TY - JOUR

T1 - Possible global minimum lattice configurations for Thomson’s problem of charges on a sphere

AU - Altschuler, Eric Lewin

AU - Williams, Timothy J.

AU - Ratner, Edward R.

AU - Tipton, Robert

AU - Stong, Richard

AU - Dowla, Farid

AU - Wooten, Frederick

PY - 1997/4/7

Y1 - 1997/4/7

N2 - What configuration of N point charges on a conducting sphere minimizes the Coulombic energy? J. J. Thomson posed this question in 1904. For N ≤ 112, numerical methods have found apparent global minimum-energy configurations; but the number of local minima appears to grow exponentially with N, making many such methods impractical. Here we describe a topological/numerical procedure that we believe gives the global energy minimum lattice configuration for N of the form N = 10(m2+n2+mn)+2(m, n positive integers). For those N with more than one lattice, we give a rule to choose the minimum one.

AB - What configuration of N point charges on a conducting sphere minimizes the Coulombic energy? J. J. Thomson posed this question in 1904. For N ≤ 112, numerical methods have found apparent global minimum-energy configurations; but the number of local minima appears to grow exponentially with N, making many such methods impractical. Here we describe a topological/numerical procedure that we believe gives the global energy minimum lattice configuration for N of the form N = 10(m2+n2+mn)+2(m, n positive integers). For those N with more than one lattice, we give a rule to choose the minimum one.

UR - http://www.scopus.com/inward/record.url?scp=0000142722&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.78.2681

DO - 10.1103/PhysRevLett.78.2681

M3 - Article

AN - SCOPUS:0000142722

SN - 0031-9007

VL - 78

SP - 2681

EP - 2685

JO - Physical Review Letters

JF - Physical Review Letters

IS - 14

ER -