32,090 research outputs found
Eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method: Real eigenvalue analysis
The development of the tridiagonal reduction method and its implementation in NASTRAN are described for real eigenvalue analysis as typified by structural vibration and buckling problems. This method is an automatic matrix reduction scheme whereby the eigensolutions in the neighborhood of a specified point in the eigenspectrum can be accurately extracted from a tridiagonal eigenvalue problem whose order is much lower than that of the full problem. The process is effected without orbitrary lumping of masses or other physical quantities at selected node points and thus avoids one of the basic weaknesses of other techniques
Extension of the tridiagonal reduction (FEER) method for complex eigenvalue problems in NASTRAN
As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum were extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order was much lower than that of the full size problem. The reduction process was effected automatically, and thus avoided the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admitted mass, damping, and stiffness matrices which were unrestricted in character, i.e., they might be real, symmetric or nonsymmetric, singular or nonsingular
Clusters and Recurrence in the Two-Dimensional Zero-Temperature Stochastic Ising Model
We analyze clustering and (local) recurrence of a standard Markov process
model of spatial domain coarsening. The continuous time process, whose state
space consists of assignments of +1 or -1 to each site in , is the
zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with
Glauber dynamics): the initial state is chosen uniformly at random and then
each site, at rate one, polls its 4 neighbors and makes sure it agrees with the
majority, or tosses a fair coin in case of a tie. Among the main results
(almost sure, with respect to both the process and initial state) are: clusters
(maximal domains of constant sign) are finite for times , but the
cluster of a fixed site diverges (in diameter) as ; each of the
two constant states is (positive) recurrent. We also present other results and
conjectures concerning positive and null recurrence and the role of absorbing
states.Comment: 16 pages, 1 figur
Two-Dimensional Scaling Limits via Marked Nonsimple Loops
We postulate the existence of a natural Poissonian marking of the double
(touching) points of SLE(6) and hence of the related continuum nonsimple loop
process that describes macroscopic cluster boundaries in 2D critical
percolation. We explain how these marked loops should yield continuum versions
of near-critical percolation, dynamical percolation, minimal spanning trees and
related plane filling curves, and invasion percolation. We show that this
yields for some of the continuum objects a conformal covariance property that
generalizes the conformal invariance of critical systems. It is an open problem
to rigorously construct the continuum objects and to prove that they are indeed
the scaling limits of the corresponding lattice objects.Comment: 25 pages, 5 figure
Interfaces (and Regional Congruence?) in Spin Glasses
We present a general theorem restricting properties of interfaces between
thermodynamic states and apply it to the spin glass excitations observed
numerically by Krzakala-Martin and Palassini-Young in spatial dimensions d=3
and 4. We show that such excitations, with interface dimension smaller than d,
cannot yield regionally congruent thermodynamic states. More generally, zero
density interfaces of translation-covariant excitations cannot be pinned (by
the disorder) in any d but rather must deflect to infinity in the thermodynamic
limit. Additional consequences concerning regional congruence in spin glasses
and other systems are discussed.Comment: 4 pages (ReVTeX); 1 figure; submitted to Physical Review Letter
Real eigenvalue analysis in NASTRAN by the tridiagonal reduction (FEER) method
Implementation of the tridiagonal reduction method for real eigenvalue extraction in structural vibration and buckling problems is described. The basic concepts underlying the method are summarized and special features, such as the computation of error bounds and default modes of operation are discussed. In addition, the new user information and error messages and optional diagnostic output relating to the tridiagonal reduction method are presented. Some numerical results and initial experiences relating to usage in the NASTRAN environment are provided, including comparisons with other existing NASTRAN eigenvalue methods
A statistical network analysis of the HIV/AIDS epidemics in Cuba
The Cuban contact-tracing detection system set up in 1986 allowed the
reconstruction and analysis of the sexual network underlying the epidemic
(5,389 vertices and 4,073 edges, giant component of 2,386 nodes and 3,168
edges), shedding light onto the spread of HIV and the role of contact-tracing.
Clustering based on modularity optimization provides a better visualization and
understanding of the network, in combination with the study of covariates. The
graph has a globally low but heterogeneous density, with clusters of high
intraconnectivity but low interconnectivity. Though descriptive, our results
pave the way for incorporating structure when studying stochastic SIR epidemics
spreading on social networks
Assembling thefacebook: Using heterogeneity to understand online social network assembly
Online social networks represent a popular and diverse class of social media
systems. Despite this variety, each of these systems undergoes a general
process of online social network assembly, which represents the complicated and
heterogeneous changes that transform newly born systems into mature platforms.
However, little is known about this process. For example, how much of a
network's assembly is driven by simple growth? How does a network's structure
change as it matures? How does network structure vary with adoption rates and
user heterogeneity, and do these properties play different roles at different
points in the assembly? We investigate these and other questions using a unique
dataset of online connections among the roughly one million users at the first
100 colleges admitted to Facebook, captured just 20 months after its launch. We
first show that different vintages and adoption rates across this population of
networks reveal temporal dynamics of the assembly process, and that assembly is
only loosely related to network growth. We then exploit natural experiments
embedded in this dataset and complementary data obtained via Internet
archaeology to show that different subnetworks matured at different rates
toward similar end states. These results shed light on the processes and
patterns of online social network assembly, and may facilitate more effective
design for online social systems.Comment: 13 pages, 11 figures, Proceedings of the 7th Annual ACM Web Science
Conference (WebSci), 201
The Architecture of a Novel Weighted Network: Knowledge Network
Networked structure emerged from a wide range of fields such as biological
systems, World Wide Web and technological infrastructure. A deeply insight into
the topological complexity of these networks has been gained. Some works start
to pay attention to the weighted network, like the world-wide airport network
and the collaboration network, where links are not binary, but have
intensities. Here, we construct a novel knowledge network, through which we
take the first step to uncover the topological structure of the knowledge
system. Furthermore, the network is extended to the weighted one by assigning
weights to the edges. Thus, we also investigate the relationship between the
intensity of edges and the topological structure. These results provide a novel
description to understand the hierarchies and organizational principles in
knowledge system, and the interaction between the intensity of edges and
topological structure. This system also provides a good paradigm to study
weighted networks.Comment: 5 figures 11 page
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