Triangle Seminars
Tuesday, 10 Nov 2009
Parametrically forced patterns and quasipatterns
Alastair Rucklidge
(University of Leeds)
Abstract:
The classic Faraday wave experiment consists of a horizontal layer of fluid that spontaneously develops a pattern of standing waves on its surface as it is driven by vertical oscillation with amplitude exceeding a critical value. Faraday wave experiments have consistently produced patterns with remarkably high degrees of symmetry. Quasipatterns, which are quasiperiodic in any spatial direction, are particularly interesting since there is, as yet, no satisfactory theoretical understanding of their formation. We use multi-frequency parametric forcing to investigate the formation of patterns and approximate quasipatterns in a model partial differential equation, which plays the same role for the Faraday wave experiment that the Swift–Hohenberg equation plays for convection. We exploit three-wave resonant interactions to design forcing functions that ought to produce complex patterns, and make quantitative comparisons between weakly nonlinear predictions and the solutions of the PDE. This comparison reveals the limitations of the theory, and we explore ways in which these limitations can be addressed.
Based on:
Design of parametrically forced patterns and quasipatterns, by A.M. Rucklidge and M. Silber. SIAM J. Applied Dynamical Systems 8 (2009) 298-347.
The classic Faraday wave experiment consists of a horizontal layer of fluid that spontaneously develops a pattern of standing waves on its surface as it is driven by vertical oscillation with amplitude exceeding a critical value. Faraday wave experiments have consistently produced patterns with remarkably high degrees of symmetry. Quasipatterns, which are quasiperiodic in any spatial direction, are particularly interesting since there is, as yet, no satisfactory theoretical understanding of their formation. We use multi-frequency parametric forcing to investigate the formation of patterns and approximate quasipatterns in a model partial differential equation, which plays the same role for the Faraday wave experiment that the Swift–Hohenberg equation plays for convection. We exploit three-wave resonant interactions to design forcing functions that ought to produce complex patterns, and make quantitative comparisons between weakly nonlinear predictions and the solutions of the PDE. This comparison reveals the limitations of the theory, and we explore ways in which these limitations can be addressed.
Based on:
Design of parametrically forced patterns and quasipatterns, by A.M. Rucklidge and M. Silber. SIAM J. Applied Dynamical Systems 8 (2009) 298-347.
Posted by: KCL
Directed polymers and the quantum Toda lattice
Neil O'Connell
(Warwick)
Wednesday, 11 Nov 2009
Superconductors and quantum criticality in M-theory
📍 London
Julian Sonner
(Imperial)
Abstract:
Quantum phase transitions imply certain scaling relations among space and time. A subclass of quantum critical systems is in fact invariant under relativstic conformal symmetries. Such theories have recently been studied as a new class of duals in AdS/CFT. I will describe how one can exactly embed so-called holographic superconductors in M-theory and how this embedding has already lead to new insights about the low-temperature behaviour of holgraphic superconductors with an underlying quantum critical point.
Quantum phase transitions imply certain scaling relations among space and time. A subclass of quantum critical systems is in fact invariant under relativstic conformal symmetries. Such theories have recently been studied as a new class of duals in AdS/CFT. I will describe how one can exactly embed so-called holographic superconductors in M-theory and how this embedding has already lead to new insights about the low-temperature behaviour of holgraphic superconductors with an underlying quantum critical point.
Posted by: KCL
Toy Models of CFT/AdS: Matrix Models Approach
Norihiro Iizuka
(Santa Barbara)
Abstract:
We study various matrix models as toy models of the gauge dual of the AdS spacetime
and black hole. I will summarize what these matrix models teach us about
the information paradox and emergence of the light speed limit.
We study various matrix models as toy models of the gauge dual of the AdS spacetime
and black hole. I will summarize what these matrix models teach us about
the information paradox and emergence of the light speed limit.
Posted by: IC
Thursday, 12 Nov 2009
Gauge threshold corrections for local string models
Joseph Conlon
(Oxford)
Abstract:
Local string models are those where Standard Model degrees of freedom arise on a small region inside a large bulk volume. I study threshold effects on gauge coupling running for such models. The Kaplunovsky-Louis formula for locally supersymmetric gauge theories predicts the unification scale should be the bulk winding mode scale, parametrically large than the string scale where divergences are naively cut off. Analysis of explicit string models on orbifold/orientifold geometries confirms this. The winding mode scale arises from the presence of tadpoles uncancelled in the local model. I briefly discuss phenomenological applications to supersymmetry breaking and gauge coupling unification.
Local string models are those where Standard Model degrees of freedom arise on a small region inside a large bulk volume. I study threshold effects on gauge coupling running for such models. The Kaplunovsky-Louis formula for locally supersymmetric gauge theories predicts the unification scale should be the bulk winding mode scale, parametrically large than the string scale where divergences are naively cut off. Analysis of explicit string models on orbifold/orientifold geometries confirms this. The winding mode scale arises from the presence of tadpoles uncancelled in the local model. I briefly discuss phenomenological applications to supersymmetry breaking and gauge coupling unification.
Posted by: QMW