The Method of Particular Solutions Using Trigonometric Basis Functions

In this paper, the method of particular solutions (MPS) using trigonometric functions as the basis functions is proposed to solve two-dimensional elliptic partial differential equations. The inhomogeneous term of the governing equation is approximated by Fourier series and the closed-form particular solutions of trigonometric functions are derived using the method of undetermined coefficients. Once the particular solutions for the trigonometric basis functions are derived, the standard MPS can be applied for solving partial differential equations. In comparing with the use of radial basis functions and polynomials in the MPS, our proposed approach provides another simple approach to effectively solving two-dimensional elliptic partial differential equations. Five numerical examples are provided in this paper to validate the merits of the proposed meshless method

Non-geometric backgrounds, doubled geometry and generalised T-duality

String backgrounds with a local torus fibration such as T-folds are naturally formulated in a doubled formalism in which the torus fibres are doubled to include dual coordinates conjugate to winding number. Here we formulate and explore a generalisation of this construction in which all coordinates are doubled, so that the doubled space is a twisted torus, i.e. a compact space constructed from identifying a group manifold under a discrete subgroup. This incorporates reductions with duality twists, T-folds and a class of flux compactifications, together with the non-geometric backgrounds expected to arise from these through T-duality. It also incorporates backgrounds that are not even locally geometric, and suggests a generalisation of T-duality to a more general context. We discuss the effective field theory arising from such an internal sector, give a world-sheet sigma model formulation of string theory on such backgrounds and illustrate our discussion with detailed examples.Comment: 81 page

Optimal control theory for unitary transformations

The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory (OCT) is used to solve the inversion problem irrespective of the initial input state. A unified formalism, based on the Krotov method is developed leading to a new scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X^1\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\Sigma^+_u$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Out of the schemes studied the square modulus scheme converges fastest. A study of the implementation of the $Q$ qubit Fourier transform in the Na$_2$ molecule was carried out for up to 5 qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.Comment: 32 pages, 6 figure

Localization by disorder in the infrared conductivity of (Y,Pr)Ba2Cu3O7 films

The ab-plane reflectivity of (Y{1-x}Prx)Ba2Cu3O7 thin films was measured in the 30-30000 cm-1 range for samples with x = 0 (Tc = 90 K), x = 0.4 (Tc = 35 K) and x = 0.5 (Tc = 19 K) as a function of temperature in the normal state. The effective charge density obtained from the integrated spectral weight decreases with increasing x. The variation is consistent with the higher dc resistivity for x = 0.4, but is one order of magnitude smaller than what would be expected for x = 0.5. In the latter sample, the conductivity is dominated at all temperatures by a large localization peak. Its magnitude increases as the temperature decreases. We relate this peak to the dc resistivity enhancement. A simple localization-by-disorder model accounts for the optical conductivity of the x = 0.5 sample.Comment: 7 pages with (4) figures include

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

Quantum computing implementations with neutral particles

We review quantum information processing with cold neutral particles, that is, atoms or polar molecules. First, we analyze the best suited degrees of freedom of these particles for storing quantum information, and then we discuss both single- and two-qubit gate implementations. We focus our discussion mainly on collisional quantum gates, which are best suited for atom-chip-like devices, as well as on gate proposals conceived for optical lattices. Additionally, we analyze schemes both for cold atoms confined in optical cavities and hybrid approaches to entanglement generation, and we show how optimal control theory might be a powerful tool to enhance the speed up of the gate operations as well as to achieve high fidelities required for fault tolerant quantum computation.Comment: 19 pages, 12 figures; From the issue entitled "Special Issue on Neutral Particles

Break-taking behaviour pattern of long-distance freight vehicles based on GPS trajectory data

This paper focuses on the break-taking behaviour pattern of long-distance freight vehicles, providing a new perspective on the study of behaviour patterns and simultaneously providing a reference for transport management departments and related enterprises. Based on Global Positioning System (GPS) trajectory data, we select stopping points as break-taking sites of long-distance freight vehicles and then classify the stopping points into three different classes based on the break-taking duration. We then explore the relationship of the distribution of the break-taking frequency between the three single classifications and their combinations, on the basis of the break-taking duration distribution. We find that the combination is a Gaussian distribution when each of the three individual classes is a Gaussian distribution, contrasting with the power-law distribution of the break-taking duration. Then we experimental analysis the distribution of the break-taking durations and frequencies, and find that, for the durations, the three single classifications can be fitted individually by an Exponential distribution and together by a Power-law distribution, for the frequencies, both the three single classifications and together can be fitted by a Gaussian distribution,so that can validate the above theoretical analysis. Key words: break-taking behaviour, long-distance freight vehicle, statistical analysi

Single Spin Asymmetry ANA_N in Polarized Proton-Proton Elastic Scattering at s=200\sqrt{s}=200 GeV

We report a high precision measurement of the transverse single spin asymmetry $A_N$ at the center of mass energy $\sqrt{s}=200$ GeV in elastic proton-proton scattering by the STAR experiment at RHIC. The $A_N$ was measured in the four-momentum transfer squared $t$ range $0.003 \leqslant |t| \leqslant 0.035$ \GeVcSq, the region of a significant interference between the electromagnetic and hadronic scattering amplitudes. The measured values of $A_N$ and its $t$-dependence are consistent with a vanishing hadronic spin-flip amplitude, thus providing strong constraints on the ratio of the single spin-flip to the non-flip amplitudes. Since the hadronic amplitude is dominated by the Pomeron amplitude at this $\sqrt{s}$, we conclude that this measurement addresses the question about the presence of a hadronic spin flip due to the Pomeron exchange in polarized proton-proton elastic scattering.Comment: 12 pages, 6 figure

Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012