On a magnetic characterization of spectral minimal partitions
نویسندگان
چکیده
منابع مشابه
Spectral Minimal Partitions for a Family of Tori
We study partitions of the two-dimensional flat torus (R/Z) × (R/bZ) into k domains, with b a real parameter in (0, 1] and k an integer. We look for partitions which minimize the energy, defined as the largest first eigenvalue of the Dirichlet Laplacian on the domains of the partition. We are in particular interested in the way these minimal partitions change when b is varied. We present here a...
متن کاملA note on limit shapes of minimal difference partitions
We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. This paper is dedicated to Professor Leonid Pastur for his 70th anniversary. A partition of a natural integer E [1] is a decomposition of E as a sum of a nonincreasing sequence of positive integers {hj}, i.e., E = ∑ j hj such that hj ≥ hj+1, for j = 1, 2 . . .....
متن کاملMinimal r-Complete Partitions
A minimal r-complete partition of an integer m is a partition of m with as few parts as possible, such that all the numbers 1, . . . , rm can be written as a sum of parts taken from the partition, each part being used at most r times. This is a generalization of M-partitions (minimal 1-complete partitions). The number of M-partitions of m was recently connected to the binary partition function ...
متن کاملA Convex Approach to Minimal Partitions
We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically, we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solution: we give some arguments to explain why it should be so, and also discuss some situation wher...
متن کاملA convex approach for computing minimal partitions
We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically, we describe an algorithm and show some results. In most cases, our relaxed problem nds a correct (approximate) solution: we give some arguments to explain why it should be so, and also discuss some situation where it fails.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2013
ISSN: 1435-9855
DOI: 10.4171/jems/415