voronoi diagram matlab voronoi function  (MathWorks Inc)

Journal: Materials

Article Title: Modeling of Polycrystalline Material Microstructure with 3D Grain Boundary Based on Laguerre–Voronoi Tessellation

doi: 10.3390/ma15061996

Figure Lengend Snippet: Schematic of the improved Laguerre–Voronoi tessellation, R i , R j are the radii of the power circles corresponding to the adjacent nucleus, D i j is the distance between nuclei, h is the thickness of the grain boundary, and the point S is the location of the cutting plane between two nuclei, λ is the ratio of the distance from point S to nucleus i to D i j , d L is the tangential distance from point S to two spheres.

Article Snippet: A large amount of grain information data is generated through the Voronoi diagram function in MATLAB, and then the polycrystalline microstructure can be modeled by reverse topological reconstruction using grain information (such as vertices, lines, surfaces, bodies) in the ABAQUS package.

Techniques:

Journal: Materials

Article Title: Modeling of Polycrystalline Material Microstructure with 3D Grain Boundary Based on Laguerre–Voronoi Tessellation

doi: 10.3390/ma15061996

Figure Lengend Snippet: Examples of arbitrary solid shapes with Voronoi cells.

Article Snippet: A large amount of grain information data is generated through the Voronoi diagram function in MATLAB, and then the polycrystalline microstructure can be modeled by reverse topological reconstruction using grain information (such as vertices, lines, surfaces, bodies) in the ABAQUS package.

Techniques:

Journal: Materials

Article Title: Modeling of Polycrystalline Material Microstructure with 3D Grain Boundary Based on Laguerre–Voronoi Tessellation

doi: 10.3390/ma15061996

Figure Lengend Snippet: ( a ) Grain size distribution of the Laguerre–Voronoi tessellation polycrystalline model with 500 grains; ( b ) grain size distribution of the Laguerre–Voronoi tessellation polycrystalline model with 125 grains; ( c ) grain size distribution of the Voronoi tessellation polycrystalline model with 500 grains; ( d ) grain size distribution of the Voronoi tessellation polycrystalline model with 125 grains.

Article Snippet: A large amount of grain information data is generated through the Voronoi diagram function in MATLAB, and then the polycrystalline microstructure can be modeled by reverse topological reconstruction using grain information (such as vertices, lines, surfaces, bodies) in the ABAQUS package.

Techniques:

Journal: Materials

Article Title: Modeling of Polycrystalline Material Microstructure with 3D Grain Boundary Based on Laguerre–Voronoi Tessellation

doi: 10.3390/ma15061996

Figure Lengend Snippet: ( a ) Distribution of the number of grains faces, ( b ) distribution of the number of single grain edges by Voronoi tessellation, ( c ) distribution of the number of single grain faces, ( d ) distribution of the number of single grain edges by Laguerre–Voronoi tessellation.

Article Snippet: A large amount of grain information data is generated through the Voronoi diagram function in MATLAB, and then the polycrystalline microstructure can be modeled by reverse topological reconstruction using grain information (such as vertices, lines, surfaces, bodies) in the ABAQUS package.

Techniques:

Journal: bioRxiv

Article Title: Pressure drives rapid burst-like collective migration from 3D cancer aggregates

doi: 10.1101/2021.04.25.441311

Figure Lengend Snippet: a) Schematic representation of aggregate preparation and imaging process. b) Over 12 h, aggregates in 0.5 mg ml − 1 collagen (LCC; top) burst into the matrix, whereas aggregates embedded in 2.5 mg ml − 1 collagen (HCC; bottom) did not. Nuclei tracks at 12 h from each condition are shown, scale bars = 50 µ m. c) Comparison of average absolute cell velocities ⟨ V t ⟩ within aggregates embedded in LCC & HCC at different time points (N = 10 each, standard error of the mean (s.e.m.)). d) Average MSD for three time windows (N = 10 each). Inset shows the MSD in log scale between 4-8 h for LCC and HCC, with their corresponding slopes (s.e.m.). e) Zoomed-in view of the bursts (red box) and non-invasive (blue box) regions from (b) (scale bars = 20 µ m). f) Averages of diffusivity (D) and powerlaw exponent α obtained by fitting f(x) = α x + 6 D onto the log of window MSDs (N = 10 each, s.e.m.). g) Representation of both the early random and later collective migration as observed in LCC. h) Velocity correlation ⟨C⟩ binned over distances (N = 10, bin size = 20 µ m). Exponential decay function fit on distances up to 150 µ m at 8 h (inset). i) Mean velocity correlation length acquired over time (median smoothed, N = 10, s.e.m.). j) Contractile stresses exerted by aggregates in LCC and HCC on their ECM (N =5 each, s.e.m.). k) Mean Voronoi volume of cells within aggregate acquired over time (N = 10, s.e.m.).

Article Snippet: Based on tracked nuclei positions, a MATLAB function ‘N-D Voronoi diagram’ was applied to retrieve an estimate for the cell borders.

Techniques: Imaging, Comparison, Migration