1,225 research outputs found
A quantum Peierls-Nabarro barrier
Kink dynamics in spatially discrete nonlinear Klein-Gordon systems is
considered. For special choices of the substrate potential, such systems
support continuous translation orbits of static kinks with no (classical)
Peierls-Nabarro barrier. It is shown that these kinks experience, nevertheless,
a lattice-periodic confining potential, due to purely quantum effects anaolgous
to the Casimir effect of quantum field theory. The resulting ``quantum
Peierls-Nabarro potential'' may be calculated in the weak coupling
approximation by a simple and computationally cheap numerical algorithm, which
is applied, for purposes of illustration, to a certain two-parameter family of
substrates.Comment: 13 pages LaTeX, 7 figure
Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets
The dynamics of magnetic bubble solitons in a two-dimensional isotropic
antiferromagnetic spin lattice is studied, in the case where the exchange
integral J(x,y) is position dependent. In the near continuum regime, this
system is described by the relativistic O(3) sigma model on a spacetime with a
spatially inhomogeneous metric, determined by J. The geodesic approximation is
used to describe low energy soliton dynamics in this system: n-soliton motion
is approximated by geodesic motion in the moduli space of static n-solitons,
equipped with the L^2 metric. Explicit formulae for this metric for various
natural choices of J(x,y) are obtained. From these it is shown that single
soliton trajectories experience refraction, with 1/J analogous to the
refractive index, and that this refraction effect allows the construction of
simple bubble lenses and bubble guides. The case where J has a disk
inhomogeneity (taking the value J_1 outside a disk, and J_2<J_1 inside) is
considered in detail. It is argued that, for sufficiently large J_1/J_2 this
type of antiferromagnet supports approximate quasibreathers: two or more
coincident bubbles confined within the disk which spin internally while their
shape undergoes periodic oscillations with a generically incommensurate period.Comment: Conference proceedings paper for talk given at Nonlinear Physics
Theory and Experiment IV, Gallipoli, Italy, June 200
Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent systems
Traditionally, superconductors are categorized as type-I or type-II. Type-I
superconductors support only Meissner and normal states, while type-II
superconductors form magnetic vortices in sufficiently strong applied magnetic
fields. Recently there has been much interest in superconducting systems with
several species of condensates, in fields ranging from Condensed Matter to High
Energy Physics. Here we show that the type-I/type-II classification is
insufficient for such multicomponent superconductors. We obtain solutions
representing thermodynamically stable vortices with properties falling outside
the usual type-I/type-II dichotomy, in that they have the following features:
(i) Pippard electrodynamics, (ii) interaction potential with long-range
attractive and short-range repulsive parts, (iii) for an n-quantum vortex, a
non-monotonic ratio E(n)/n where E(n) is the energy per unit length, (iv)
energetic preference for non-axisymmetric vortex states, "vortex molecules".
Consequently, these superconductors exhibit an emerging first order transition
into a "semi-Meissner" state, an inhomogeneous state comprising a mixture of
domains of two-component Meissner state and vortex clusters.Comment: in print in Phys. Rev. B Rapid Communications. v2: presentation is
made more accessible for a general reader. Latest updates and links to
related papers are available at the home page of one of the authors:
http://people.ccmr.cornell.edu/~egor
Kinks in dipole chains
It is shown that the topological discrete sine-Gordon system introduced by
Speight and Ward models the dynamics of an infinite uniform chain of electric
dipoles constrained to rotate in a plane containing the chain. Such a chain
admits a novel type of static kink solution which may occupy any position
relative to the spatial lattice and experiences no Peierls-Nabarro barrier.
Consequently the dynamics of a single kink is highly continuum like, despite
the strongly discrete nature of the model. Static multikinks and kink-antikink
pairs are constructed, and it is shown that all such static solutions are
unstable. Exact propagating kinks are sought numerically using the
pseudo-spectral method, but it is found that none exist, except, perhaps, at
very low speed.Comment: Published version. 21 pages, 5 figures. Section 3 completely
re-written. Conclusions unchange
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
Come to the dark side! The role of functional traits in shaping dark diversity patterns of south-eastern European hoverflies
1. Dark diversity represents the set of species that can potentially inhabit a given area under particular ecological conditions, but are currently 'missing' from a site. This concept allows characterisation of the mechanisms determining why species are sometimes absent from an area that seems ecologically suitable for them. 2. The aim of this study was to determine the dark diversity of hoverflies in south-eastern Europe and to discuss the role of different functional traits that might increase the likelihood of species contributing to dark diversity. Based on expert opinion, the Syrph the Net database and known occurrences of species, the study estimated species pools, and observed and dark diversities within each of 11 defined vegetation types for 564 hoverfly species registered in south-eastern Europe. To detect the most important functional traits contributing to species being in dark diversity across different vegetation types, a random forest algorithm and respective statistics for variable importance were used. 3. The highest dark diversity was found for southwest Balkan sub-Mediterranean mixed oak forest type, whereas the lowest was in Mediterranean mixed forest type. Three larval feeding modes (saproxylic, and phytophagous on bulbs or roots) were found to be most important for determining the probability of a species contributing to hoverfly dark diversity, based on univariate correlations and random forest analysis. 4. This study shows that studying dark diversity might provide important insights into what drives community assembly in south-eastern European hoverflies, especially its missing components, and contributes to more precise conservation prioritisation of both hoverfly species and their habitats.Peer reviewe
The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps
The most fruitful approach to studying low energy soliton dynamics in field
theories of Bogomol'nyi type is the geodesic approximation of Manton. In the
case of vortices and monopoles, Stuart has obtained rigorous estimates of the
errors in this approximation, and hence proved that it is valid in the low
speed regime. His method employs energy estimates which rely on a key
coercivity property of the Hessian of the energy functional of the theory under
consideration. In this paper we prove an analogous coercivity property for the
Hessian of the energy functional of a general sigma model with compact K\"ahler
domain and target. We go on to prove a continuity property for our result, and
show that, for the CP^1 model on S^2, the Hessian fails to be globally coercive
in the degree 1 sector. We present numerical evidence which suggests that the
Hessian is globally coercive in a certain equivariance class of the degree n
sector for n>1. We also prove that, within the geodesic approximation, a single
CP^1 lump moving on S^2 does not generically travel on a great circle.Comment: 29 pages, 1 figure; typos corrected, references added, expanded
discussion of the main function spac
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
Long-lived oscillons from asymmetric bubbles
The possibility that extremely long-lived, time-dependent, and localized
field configurations (``oscillons'') arise during the collapse of asymmetrical
bubbles in 2+1 dimensional phi^4 models is investigated. It is found that
oscillons can develop from a large spectrum of elliptically deformed bubbles.
Moreover, we provide numerical evidence that such oscillons are: a) circularly
symmetric; and b) linearly stable against small arbitrary radial and angular
perturbations. The latter is based on a dynamical approach designed to
investigate the stability of nonintegrable time-dependent configurations that
is capable of probing slowly-growing instabilities not seen through the usual
``spectral'' method.Comment: RevTeX 4, 9 pages, 11 figures. Revised version with a new approach to
stability. Accepted to Phys. Rev.
Clinical use, challenges, and barriers to implementation of deformable image registration in radiotherapy – the need for guidance and QA tools
OBJECTIVE: The aim of this study was to evaluate the current status of the clinical use of deformable image registration (DIR) in radiotherapy and to gain an understanding of the challenges faced by centres in clinical implementation of DIR, including commissioning and quality assurance (QA), and to determine the barriers faced. The goal was to inform whether additional guidance and QA tools were needed. METHODS: A survey focussed on clinical use, metrics used, how centres would like to use DIR in the future and challenges faced, was designed and sent to 71 radiotherapy centres in the UK. Data were gathered specifically on which centres we using DIR clinically, which applications were being used, what commissioning and QA tests were performed, and what barriers were preventing the integration of DIR into the clinical workflow. Centres that did not use DIR clinically were encouraged to fill in the survey and were asked if they have any future plans and in what timescale. RESULTS: 51 out of 71 (70%) radiotherapy centres responded. 47 centres reported access to a commercial software that could perform DIR. 20 centres already used DIR clinically, and 22 centres had plans to implement an application of DIR within 3 years of the survey. The most common clinical application of DIR was to propagate contours from one scan to another (19 centres). In each of the applications, the types of commissioning and QA tests performed varied depending on the type of application and between centres. Some of the key barriers were determining when a DIR was satisfactory including which metrics to use, and lack of resources. CONCLUSION: The survey results highlighted that there is a need for additional guidelines, training, better tools for commissioning DIR software and for the QA of registration results, which should include developing or recommending which quantitative metrics to use. ADVANCES IN KNOWLEDGE: This survey has given a useful picture of the clinical use and lack of use of DIR in UK radiotherapy centres. The survey provided useful insight into how centres commission and QA DIR applications, especially the variability among centres. It was also possible to highlight key barriers to implementation and determine factors that may help overcome this which include the need for additional guidance specific to different applications, better tools and metrics
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