75,572 research outputs found
Combination of Conventional and Optimisation Techniques for Performance Prediction in Large Waterflood Projects
Imperial Users onl
Stabilising Model Predictive Control for Discrete-time Fractional-order Systems
In this paper we propose a model predictive control scheme for constrained
fractional-order discrete-time systems. We prove that all constraints are
satisfied at all time instants and we prescribe conditions for the origin to be
an asymptotically stable equilibrium point of the controlled system. We employ
a finite-dimensional approximation of the original infinite-dimensional
dynamics for which the approximation error can become arbitrarily small. We use
the approximate dynamics to design a tube-based model predictive controller
which steers the system state to a neighbourhood of the origin of controlled
size. We finally derive stability conditions for the MPC-controlled system
which are computationally tractable and account for the infinite dimensional
nature of the fractional-order system and the state and input constraints. The
proposed control methodology guarantees asymptotic stability of the
discrete-time fractional order system, satisfaction of the prescribed
constraints and recursive feasibility
Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects
An acoustic oscillation of the primeval photon-baryon fluid around the
decoupling time imprints a characteristic scale in the galaxy distribution
today, known as the baryon acoustic oscillation (BAO) scale. Several on-going
and/or future galaxy surveys aim at detecting and precisely determining the BAO
scale so as to trace the expansion history of the universe. We consider
nonlinear and redshift-space distortion effects on the shifts of the BAO scale
in -space using perturbation theory. The resulting shifts are indeed
sensitive to different choices of the definition of the BAO scale, which needs
to be kept in mind in the data analysis. We present a toy model to explain the
physical behavior of the shifts. We find that the BAO scale defined as in
Percival et al. (2007) indeed shows very small shifts ( 1%) relative
to the prediction in {\it linear theory} in real space. The shifts can be
predicted accurately for scales where the perturbation theory is reliable.Comment: 21 pages, 9 figures, references and supplementary sections added,
accepted for publication in PAS
Non-linear Evolution of Baryon Acoustic Oscillations from Improved Perturbation Theory in Real and Redshift Spaces
We study the non-linear evolution of baryon acoustic oscillations in the
matter power spectrum and correlation function from the improved perturbation
theory (PT). Based on the framework of renormalized PT, we apply the {\it
closure approximation} that truncates the infinite series of loop contributions
at one-loop order, and obtain a closed set of integral equations for power
spectrum and non-linear propagator. The resultant integral expressions keep
important non-perturbative properties which can dramatically improve the
prediction of non-linear power spectrum. Employing the Born approximation, we
then derive the analytic expressions for non-linear power spectrum and the
predictions are made for non-linear evolution of baryon acoustic oscillations
in power spectrum and correlation function. A detailed comparison between
improved PT results and N-body simulations shows that a percent-level agreement
is achieved in a certain range in power spectrum and in a rather wider range in
correlation function. Combining a model of non-linear redshift-space
distortion, we also evaluate the power spectrum and correlation function in
correlation function. In contrast to the results in real space, the agreement
between N-body simulations and improved PT predictions tends to be worse, and a
more elaborate modeling for redshift-space distortion needs to be developed.
Nevertheless, with currently existing model, we find that the prediction of
correlation function has a sufficient accuracy compared with the
cosmic-variance errors for future galaxy surveys with volume of a few (Gpc/h)^3
at z>=0.5.Comment: 25 pages, 15 figures, accepted for publication in Phys.Rev.
Multigrid waveform relaxation for the time-fractional heat equation
In this work, we propose an efficient and robust multigrid method for solving
the time-fractional heat equation. Due to the nonlocal property of fractional
differential operators, numerical methods usually generate systems of equations
for which the coefficient matrix is dense. Therefore, the design of efficient
solvers for the numerical simulation of these problems is a difficult task. We
develop a parallel-in-time multigrid algorithm based on the waveform relaxation
approach, whose application to time-fractional problems seems very natural due
to the fact that the fractional derivative at each spatial point depends on the
values of the function at this point at all earlier times. Exploiting the
Toeplitz-like structure of the coefficient matrix, the proposed multigrid
waveform relaxation method has a computational cost of
operations, where is the number of time steps and is the number of
spatial grid points. A semi-algebraic mode analysis is also developed to
theoretically confirm the good results obtained. Several numerical experiments,
including examples with non-smooth solutions and a nonlinear problem with
applications in porous media, are presented
Reaction Front in an A+B -> C Reaction-Subdiffusion Process
We study the reaction front for the process A+B -> C in which the reagents
move subdiffusively. Our theoretical description is based on a fractional
reaction-subdiffusion equation in which both the motion and the reaction terms
are affected by the subdiffusive character of the process. We design numerical
simulations to check our theoretical results, describing the simulations in
some detail because the rules necessarily differ in important respects from
those used in diffusive processes. Comparisons between theory and simulations
are on the whole favorable, with the most difficult quantities to capture being
those that involve very small numbers of particles. In particular, we analyze
the total number of product particles, the width of the depletion zone, the
production profile of product and its width, as well as the reactant
concentrations at the center of the reaction zone, all as a function of time.
We also analyze the shape of the product profile as a function of time, in
particular its unusual behavior at the center of the reaction zone
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