HTML_EDITOR Intro Page true true The original version of this program was written by Morten Brydensholt in collaboration with J. Hasbun during the OSP Summer 2003 workshop at Davidson College. This version of the program has most recently been modified by J. Hasbun. -Brownian Motion (Robert Brown, 1828) refers to the motion developed by a particle supended in a liquid. The random motion seen is due to random collisions suffered by the suspended particle with the molecules in the liquid. The molecules in the liquid move about in a random way and when they encounter the suspended particle and collide, the suspended particle's momentum is changed. -In this simulation, the suspended particle is colored red. Its mass can be changed to see its effect. Basically, if the particle's mass is large, the motion is less random because of it large momentum. But, as the particle's mass decreases, the motion is susceptible to more random changes than if the particle's mass is large. Such effect might play an important role in nanotechnology issues. -The simulation starts with random positions and velocities of the molecules as well as the particle. The suspended particle is visible at all times, but the liquid's molecules can only be seen if desired. Momentum is conserved by looking at collisions due to particle pairs, such that during a pair collision, v1=( 2*m2*v2 + (m1-m2)*v1 )/(m1+m2), and v2=( 2*m1*v1 + (m2-m1)*v2 )/(m1+m1). The motion is modeled by solving the differential equations dVx/dt=Fx/m, and dVy/dt=Fy/m, with Fx, and Fy being the forces due to the walls. We let these forces take a constant value when the particle enters the wall region. For example, Fx=Fo if x <= left wall and Fx=-Fo if x>=right wall; Fy=Fo if y<=bottom wall, and Fy=-Fo if y>= top wall position. Note, there are times when the particles gain too much momentum and looks like they want to get out of the box. In such case, one needs to reset the simulation because the conservation of energy property is not stricktly enforced thus far. ]]> 25 false VARIABLE_EDITOR Var Table true true n int N int m double [N] M double d double x double [N] y double [N] vy double [N] vx double [N] color Object [N] t double Lx double Ly double f double v0 double visible boolean [N] x0 double y0 double double CODE_EDITOR particles true true ODE_EDITOR Evol Page true true t 0.005 vx[i] vy[i] Fx(i,x,y,vx,vy)/m[i] Fy(i,x,y,vx,vy)/m[i] RungeKutta CODE_EDITOR Collisions true true LIBRARY_EDITOR force true true =0+d/4 || y[i] <= Ly-d/4)) return f; if (x[i]>=Lx-d/4 && (y[i]>=0+d/4 || y[i] <= Ly-d/4)) return -f; if (y[i]<=0.0+d/4 && (x[i]>=0+d/4 || x[i] <= Lx-d/4)) return 0; if (y[i]>=Ly-d/4 && (x[i]>=0+d/4 || x[i] <= Lx-d/4)) return 0; return 0.0; } public double Fy(int i, double x[], double y[],double vx[],double vy[]) { if (x[i]<=0.0+d/4 && (y[i]>=0+d/4 || y[i] <= Ly-d/4)) return 0; if (x[i]>=Lx-d/4 && (y[i]>=0+d/4 || y[i] <= Ly-d/4)) return 0; if (y[i]<=0.0+d/4 && (x[i]>=0+d/4 || x[i] <= Lx-d/4)) return f; if (y[i]>=Ly-d/4 && (x[i]>=0+d/4 || x[i] <= Lx-d/4)) return -f; return 0.0; } ]]> LIBRARY_EDITOR visible true true true Elements.Frame Frame true Frame border true 340,400 true Elements.Panel buttonspanel Frame south border:0,0 500,70 true Elements.Panel Panel1 buttonspanel center flow:left,0,0 200,50 Elements.Button Play Panel1 center Play _play() Elements.Button Pause Panel1 Pause _pause() Elements.Button Initialize Panel1 Initialize _initialize() Elements.Button reset Panel1 reset _reset() Elements.CheckBox visible Panel1 visible false visibleOn() visibleOff() true Elements.Panel Panel2 buttonspanel south grid:1,3,0,0 200,40 Elements.Slider N Panel2 n 1 N _initialize() n=0 100,30 Elements.Slider v0 Panel2 v0 0.0 10.0 _initialize() vO=#0.00 100,30 Elements.Slider M Panel2 M 1.0 100.0 M=0.00 100,30 true Elements.Panel drawing Frame north border 500,500 true Elements.DrawingPanel DrawingPanel drawing north false false -5.0 Lx+5.0 -5.0 Ly+5.0 500,320 Elements.Arrow wall_left DrawingPanel 0.0-0.5*d 0.0-0.5*d 0 Ly+d SEGMENT lightGray Elements.Arrow wall_top DrawingPanel 0.0-0.5*d Ly+0.5*d Lx+d 0 SEGMENT lightGray Elements.Arrow wall_right DrawingPanel Lx+0.5*d 0.0-0.5*d 0 Ly+d SEGMENT lightGray Elements.Arrow wall_bottom DrawingPanel 0.0-0.5*d 0.0-0.5*d Lx+d 0 SEGMENT lightGray Elements.ParticleSet ParticleSet DrawingPanel n x y d d visible FILLED_CIRCLE color Elements.Trace Particle_Trace DrawingPanel 2000 x0 y0 true 0,64,128 NO_MARKER true