2016, Klein, Olaf, Recupero, Vincenzo

Sweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of rate independent operator. As a particular case we get the so called play operator, which is a typical example of a hysteresis operator. The continuity properties of these operators were studied in several works. In this note we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide counterexamples showing that for all BV-formulations of the sweeping process the corresponding solution operator is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1-topology. This is at variance with the play operator which has a BV-extension that is continuous in this case.

2016, Reichelt, Sina

We derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling the microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms and we allow for different diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1 other species may diffuse with the order of the characteristic microstructure-length scale. We consider an effective system, which is rigorously obtained via two-scale convergence, and we derive quantitative error estimates.

2016, Hellmann, F., Kamiński, W., Kostecki, R.P.

2015, Lindenfelser, F., Keitch, B., Kienzler, D., Bykov, D., Uebel, P., Schmidt, M.A., Russell, P.St.J., Home, J.P.

We demonstrate a surface-electrode ion trap fabricated using techniques transferred from the manufacture of photonic-crystal fibres. This provides a relatively straightforward route for realizing traps with an electrode structure on the 100 micron scale with high optical access. We demonstrate the basic functionality of the trap by cooling a single ion to the quantum ground state, allowing us to measure a heating rate from the ground state of 787 ± 24 quanta/s. Variation of the fabrication procedure used here may provide access to traps in this geometry with trap scales between 100 μm and 10 μm

2012, Cerda-Méndez, E.A., Krizhanovskii, D.N., Biermann, K., Hey, R., Skolnick, M.S., Santos, P.V.

We study the spatial coherence of polariton condensates subjected to coherent modulation by a one-dimensional tunable acoustic potential.We use an interferometric technique to measure the amplitude and phase of the macroscopic condensate wavefunction. By increasing the acoustic modulation amplitude, we track the transition from the extended wavefunction of the unperturbed condensate to a regime where the wavefunction is spatially modulated and then to a fully confined regime, where independent condensates form at the minima of the potential with negligible particle tunneling between adjacent sites.

2016, Lazzaroni, Giuliano, Rossi, Riccarda, Thomas, Marita, Toader, Rodica

This note deals with the analysis of a model for partial damage, where the rate- independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1, 2] with the methods from Lazzaroni/Rossi/Thomas/Toader [3]. The present analysis encompasses, differently from [2], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [3], a nonconstant heat capacity and a time-dependent Dirichlet loading.

2015, Gentile, Paola, Cuoco, Mario, Ortix, Carmine

We prove that curvature effects in low-dimensional nanomaterials can promote the generation of topological states of matter by considering the paradigmatic example of quantum wires with Rashba spin-orbit coupling, which are bent in a nanoscale periodic serpentine structure. The effect of the periodic curvature generally results in the appearance of insulating phases with a corresponding novel butterfly spectrum characterized by the formation of finite measure complex regions of forbidden energies. When the Fermi energy lies in the gaps, the system displays localized end states protected by topology. We further show that for certain superstructure periods the system possesses topologically nontrivial insulating phases at half filling. Our results suggest that the local curvature and the topology of the electronic states are inextricably intertwined in geometrically deformed nanomaterials.

2016, Pimenov, Alexander, Rachinskii, Dmitrii

We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically.

2015, Zimmermann, Henri, Eilzer, Sebastian, Eichmann, Ulli

We investigated the principal quantum number n distribution of excited states resulting from the interaction of Helium with strong, short laser pulses. We find excellent agreement with predictions of the semiclassical frustrated tunneling ionization (FTI) model [1] as well as fully quantum mechanical calculations. Furthermore, the excitation process directly populates triplet excited states due to the breakdown of the Russel-Saunders coupling scheme for high orbital angular momentum l states of Helium, which are predominantly populated in the strong laser field.

2011, Hrauda, N., Zhang, J., Wintersberger, E., Etzelstorfer, T., Mandl, B., Stangl, J., Carbone, D., Holý, V., Jovanović, V., Biasotto, C., Nanver, L.K., Moers, J., Grützmacher, D., Bauer, G.

For advanced electronic, optoelectronic, or mechanical nanoscale devices a detailed understanding of their structural properties and in particular the strain state within their active region is of utmost importance. We demonstrate that X-ray nanodiffraction represents an excellent tool to investigate the internal structure of such devices in a nondestructive way by using a focused synchotron X-ray beam with a diameter of 400 nm. We show results on the strain fields in and around a single SiGe island, which serves as stressor for the Si-channel in a fully functioning Si-metal-oxide semiconductor field-effect transistor.