Personally, I would like to introduce a WEB site I found recently, which offers some excellent material which impacts on many areas of contemporary Physics:
The Center for Polymer Studies, located in the Physics Department at Boston University has an excellent Web site which deserves attention. The site describes the Center's research focus, and most importantly offers extensive online information and downloadable simulation software. This site is a must-see for those interested in: polymer interactions, randomness, percolation and general fractal systems, as well as the experimental methods used to study such systems.
Importantly there is also extensive interactive information concerning current and planned Research Projects which are suitable for Undergraduate and High School Science Education. For example, one project investigates: "The Random Universe: An Interdisciplinary Approach to Investigating Patterns in Nature.
For those of you planning on teaching a course on Fractals in Physics or even introducing your students to stochastic behaviour and non-linear systems then you should take a look at a forthcoming book currently available in a pilot edition called: Fractals in Science: An Introductory Course. This is planned for release in the Summer of 1997, and includes course material, software and a guided hands-on introduction to natural fractals including such topics as: fractal behaviour in nerve cells, forest fires, mountain ranges, and cloud shapes.
There is also a regular newsletter called the: "Patterns In Nature Newsletter" aimed at informing High School and early Undergraduate students and their teachers about new experiments, and teaching tools and materials. The Winter 1996 "Patterns in Nature Newsletter" is available online.
There is also substantial cutting-edge Research progress reports which detail current work carried out by the researchers from the Center for Polymer Studies. For example, one report concerns the Theories of Diffusion -Limited Aggregation, while another explores Long-Range Correlations in DNA Base Pair Sequences.
For those students intersted in getting involved with fractals, and the analysis of random phenomena - there are patterns in Nature Student Activity Guides. These demonstrate an actual experiment, and include fully stated aims, hypotheses, methods, results and conclusions. Typical examples include: the generation of silver fractals using a straightforward chemical reaction which produces ramified, branching fractal shapes. Another example, investigates the fractal patterns in leaves.
A stunning set of Java-Powered Simulations are also available for viewing, and selected simulations can be downloaded for both Windows or Macintosh platforms. These include: one and two dimensional random walks, molecular motion, a sandpile simulation, diffusion-limited aggregation and a polymer simulation.
Check out the set of Simulation Software for visualizing aspects of Molecular Dynamics. Note however that a UNIX operating environment is required.
Finally, I urge all of you to take a look at the following FTP directory which provides downloadable simulation software for both the Windows and Macintosh platforms. Many of the programs (i.e. OGAFSAMP.ZIP) offer an excellent, graphic introduction to forest fires simulations, and generation of diffusion-limited aggregates; while another (DP.ZIP) provides software tools to calculate the mass fractal dimension of a two dimensional digital object in the plane.
ftp://erato.bu.edu/pub/OGAF/pc WINDOWS SOFTWARE
ftp://erato.bu.edu/pub/OGAF/mac MACINTOSH SOFTWARE
(Submitted to Virtual Physics: January 2, 1997)
Table 1. Amplitudes of absorption and power spectra obtained from the ethylene glycol sample.
Table 2. Calculated values of 180o pulse, 90o amplitude, and pulse inhomogeneity.
PROGRAM SINMAC REAL C(100),S(100),F(100),K(100),P(100) COMMON C,S,F,K,P,N,IFLAG,C1,C2,C3,C4,C5,C6,R1,R2,R3 WRITE(*,1001) READ(*,*)N WRITE(*,1002) READ(*,*) A0 WRITE(*,1003) READ(*,*)B0 WRITE(*,1004) READ(*,*)T0 WRITE(*,1005) READ(*,*)(C(I),I=1,N) WRITE(*,1006) READ(*,*)(S(I),I=1,N) 1001 FORMAT(2X,'Number of experimental points = '\) 1002 FORMAT(2X,'Estimated amplitude of signal at 90deg. = '\) 1003 FORMAT(2X,'Correction parameter B (usually B=0) = '\) 1004 FORMAT(2X,'Estimated duration of 180 deg. pulse = '\) 1005 FORMAT(2X,'Pulse durations') 1006 FORMAT(2X,'Amplitudes') C Estimated values E1=0.1 E2=1.0E-4 E3=0.1 DA=0.0 DB=0.0 DT=0.0 A=A0 B=B0 T=T0 L=1 C Iteration 200 CONTINUE A=A+DA B=B+DB T=T+DT CALL POWER(A,B,T) D=2.0*C2*C3*C5-C3*C3*C4-C1*C5*C5+C1*C4*C6-C2*C2*C6 D=1.0/D DA=D*(C3*C5*R2-C3*C4*R3+C2*C5*R3-C2*C6*R2+R1*(C4*C6-C5*C5)) DB=D*(C2*C3*R3+R2*(C1*C6-C3*C3)+C3*C5*R1-C1*C5*R3-C2*C6*R1) DT=D*(C2*C5*R1-C3*C4*R1+C2*C3*R2-C1*C5*R2+R3*(C1*C4-C2*C2)) IF(DA.GT.E1.OR.DB.GT.E2.OR.DT.GT.E3)GOTO 200 C Calculated values SI=0.0 DO 10 I=1,N SI=SI+P(I)**2 10 CONTINUE SI=SQRT(SI/FLOAT(N-3)) SA=SI*SQRT(D*(C4*C6-C5*C5)) SB=SI*SQRT(D*(C1*C6-C3*C3)) T9=SI*SQRT(D*(C1*C4-C2*C2)) C Correlation parameters AT=C3/SQRT(C1*C6) AB=C2/SQRT(C1*C4) BT=C5/SQRT(C4*C6) A=A*A PN=(1.0+(1.0-B*2.25*T**2)) PN=0.5*(PN/(1.0-B*0.25*T*T)) PNPLS=ACOS(PN)*180.0/ACOS(-1.0) C Results WRITE(*,2001) WRITE(*,2002)A,SA,AT WRITE(*,2003)B,SB,BT WRITE(*,2004)T,T9,BT WRITE(*,2005)PNPLS STOP 2001 FORMAT(//2X,'Results of calculation:') 2002 FORMAT(2X,'A,SA,AT: ',3F16.8) 2003 FORMAT(2X,'B,SB,AB: ',3F16.8) 2004 FORMAT(2X,'T,ST,BT: ',3F16.8) 2005 FORMAT(2X,'PN: ',F16.8) END SUBROUTINE POWER(A,B,T) REAL C(100),S(100),P(100),K(100),F(100) COMMON C,S,F,K,P,N,IFLAG,C1,C2,C3,C4,C5,C6,R1,R2,R3 C1=0.0 C2=0.0 C3=0.0 C4=0.0 C5=0.0 C6=0.0 R1=0.0 R2=0.0 R3=0.0 DO 10 I=1,N AL=ACOS(-1.0)*C(I)/T K(I)=1.0-B*C(I)**2 F(I)=(A*K(I)*SIN(AL))**2 FB=-2.0*A*A*C(I)**2*K(I)*(SIN(AL))**2 FT=-ACOS(-1.0)*C(I)*(A*K(I)/T)**2*SIN(2.0*AL) FA=2.0*A*K(I)**2*(SIN(AL))**2 C1=C1+FA*FA C2=C2+FA*FB C3=C3+FA*FT C4=C4+FB*FB C5=C5+FB*FT C6=C6*FT*FT P(I)=S(I)-F(I) R1=R1+P(I)*FA R2=R2+P(I)*FB R3=R3+P(I)*FT 10 CONTINUE RETURN END