5,702 research outputs found
On the Convergence of the Born Series in Optical Tomography with Diffuse Light
We provide a simple sufficient condition for convergence of Born series in
the forward problem of optical diffusion tomography. The condition does not
depend on the shape or spatial extent of the inhomogeneity but only on its
amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem
An Efficient Algorithm for Classical Density Functional Theory in Three Dimensions: Ionic Solutions
Classical density functional theory (DFT) of fluids is a valuable tool to
analyze inhomogeneous fluids. However, few numerical solution algorithms for
three-dimensional systems exist. Here we present an efficient numerical scheme
for fluids of charged, hard spheres that uses operations
and memory, where is the number of grid points. This
system-size scaling is significant because of the very large required for
three-dimensional systems. The algorithm uses fast Fourier transforms (FFT) to
evaluate the convolutions of the DFT Euler-Lagrange equations and Picard
(iterative substitution) iteration with line search to solve the equations. The
pros and cons of this FFT/Picard technique are compared to those of alternative
solution methods that use real-space integration of the convolutions instead of
FFTs and Newton iteration instead of Picard. For the hard-sphere DFT we use
Fundamental Measure Theory. For the electrostatic DFT we present two
algorithms. One is for the \textquotedblleft bulk-fluid\textquotedblright
functional of Rosenfeld [Y. Rosenfeld. \textit{J. Chem. Phys.} 98, 8126 (1993)]
that uses operations. The other is for the
\textquotedblleft reference fluid density\textquotedblright (RFD) functional
[D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)]. This
functional is significantly more accurate than the bulk-fluid functional, but
the RFD algorithm requires operations.Comment: 23 pages, 4 figure
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