8,548 research outputs found
Self-adjoint symmetry operators connected with the magnetic Heisenberg ring
We consider symmetry operators a from the group ring C[S_N] which act on the
Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We
investigate such symmetry operators a which are self-adjoint (in a sence
defined in the paper) and which yield consequently observables of the
Heisenberg model. We prove the following results: (i) One can construct a
self-adjoint idempotent symmetry operator from every irreducible character of
every subgroup of S_N. This leads to a big manifold of observables. In
particular every commutation symmetry yields such an idempotent. (ii) The set
of all generating idempotents of a minimal right ideal R of C[S_N] contains one
and only one idempotent which ist self-adjoint. (iii) Every self-adjoint
idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k
which are also self-adjoint and pairwise orthogonal. We give a computer
algorithm for the calculation of such decompositions. Furthermore we present 3
additional algorithms which are helpful for the calculation of self-adjoint
operators by means of discrete Fourier transforms of S_N. In our investigations
we use computer calculations by means of our Mathematica packages PERMS and
HRing.Comment: 13 page
Aluminide coatings for nickel base alloys
The metalliding process was used to aluminide IN-100 and TD NiCr. Aluminum was deposited over a broad range of deposition rates, with two types of coating structures resulting. Chromium, silicon, titanium and yttrium were also individually deposited simutaneously with aluminum on IN-100. None of these had a marked effect on the oxidation resistance of the aluminide coating. Porosity-free aluminide coatings with good oxidation resistance were formed on TD NiCr providing the aluminum concentration did not exceed 8 percent, the limit of solubility in the gamma phase
Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions
Turbulent Rayleigh-Benard convection with phase changes in an extended layer
between two parallel impermeable planes is studied by means of
three-dimensional direct numerical simulations for Rayleigh numbers between
10^4 and 1.5\times 10^7 and for Prandtl number Pr=0.7. Two different sets of
boundary conditions of temperature and total water content are compared:
imposed constant amplitudes which translate into Dirichlet boundary conditions
for the scalar field fluctuations about the quiescent diffusive equilibrium and
constant imposed flux boundary conditions that result in Neumann boundary
conditions. Moist turbulent convection is in the conditionally unstable regime
throughout this study for which unsaturated air parcels are stably and
saturated air parcels unstably stratified. A direct comparison of both sets of
boundary conditions with the same parameters requires to start the turbulence
simulations out of differently saturated equilibrium states. Similar to dry
Rayleigh-Benard convection the differences in the turbulent velocity
fluctuations, the cloud cover and the convective buoyancy flux decrease across
the layer with increasing Rayleigh number. At the highest Rayleigh numbers the
system is found in a two-layer regime, a dry cloudless and stably stratified
layer with low turbulence level below a fully saturated and cloudy turbulent
one which equals classical Rayleigh-Benard convection layer. Both are separated
by a strong inversion that gets increasingly narrower for growing Rayleigh
number.Comment: 19 pages, 13 Postscript figures, Figures 10,11,12,13, in reduced
qualit
Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation
The detection of community structure in networks is intimately related to
finding a concise description of the network in terms of its modules. This
notion has been recently exploited by the Map equation formalism (M. Rosvall
and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an
information-theoretic description of the process of coding inter- and
intra-community transitions of a random walker in the network at stationarity.
However, a thorough study of the relationship between the full Markov dynamics
and the coding mechanism is still lacking. We show here that the original Map
coding scheme, which is both block-averaged and one-step, neglects the internal
structure of the communities and introduces an upper scale, the `field-of-view'
limit, in the communities it can detect. As a consequence, Map is well tuned to
detect clique-like communities but can lead to undesirable overpartitioning
when communities are far from clique-like. We show that a signature of this
behavior is a large compression gap: the Map description length is far from its
ideal limit. To address this issue, we propose a simple dynamic approach that
introduces time explicitly into the Map coding through the analysis of the
weighted adjacency matrix of the time-dependent multistep transition matrix of
the Markov process. The resulting Markov time sweeping induces a dynamical
zooming across scales that can reveal (potentially multiscale) community
structure above the field-of-view limit, with the relevant partitions indicated
by a small compression gap.Comment: 10 pages, 6 figure
Approximating Spectral Impact of Structural Perturbations in Large Networks
Determining the effect of structural perturbations on the eigenvalue spectra
of networks is an important problem because the spectra characterize not only
their topological structures, but also their dynamical behavior, such as
synchronization and cascading processes on networks. Here we develop a theory
for estimating the change of the largest eigenvalue of the adjacency matrix or
the extreme eigenvalues of the graph Laplacian when small but arbitrary set of
links are added or removed from the network. We demonstrate the effectiveness
of our approximation schemes using both real and artificial networks, showing
in particular that we can accurately obtain the spectral ranking of small
subgraphs. We also propose a local iterative scheme which computes the relative
ranking of a subgraph using only the connectivity information of its neighbors
within a few links. Our results may not only contribute to our theoretical
understanding of dynamical processes on networks, but also lead to practical
applications in ranking subgraphs of real complex networks.Comment: 9 pages, 3 figures, 2 table
Molecular Clock on a Neutral Network
The number of fixed mutations accumulated in an evolving population often
displays a variance that is significantly larger than the mean (the
overdispersed molecular clock). By examining a generic evolutionary process on
a neutral network of high-fitness genotypes, we establish a formalism for
computing all cumulants of the full probability distribution of accumulated
mutations in terms of graph properties of the neutral network, and use the
formalism to prove overdispersion of the molecular clock. We further show that
significant overdispersion arises naturally in evolution when the neutral
network is highly sparse, exhibits large global fluctuations in neutrality, and
small local fluctuations in neutrality. The results are also relevant for
elucidating the topological structure of a neutral network from empirical
measurements of the substitution process.Comment: 10 page
Finding community structure in very large networks
The discovery and analysis of community structure in networks is a topic of
considerable recent interest within the physics community, but most methods
proposed so far are unsuitable for very large networks because of their
computational cost. Here we present a hierarchical agglomeration algorithm for
detecting community structure which is faster than many competing algorithms:
its running time on a network with n vertices and m edges is O(m d log n) where
d is the depth of the dendrogram describing the community structure. Many
real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in
which case our algorithm runs in essentially linear time, O(n log^2 n). As an
example of the application of this algorithm we use it to analyze a network of
items for sale on the web-site of a large online retailer, items in the network
being linked if they are frequently purchased by the same buyer. The network
has more than 400,000 vertices and 2 million edges. We show that our algorithm
can extract meaningful communities from this network, revealing large-scale
patterns present in the purchasing habits of customers
Global interlaboratory assessments of perfluoroalkyl substances under the Stockholm Convention on persistent organic pollutants
The Global Monitoring Plan (GMP) according to article 16 of the Stockholm Convention on Persistent Organic Pollutants (POPs) requires that POP laboratories must be capable – at any time – to analyse samples for POPs within a variation of ±25%. Based on this target error of 25%, a statistical model using z-scores was applied to assess the performance of analytical laboratories for POPs and a number of matrices. Since the second round of these ‘Bi-ennial Global Interlaboratory Assessment on Persistent Organic Pollutants (POPs)’, carried out in 2012/2013, perfluoroalkyl substances (PFASs) have been included into the proficiency tests. The third round was carried out in 2016/2017. The test materials included test solutions of PFASs analytical standards, the abiotic matrices sediment, air (extract) and water and the biotic matrices fish, human milk and human plasma. The number of laboratories submitting results for PFASs remained quite stable (IL2 = 27 laboratories; IL3 = 29), but there was broader geographic distribution observed in IL3: in addition to the laboratories from Asia and the Western Europe/other groups, two laboratories from Africa participated, two from Central-Eastern Europe and one from the Latin American/Caribbean region. Considering that PFASs were introduced for the first time in round 2, the results were good to reasonable compared to those of a number of other POPs included in the same study. However, it shall also be mentioned that for some matrices and PFASs, the number of laboratories submitting results was too small and the results too scattered to derive a consensus value. This was especially true for the PFOS precursor compounds and the air matrix. Also, laboratories struggle with the analysis of the branched PFOS isomers. These interlaboratory assessments on PFASs gave promising results and demonstrated the importance of proficiency tests in an international environment to generate trust in laboratory results. The need to participate regularly in such intercomparison assessments is highlighted. The results show the current level of PFAS analysis, which varies by laboratory and by matrix rather than per geographic region
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