672 research outputs found
On Binary Codes from Conics in PG(2,q)
Let A be the incidence matrix of passant lines and internal points with
respect to a conic in PG(2, q), where q is an odd prime power. In this article,
we study both geometric and algebraic properties of the column null space L of
A over the finite field of 2 elements. In particular, using methods from both
finite geometry and modular presentation theory, we manage to compute the
dimension of L, which provides a proof for the conjecture on the dimension of
the binary code generated by L
Exact and heuristic approaches for multi-component optimisation problems
Modern real world applications are commonly complex, consisting of multiple subsystems
that may interact with or depend on each other. Our case-study about wave
energy converters (WEC) for the renewable energy industry shows that in such a
multi-component system, optimising each individual component cannot yield global
optimality for the entire system, owing to the influence of their interactions or the
dependence on one another. Moreover, modelling a multi-component problem is
rarely easy due to the complexity of the issues, which leads to a desire for existent
models on which to base, and against which to test, calculations. Recently,
the travelling thief problem (TTP) has attracted significant attention in the Evolutionary
Computation community. It is intended to offer a better model for multicomponent
systems, where researchers can push forward their understanding of
the optimisation of such systems, especially for understanding of the interconnections
between the components. The TTP interconnects with two classic NP-hard
problems, namely the travelling salesman problem and the 0-1 knapsack problem,
via the transportation cost that non-linearly depends on the accumulated weight
of items. This non-linear setting introduces additional complexity. We study this
nonlinearity through a simplified version of the TTP - the packing while travelling
(PWT) problem, which aims to maximise the total reward for a given travelling tour.
Our theoretical and experimental investigations demonstrate that the difficulty of a
given problem instance is significantly influenced by adjusting a single parameter,
the renting rate, which prompted our method of creating relatively hard instances
using simple evolutionary algorithms. Our further investigations into the PWT
problem yield a dynamic programming (DP) approach that can solve the problem in
pseudo polynomial time and a corresponding approximation scheme. The experimental
investigations show that the new approaches outperform the state-of-the-art
ones. We furthermore propose three exact algorithms for the TTP, based on the DP
of the PWT problem. By employing the exact DP for the underlying PWT problem
as a subroutine, we create a novel indicator-based hybrid evolutionary approach for
a new bi-criteria formulation of the TTP. This hybrid design takes advantage of the
DP approach, along with a number of novel indicators and selection mechanisms
to achieve better solutions. The results of computational experiments show that the
approach is capable to outperform the state-of-the-art results.Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 201
Superior thermal conductivity and extremely high mechanical strength in polyethylene chains from {\it ab initio} calculation
The upper limit of the thermal conductivity and the mechanical strength are
predicted for the polyethylene chain, by performing the {\it ab initio}
calculation and applying the quantum mechanical non-equilibrium Green's
function approach. Specially, there are two main findings from our calculation:
(1). the thermal conductivity can reach a high value of 310 W/K/m in a 100 nm
polyethylene chain at room temperature; (2). the Young's modulus in the
polyethylene chain is as high as 374.5 GPa, and the polyethylene chain can
sustain (ultimate) strain before undergoing structural phase
transition into gaseous ethylene.Comment: published in J. Appl. Phys. (2012
Chandra Observation of a Weak Shock in the Galaxy Cluster A2556
Based on a 21.5 ks \chandra\ observation of A2556, we identify an edge on the
surface brightness profile (SBP) at about 160 kpc northeast of the
cluster center, and it corresponds to a shock front whose Mach number
is calculated to be . No prominent
substructure, such as sub-cluster, is found in either optical or X-ray band
that can be associated with the edge, suggesting that the conventional
super-sonic motion mechanism may not work in this case. As an alternative
solution, we propose that the nonlinear steepening of acoustic wave, which is
induced by the turbulence of the ICM at the core of the cluster, can be used to
explain the origin of the shock front. Although nonlinear steepening weak shock
is expected to occur frequently in clusters, why it is rarely observed still
remains a question that requires further investigation, including both deeper
X-ray observation and extensive theoretical studies.Comment: 15 pages, 4 figures, accepted by Ap
Dimensions of some binary codes arising from a conic in PG(2,q)
AbstractLet O be a conic in the classical projective plane PG(2,q), where q is an odd prime power. With respect to O, the lines of PG(2,q) are classified as passant, tangent, and secant lines, and the points of PG(2,q) are classified as internal, absolute and external points. The incidence matrices between the secant/passant lines and the external/internal points were used in Droms et al. (2006) [6] to produce several classes of structured low-density parity-check binary codes. In particular, the authors of Droms et al. (2006) [6] gave conjectured dimension formula for the binary code L which arises as the F2-null space of the incidence matrix between the secant lines and the external points to O. In this paper, we prove the conjecture on the dimension of L by using a combination of techniques from finite geometry and modular representation theory
A comparative study of two molecular mechanics models based on harmonic potentials
We show that the two molecular mechanics models, the stick-spiral and the
beam models, predict considerably different mechanical properties of materials
based on energy equivalence. The difference between the two models is
independent of the materials since all parameters of the beam model are
obtained from the harmonic potentials. We demonstrate this difference for
finite width graphene nanoribbons and a single polyethylene chain comparing
results of the molecular dynamics (MD) simulations with harmonic potentials and
the finite element method with the beam model. We also find that the difference
strongly depends on the loading modes, chirality and width of the graphene
nanoribbons, and it increases with decreasing width of the nanoribbons under
pure bending condition. The maximum difference of the predicted mechanical
properties using the two models can exceed 300% in different loading modes.
Comparing the two models with the MD results of AIREBO potential, we find that
the stick-spiral model overestimates and the beam model underestimates the
mechanical properties in narrow armchair graphene nanoribbons under pure
bending condition.Comment: 40 pages, 21 figure
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