111,194 research outputs found
The optimization of profiled diffusers
Methods have been developed to produce profiled diffusers that create a large amount of diffusion. The methods are iterative and required the development of a new parameter to measure diffusion. Achieving scattering independent of angle has been attempted over a wide bandwidth. The methods are also applicable to other diffusion criteria. The diffusers consists of a series of wells of the same width but of different depths similar to Schroeder diffusers. Applications include concert halls, theatres, and studio monitor rooms. The new diffusers have been shown to create better, more uniform diffusion than the previous designs of Schroeder. This is due to the new designs being reliant on accurate boundary element prediction methods rather than more approximate techniques
Networks for Nonlinear Diffusion Problems in Imaging
A multitude of imaging and vision tasks have seen recently a major
transformation by deep learning methods and in particular by the application of
convolutional neural networks. These methods achieve impressive results, even
for applications where it is not apparent that convolutions are suited to
capture the underlying physics.
In this work we develop a network architecture based on nonlinear diffusion
processes, named DiffNet. By design, we obtain a nonlinear network architecture
that is well suited for diffusion related problems in imaging. Furthermore, the
performed updates are explicit, by which we obtain better interpretability and
generalisability compared to classical convolutional neural network
architectures. The performance of DiffNet tested on the inverse problem of
nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset.
We obtain competitive results to the established U-Net architecture, with a
fraction of parameters and necessary training data
Parabolic and Hyperbolic Contours for Computing the Bromwich Integral
Some of the most effective methods for the numerical inversion of the Laplace transform are based on the approximation of the Bromwich contour integral. The accuracy of these methods often hinges on a good choice of contour, and several such contours have been proposed in the literature. Here we analyze two recently proposed contours, namely a parabola and a hyperbola. Using a representative model problem, we determine estimates for the optimal parameters that define these contours. An application to a fractional diffusion equation is presented.\ud
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JACW was supported by the National Research Foundation in South Africa under grant FA200503230001
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Competitive effects between stationary chemical reaction centres: a theory based on off-center monopoles.
The subject of this paper is competitive effects between multiple reaction sinks. A theory based on off-center monopoles is developed for the steady-state diffusion equation and for the convection-diffusion equation with a constant flow field. The dipolar approximation for the diffusion equation with two equal reaction centres is compared with the exact solution. The former turns out to be remarkably accurate, even for two touching spheres. Numerical evidence is presented to show that the same holds for larger clusters (with more than two spheres). The theory is extended to the convection-diffusion equation with a constant flow field. As one increases the convective velocity, the competitive effects between the reactive centres gradually become less significant. This is demonstrated for a number of cluster configurations. At high flow velocities, the current methodology breaks down. Fixing this problem will be the subject of future research. The current method is useful as an easy-to-use tool for the calibration of other more complicated models in mass and/or heat transfer
The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur
Dynamical instrument limitations, such as finite detection bandwidth, do not
simply add statistical errors to fluctuation measurements, but can create
significant systematic biases that affect the measurement of steady-state
properties. Such effects must be considered when calibrating ultra-sensitive
force probes by analyzing the observed Brownian fluctuations. In this article,
we present a novel method for extracting the true spring constant and diffusion
coefficient of a harmonically confined Brownian particle that extends the
standard equipartition and power spectrum techniques to account for video-image
motion blur. These results are confirmed both numerically with a Brownian
dynamics simulation, and experimentally with laser optical tweezers.Comment: 12 pages, 6 figures, revtex4; published in Optics Express.
http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-25-1251
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