Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion

A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the ``mesoscopic'' level and is derived from the ``microscopic'' wave equation. A precise treatment of the diffuse intensity is derived which automatically includes the effects of boundary layers. Effects such as the enhanced backscatter cone and imaging of objects in opaque media are also discussed within this framework. In the second part the approach is extended to mesoscopic correlations between multiple scattered intensities which arise when scattering is strong. These correlations arise from the underlying wave character. The derivation of correlation functions and intensity distribution functions is given and experimental data are discussed. Although the focus is on light scattering, the theory is also applicable to micro waves, sound waves and non-interacting electrons.Comment: Review. 86 pages Latex, 32 eps-figures included. To appear in Rev. Mod. Phy

Optimal learning rules for discrete synapses

There is evidence that biological synapses have a limited number of discrete weight states. Memory storage with such synapses behaves quite differently from synapses with unbounded, continuous weights, as old memories are automatically overwritten by new memories. Consequently, there has been substantial discussion about how this affects learning and storage capacity. In this paper, we calculate the storage capacity of discrete, bounded synapses in terms of Shannon information. We use this to optimize the learning rules and investigate how the maximum information capacity depends on the number of synapses, the number of synaptic states, and the coding sparseness. Below a certain critical number of synapses per neuron (comparable to numbers found in biology), we find that storage is similar to unbounded, continuous synapses. Hence, discrete synapses do not necessarily have lower storage capacity

Magnetic properties of amorphous thin films produced by ion mixing

We have produced several magnetic amorphous alloys by ion mixing of thin multilayer films. Our results show that the ion mixing technique is able to produce amorphous films of the various categories (transition metal-metalloid, transition metal pairs) at the composition appropriate for the appearance of magnetic ordering. A comparison of their saturation magnetization with that of related vapor quenched films suggests similar nearest-neighbor coordination in both kinds of samples

A Novel Spike Distance

The discrimination between two spike trains is a fundamental problem for both experimentalists and the nervous system itself. We introduce a measure for the distance between two spike trains. The distance has a time constant as a parameter. Depending on this parameter, the distance interpolates between a coincidence detector and a rate difference counter. The dependence of the distance on noise is studied with an integrate-and-fire model. For an intermediate range of the time constants, the distance depends linearly on the noise. This property can be used to determine the intrinsic noise of a neuron

Mesoscopic phenomena in multiple light scattering

In my thesis I study mesoscopic corrections on diffuse transport. I first describe the diffuse transport of light, using the scalar approximation and the radiative transfer approach. Next, I focus on the correlations in transmission, I discuss the so called C_1, C_2, C_3 decomposition and calculate each term in detail. Finally, I discuss the full distribution functions in the transmission. Many references and figures are included. Note, however, that much of the work was already published or is present on the cond-mat archive. A limited number is available as hardcopy on request ([email protected]) else 132 pages Postscript.Comment: Ph.D. thesis. 132 pages postscript; hardcopy available on reques

Third Cumulant of the total Transmission of diffuse Waves

The probability distribution of the total transmission is studied for waves multiple scattered from a random, static configuration of scatterers. A theoretical study of the second and third cumulant of this distribution is presented. Within a diagrammatic approach a theory is developed which relates the third cumulant normalized to the average, $\langle \langle T_a^3 \rangle \rangle$, to the normalized second cumulant $\langle \langle T_a^2 \rangle \rangle$. For a broad Gaussian beam profile it is found that $\langle \langle T_a^3 \rangle \rangle= \frac{16}{5} \langle \langle T_a^2 \rangle \rangle^2$. This is in good agreement with data of optical experiments.Comment: 16 pages revtex, 8 separate postscript figure

rPICARD: A CASA-based Calibration Pipeline for VLBI Data

Currently, HOPS and AIPS are the primary choices for the time-consuming process of (millimeter) Very Long Baseline Interferometry (VLBI) data calibration. However, for a full end-to-end pipeline, they either lack the ability to perform easily scriptable incremental calibration or do not provide full control over the workflow with the ability to manipulate and edit calibration solutions directly. The Common Astronomy Software Application (CASA) offers all these abilities, together with a secure development future and an intuitive Python interface, which is very attractive for young radio astronomers. Inspired by the recent addition of a global fringe-fitter, the capability to convert FITS-IDI files to measurement sets, and amplitude calibration routines based on ANTAB metadata, we have developed the the CASA-based Radboud PIpeline for the Calibration of high Angular Resolution Data (rPICARD). The pipeline will be able to handle data from multiple arrays: EHT, GMVA, VLBA and the EVN in the first release. Polarization and phase-referencing calibration are supported and a spectral line mode will be added in the future. The large bandwidths of future radio observatories ask for a scalable reduction software. Within CASA, a message passing interface (MPI) implementation is used for parallelization, reducing the total time needed for processing. The most significant gain is obtained for the time-consuming fringe-fitting task where each scan be processed in parallel.Comment: 6 pages, 1 figure, EVN 2018 symposium proceeding

A New Type of Intensity Correlation in Random Media

A monochromatic point source, embedded in a three-dimensional disordered medium, is considered. The resulting intensity pattern exhibits a new type of long-range correlations. The range of these correlations is infinite and their magnitude, normalized to the average intensity, is of order $1/k_0 \ell$, where $k_0$ and $\ell$ are the wave number and the mean free path respectively.Comment: RevTeX, 8 pages, 3 figures, Accepted to Phys. Rev. Let