1,769 research outputs found
Bogoliubov modes of a dipolar condensate in a cylindrical trap
The calculation of properties of Bose-Einstein condensates with dipolar
interactions has proven a computationally intensive problem due to the long
range nature of the interactions, limiting the scope of applications. In
particular, the lowest lying Bogoliubov excitations in three dimensional
harmonic trap with cylindrical symmetry were so far computed in an indirect
way, by Fourier analysis of time dependent perturbations, or by approximate
variational methods. We have developed a very fast and accurate numerical
algorithm based on the Hankel transform for calculating properties of dipolar
Bose-Einstein condensates in cylindrically symmetric traps. As an application,
we are able to compute many excitation modes by directly solving the
Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in
different trap geometries. We use these results to calculate the quantum
depletion of the condensate by a combination of a computation of the exact
modes and the use of a local density approximation
Computation of a combined spherical-elastic and viscous-half-space earth model for ice sheet simulation
This report starts by describing the continuum model used by Lingle & Clark
(1985) to approximate the deformation of the earth under changing ice sheet and
ocean loads. That source considers a single ice stream, but we apply their
underlying model to continent-scale ice sheet simulation. Their model combines
Farrell's (1972) elastic spherical earth with a viscous half-space overlain by
an elastic plate lithosphere. The latter half-space model is derivable from
calculations by Cathles (1975). For the elastic spherical earth we use
Farrell's tabulated Green's function, as do Lingle & Clark. For the half-space
model, however, we propose and implement a significantly faster numerical
strategy, a spectral collocation method (Trefethen 2000) based directly on the
Fast Fourier Transform. To verify this method we compare to an integral formula
for a disc load. To compare earth models we build an accumulation history from
a growing similarity solution from (Bueler, et al.~2005) and and simulate the
coupled (ice flow)-(earth deformation) system. In the case of simple isostasy
the exact solution to this system is known. We demonstrate that the magnitudes
of numerical errors made in approximating the ice-earth system are
significantly smaller than pairwise differences between several earth models,
namely, simple isostasy, the current standard model used in ice sheet
simulation (Greve 2001, Hagdorn 2003, Zweck & Huybrechts 2005), and the Lingle
& Clark model. Therefore further efforts to validate different earth models
used in ice sheet simulations are, not surprisingly, worthwhile.Comment: 36 pages, 16 figures, 3 Matlab program
Intergration of system identification and robust controller designs for flexible structures in space
An approach is developed using experimental data to identify a reduced-order model and its model error for a robust controller design. There are three steps involved in the approach. First, an approximately balanced model is identified using the Eigensystem Realization Algorithm, which is an identification algorithm. Second, the model error is calculated and described in frequency domain in terms of the H(infinity) norm. Third, a pole placement technique in combination with a H(infinity) control method is applied to design a controller for the considered system. A set experimental data from an existing setup, namely the Mini-Mast system, is used to illustrate and verify the approach
Optimization Techniques for the Power Beaming Analysis of Microwave Transmissions from a Space-Based Solar Power Satellite
In the 21st century, the development of technologies to produce carbon free power sources remains paramount. In this paper, we study an optimal power transmission strategy from a space-based satellite generation station to Earth using scalar diffraction theory. The resulting model is then solved via a spectral method that guarantees a compactly supposed profile from the transmitting antenna. Finally, the problem is then solved via a more general pseudo-spectral method using control theory
Variable-step finite difference schemes for the solution of Sturm-Liouville problems
We discuss the solution of regular and singular Sturm-Liouville problems by
means of High Order Finite Difference Schemes. We describe a code to define a
discrete problem and its numerical solution by means of linear algebra
techniques. Different test problems are proposed to emphasize the behaviour of
the proposed algorithm
Calculation of the T-matrix: general considerations and application of the point-matching method
The T-matrix method is widely used for the calculation of scattering by
particles of sizes on the order of the illuminating wavelength. Although the
extended boundary condition method (EBCM) is the most commonly used technique
for calculating the T-matrix, a variety of methods can be used.
We consider some general principles of calculating T-matrices, and apply the
point-matching method to calculate the T-matrix for particles devoid of
symmetry. This method avoids the time-consuming surface integrals required by
the EBCM.Comment: 10 pages. 2 figures, 1 tabl
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