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'Sudoku' X-Ray Uncovers Movements within Opaque Materials

posted by martyb on Friday November 30 2018, @09:43PM   
from the ♫♫♩♩♫♪♪-I-feel-the-Earth-move-under-my-feet dept.

Phoenix666 writes in with a story from ScienceDaily:

[...] academics from the Sydney Centre in Geomechanics and Mining Materials (SciGEM) including Professor of Civil Engineering, Itai Einav and Postdoctoral Research Associate, Dr James Baker have developed a new X-ray method which allows scientists to see inside granular flows. Named X-ray rheography, or "writing flow," their approach gathers information using 3-point high-speed radiography, and then assembles this information by solving a Sudoku-style puzzle.

[...] The new X-ray rheography technique has the ability to form a three dimensional image of moving grains, which has helped the researchers better understand how particles flow and behave in various circumstances. In many examples they have found that granular media tends to flow in unique patterns and waves.

"Unlike fluids, we discovered that confined, three-dimensional steady granular flows arise through cycles of contraction and expansion, à la 'granular lungs'. Again, unlike fluids, we also found that grains tend to travel along parallel lines, even near curved boundaries.

[...] Journal Reference:
James Baker, François Guillard, Benjy Marks, Itai Einav. X-ray rheography uncovers planar granular flows despite non-planar walls. Nature Communications, 2018; 9 (1) DOI: 10.1038/s41467-018-07628-6

At last we can know exactly how the Days of our Lives move.

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Original Submission

• But how? (Score: 2) by edIII on Saturday December 01 2018, @01:23AM

  by edIII (791) on Saturday December 01 2018, @01:23AM (#768536)

  their approach gathers information using 3-point high-speed radiography, and then assembles this information by solving a Sudoku-style puzzle.

  You bastard. You made me read TFA to find out how.

  Next, both the real experimental and artificially generated radiographs are analysed by first dividing into 32 × 32 interrogation windows. For a given window, the auto- and cross-correlation functions are computed and, by solving a deconvolution inverse problem, used to calculate the probability density functions (PDFs) of in-plane displacements in that window (Fig. 3a). These PDFs give the distribution, along the path of the X-ray beam, of the in-plane velocities, which we discretise by taking equally spaced percentiles (Fig. 3b) into vectors of candidate velocities, considering the two planar components separately. For each window and component this tells us the different displacements perpendicular to the beam that occur through the direction of the beam, but does not give the relative out-of-plane position of each such component. An orthogonal scanning angle provides the additional information required to reconstruct a 3D map of the velocity component in plane with both detectors, by combining the two sets of candidate arrays. For example, scanning directions 1 and 2 (as shown in Fig. 1) are used for the vertical component. Given these two candidate arrays, the problem becomes a question of how best to consistently arrange the vectors in the internal grid. This may be thought of as a generalised Sudoku-style puzzle because we know the numbers that should be placed in each row and column but not how to arrange them. However, unlike a Sudoku problem, we are not given any filled-in cells to start the process, and the row and column information may not perfectly match each other. Nevertheless, it can be formulated into a simple optimisation problem, where one aims to minimise discrepancies between the two sets of observations, which we solve with a fast, constructive algorithm to find the arrangement of the two sets of candidate arrays. Taking the mean of these two vectors in each cell gives the output solution value. Note that the solution of this algorithm is not unique, being dependent on the order in which each internal grid point is calculated. This problem is overcome by computing several comparable solutions using different random paths through this grid and averaging over these values. The other two components of the velocity are reconstructed in the same manner by repeating with other pairs of scanning directions.

  The article is worth the read.

  --
  Technically, lunchtime is at any moment. It's just a wave function.

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