Three-year project studentship, funded by EPSRC, on
Critical points of discrete potentials in the plane and in space.
The successful applicant will carry out research on the above project, leading to the degree of Ph.D.
The research will be supervised by
Professor J.K. Langley, School of Mathematical Sciences, University of Nottingham. Tel. 0115 951 4964.
Brief description of the project: the equilibrium points of the electrostatic field generated by an infinite set of point charges or charged wires correspond, subject to convergence conditions, to critical points of certain potentials. The aim is to determine sufficient conditions for the existence of such critical points. The methods involve complex analysis and potential theory.
To be slightly more precise, assume a distribution of charged wires, each carrying charge density a_k > 0 and perpendicular to the complex plane at z_k. Assume that \sum |a_k/ z_k| is finite. The force acting on a unit charge at z is then proportional to the complex conjugate of
f(z) = \sum a_k/(z - z_k) .
It is conjectured that such meromorphic functions always have zeros, in which case the electrostatic field always has equilibrium points. There are analogous conjectures for point charges in space.
For a more detailed description, see:
Applicants should be EU citizens and hold, or be about to obtain, a good first degree, including courses in real and complex analysis.
For more information please contact Professor Langley.
July 2004: this studentship has been filled. Further applications for PhD work in analysis at Nottingham are, however, always welcome.