The  Weizmann  Institute  of  Science
                  Faculty of Mathematics and Computer Science
 
                 Mathematical Analysis and Applications Seminar
 
                     Lecture Hall, Room 1, Ziskind Building
                          on Tuesday, January 18, 2011
                                  11:00 - noon
 
                                    Ram Band
                               Bristol University
 
                                 will speak on
 
                  Finding the nodal points on a quantum graph
 
Abstract:
The investigation of nodal patterns on manifolds has began already in the 19th
century by the pioneering work of Chladni on the nodal structures of vibrating
plates.  Sturm's oscillation theorem states that the $n$-th vibrational mode of
a string has $n-1$ nodal points equally distributed on the string.  However,
finding the location of the nodal points on a general quantum graphs is far
less trivial task. This is despite a quantum graph being nothing more than a
structure of strings attached to each other.  We manage to study the number of
nodal points and their location without solving the full eigenvalue problem on
the graph.  This is done by defining an energy function on the space of nodal
points' possible locations and examining its critical points.
 
This work follows the approach taken by Helffer, Hoffmann-Ostenhof and
Terracini to study Schroedinger operators on two-dimensional domains.  Quantum
graphs obey the analogue of the results by Helffer et al, and are used to
further generalize them.
 
This is a joint work with Gregory Berkolaiko, Hillel Raz and Uzy Smilansky.
 
            Mathematical Analysis and Applications Seminar Web Page:
               <http://www.wisdom.weizmann.ac.il/~vered/analsem.html>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Diana Mandelik   <diana.mandelik@weizmann.ac.il>