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Michael C.
United States
Registrace 10. 07. 2015
Lover of math and physics
Phased Array Diffraction Demonstration
This is a rudimentary approximation of phased array behavior based off of the Fraunhofer approximation taking the generated pattern as the Fourier transform of the input signal. What this represents is two simple facts about phased arrays which are easily understood in the Fraunhofer approximation; that is:
-a linearly (spatially) varying phase function results in a spatial shifting of the pattern; this is the primary reason we care about phased arrays as it allows us to steer radiation sheerly by manipulating the phase of our emitters.
-a quadratically varying phase has the effect of a concave mirror. This seems odd maybe at first glance but if one consider the approximation of the height profile of such a lens as corresponding directly to phase changes, then it should be obvious that having such a spatially varying phase achieves this effect
-a linearly (spatially) varying phase function results in a spatial shifting of the pattern; this is the primary reason we care about phased arrays as it allows us to steer radiation sheerly by manipulating the phase of our emitters.
-a quadratically varying phase has the effect of a concave mirror. This seems odd maybe at first glance but if one consider the approximation of the height profile of such a lens as corresponding directly to phase changes, then it should be obvious that having such a spatially varying phase achieves this effect
zhlédnutí: 60
Video
Brute Force Recursion Algorithm for Connected Component Traversal
zhlédnutí 161Před 4 měsíci
This is a brute force non-optimized bit of code I wrote to move a scribe across a microscope slide in order to "print" an aperture for producing particular diffraction patterns. In principle, it couldbe highly optimized for backtracking speed by just taking a shortest path to the nearest unvisited pixel and restarting the recursion but I'm too lazy and the project is due next week.
Producing an aperture with a specified diffraction pattern through genetic algorithm
zhlédnutí 41Před 4 měsíci
Producing an aperture with a specified diffraction pattern through genetic algorithm
Crystallization Visual
zhlédnutí 56Před 7 měsíci
3D basic simulation of crystalization using 2 species of charged particles. The legend displays weird so just ignore it
Beginning of PDE-based high-particle gravity simulation.
zhlédnutí 773Před 11 měsíci
This is proof of concept for a PDE-based gravity simulation which for being able to theoretically remove the issue of having to compute inverse-squares for large numbers of particles. This aims instead to simulate the broad strokes and gain particle data from the velocity field rather than through pairwise computation. Furthermore, this method allows one to seemlessly adjust for collisions by i...
Exponentiation of the complex plane from from -2 to 2
zhlédnutí 40Před rokem
lines=60; griddens=0.3; xi=linspace(-lines,lines,10000); x=xi; for n=-lines:lines x=[x,xi n*i*griddens]; end for n=-lines:lines x=[x,xi*i n*griddens]; end bounds=5; for n=0:240 expo=-2 4/240*n; %expo is the value that's changing that you're animating xn=x.^expo; %xn is a list of complex points that are being plotted where x is the initial grid scatter(real(xn),imag(xn),0.035,Marker="."); title(...
Effect of exponentiation from 1 to -1 on the complex plane
zhlédnutí 43Před rokem
I had to make animation to earlier to to describe why a negative times a negative is a positive and found that the program I made was well suited to doing this kind of complex transformation animation. So here it is and here's the code I used to do it in a Matlab live script: lines=100; griddens=0.2; xi=linspace(-lines,lines,10000); x=xi; for n=-lines:lines x=[x,xi n*i*griddens]; end for n=-lin...
Neural Net Learning to predict a sine wave
zhlédnutí 122Před rokem
I suggest watching on a slower speed or else it's just pure chaos
Laplacian-based smoothing algorithm
zhlédnutí 928Před rokem
I was dealing with error data corresponding to a parabolic interpolation estimation of pi and ended up with some very noisy (but interestingly repetitive) data corresponding to error vs. resolution. Afterwards, I decided to try out an algorithm I had thought of prior which is basically a discretization of an equation that relates a surface's (or in this case a curve's) concavity to its velocity...
Preliminary test for simulating pheromone trails of evolving cells
zhlédnutí 33Před 2 lety
Pretty much exactly what the title cells. This is part of a project to create an accurate simulation of evolution of creatures. I thought it contrived to try to automatically give cells the ability to sense other cells, so instead I allow them to detect the concentration of various chemical signals such as CO2, O2, and 3 arbitrary pheromones. These computations were performed with a neural netw...