23,069 research outputs found
Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata
Functions which are equivariant or invariant under the transformations of a
compact linear group acting in an euclidean space , can profitably
be studied as functions defined in the orbit space of the group. The orbit
space is the union of a finite set of strata, which are semialgebraic manifolds
formed by the -orbits with the same orbit-type. In this paper we provide a
simple recipe to obtain rational parametrizations of the strata. Our results
can be easily exploited, in many physical contexts where the study of
equivariant or invariant functions is important, for instance in the
determination of patterns of spontaneous symmetry breaking, in the analysis of
phase spaces and structural phase transitions (Landau theory), in equivariant
bifurcation theory, in crystal field theory and in most areas where use is made
of symmetry adapted functions.
A physically significant example of utilization of the recipe is given,
related to spontaneous polarization in chiral biaxial liquid crystals, where
the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing
in J. Phys. A: Math. Ge
Scale dependence of cosmological backreaction
Due to the non-commutation of spatial averaging and temporal evolution,
inhomogeneities and anisotropies (cosmic structures) influence the evolution of
the averaged Universe via the cosmological backreaction mechanism. We study the
backreaction effect as a function of averaging scale in a perturbative approach
up to higher orders. We calculate the hierarchy of the critical scales, at
which 10% effects show up from averaging at different orders. The dominant
contribution comes from the averaged spatial curvature, observable up to scales
of 200 Mpc. The cosmic variance of the local Hubble rate is 10% (5%) for
spherical regions of radius 40 (60) Mpc. We compare our result to the one from
Newtonian cosmology and Hubble Space Telescope Key Project data.Comment: 6 pages, 2 figures; v3: substantial modifications, new figure
Solomon Islands: Essential aspects of governance for Aquatic Agricultural Systems in Malaita Hub
In late 2012, a governance assessment was carried out as part of the diagnosis phase of rollout of the CGIAR Aquatic Agricultural Systems Program in Malaita Hub in Solomon Islands. The purpose of the assessment was to identify and provide a basic understanding of essential aspects of governance related to Aquatic Agricultural Systems in general, and more specifically as a case study in natural resource management. The underlying principles of the approach we have taken are drawn from an approach known as “Collaborating for Resilience” (CORE), which is based on bringing all key stakeholders into a process to ensure that multiple perspectives are represented (a listening phase), that local actors have opportunities to influence each other’s understanding (a dialogue phase), and that ultimately commitments to action are built (a choice phase) that would not be possible through an outsider’s analysis alone. This report begins to address governance from an AAS perspective, using input from AAS households and other networked stakeholders. We attempt to summarize governance issues that are found not only within the community but also, and especially, those that are beyond the local level, both of which may need to be addressed by the AAS program
Image interpolation using Shearlet based iterative refinement
This paper proposes an image interpolation algorithm exploiting sparse
representation for natural images. It involves three main steps: (a) obtaining
an initial estimate of the high resolution image using linear methods like FIR
filtering, (b) promoting sparsity in a selected dictionary through iterative
thresholding, and (c) extracting high frequency information from the
approximation to refine the initial estimate. For the sparse modeling, a
shearlet dictionary is chosen to yield a multiscale directional representation.
The proposed algorithm is compared to several state-of-the-art methods to
assess its objective as well as subjective performance. Compared to the cubic
spline interpolation method, an average PSNR gain of around 0.8 dB is observed
over a dataset of 200 images
Dynamics of the DBI Spike Soliton
We compare oscillations of a fundamental string ending on a D3-brane in two
different settings: (1) a test-string radially threading the horizon of an
extremal black D3-brane and (2) the spike soliton of the DBI effective action
for a D3-brane. Previous work has shown that overall transverse modes of the
test-string appear as l=0 modes of the transverse scalar fields of the DBI
system. We identify DBI world-volume degrees of freedom that have dynamics
matching those of the test-string relative transverse modes. We show that there
is a map, resembling T-duality, between relative and overall transverse modes
for the test-string that interchanges Neumann and Dirichlet boundary conditions
and implies equality of the absorption coefficients for both modes. We give
general solutions to the overall and relative transverse parts of the DBI
coupled gauge and scalar system and calculate absorption coefficients for the
higher angular momentum modes in the low frequency limit. We find that there is
a nonzero amplitude for l>0 modes to travel out to infinity along the spike,
demonstrating that the spike remains effectively 3+1-dimensional.Comment: 15 pages, 1 figur
Polarizations and Nullcone of Representations of Reductive Groups
The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.
On historical earthquakes in Switzerland: summary of compilations and investigations
Studies of historical earthquakes in Switzerland are contained in monographs, chronological collections of effects and parametric catalogues. The systematic collection of macroseismic material started with the creation of the Swiss Seismological Commission in 1878. All parametric catalogues since 1975 have been prepared for seismic hazard assessment. The most up-to-date investigation of macroseismic data and compilation into a catalogue (ECOS) was made in the 2002 in context of the re-assessment of seismic hazard for nuclear sites
The loss of anisotropy in MgB2 with Sc substitution and its relationship with the critical temperature
The electrical conductivity anisotropy of the sigma-bands is calculated for
the (Mg,Sc)B2 system using a virtual crystal model. Our results reveal that
anisotropy drops with relatively little scandium content (< 30%); this
behaviour coincides with the lowering of Tc and the reduction of the Kohn
anomaly. This anisotropy loss is also found in the Al and C doped systems. In
this work it is argued that the anisotropy, or 2D character, of the sigma-bands
is an important parameter for the understanding of the high Tc found in MgB2
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