4,441 research outputs found
The development of precipitation-hardened chromium-base alloys Final report
Precipitation with refractory metal carbides for creep resistant chromium-base alloy
Truncation method for Green's functions in time-dependent fields
We investigate the influence of a time dependent, homogeneous electric field
on scattering properties of non-interacting electrons in an arbitrary static
potential. We develop a method to calculate the (Keldysh) Green's function in
two complementary approaches. Starting from a plane wave basis, a formally
exact solution is given in terms of the inverse of a matrix containing
infinitely many 'photoblocks' which can be evaluated approximately by
truncation. In the exact eigenstate basis of the scattering potential, we
obtain a version of the Floquet state theory in the Green's functions language.
The formalism is checked for cases such as a simple model of a double barrier
in a strong electric field. Furthermore, an exact relation between the
inelastic scattering rate due to the microwave and the AC conductivity of the
system is derived which in particular holds near or at a metal-insulator
transition in disordered systems.Comment: to appear in Phys. Rev. B., 21 pages, 3 figures (ps-files
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
Multifractal wave functions of simple quantum maps
We study numerically multifractal properties of two models of one-dimensional
quantum maps, a map with pseudointegrable dynamics and intermediate spectral
statistics, and a map with an Anderson-like transition recently implemented
with cold atoms. Using extensive numerical simulations, we compute the
multifractal exponents of quantum wave functions and study their properties,
with the help of two different numerical methods used for classical
multifractal systems (box-counting method and wavelet method). We compare the
results of the two methods over a wide range of values. We show that the wave
functions of the Anderson map display a multifractal behavior similar to
eigenfunctions of the three-dimensional Anderson transition but of a weaker
type. Wave functions of the intermediate map share some common properties with
eigenfunctions at the Anderson transition (two sets of multifractal exponents,
with similar asymptotic behavior), but other properties are markedly different
(large linear regime for multifractal exponents even for strong
multifractality, different distributions of moments of wave functions, absence
of symmetry of the exponents). Our results thus indicate that the intermediate
map presents original properties, different from certain characteristics of the
Anderson transition derived from the nonlinear sigma model. We also discuss the
importance of finite-size effects.Comment: 15 pages, 21 figure
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