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 $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

A comparative study of benchmarking approaches for non-domestic buildings: Part 1 – Top-down approach

Benchmarking plays an important role in improving energy efficiency of non-domestic buildings. A review of energy benchmarks that underpin the UK’s 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 $D_{M}=1.33$. We also found that the stiffness exponent $\alpha =-0.25$ is universal, but varies with the plasticity parameters $s$ and $\theta_{p}$. 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 AdS5×S5AdS_5 \times S^5 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 $AdS_5 \times S^5$. We adopt an ansatz to find the classical string solution which is rotating in the deformed $S^5$ 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.