Hybridization for stability verification of nonlinear switched systems

We propose a novel hybridization method for stability analysis that over-approximates nonlinear dynamical systems by switched systems with linear inclusion dynamics. We observe that existing hybridization techniques for safety analysis that over-approximate nonlinear dynamical systems by switched affine inclusion dynamics and provide fixed approximation error, do not suffice for stability analysis. Hence, we propose a hybridization method that provides a state-dependent error which converges to zero as the state tends to the equilibrium point. The crux of our hybridization computation is an elegant recursive algorithm that uses partial derivatives of a given function to obtain upper and lower bound matrices for the over-approximating linear inclusion. We illustrate our method on some examples to demonstrate the application of the theory for stability analysis. In particular, our method is able to establish stability of a nonlinear system which does not admit a polynomial Lyapunov function

Formal synthesis of stabilizing controllers for periodically controlled linear switched systems

In this paper, we address the problem of synthesizing periodic switching controllers for stabilizing a family of linear systems. Our broad approach consists of constructing a finite game graph based on the family of linear systems such that every winning strategy on the game graph corresponds to a stabilizing switching controller for the family of linear systems. The construction of a (finite) game graph, the synthesis of a winning strategy and the extraction of a stabilizing controller are all computationally feasible. We illustrate our method on an example

Exchange coupling in transition-metal nano-clusters on Cu(001) and Cu(111) surfaces

We present results of density-functional calculations on the magnetic properties of Cr, Mn, Fe and Co nano-clusters (1 to 9 atoms large) supported on Cu(001) and Cu(111). The inter-atomic exchange coupling is found to depend on competing mechanisms, namely ferromagnetic double exchange and antiferromagnetic kinetic exchange. Hybridization-induced broadening of the resonances is shown to be important for the coupling strength. The cluster shape is found to weaken the coupling via a mechanism that comprises the different orientation of the atomic d-orbitals and the strength of nearest-neighbour hopping. Especially in Fe clusters, a correlation of binding energy and exchange coupling is also revealed

Engineering elliptical spin-excitations by complex anisotropy fields in Fe adatoms and dimers on Cu(111)

We investigate the dynamics of Fe adatoms and dimers deposited on the Cu(111) metallic surface in the presence of spin-orbit coupling, within time-dependent density functional theory. The \textit{ab initio} results provide material-dependent parameters that can be used in semiclassical approaches, which are used for insightful interpretations of the excitation modes. By manipulating the surroundings of the magnetic elements, we show that elliptical precessional motion may be induced through the modification of the magnetic anisotropy energy. We also demonstrate how different kinds of spin precession are realized, considering the symmetry of the magnetic anisotropy energy, the ferro- or antiferromagnetic nature of the exchange coupling between the impurities, and the strength of the magnetic damping. In particular, the normal modes of a dimer depend on the initial magnetic configuration, changing drastically by going from a ferromagnetic metastable state to the antiferromagnetic ground state. By taking into account the effect of the damping into their resonant frequencies, we reveal that an important contribution arises for strongly biaxial systems and specially for the antiferromagnetic dimers with large exchange couplings. Counter intuitively, our results indicate that the magnetic damping influences the quantum fluctuations by decreasing the zero-point energy of the system

Ultrafast switching of composite order in A3_3C60_{60}

We study the controlled manipulation of the Jahn-Teller metal state of fulleride compounds using nonequilibrium dynamical mean field theory. This anomalous metallic state is a spontaneous orbital-selective Mott phase, which is characterized by one metallic and two insulating orbitals. Using protocols based on transiently reduced hopping amplitudes or periodic electric fields, we demonstrate the possibility to switch orbitals between Mott insulating and metallic on a sub-picosecond timescale, and to rotate the order parameter between three equivalent states that can be distinguished by their anisotropic conductance. The Jahn-Teller metal phase of alkali-doped fullerides thus provides a promising platform for ultrafast persistent memory devices

Compressed Sensing - A New mode of Measurement

After introducing the concept of compressed sensing as a complementary measurement mode to the classical Shannon-Nyquist approach, I discuss some of the drivers, potential challenges and obstacles to its implementation. I end with a speculative attempt to embed compressed sensing as an enabling methodology within the emergence of data-driven discovery. As a consequence I predict the growth of non-nomological sciences where heuristic correlations will find applications but often bypass conventional pure basic and use-inspired basic research stages due to the lack of verifiable hypotheses

Non-equilibrium steady state in a periodically driven Kondo model

We investigate the Kondo model with time-dependent couplings that are periodically switched on and off. On the Toulouse line we derive exact analytical results for the spin dynamics in the steady state that builds up after an infinite number of switching periods. Remarkably, the algebraic long time behavior of the spin-spin correlation function remains completely unaffected by the driving. In the limit of slow driving the dynamics become equivalent to that of a single interaction quench. In the limit of fast driving one can show that the steady state cannot be described by some effective equilibrium Hamiltonian since a naive implementation of the Trotter formula gives wrong results. As a consequence, the steady state in the limit of fast switching serves as an example for the emergence of new quantum states not accessible in equilibrium.Comment: 13 pages, 4 figures; minor changes, version as publishe