2,368 research outputs found
High order variational integrators in the optimal control of mechanical systems
In recent years, much effort in designing numerical methods for the
simulation and optimization of mechanical systems has been put into schemes
which are structure preserving. One particular class are variational
integrators which are momentum preserving and symplectic. In this article, we
develop two high order variational integrators which distinguish themselves in
the dimension of the underling space of approximation and we investigate their
application to finite-dimensional optimal control problems posed with
mechanical systems. The convergence of state and control variables of the
approximated problem is shown. Furthermore, by analyzing the adjoint systems of
the optimal control problem and its discretized counterpart, we prove that, for
these particular integrators, dualization and discretization commute.Comment: 25 pages, 9 figures, 1 table, submitted to DCDS-
Improving optimal control of grid-connected lithium-ion batteries through more accurate battery and degradation modelling
The increased deployment of intermittent renewable energy generators opens up
opportunities for grid-connected energy storage. Batteries offer significant
flexibility but are relatively expensive at present. Battery lifetime is a key
factor in the business case, and it depends on usage, but most techno-economic
analyses do not account for this. For the first time, this paper quantifies the
annual benefits of grid-connected batteries including realistic physical
dynamics and nonlinear electrochemical degradation. Three lithium-ion battery
models of increasing realism are formulated, and the predicted degradation of
each is compared with a large-scale experimental degradation data set
(Mat4Bat). A respective improvement in RMS capacity prediction error from 11\%
to 5\% is found by increasing the model accuracy. The three models are then
used within an optimal control algorithm to perform price arbitrage over one
year, including degradation. Results show that the revenue can be increased
substantially while degradation can be reduced by using more realistic models.
The estimated best case profit using a sophisticated model is a 175%
improvement compared with the simplest model. This illustrates that using a
simplistic battery model in a techno-economic assessment of grid-connected
batteries might substantially underestimate the business case and lead to
erroneous conclusions
The effect of a nucleating agent on lamellar growth in melt-crystallizing polyethylene oxide
The effects of a (non co-crystallizing) nucleating agent on secondary
nucleation rate and final lamellar thickness in isothermally melt-crystallizing
polyethylene oxide are considered. SAXS reveals that lamellae formed in
nucleated samples are thinner than in the pure samples crystallized at the same
undercoolings. These results are in quantitative agreement with growth rate
data obtained by calorimetry, and are interpreted as the effect of a local
decrease of the basal surface tension, determined mainly by the nucleant
molecules diffused out of the regions being about to crystallize. Quantitative
agreement with a simple lattice model allows for some interpretation of the
mechanism.Comment: submitted to Journal of Applied Physics (first version on 22 Apr
2002
Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids
In the past twenty years, shear-banding flows have been probed by various
techniques, such as rheometry, velocimetry and flow birefringence. In micellar
solutions, many of the data collected exhibit unexplained spatio-temporal
fluctuations. Recently, it has been suggested that those fluctuations originate
from a purely elastic instability of the flow. In cylindrical Couette geometry,
the instability is reminiscent of the Taylor-like instability observed in
viscoelastic polymer solutions. In this letter, we describe how the criterion
for purely elastic Taylor-Couette instability should be adapted to
shear-banding flows. We derive three categories of shear-banding flows with
curved streamlines, depending on their stability.Comment: 6 pages, 3 figure
Potential "ways of thinking" about the shear-banding phenomenon
Shear-banding is a curious but ubiquitous phenomenon occurring in soft
matter. The phenomenological similarities between the shear-banding transition
and phase transitions has pushed some researchers to adopt a 'thermodynamical'
approach, in opposition to the more classical 'mechanical' approach to fluid
flows. In this heuristic review, we describe why the apparent dichotomy between
those approaches has slowly faded away over the years. To support our
discussion, we give an overview of different interpretations of a single
equation, the diffusive Johnson-Segalman (dJS) equation, in the context of
shear-banding. We restrict ourselves to dJS, but we show that the equation can
be written in various equivalent forms usually associated with opposite
approaches. We first review briefly the origin of the dJS model and its initial
rheological interpretation in the context of shear-banding. Then we describe
the analogy between dJS and reaction-diffusion equations. In the case of
anisotropic diffusion, we show how the dJS governing equations for steady shear
flow are analogous to the equations of the dynamics of a particle in a quartic
potential. Going beyond the existing literature, we then draw on the Lagrangian
formalism to describe how the boundary conditions can have a key impact on the
banding state. Finally, we reinterpret the dJS equation again and we show that
a rigorous effective free energy can be constructed, in the spirit of early
thermodynamic interpretations or in terms of more recent approaches exploiting
the language of irreversible thermodynamics.Comment: 14 pages, 6 figures, tutorial revie
Minkowski Functionals of Abell/ACO Clusters
We determine the Minkowski functionals for a sample of Abell/ACO clusters,
401 with measured and 16 with estimated redshifts. The four Minkowski
functionals (including the void probability function and the mean genus)
deliver a global description of the spatial distribution of clusters on scales
from to 60\hMpc with a clear geometric interpretation. Comparisons with
mock catalogues of N--body simulations using different variants of the CDM
model demonstrate the discriminative power of the description. The standard CDM
model and the model with tilted perturbation spectrum cannot generate the
Minkowski functionals of the cluster data, while a model with a cosmological
constant and a model with breaking of the scale invariance of perturbations
(BSI) yield compatible results.Comment: 10 pages, 13 Postscript figures, uses epsf.sty and mn.sty (included),
submitted to MNRA
Higher Order Variational Integrators: a polynomial approach
We reconsider the variational derivation of symplectic partitioned
Runge-Kutta schemes. Such type of variational integrators are of great
importance since they integrate mechanical systems with high order accuracy
while preserving the structural properties of these systems, like the
symplectic form, the evolution of the momentum maps or the energy behaviour.
Also they are easily applicable to optimal control problems based on mechanical
systems as proposed in Ober-Bl\"obaum et al. [2011].
Following the same approach, we develop a family of variational integrators
to which we refer as symplectic Galerkin schemes in contrast to symplectic
partitioned Runge-Kutta. These two families of integrators are, in principle
and by construction, different one from the other. Furthermore, the symplectic
Galerkin family can as easily be applied in optimal control problems, for which
Campos et al. [2012b] is a particular case.Comment: 12 pages, 1 table, 23rd Congress on Differential Equations and
Applications, CEDYA 201
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