57,031 research outputs found
A version of the Glimm method based on generalized Riemann problems
We introduce a generalization of Glimm's random choice method, which provides
us with an approximation of entropy solutions to quasilinear hyperbolic system
of balance laws. The flux-function and the source term of the equations may
depend on the unknown as well as on the time and space variables. The method is
based on local approximate solutions of the generalized Riemann problem, which
form building blocks in our scheme and allow us to take into account naturally
the effects of the flux and source terms. To establish the nonlinear stability
of these approximations, we investigate nonlinear interactions between
generalized wave patterns. This analysis leads us to a global existence result
for quasilinear hyperbolic systems with source-term, and applies, for instance,
to the compressible Euler equations in general geometries and to hyperbolic
systems posed on a Lorentzian manifold.Comment: 34 page
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
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
Selecting Finite Unified Theories with Current Data
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories
that can be made all-loop finite, leading to a severe reduction of the free
parameters. We review the investigation of FUTs based on SU(5) in the context
of low-energy phenomenology observables. Using the restrictions from the top
and bottom quark masses, it is possible to discriminate between different
models. Including further low-energy constraints such as B-physics observables,
the bound on the lightest Higgs boson mass and the cold dark matter density, we
derive the predictions for the supersymmetric particle spectrum and the
prospects for discoveries at the LHC.Comment: 3 pages, 3 figures, talk given at SUSY08, Seoul, Kore
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
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
Micro Balloon Actuators for Aerodynamic Control
A robust, large-force, large-deflection micro balloon actuator for aerodynamic (manoeuvring) control of transonic aircraft has been developed. Using a novel process, high yield linear arrays of silicone balloons on a robust silicon substrate have been fabricated that can deflect vertically in excess of one mm. Balloon actuators have been tested under cyclic conditions to assess reliability. The actuators have been characterized in a wind tunnel to assess their suitability as aerodynamic control surfaces and flight-tested on a jet fighter to assess their resistance to varied temperatures and pressures at high velocity
Interlayer Exchange Coupling Beyond the Proximity Force Approximation
Ion bombardment has been shown to be capable of enhancing the interlayer
exchange coupling in a trilayer system that exhibits giant magnetoresistance.
We demonstrate that this phenomenon can be derived from the phase coherence
among scattered paths within the two rough interfaces when their topographies
are correlated. In the case of mild corrugations, our method reproduces the
predictions by the proximity force approximation which does not consider the
interference. When the characteristic Fourier conjugate of the tomography
becomes large and comparable to the Fermi momentum, interesting new features
arise and can only be captured by our more general approach. Among our
findings, the scenario of an enhanced interlayer exchange coupling due to the
interface roughness is explained, along with how it depends on the sample
parameters. An additional channel for the resonant transmission is identified
due to extra scattering paths from the roughness.Comment: 9 pages, 7 figures, submitted to PRB (2010
Semiclassical Strings in Electric and Magnetic Fields Deformed Spacetimes
We first apply the transformation of mixing azimuthal and internal coordinate
or mixing time and internal coordinate to the 11D M-theory with a stack N
M2-branes to find the spacetime of a stack of N D2-branes with magnetic or
electric flux in 10 D IIA string theory, after the Kaluza-Klein reduction. We
then perform the T duality to the spacetime to find the background of a stack
of N D3-branes with magnetic or electric flux. In the near-horizon limit the
background becomes the magnetic or electric field deformed .
We adopt an ansatz to find the classical string solution which is rotating in
the deformed with three angular momenta in the three rotation planes. The
relations between the classical string energy and its angular momenta are found
and results show that the external magnetic and electric fluxes will increase
the string energy. Therefore, from the AdS/CFT point of view, the corrections
of the anomalous dimensions of operators in the dual SYM theory will be
positive. We also investigate the small fluctuations in these solutions and
discuss the effects of magnetic and electric fields on the stability of these
classical rotating string solutions. Finally, we find the possible solutions of
string pulsating on the deformed spacetimes and show that the corrections to
the anomalous dimensions of operators in the dual SYM theory are non-negative.Comment: Latex 18 pages, correct sec. 3.
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