129,558 research outputs found
Loop equations for multi-cut matrix models
The loop equation for the complex one-matrix model with a multi-cut structure
is derived and solved in the planar limit. An iterative scheme for higher
genus contributions to the free energy and the multi-loop correlators is presented
for the two-cut model, where explicit results are given up to and including
genus two. The double-scaling limit is analyzed and the relation to the
one-cut solution of the hermitian and complex one-matrix model is discussed
Geometrically Induced Phase Transitions at Large N
Utilizing the large N dual description of a metastable system of branes and
anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau
threefold, we study phase transitions induced by changing the positions of the
S^2's. At leading order in 1/N the effective potential for this system is
computed by the planar limit of an auxiliary matrix model. Beginning at the two
loop correction, the degenerate vacuum energy density of the discrete confining
vacua split, and a potential is generated for the axion. Changing the relative
positions of the S^2's causes discrete jumps in the energetically preferred
confining vacuum and can also obstruct direct brane/anti-brane annihilation
processes. The branes must hop to nearby S^2's before annihilating, thus
significantly increasing the lifetime of the corresponding non-supersymmetric
vacua. We also speculate that misaligned metastable glueball phases may
generate a repulsive inter-brane force which stabilizes the radial mode present
in compact Calabi-Yau threefolds.Comment: 47 pages, 7 figure
Universal correlators for multi-arc complex matrix models
The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the Hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result for one arc. The basic tool is the iterative solution of the loop equation for the complex matrix model with multiple arcs, which provides all multi-loop correlators up to an arbitrary genus. Explicit results for genus one are given for any number of arcs. The two-arc solution is investigated in detail, including the double-scaling limit. In addition universal expressions for the string susceptibility are given for both the complex and Hermitian model
Control of Towing Kites for Seagoing Vessels
In this paper we present the basic features of the flight control of the
SkySails towing kite system. After introduction of coordinate definitions and
basic system dynamics we introduce a novel model used for controller design and
justify its main dynamics with results from system identification based on
numerous sea trials. We then present the controller design which we
successfully use for operational flights for several years. Finally we explain
the generation of dynamical flight patterns.Comment: 12 pages, 18 figures; submitted to IEEE Trans. on Control Systems
Technology; revision: Fig. 15 corrected, minor text change
Entropy of Operator-valued Random Variables: A Variational Principle for Large N Matrix Models
We show that, in 't Hooft's large N limit, matrix models can be formulated as
a classical theory whose equations of motion are the factorized
Schwinger--Dyson equations. We discover an action principle for this classical
theory. This action contains a universal term describing the entropy of the
non-commutative probability distributions. We show that this entropy is a
nontrivial 1-cocycle of the non-commutative analogue of the diffeomorphism
group and derive an explicit formula for it. The action principle allows us to
solve matrix models using novel variational approximation methods; in the
simple cases where comparisons with other methods are possible, we get
reasonable agreement.Comment: 45 pages with 1 figure, added reference
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