On stability of switched differential algebraic systems – conditions and applications

We obtain an efficient parametrization that ensures stability of switched linear systems under arbitrary switching. Apart from stability analysis, our results are useful for addressing several important system theoretic problems, e.g. designing controllers that ensure robustness against arbitrary combinations of sensor or actuator failure. We illustrate our results by considering control of a distillation column

Theoretical Characterization of the Interface in a Nonequilibrium Lattice System

The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by a kinetic Ising--like model system with nonequilibrium steady states is studied. The system is maintained out of equilibrium by perturbing the familiar spin--flip dynamics at temperature T with completely--random flips; one may interpret these as ideally simulating some (dynamic) impurities. We find evidence that, in the present case, the nonequilibrium mechanism adds to the basic thermal one resulting on a renormalization of microscopic parameters such as the probability of interfacial broken bonds. On this assumption, we develop theory for the nonequilibrium "surface tension", which happens to show a non--monotonous behavior with a maximum at some finite T. It ensues, in full agreement with Monte Carlo simulations, that interface fluctuations differ qualitatively from the equilibrium case, e.g., the interface remains rough at zero--T. We discuss on some consequences of these facts for nucleation theory, and make some explicit predictions concerning the nonequilibrium droplet structure.Comment: 10 pages, 7 figures, submitted to Phys. Re

Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev stability, and we explain the transitions between these. We apply our results to the Kirchhoff model for the motion of an axisymmetric underwater vehicle, and we numerically study dissipation induced instability of KAM stable relative equilibria for this system.Comment: Minor revisions. Typographical errors correcte

More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds

In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained form of the Lax connection is that it is invariant under Z_4-transformations of the superisometry generators and the spectral parameter. This demonstrates that the contribution of the non-coset fermions does not spoil the Z_4-symmetry of the super-coset Lax connection which is of crucial importance for the application of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a very similar form. This is because their amount of target-space supersymmetries complement each other to 32=24+8, the maximal number of 10d type II supersymmetries. As a byproduct, this similarity has allowed us to obtain the form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace to all orders in the coset fermions and to the second order in the non-coset ones.Comment: 28 pages; v2: References adde

Temperature Dependence of Facet Ridges in Crystal Surfaces

The equilibrium crystal shape of a body-centered solid-on-solid (BCSOS) model on a honeycomb lattice is studied numerically. We focus on the facet ridge endpoints (FRE). These points are equivalent to one dimensional KPZ-type growth in the exactly soluble square lattice BCSOS model. In our more general context the transfer matrix is not stochastic at the FRE points, and a more complex structure develops. We observe ridge lines sticking into the rough phase where thesurface orientation jumps inside the rounded part of the crystal. Moreover, the rough-to-faceted edges become first-order with a jump in surface orientation, between the FRE point and Pokrovsky-Talapov (PT) type critical endpoints. The latter display anisotropic scaling with exponent $z=3$ instead of familiar PT value $z=2$.Comment: 12 pages, 19 figure

Type IIB tensionless superstrings in a pp-wave background

We solve the tensionless string in a constant plane wave background and obtain a hugely degenerate spectrum. This is the case for a large class of plane wave backgrounds. We show that the solution can also be derived as a consistent limit of the quantized tensile theory of IIB strings in a pp-wave. This is in contrast to the situation for several other backgrounds.Comment: 1+17 pages, LaTeX, minor corrections, added new reference

Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality

We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti-de Sitter space and the Schroedinger spacetime. These models can be obtained via T-duality from integrable models. We construct an infinite family of non-local conserved charges from the T-dual Lax currents, enhancing the symmetry of warped anti-de Sitter space and the Schroedinger spacetime to sl2(R)+sl2(R).Comment: 29 Pages, 3 appendices. Minor changes: added references, footnot