534 research outputs found
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
Standing Posture Modeling and Control for a Humanoid Robot
Master'sMASTER OF ENGINEERIN
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
electronic state of Na. Raman-like transitions through the
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 qubit Fourier transform in the Na
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
Robust car-following control of connected and autonomous vehicles: a Stochastic Model Predictive Control approach
Vehicle platooning has attracted growing attention for its potential to enhance traffic capacity and road safety. This paper proposes an innovative distributed Stochastic Model Predictive Control (SMPC) for a vehicle platoon system to enhance the robustness and safety of the vehicles in uncertain traffic environments. In particular, considering the similarity between the acceleration or deceleration behaviour of neighbouring vehicles and the spring-scale properties, we use a two-mass spring system for the first time to construct an uncertain dynamic model of a formation system. In the presence of uncertain perturbations with known distributional attributes (expectation, variance), we propose an objective function in the form of expectation along with probabilistic chance constraints. Subsequently, a state feedback control mechanism is devised accordingly. Under the cumulative probability distribution function of stochastic perturbations, we theoretically derive a computationally tractable equivalent of the SMPC model. Finally, simulation experiments are designed to validate the control performance of the SMPC platoon controllers, along with an analysis of the stability performance under varying probabilities. The experimental findings demonstrate that the model can be efficiently solved in real-time with appropriately chosen prediction horizon lengths, ensuring robust and safe longitudinal vehicle formation control
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 -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 in Polarized Proton-Proton Elastic Scattering at GeV
We report a high precision measurement of the transverse single spin
asymmetry at the center of mass energy GeV in elastic
proton-proton scattering by the STAR experiment at RHIC. The was measured
in the four-momentum transfer squared range \GeVcSq, the region of a significant interference between the
electromagnetic and hadronic scattering amplitudes. The measured values of
and its -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 , 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
- …