barcode assessment and population structure of aphidophagous hoverfly <i>Sphaerophoria scripta</i>:Implications for conservation biological control

With the advent of integrated pest management, the conservation of indigenous populations of natural enemies of pest species has become a relevant practice, necessitating the accurate identification of beneficial species and the inspection of evolutionary mechanisms affecting the long-time persistence of their populations. The long hoverfly,Sphaerophoria scripta, represents one of the most potent aphidophagous control agents due to a worldwide distribution and a favorable constellation of biological traits. Therefore, we assessed five EuropeanS. scriptapopulations by combining molecular (cytochromecoxidase subunit I-COI, internal transcribed spacer 2-ITS2, and allozyme loci) and morphological (wing size and shape) characters.COIsequences retrieved in this study were conjointly analyzed with BOLD/GenBank sequences of the otherSphaerophoriaspecies to evaluate whetherCOIpossessed a sufficient diagnostic value as a DNA barcode marker to consistently delimit allospecific individuals. Additionally, the aforementioned characters were used to inspect the population structure ofS. scriptain Europe using methods based on individual- and population-based genetic differences, as well as geometric morphometrics of wing traits. The results indicate numerous sharedCOIhaplotypes among differentSphaerophoriaspecies, thus disqualifying this marker from being an adequate barcoding region in this genus. Conversely, the analyses of population structuring revealed high population connectivity across Europe, therefore indicating strong tolerance ofS. scriptato environmental heterogeneity. The results imply a multilocus approach as the next step in molecular identification of differentSphaerophoriaspecies, while confirming the status ofS. scriptaas a powerful biocontrol agent of economically relevant aphid pests

Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure