46,356 research outputs found
Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms
Let and be two integers with , and let and be
integers with and . In this paper, we prove that , where is a constant depending on and .Comment: 8 pages. To appear in Archiv der Mathemati
A comparative study of benchmarking approaches for non-domestic buildings: Part 1 ā Top-down approach
Benchmarking plays an important role in improving energy efficiency of non-domestic buildings. A review of energy benchmarks that underpin the UKās Display Energy Certificate (DEC) scheme have prompted necessities to explore the benefits and limitations of using various methods to derive energy benchmarks. The existing methods were reviewed and grouped into top-down and bottom-up approaches based on the granularity of the data used. In the study, two top-down methods, descriptive statistics and artificial neural networks (ANN), were explored for the purpose of benchmarking energy performances of schools. The results were used to understand the benefits of using these benchmarks for assessing energy efficiency of buildings and the limitations that affect the robustness of the derived benchmarks. Compared to the bottom-up approach, top-down approaches were found to be beneficial in gaining insight into how peers perform. The relative rather than absolute feedback on energy efficiency meant that peer pressure was a motivator for improvement. On the other hand, there were limitations with regard to the extent to which the energy efficiency of a building could be accurately assessed using the top-down benchmarks. Moreover, difficulties in acquiring adequate data were identified as a key limitation to using the top-down approach for benchmarking non-domestic buildings. The study suggested that there are benefits in rolling out of DECs to private sector buildings and that there is a need to explore more complex methods to provide more accurate indication of energy efficiency in non-domestic buildings
Measurement of micro synthetic jet actuation using intensity of disturbance
Synthetic jet actuator (SJA), as a zero-net-mass but non-zero momentum device, has shown great potential in controlling laminar separation caused by adverse pressure gradient in a boundary layer flow. The effectiveness of a SJA has been evaluated in different ways. However, the strategy of using SJAs in controlling boundary layer flow separation is to disturb the boundary layer flow and consequently to accelerate the transition from laminar to turbulence which has greater momentum than laminar flow to resist flow separation. Therefore, the level of disturbance originated by a SJA may be used to evaluate the ability of the SJA to control laminar separation. Intensity of disturbance, originally defined for measuring the ādegree of disturbanceā in the external flow in boundary layer theories, has been first time used to quantitatively evaluate the level of disturbance triggered by a SJA. This paper reports the intensity of disturbance triggered by three micro synthetic jet actuators which were installed at three streamwise locations and driven at two forcing frequencies. Quantitatively measured by the intensity of disturbance, the results will show the dependency of the SJAās actuation on the streamwise position, on the forcing frequency and on the forcing amplitude
Straight-line Drawability of a Planar Graph Plus an Edge
We investigate straight-line drawings of topological graphs that consist of a
planar graph plus one edge, also called almost-planar graphs. We present a
characterization of such graphs that admit a straight-line drawing. The
characterization enables a linear-time testing algorithm to determine whether
an almost-planar graph admits a straight-line drawing, and a linear-time
drawing algorithm that constructs such a drawing, if it exists. We also show
that some almost-planar graphs require exponential area for a straight-line
drawing
Crumpling wires in two dimensions
An energy-minimal simulation is proposed to study the patterns and mechanical
properties of elastically crumpled wires in two dimensions. We varied the
bending rigidity and stretching modulus to measure the energy allocation,
size-mass exponent, and the stiffness exponent. The mass exponent is shown to
be universal at value . We also found that the stiffness exponent
is universal, but varies with the plasticity parameters and
. These numerical findings agree excellently with the experimental
results
Quantum Speed Limit for Perfect State Transfer in One Dimension
The basic idea of spin chain engineering for perfect quantum state transfer
(QST) is to find a set of coupling constants in the Hamiltonian, such that a
particular state initially encoded on one site will evolve freely to the
opposite site without any dynamical controls. The minimal possible evolution
time represents a speed limit for QST. We prove that the optimal solution is
the one simulating the precession of a spin in a static magnetic field. We also
argue that, at least for solid-state systems where interactions are local, it
is more realistic to characterize the computation power by the couplings than
the initial energy.Comment: 5 pages, no figure; improved versio
Single Top Quark Production and Decay at Next-to-leading Order in Hadron Collision
We present a calculation of the next-to-leading order QCD corrections, with
one-scale phase space slicing method, to single top quark production and decay
process at hadron colliders.
Using the helicity amplitude method, the angular correlation of the final state
partons and the spin correlation of the top quark are preserved. The effect of
the top quark width is also examined.Comment: 47 pages, 9 figure
Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time
Thomassen characterized some 1-plane embedding as the forbidden configuration
such that a given 1-plane embedding of a graph is drawable in straight-lines if
and only if it does not contain the configuration [C. Thomassen, Rectilinear
drawings of graphs, J. Graph Theory, 10(3), 335-341, 1988].
In this paper, we characterize some 1-plane embedding as the forbidden
configuration such that a given 1-plane embedding of a graph can be re-embedded
into a straight-line drawable 1-plane embedding of the same graph if and only
if it does not contain the configuration. Re-embedding of a 1-plane embedding
preserves the same set of pairs of crossing edges.
We give a linear-time algorithm for finding a straight-line drawable 1-plane
re-embedding or the forbidden configuration.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016). This is an extended
abstract. For a full version of this paper, see Hong S-H, Nagamochi H.:
Re-embedding a 1-Plane Graph into a Straight-line Drawing in Linear Time,
Technical Report TR 2016-002, Department of Applied Mathematics and Physics,
Kyoto University (2016
Low thrust orbit determination program
Logical flow and guidelines are provided for the construction of a low thrust orbit determination computer program. The program, tentatively called FRACAS (filter response analysis for continuously accelerating spacecraft), is capable of generating a reference low thrust trajectory, performing a linear covariance analysis of guidance and navigation processes, and analyzing trajectory nonlinearities in Monte Carlo fashion. The choice of trajectory, guidance and navigation models has been made after extensive literature surveys and investigation of previous software. A key part of program design relied upon experience gained in developing and using Martin Marietta Aerospace programs: TOPSEP (Targeting/Optimization for Solar Electric Propulsion), GODSEP (Guidance and Orbit Determination for SEP) and SIMSEP (Simulation of SEP)
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