415 research outputs found
Computation of unsteady transonic flows through rotating and stationary cascades. 1: Method of analysis
A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator) or a single blade row of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite difference method is employed in the interior of the passage, and a method of characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors and compared with available experimental data, consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed
Computation of unsteady transonic flows through rotating and stationary cascades. 3: Acoustic far-field analysis
A small perturbation type analysis has been developed for the acoustic far field in an infinite duct extending upstream and downstream of an axial turbomachinery stage. The analysis is designed to interface with a numerical solution of the near field of the blade rows and, thereby, to provide the necessary closure condition to complete the statement of infinite duct boundary conditions for the subject problem. The present analysis differs from conventional inlet duct analyses in that a simple harmonic time dependence was not assumed, since a transient signal is generated by the numerical near-field solution and periodicity is attained only asymptotically. A description of the computer code developed to carry out the necessary convolutions numerically is included, as well as the results of a sample application using an impulsively initiated harmonic signal
Random Topologies and the emergence of cooperation: the role of short-cuts
We study in detail the role of short-cuts in promoting the emergence of
cooperation in a network of agents playing the Prisoner's Dilemma Game (PDG).
We introduce a model whose topology interpolates between the one-dimensional
euclidean lattice (a ring) and the complete graph by changing the value of one
parameter (the probability p to add a link between two nodes not already
connected in the euclidean configuration). We show that there is a region of
values of p in which cooperation is largely enhanced, whilst for smaller values
of p only a few cooperators are present in the final state, and for p
\rightarrow 1- cooperation is totally suppressed. We present analytical
arguments that provide a very plausible interpretation of the simulation
results, thus unveiling the mechanism by which short-cuts contribute to promote
(or suppress) cooperation
Network Structures from Selection Principles
We present an analysis of the topologies of a class of networks which are
optimal in terms of the requirements of having as short a route as possible
between any two nodes while yet keeping the congestion in the network as low as
possible. Strikingly, we find a variety of distinct topologies and novel phase
transitions between them on varying the number of links per node. Our results
suggest that the emergence of the topologies observed in nature may arise both
from growth mechanisms and the interplay of dynamical mechanisms with a
selection process.Comment: 4 pages, 5 figure
Spectral Theory of Sparse Non-Hermitian Random Matrices
Sparse non-Hermitian random matrices arise in the study of disordered
physical systems with asymmetric local interactions, and have applications
ranging from neural networks to ecosystem dynamics. The spectral
characteristics of these matrices provide crucial information on system
stability and susceptibility, however, their study is greatly complicated by
the twin challenges of a lack of symmetry and a sparse interaction structure.
In this review we provide a concise and systematic introduction to the main
tools and results in this field. We show how the spectra of sparse
non-Hermitian matrices can be computed via an analogy with infinite dimensional
operators obeying certain recursion relations. With reference to three
illustrative examples --- adjacency matrices of regular oriented graphs,
adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency
matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the
use of these methods to obtain both analytic and numerical results for the
spectrum, the spectral distribution, the location of outlier eigenvalues, and
the statistical properties of eigenvectors.Comment: 60 pages, 10 figure
Diffusion Processes on Small-World Networks with Distance-Dependent Random-Links
We considered diffusion-driven processes on small-world networks with
distance-dependent random links. The study of diffusion on such networks is
motivated by transport on randomly folded polymer chains, synchronization
problems in task-completion networks, and gradient driven transport on
networks. Changing the parameters of the distance-dependence, we found a rich
phase diagram, with different transient and recurrent phases in the context of
random walks on networks. We performed the calculations in two limiting cases:
in the annealed case, where the rearrangement of the random links is fast, and
in the quenched case, where the link rearrangement is slow compared to the
motion of the random walker or the surface. It has been well-established that
in a large class of interacting systems, adding an arbitrarily small density
of, possibly long-range, quenched random links to a regular lattice interaction
topology, will give rise to mean-field (or annealed) like behavior. In some
cases, however, mean-field scaling breaks down, such as in diffusion or in the
Edwards-Wilkinson process in "low-dimensional" small-world networks. This
break-down can be understood by treating the random links perturbatively, where
the mean-field (or annealed) prediction appears as the lowest-order term of a
naive perturbation expansion. The asymptotic analytic results are also
confirmed numerically by employing exact numerical diagonalization of the
network Laplacian. Further, we construct a finite-size scaling framework for
the relevant observables, capturing the cross-over behaviors in finite
networks. This work provides a detailed account of the
self-consistent-perturbative and renormalization approaches briefly introduced
in two earlier short reports.Comment: 36 pages, 27 figures. Minor revisions in response to the referee's
comments. Furthermore, some typos were fixed and new references were adde
Transmission and Spectral Aspects of Tight Binding Hamiltonians for the Counting Quantum Turing Machine
It was recently shown that a generalization of quantum Turing machines
(QTMs), in which potentials are associated with elementary steps or transitions
of the computation, generates potential distributions along computation paths
of states in some basis B. The distributions are computable and are thus
periodic or have deterministic disorder. These generalized machines (GQTMs) can
be used to investigate the effect of potentials in causing reflections and
reducing the completion probability of computations. This work is extended here
by determination of the spectral and transmission properties of an example GQTM
which enumerates the integers as binary strings. A potential is associated with
just one type of step. For many computation paths the potential distributions
are initial segments of a quasiperiodic distribution that corresponds to a
substitution sequence. The energy band spectra and Landauer Resistance (LR) are
calculated for energies below the barrier height by use of transfer matrices.
The LR fluctuates rapidly with momentum with minima close to or at band-gap
edges. For several values of the parameters, there is good transmission over
some momentum regions.Comment: 22 pages Latex, 13 postscript figures, Submitted to Phys. Rev.
Genome-wide association scan meta-analysis identifies three Loci influencing adiposity and fat distribution.
To identify genetic loci influencing central obesity and fat distribution, we performed a meta-analysis of 16 genome-wide association studies (GWAS, N = 38,580) informative for adult waist circumference (WC) and waist-hip ratio (WHR). We selected 26 SNPs for follow-up, for which the evidence of association with measures of central adiposity (WC and/or WHR) was strong and disproportionate to that for overall adiposity or height. Follow-up studies in a maximum of 70,689 individuals identified two loci strongly associated with measures of central adiposity; these map near TFAP2B (WC, P = 1.9x10(-11)) and MSRA (WC, P = 8.9x10(-9)). A third locus, near LYPLAL1, was associated with WHR in women only (P = 2.6x10(-8)). The variants near TFAP2B appear to influence central adiposity through an effect on overall obesity/fat-mass, whereas LYPLAL1 displays a strong female-only association with fat distribution. By focusing on anthropometric measures of central obesity and fat distribution, we have identified three loci implicated in the regulation of human adiposity
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