1,279 research outputs found
Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models
The lower-critical dimension for the existence of the Ising spin-glass phase
is calculated, numerically exactly, as for a family of
hierarchical lattices, from an essentially exact (correlation coefficent ) near-linear fit to 23 different diminishing fractional dimensions.
To obtain this result, the phase transition temperature between the disordered
and spin-glass phases, the corresponding critical exponent , and the
runaway exponent of the spin-glass phase are calculated for consecutive
hierarchical lattices as dimension is lowered.Comment: 5 pages, 2 figures, 1 tabl
On micro-structural effects in dielectric mixtures
The paper presents numerical simulations performed on dielectric properties
of two-dimensional binary composites on eleven regular space filling
tessellations. First, significant contributions of different parameters, which
play an important role in the electrical properties of the composite, are
introduced both for designing and analyzing material mixtures. Later, influence
of structural differences and intrinsic electrical properties of constituents
on the composite's over all electrical properties are investigated. The
structural differences are resolved by the spectral density representation
approach. The numerical technique, without any {\em a-priori} assumptions, for
extracting the spectral density function is also presented.Comment: 24 pages, 8 figure and 7 tables. It is submitted to IEEE Transactions
on Dielectrics and Electrical Insulatio
Signs of low frequency dispersions in disordered binary dielectric mixtures (50-50)
Dielectric relaxation in disordered dielectric mixtures are presented by
emphasizing the interfacial polarization. The obtained results coincide with
and cause confusion with those of the low frequency dispersion behavior. The
considered systems are composed of two phases on two-dimensional square and
triangular topological networks. We use the finite element method to calculate
the effective dielectric permittivities of randomly generated structures. The
dielectric relaxation phenomena together with the dielectric permittivity
values at constant frequencies are investigated, and significant differences of
the square and triangular topologies are observed. The frequency dependent
properties of some of the generated structures are examined. We conclude that
the topological disorder may lead to the normal or anomalous low frequency
dispersion if the electrical properties of the phases are chosen properly, such
that for ``slightly'' {\em reciprocal mixture}--when , and
--normal, and while for ``extreme'' {\em reciprocal
mixture}--when , and --anomalous
low frequency dispersions are obtained. Finally, comparison with experimental
data indicates that one can obtain valuable information from simulations when
the material properties of the constituents are not available and of
importance.Comment: 13 pages, 7 figure
Itineraries of walking and footwear on film:[Review of: T.D. Tucker (2020) The Peripatetic Frame: Images of Walking in Film; E. Ezra, C. Wheatley (2020) Shoe Reels: The History and Philosophy of Footwear in Film]
Extracting spectral density function of a binary composite without a-priori assumption
The spectral representation separates the contributions of geometrical
arrangement (topology) and intrinsic constituent properties in a composite. The
aim of paper is to present a numerical algorithm based on the Monte Carlo
integration and contrainted-least-squares methods to resolve the spectral
density function for a given system. The numerical method is verified by
comparing the results with those of Maxwell-Garnett effective permittivity
expression. Later, it is applied to a well-studied rock-and-brine system to
instruct its utility. The presented method yields significant microstructural
information in improving our understanding how microstructure influences the
macroscopic behaviour of composites without any intricate mathematics.Comment: 4 pages, 5 figures and 1 tabl
Projected finite elements for reaction-diffusion systems on stationary closed surfaces
This paper presents a robust, efficient and accurate finite element method for solving reaction-diffusion systems on stationary spheroidal surfaces (these are surfaces which are deformations of the sphere such as ellipsoids, dumbbells, and heart-shaped surfaces) with potential applications in the areas of developmental biology, cancer research, wound healing, tissue regeneration, and cell motility among many others where such models are routinely used. Our method is inspired by the radially projected finite element method introduced by Meir and Tuncer (2009), hence the name ``projected'' finite element method. The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization which is ``logically'' rectangular. To demonstrate the robustness, applicability and generality of this numerical method, we present solutions of reaction-diffusion systems on various spheroidal surfaces. We show that the method presented in this paper preserves positivity of the solutions of reaction-diffusion equations which is not generally true for Galerkin type methods. We conclude that surface geometry plays a pivotal role in pattern formation. For a fixed set of model parameter values, different surfaces give rise to different pattern generation sequences of either spots or stripes or a combination (observed as circular spot-stripe patterns). These results clearly demonstrate the need for detailed theoretical analytical studies to elucidate how surface geometry and curvature influence pattern formation on complex surfaces
Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models
Hierarchical lattices that constitute spatially anisotropic systems are
introduced. These lattices provide exact solutions for hierarchical models and,
simultaneously, approximate solutions for uniaxially or fully anisotropic d=3
physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers,
are obtained for Ising, XY magnetic models and percolation systems, including
crossovers from algebraic order to true long-range order.Comment: 7 pages, 12 figures. Corrected typos, added publication informatio
Online Fault Classification in HPC Systems through Machine Learning
As High-Performance Computing (HPC) systems strive towards the exascale goal,
studies suggest that they will experience excessive failure rates. For this
reason, detecting and classifying faults in HPC systems as they occur and
initiating corrective actions before they can transform into failures will be
essential for continued operation. In this paper, we propose a fault
classification method for HPC systems based on machine learning that has been
designed specifically to operate with live streamed data. We cast the problem
and its solution within realistic operating constraints of online use. Our
results show that almost perfect classification accuracy can be reached for
different fault types with low computational overhead and minimal delay. We
have based our study on a local dataset, which we make publicly available, that
was acquired by injecting faults to an in-house experimental HPC system.Comment: Accepted for publication at the Euro-Par 2019 conferenc
Numerical calculations of effective elastic properties of two cellular structures
Young's moduli of regular two-dimensional truss-like and eye-shape-like
structures are simulated by using the finite element method. The structures are
the idealizations of soft polymeric materials used in the electret
applications. In the simulations size of the representative smallest units are
varied, which changes the dimensions of the cell-walls in the structures. A
power-law expression with a quadratic as the exponential term is proposed for
the effective Young's moduli of the systems as a function of the solid volume
fraction. The data is divided into three regions with respect to the volume
fraction; low, intermediate and high concentrations. The parameters of the
proposed power-law expression in each region are later represented as a
function of the structural parameters, unit-cell dimensions. The presented
expression can be used to predict structure/property relationship in materials
with similar cellular structures. It is observed that the structures with
volume fractions of solid higher than 0.15 exhibit the importance of the
cell-wall thickness contribution in the elastic properties. The cell-wall
thickness is the most significant factor to predict the effective Young's
modulus of regular cellular structures at high volume fractions of solid. At
lower concentrations of solid, eye-like structure yields lower Young's modulus
than the truss-like structure with the similar anisotropy. Comparison of the
numerical results with those of experimental data of poly(propylene) show good
aggreement regarding the influence of cell-wall thickness on elastic properties
of thin cellular films.Comment: 7 figures and 2 table
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