 1D: you can keep a steady line; with a velocity in the x=1
 2D: you can keep a stationary formations: square, circle … or a wavy path; the velocity becomes a combination of xy
 3D: to move those rotating 2D formations forward you need a 3th dimension (xyz). Because if you move a rotating formation forward in 2D, every particle starts to have a different velocity, only by adding an extra dimension is it possible to move them together forward in a particular direction, and keep their formation rotation going.
 4D: to move those round or forward moving formations, one needs again an extra dimension; xyza
Friday, August 15, 2014
Extra Dimensions (V=1)
Saturday, August 2, 2014
Closed Hilbert Curve
After finding a topic on Continuous Fractal SpaceFilling (Hilbert) Curves ...
... in a mathbook in the library this week ...
... I started looking for them on the internet and came across a neat tool on the Wolframsite:
(CDF player: http://www.wolfram.com/cdfplayer/  200 Mb or so)
But because the curve was open, I asked the developer Dr. Michael Trott if he could ad a closing option, like the picture in the book … and hey! he send me this adjusted cdffile/code where the loop is closed ... et voilà there was the Fig. 8 knot, check it out:
http://800million.org/InterpolatingTheHilbertCurveWithABSplineClosed.cdf
Friday, July 11, 2014
Wednesday, July 2, 2014
Two ellipses scanning for contact
Simulation made by Krypt0n
Yellow and purple are the tangent at the closest points, white connecting line is the shortest distance between ellipses, long white lines are tests for: http://en.wikipedia.org/wiki/Hyperplane_separation_theorem
Yellow and purple are the tangent at the closest points, white connecting line is the shortest distance between ellipses, long white lines are tests for: http://en.wikipedia.org/wiki/Hyperplane_separation_theorem
Saturday, April 26, 2014
War of the Ants
TV noise is a fun reference for the Aether medium.
See post: Spiraling Figure 8
Noise, in analog video and television, is a random dot pattern of static displayed when no transmission signal is obtained by the antenna receiver of television sets and other display devices. The random pattern superimposed on the picture, visible as a random flicker of "dots" or "snow", is the result of electronic noise and radiated electromagnetic noise accidentally picked up by the antenna.
Since one impression of the "snow" is of fastflickering black bugs on a cool white background, in Sweden, Denmark and Hungary the phenomenon is often called myrornas krig in Swedish, myrekrig in Danish, hangyák háborúja in Hungarian, and semut bertengkar in Indonesian, which translate to "War of the Ants" or sometimes hangyafoci which means "ant soccer", and in Romanian, purici, which translates into "fleas".
Tuesday, March 11, 2014
Tippy Top
A 'Tippy Top' is a spherical object like an oval/ellipse with its center of mass out of the middle when spun. The reason it tip's over has got to do with Momentum of inertia, Torque and Force of friction.
Monday, March 3, 2014
Thursday, February 13, 2014
Extreme Vortex Confinement
Simulation made by JAHC
Vorticity Confinement has a basic familiarity to solitary wave approach which is extensively used in many condensed matter physics applications. The effect of VC is to capture the small scale features over as few as 2 grid cells as they convect through the flow.
Thursday, February 6, 2014
Granular Medium
GranularMedium simulations made by Nicholas Guttenberg with his GRNLR particle simulator. The program was orignally used for studying granular jets, wet granular droplet impact, and tipping icebergs.
Ref. "An approximate hard sphere method for densely packed granular flows" (link  283 kb)
Ref.: "Grains and gas flow: Molecular dynamics with hydrodynamic interactions" (link  207 kb)
Ref. "An approximate hard sphere method for densely packed granular flows" (link  283 kb)
Ref.: "Grains and gas flow: Molecular dynamics with hydrodynamic interactions" (link  207 kb)
In WooDEM we had the problem that particles slowed down due to dissipation (Coefficient of Restitution < 1). So energy was being constantly removed from the simulation due to collisions, to keep the particles going Nicholas used 3 solutions in his program for adding energy:
A. Swimmers: after interaction a force is added to keep the particle's velocity close to 1
F=a*v*(1v^2)
 The first ‘v’ is a vector,
 v^2 is a scalar,
 ’a’ is a scalar that controls how strong this force is.
This turns the particles into active swimmers, and you can create interesting structure by doing this in the presence of a high density of particles (basically they have to move because of the force, but they want to be still because they're near the jamming point, so they end up moving in largescale vortices similar to those in the Twirls video).

B. Thermalisation: adding a force to keep energy despite dissipation
F=sqrt(T)*eta/sqrt(dt)
 ’T’ is the desired temperature (normally there'd be a measure of dissipation, but your dissipation is due to inelastic collisions),
 ‘dt’ a timestep used by the algorithm (needed for of how noise scales),
 ‘eta’ a random number generated every time you call the function to get the force.
This will cause the particle motions to have some relatively constant level of energy despite dissipation.

C. Rescale timestep: so motion occurs at a constant velocity
For hard grains there is no inherent energy scale, so a system of grains moving at 1mm/year and a system of grains moving at 100 m/s have the same physics, just strewn out over a different time scale.
What you could do is snap a frame at irregular intervals. First at every second, as the grains slow down, then every 2, 4, 8, ... The right interval to use would be based on the square root of the system's average energy (e.g. sum up v^2 for every grain, divide by the number of grains, then take the square root and multiply by a constant to make it look good).
For hard grains there is no inherent energy scale, so a system of grains moving at 1mm/year and a system of grains moving at 100 m/s have the same physics, just strewn out over a different time scale.
What you could do is snap a frame at irregular intervals. First at every second, as the grains slow down, then every 2, 4, 8, ... The right interval to use would be based on the square root of the system's average energy (e.g. sum up v^2 for every grain, divide by the number of grains, then take the square root and multiply by a constant to make it look good).
GRNLR  GUI
Wednesday, January 29, 2014
LC : Nemantic, Smectic and Chiral Phase
I. NEMANTIC PHASE
"One of the most common Liquid Crystal (LC) phases is the nematic. The word nematic comes from the Greek νήμα (nema), which means "thread". This term originates from the threadlike topological defects observed in nematics, which are formally called 'disclinations'. Nematics also exhibit socalled "hedgehog" topological defects. In a nematic phase, the calamitic or rodshaped organic molecules have no positional order, but they selfalign to have longrange directional order with their long axes roughly parallel. Thus, the molecules are free to flow and their center of mass positions are randomly distributed as in a liquid, but still maintain their longrange directional order."
http://en.wikipedia.org/wiki/Nematic#Nematic_phase

"Colloidal dispersions in liquid crystals can serve as asoftmatter toolkit for the selfassembly of composite materials with preengineered properties and structures that are highly dependent on particleinduced topological defects. Here, we demonstrate that bulk and surface defects in nematic fluids can be patterned by tuning the topology of colloidal particles dispersed in them. In particular, by taking advantage of twophoton photopolymerization techniques to make knotshaped microparticles, we show that the interplay of the topologies of the knotted particles, the nematic field and the induced defects leads to knotted, linked and other topologically nontrivial field configurations."
http://www.nature.com/nmat/journal/vaop/ncurrent/full/nmat3840.html

"Elasticity of LCrich nematic phase affects the phase separated domain pattern significantly. For examples, we often observed the triangle and tear shaped droplets of isotropic phase. We demonstrated the two types of ordering processes, which we called isotropic and nematic spinoidal decompositions."http://statphys.scphys.kyotou.ac.jp/~araki/e_sim_pdlc.html

Möbius strip ties liquid crystal in knots
 Liquid crystal are composed of long, thin, rodlike molecules which align themselves so they all point in the same direction. By controlling the alignment of these molecules, scientists can literally tie them in a knot.
 To do this, they simulated adding a micron sized silica particle  or colloid  to the liquid crystal. This disrupts the orientation of the liquid crystal molecules.
 For example, a colloid in the shape of a sphere will cause the liquid crystal molecules to align perpendicular to the surface of the sphere, a bit like a hedgehog’s spikes.
 Using a theoretical model, the University of Warwick scientists have taken this principle and extended it to colloids which have a knotted shape in the form a Möbius strip. http://www2.warwick.ac.uk/newsandevents/pressreleases/m246bius_strip_ties

Liquidcrystalmediated selfassembly at nanodroplet interfaces
Technological applications of liquid crystals have generally relied on control of molecular orientation at a surface or an interface. Such control has been achieved through topography, chemistry and the adsorption of monolayers or surfactants. The role of the substrate or interface has been to impart order over visible length scales and to confine the liquid crystal in a device. Here, we report results from a computational study of a liquidcrystalbased system in which the opposite is true: the liquid crystal is used to impart order on the interfacial arrangement of a surfactant.

II. SMECTIC PHASE
http://en.wikipedia.org/wiki/Nematic#Smectic_phases

The Growth and Buckling of a Smectic Liquid Crystal Filament
Growth by permeation and draginduced buckling instabilities have been observed in the dynamics of thin filaments in an isotropicSmectic A ($IS_A$) phase transition of liquid crystal fluid, and in lipid bilayer tubes evolving in a fluid medium. With motivation from the experiments with liquid crystal, we have been studying the dynamics of a growing elastic filament immersed in a Stokes fluid. By combining results from slender body theory, Green's function methods, and elasticity theory, we express the selfinduced velocity of the filament as the nonlocal consequence of forces the filament exerts upon the incompressible fluid by its elastic response and growth.
http://math.nyu.edu/faculty/shelley/Fluids/Smectic/smectic.html

III. CHIRAL PHASE
"The chiral nematic phase exhibits chirality (handedness). This phase is often called the cholesteric phase because it was first observed for cholesterol derivatives. Only chiral molecules (i.e., those that have no internal planes of symmetry) can give rise to such a phase. This phase exhibits a twisting of the molecules perpendicular to the director, with the molecular axis parallel to the director. The finite twist angle between adjacent molecules is due to their asymmetric packing"
Tuesday, January 28, 2014
Test Results
A. One cwflow colliding against one ccwflow > forming a central Stemlike flow:
B. Ellipsoidal vs. Spherical particles:
C. Spherical: Two circular flows (cw  ccw) quickly smoothing out into one circular flow:
D. Ellipsoidal: Out of the tessellated starting setting, flows start to emerge after a few seconds:
Friday, January 24, 2014
Spin Around & Aligning with the Hertz Model
By changing the 'Material model' in the WooDEM from 'Linear' to 'Hertz' it is possible to make the particles go round, be it ClockWise or Counter ClockWise, the direction is incidental.
“The HertzMindlin model begins by assuming that contacting solids are isotropic and elastic, and that the representative dimensions of the contact area are very small compared to the various radii of curvature of the undeformed bodies. Another assumption of the HertzMindlin model is that the two solids are perfectly smooth. Only the normal pressures that arise during contact are considered (the extensions of Hertz theory for the tangential component of traction will be discussed later). The HertzMindlin contactforcedisplacement law is nonlinear elastic, with path dependence and dissipation due to slip, and omits relative roll and torsion between the two spheres. Strictly speaking, the simplified contact forcedisplacement law is thermodynamically inconsistent (i.e., unphysical), since it permits energy generation at no cost.”
http://www.cflhd.gov/programs/techDevelopment/geotech/velocity/documents/05_chapter_3_numerical_modeling.pdf

If you want you could check out the action yourself in WooDEM, the program is free (http://www.launchpad.net/woo), and it’s just a 5 to 10 minute download & installation, copy these lines into your Ubuntu Terminal and you're good:sudo addaptrepository ppa:eudoxos/woodaily
sudo aptget update
sudo aptget install pythonwoo
or use the singlecoreversion:
sudo addaptrepository ppa:eudoxos/woodaily
sudo aptget update
sudo aptget install pythonwoosinglecore
To start the program simply type in ‘woo’ and next you can press the F10key to launch the control panels. Chose at the Preprocesstab the preset plugin ‘EllGroup (woo.pre.ell2d)’, select Hertz (highlighted in yellow) to make ‘m go round and press the arrow in the lower right corner to process these settings.
Press Play (>) at ‘Simulation’ to start all the action, you can switch ‘Trace particles’ on/off at the Tracetab; for coloring the particles look at the Displaytab where you set ‘colorBy’ to ‘angVel’ and select ‘Z’ at ‘vecAxis’ or chose some other settings, have fun!
btw notice that the 'Restitution coefficient' (COR) is set to 0.7 if you boost it up to 0.99 then there's less disipation, and the particles will move more dynamic and for a longer time, but by doing so the subtle aligning interaction is gone and they become again chaotic, acting similar to the ‘Linear’ method ... and that *special* circular motion is gone. Hopefully this can be fixed.
For more info on Contact Models and Coefficient Of Restitution in Woo:
 http://woodem.eu/doc/theory/contact/index.html
 http://woodem.eu/doc/theory/contact/hertzian.html#coefficientofrestitution
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