4,888 research outputs found
Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions
In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics
(SEASD), a novel computational method for dynamic simulations of polydisperse
colloidal suspensions with full hydrodynamic interactions. SEASD is based on
the framework of Stokesian Dynamics (SD) with extension to compressible
solvents, and uses the Spectral Ewald (SE) method [Lindbo & Tornberg, J.
Comput. Phys. 229 (2010) 8994] for the wave-space mobility computation. To meet
the performance requirement of dynamic simulations, we use Graphic Processing
Units (GPU) to evaluate the suspension mobility, and achieve an order of
magnitude speedup compared to a CPU implementation. For further speedup, we
develop a novel far-field block-diagonal preconditioner to reduce the far-field
evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of
the mean-field Brownian approximation of Banchio & Brady [J. Chem. Phys. 118
(2003) 10323]. We extensively discuss implementation and parameter selection
strategies in SEASD, and demonstrate the spectral accuracy in the mobility
evaluation and the overall computation scaling. We
present three computational examples to further validate SEASD and SEASD-nf in
monodisperse and bidisperse suspensions: the short-time transport properties,
the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear
Brownian rheology. Our validation results show that the agreement between SEASD
and SEASD-nf is satisfactory over a wide range of parameters, and also provide
significant insight into the dynamics of polydisperse colloidal suspensions.Comment: 39 pages, 21 figure
Dynamics of aerospace vehicles
The focus of this research was to address the modeling, including model reduction, of flexible aerospace vehicles, with special emphasis on models used in dynamic analysis and/or guidance and control system design. In the modeling, it is critical that the key aspects of the system being modeled be captured in the model. In this work, therefore, aspects of the vehicle dynamics critical to control design were important. In this regard, fundamental contributions were made in the areas of stability robustness analysis techniques, model reduction techniques, and literal approximations for key dynamic characteristics of flexible vehicles. All these areas are related. In the development of a model, approximations are always involved, so control systems designed using these models must be robust against uncertainties in these models
Modeling the Void H I Column Density Spectrum
The equivalent width distribution function (EWDF) of \hone absorbers specific
to the void environment has been recently derived (Manning 2002), revealing a
large line density of clouds (dN/dz ~500 per unit z for Log (N_HI)> 12.4). I
show that the void absorbers cannot be diffuse (or so-called filamentary)
clouds, expanding with the Hubble flow, as suggested by N-body/hydro
simulations. Absorbers are here modeled as the baryonic remnants of
sub-galactic perturbations that have expanded away from their dark halos in
response to reionization at z ~ 6.5. A 1-D Lagrangian hydro/gravity code is
used to follow the dynamic evolution and ionization structure of the baryonic
clouds for a range of halo circular velocities. The simulation products at z=0
can be combined according to various models of the halo velocity distribution
function to form a column density spectrum that can be compared with the
observed. I find that such clouds may explain the observed EWDF if the halo
velocity distribution function is as steep as that advanced by Klypin (1999),
and the halo mass distribution is closer to isothermal than to NFW.Comment: 21 pages, 15 figures. Paper in press; ApJ 591, n
Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems
Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems
for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case) and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds
Model Reduction Using Semidefinite Programming
In this thesis model reduction methods for linear time invariant systems are investigated. The reduced models are computed using semidefinite programming. Two ways of imposing the stability constraint are considered. However, both approaches add a positivity constraint to the program. The input to the algorithms is a number of frequency response samples of the original model. This makes the computational complexity relatively low for large-scale models. Extra properties on a reduced model can also be enforced, as long as the properties can be expressed as convex conditions. Semidefinite program are solved using the interior point methods which are well developed, making the implementation simpler. A number of extensions to the proposed methods were studied, for example, passive model reduction, frequency-weighted model reduction. An interesting extension is reduction of parameterized linear time invariant models, i.e. models with state-space matrices dependent on parameters. It is assumed, that parameters do not depend on state variables nor time. This extension is valuable in modeling, when a set of parameters has to be chosen to fit the required specifications. A good illustration of such a problem is modeling of a spiral radio frequency inductor. The physical model depends nonlinearly on two parameters: wire width and wire separation. To chose optimally both parameters a low-order model is usually created. The inductor modeling is considered as a case study in this thesis
Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges
This paper discusses model order reduction of LTI systems over limited
frequency intervals within the framework of balanced truncation. Two new
\emph{frequency-dependent balanced truncation} methods were developed, one is
\emph{SF-type frequency-dependent balanced truncation} to copy with the cases
that only a single dominating point of the operating frequency interval is
pre-known, the other is \emph{interval-type frequency-dependent balanced
truncation} to deal with the cases that both of the upper and lower bound of
frequency interval are known \emph{a priori}. SF-type error bound and
interval-type error bound are derived for the first time to estimate the
desired approximation error over pre-specified frequency interval. We show that
the new methods generally lead to good in-band approximation performance, at
the same time, provide accurate error bounds under certain conditions. Examples
are included for illustration.Comment: prepared to submit for International Journal of Contro
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