67,703 research outputs found
Model reduction of controlled Fokker--Planck and Liouville-von Neumann equations
Model reduction methods for bilinear control systems are compared by means of
practical examples of Liouville-von Neumann and Fokker--Planck type. Methods
based on balancing generalized system Gramians and on minimizing an H2-type
cost functional are considered. The focus is on the numerical implementation
and a thorough comparison of the methods. Structure and stability preservation
are investigated, and the competitiveness of the approaches is shown for
practically relevant, large-scale examples
Moment free energies for polydisperse systems
A polydisperse system contains particles with at least one attribute
(such as particle size in colloids or chain length in polymers) which takes
values in a continuous range. It therefore has an infinite number of conserved
densities, described by a density {\em distribution} . The free
energy depends on all details of , making the analysis of phase
equilibria in such systems intractable. However, in many (especially
mean-field) models the {\em excess} free energy only depends on a finite number
of (generalized) moments of ; we call these models truncatable.
We show, for these models, how to derive approximate expressions for the {\em
total} free energy which only depend on such moment densities. Our treatment
unifies and explores in detail two recent separate proposals by the authors for
the construction of such moment free energies. We show that even though the
moment free energy only depends on a finite number of density variables, it
gives the same spinodals and critical points as the original free energy and
also correctly locates the onset of phase coexistence. Results from the moment
free energy for the coexistence of two or more phases occupying comparable
volumes are only approximate, but can be refined arbitrarily by retaining
additional moment densities. Applications to Flory-Huggins theory for
length-polydisperse homopolymers, and for chemically polydisperse copolymers,
show that the moment free energy approach is computationally robust and gives
new geometrical insights into the thermodynamics of polydispersity.Comment: RevTeX, 43 pages including figure
Broad boron sheets and boron nanotubes: An ab initio study of structural, electronic, and mechanical properties
Based on a numerical ab initio study, we discuss a structure model for a
broad boron sheet, which is the analog of a single graphite sheet, and the
precursor of boron nanotubes. The sheet has linear chains of sp hybridized
sigma bonds lying only along its armchair direction, a high stiffness, and
anisotropic bonds properties. The puckering of the sheet is explained as a
mechanism to stabilize the sp sigma bonds. The anisotropic bond properties of
the boron sheet lead to a two-dimensional reference lattice structure, which is
rectangular rather than triangular. As a consequence the chiral angles of
related boron nanotubes range from 0 to 90 degrees. Given the electronic
properties of the boron sheets, we demonstrate that all of the related boron
nanotubes are metallic, irrespective of their radius and chiral angle, and we
also postulate the existence of helical currents in ideal chiral nanotubes.
Furthermore, we show that the strain energy of boron nanotubes will depend on
their radii, as well as on their chiral angles. This is a rather unique
property among nanotubular systems, and it could be the basis of a different
type of structure control within nanotechnology.Comment: 16 pages, 17 figures, 2 tables, Versions: v1=preview, v2=first final,
v3=minor corrections, v4=document slightly reworke
emgr - The Empirical Gramian Framework
System Gramian matrices are a well-known encoding for properties of
input-output systems such as controllability, observability or minimality.
These so-called system Gramians were developed in linear system theory for
applications such as model order reduction of control systems. Empirical
Gramian are an extension to the system Gramians for parametric and nonlinear
systems as well as a data-driven method of computation. The empirical Gramian
framework - emgr - implements the empirical Gramians in a uniform and
configurable manner, with applications such as Gramian-based (nonlinear) model
reduction, decentralized control, sensitivity analysis, parameter
identification and combined state and parameter reduction
A Modular Regularized Variational Multiscale Proper Orthogonal Decomposition for Incompressible Flows
In this paper, we propose, analyze and test a post-processing implementation
of a projection-based variational multiscale (VMS) method with proper
orthogonal decomposition (POD) for the incompressible Navier-Stokes equations.
The projection-based VMS stabilization is added as a separate post-processing
step to the standard POD approximation, and since the stabilization step is
completely decoupled, the method can easily be incorporated into existing
codes, and stabilization parameters can be tuned independent from the time
evolution step. We present a theoretical analysis of the method, and give
results for several numerical tests on benchmark problems which both illustrate
the theory and show the proposed method's effectiveness
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