5,612 research outputs found
Two Sets of Simple Formulae to Estimating Fractal Dimension of Irregular Boundaries
Irregular boundary lines can be characterized by fractal dimension, which
provides important information for spatial analysis of complex geographical
phenomena such as cities. However, it is difficult to calculate fractal
dimension of boundaries systematically when image data is limited. An
approximation estimation formulae of boundary dimension based on square is
widely applied in urban and ecological studies. However, the boundary dimension
is sometimes overestimated. This paper is devoted to developing a series of
practicable formulae for boundary dimension estimation using ideas from
fractals. A number of regular figures are employed as reference shapes, from
which the corresponding geometric measure relations are constructed; from these
measure relations, two sets of fractal dimension estimation formulae are
derived for describing fractal-like boundaries. Correspondingly, a group of
shape indexes can be defined. A finding is that different formulae have
different merits and spheres of application, and the second set of boundary
dimensions is a function of the shape indexes. Under condition of data
shortage, these formulae can be utilized to estimate boundary dimension values
rapidly. Moreover, the relationships between boundary dimension and shape
indexes are instructive to understand the association and differences between
characteristic scales and scaling. The formulae may be useful for the
pre-fractal studies in geography, geomorphology, ecology, landscape science,
and especially, urban science.Comment: 28 pages, 2 figures, 9 table
A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing
This work introduces an innovative parallel, fully-distributed finite element
framework for growing geometries and its application to metal additive
manufacturing. It is well-known that virtual part design and qualification in
additive manufacturing requires highly-accurate multiscale and multiphysics
analyses. Only high performance computing tools are able to handle such
complexity in time frames compatible with time-to-market. However, efficiency,
without loss of accuracy, has rarely held the centre stage in the numerical
community. Here, in contrast, the framework is designed to adequately exploit
the resources of high-end distributed-memory machines. It is grounded on three
building blocks: (1) Hierarchical adaptive mesh refinement with octree-based
meshes; (2) a parallel strategy to model the growth of the geometry; (3)
state-of-the-art parallel iterative linear solvers. Computational experiments
consider the heat transfer analysis at the part scale of the printing process
by powder-bed technologies. After verification against a 3D benchmark, a
strong-scaling analysis assesses performance and identifies major sources of
parallel overhead. A third numerical example examines the efficiency and
robustness of (2) in a curved 3D shape. Unprecedented parallelism and
scalability were achieved in this work. Hence, this framework contributes to
take on higher complexity and/or accuracy, not only of part-scale simulations
of metal or polymer additive manufacturing, but also in welding, sedimentation,
atherosclerosis, or any other physical problem where the physical domain of
interest grows in time
The Fractal Dimension of Projected Clouds
The interstellar medium seems to have an underlying fractal structure which
can be characterized through its fractal dimension. However, interstellar
clouds are observed as projected two-dimensional images, and the projection of
a tri-dimensional fractal distorts its measured properties. Here we use
simulated fractal clouds to study the relationship between the tri-dimensional
fractal dimension (D_f) of modeled clouds and the dimension resulting from
their projected images. We analyze different fractal dimension estimators: the
correlation and mass dimensions of the clouds, and the perimeter-based
dimension of their boundaries (D_per). We find the functional forms relating
D_f with the projected fractal dimensions, as well as the dependence on the
image resolution, which allow to estimatethe "real" D_f value of a cloud from
its projection. The application of these results to Orion A indicates in a
self-consistent way that 2.5 < D_f < 2.7 for this molecular cloud, a value
higher than the result D_per+1 = 2.3 some times assumed in literature for
interstellar clouds.Comment: 27 pages, 13 figures, 1 table. Accepted for publication in ApJ. Minor
change
Quantum Monte Carlo Study of Strongly Correlated Electrons: Cellular Dynamical Mean-Field Theory
We study the Hubbard model using the Cellular Dynamical Mean-Field Theory
(CDMFT) with quantum Monte Carlo (QMC) simulations. We present the algorithmic
details of CDMFT with the Hirsch-Fye QMC method for the solution of the
self-consistently embedded quantum cluster problem. We use the one- and
two-dimensional half-filled Hubbard model to gauge the performance of CDMFT+QMC
particularly for small clusters by comparing with the exact results and also
with other quantum cluster methods. We calculate single-particle Green's
functions and self-energies on small clusters to study their size dependence in
one- and two-dimensions.Comment: 14 pages, 18 figure
Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium
Multifractal scaling (MFS) refers to structures that can be described as a
collection of interwoven fractal subsets which exhibit power-law spatial
scaling behavior with a range of scaling exponents (concentration, or
singularity, strengths) and dimensions. The existence of MFS implies an
underlying multiplicative (or hierarchical, or cascade) process. Panoramic
column density images of several nearby star- forming cloud complexes,
constructed from IRAS data and justified in an appendix, are shown to exhibit
such multifractal scaling, which we interpret as indirect but quantitative
evidence for nested hierarchical structure. The relation between the dimensions
of the subsets and their concentration strengths (the "multifractal spectrum'')
appears to satisfactorily order the observed regions in terms of the mixture of
geometries present: strong point-like concentrations, line- like filaments or
fronts, and space-filling diffuse structures. This multifractal spectrum is a
global property of the regions studied, and does not rely on any operational
definition of "clouds.'' The range of forms of the multifractal spectrum among
the regions studied implies that the column density structures do not form a
universality class, in contrast to indications for velocity and passive scalar
fields in incompressible turbulence, providing another indication that the
physics of highly compressible interstellar gas dynamics differs fundamentally
from incompressible turbulence. (Abstract truncated)Comment: 27 pages, (LaTeX), 13 figures, 1 table, submitted to Astrophysical
Journa
Theory and Design of Flight-Vehicle Engines
Papers are presented on such topics as the testing of aircraft engines, errors in the experimental determination of the parameters of scramjet engines, the effect of the nonuniformity of supersonic flow with shocks on friction and heat transfer in the channel of a hypersonic ramjet engine, and the selection of the basic parameters of cooled GTE turbines. Consideration is also given to the choice of optimal total wedge angle for the acceleration of aerospace vehicles, the theory of an electromagnetic-resonator engine, the dynamic characteristics of the pumps and turbines of liquid propellant rocket engines in transition regimes, and a hierarchy of mathematical models for spacecraft control engines
Phase Diagram of Bosonic Atoms in Two-Color Superlattices
We investigate the zero temperature phase diagram of a gas of bosonic atoms
in one- and two-color standing-wave lattices in the framework of the
Bose-Hubbard model. We first introduce some relevant physical quantities;
superfluid fraction, condensate fraction, quasimomentum distribution, and
matter-wave interference pattern. We then discuss the relationships between
them on the formal level and show that the superfluid fraction, which is the
relevant order parameter for the superfluid to Mott-insulator transition,
cannot be probed directly via the matter wave interference patterns. The formal
considerations are supported by exact numerical solutions of the Bose-Hubbard
model for uniform one-dimensional systems. We then map out the phase diagram of
bosons in non-uniform lattices. The emphasis is on optical two-color
superlattices which exhibit a sinusoidal modulation of the well depth and can
be easily realized experimentally. From the study of the superfluid fraction,
the energy gap, and other quantities we identify new zero-temperature phases,
including a localized and a quasi Bose-glass phase, and discuss prospects for
their experimental observation.Comment: 18 pages, 17 figures, using REVTEX
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