[ppi] [ppiindia] FW: Medali Emas

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fyi
 
----- Original Message ----- 
Sent: Wednesday, April 07, 2004 7:37 PM
Subject: Medali Emas untuk SMUN 3 Jayapura 
 
Berita dari Prof. Yohanes Surya
Vice President The First Step to Nobel Prize

Siswa Indonesia merebut Medali Emas dalam Kompetisi Riset The First Step to 
Nobel Prize in Physics.

Septinus George Saa siswa SMUN 3 Jayapura - Papua berhasil merebut medali EMAS 
(hadiah pertama) dalam kompetisi riset Fisika tingkat DUNIA untuk siswa SMU, 
The First Step to Nobel Prize in Physics 2004.

Paper Septinus menyisihkan ratusan paper yang berasal dari puluhan negara, 
setelah melalui penjurian yang dilakukan oleh juri-juri internasional. Ini 
sangat luar biasa!

Septinus membuat makalah tentang bagaimana menghitung hambatan antara dua titik 
dari suatu rangkaian resistor tak hingga yang membentuk suatu segitiga dan 
hexagonal.

Dalam menurunkan rumusnya itu Septinus memanfaatkan deret Fourier yang untuk 
anak SMU seusia Septinus mungkin masih sangat asing.

Kita harus mengacungkan jempol atas prestasi Septinus yang luar biasa ini. 
Terutama karena prestasinya ini membuktikan bahwa siswa dari daerah yang jauh 
terpencil di Jayapura ternyata mampu menjadi juara dunia jika dibimbing dan 
diarahkan dengan tepat. Ini akan menjadi dorongan yang besar bagi daerah-daerah 
lain untuk maju membangun Indonesia.



Infinite Triangle and hexagonal lattice networks of identical resistor

Septinus George Saa

National Public School 3 Jayapura, Penggalang Street No. 59 Waena Jayapura - 
Papua

INDONESIA, Phone/fax:+62 967 571506

Abstract

The resistance between two arbitrary points in an infinite triangle and 
hexagonal lattice networks of identical resistor are calculated using fourier 
series. For hexagonal networks I discover a new method of calculating the 
resistance directly from the networks instead of using D-Y transformation which 
is commonly used. The results are compared numerically to other authors that 
utilizing separation variable[1,2] or green function[3].


SUMMARY

Problem of calculating resistance between two arbitrary points in the infinite 
lattice networks has been revived recently. Several methods has been introduced 
to solve the problem. We could find the old history of this efforts and cited 
paper related with this topic in Zemanian paper[4]. One of the relatively new 
approach is developed by Giulio Venezian[1]. Venezian used a superposition 
method and explicating the symmetry of the grid. The mathematical problem 
involves the solution of an infinite set of linear, inhomogenous difference 
equations which are solved by the method of separation variables. This method 
is developed further by D. Atkinson and F.J. van Steewijk[2] to calculate the 
resistance between two arbitrary nodes in an infinite triangular and hexagonal 
lattices in two dimensions. In addition, for hexagonal lattices they used D-Y 
transformation of the triangular lattices. Doyle and Snell presented the method 
to calculate the infinite electric networks using the ran
 dom walks, though they did not show explicitly and numerically of the 
results[5]. Later on Jozsef Cserti used the lattice green function to calculate 
the resistance of infinite networks of resistors[3].

In this paper I present the alternative approach which was introduced by 
Krzysztof Giaro[6] who calculated the resistance between any two points in the 
infinite square lattices networks that utilizes the basic properties of Fourier 
series. The method has been extended for the infinite cubic lattice networks by 
Agus Wirawan[7]. I use this method to calculate the resistance between any two 
points in the infinite triangle and hexagonal lattices networks. For the 
hexagonal lattice, we use two methods: first , D-Y transformation and secondly 
the use of the fourier series directly from the hexagonal networks. In the 
analysis we use an orthogonal cartesian coordinate system (one axis is 
horizontal and the other is vertical) instead of a hexagonal/triangle 
coordinate system (one axis is horizontal and the other is inclined at 120o) 
that often used in the triangle or hexagonal analysis[2,3]. To some extent the 
orthogonal cartesian coordinate system is easier to follow both for triangu
 lar and hexagonal lattices compared to the other coordinate systems. The 
results are written in a double integral formulas which look different from the 
formula derived by some authors[2,3] However I have succesfully proved 
numerically that both results are actually the same.

Reference

[1] G. Venezian, "On the Resistance between two points on a grid," Am. J. Phys. 
62, 1000-1004 (1994).
[2] D. Atkinson and F.J. van Steenwijk. "Infinite resistive lattices," Am. J. 
Phys. 67, 486-492 (1999).
[3] Jozsef Cserti, "Application of the lattice Green's function for calculating 
the resistance of infinite networks of resistors," Am. J. Phys. 68, 896-906 
(2000)
[4] A.H. Zemanian, "Infinite Electrical Networks: A Reprise," IEEE Transraction 
on Circuits and Systems 35 No. 11, 1346-1358 (1988)
[5] P.G. Doyle and J.L. Snell, Random Walks and Electric Networks, (The Carus 
Mathematical Monograph, series 22, The Mathematical Association of America, 
USA, 1999).
[6] Krizysztof Giaro, "A Network of Resistor," Young Physicists Research 
Papers, Instytut Fizyki PAN Warszawa 1998. p 27-37.
[7] I Made Agus Wirawan, "Analysis of Cubic Infinite Network of resistors," 
Proceedings of the Seventh International Competition in Research Projects in 
Physics of High School Students 1998/1999. pp. 33-41 Warszawa 2000







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