Cubic Nonlinear Schrödinger Equation on Three Dimensional Balls with Radial Data

We prove wellposedness of the Cauchy problem for the cubic nonlinear Schrödinger equation with Dirichlet boundary conditions and radial data on 3D balls. The main argument is based on a bilinear eigenfunction estimate and the use of X ^{s, b} spaces. The last part presents a first attempt to study the non radial case. We prove bilinear estimates for the linear Schrödinger flow with particular initial data.     

Self-consistent relaxation-time models in quantum mechanics

ABSTRACT. This paper is concerned with the relaxation-time von Neumann- Poisson (or quantum Liouville-Poisson) equation in three spatial dimensions which describes the self-consistent time evolution of an open quantum me- chanical system that includes some relaxation mechanism. This model and the equivalent relaxation-time Wigner-Poisson system play an important role in the simulation of quantum semiconductor devices. For initial density matrices with finite kinetic energy, we prove that this problem, formulated in the space of Hermitian trace class operators, admits a unique global strong solution. A key ingredient for our analysis is a new generalization of the Lieb-Thirring inequality for density matrix operators.     

Capture into resonance and escape from it in a forced nonlinear pendulum

We study the dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the unperturbed pendulum’s oscillations, the pendulum can be captured into resonance. The captured pendulum oscillates in such a way that the resonance is preserved, and the amplitude of the oscillations accordingly grows. We consider this problem in the frames of a standard Hamiltonian approach to resonant phenomena in slow-fast Hamiltonian systems developed earlier, and evaluate the probability of capture into resonance. If the system passes through resonance at small enough initial amplitudes of the pendulum, the capture occurs with necessity (so-called autoresonance). In general, the probability of capture varies between one and zero, depending on the initial amplitude. We demonstrate that a pendulum captured at small values of its amplitude escapes from resonance in the domain of oscillations close to the separatrix of the pendulum, and evaluate the amplitude of the oscillations at the escape.     

Modelling and analysis of the non-iterative coupling process for co-simulation

Concerning non-iterative co-simulation, stepwise extrapolation of coupling signals is required to solve an overall system of interconnected subsystems. Each extrapolation is some kind of estimation and is directly associated with an estimation error. The introduced disturbance depends significantly on the macro-step size, i.e. the coupling step size, and influences the entire system behaviour. In addition, for synchronization purposes, sampling of the coupling signals can cause aliasing. Instead of analysing the coupling effects in the time domain, as it is commonly practised, we concentrate on a model-based approach to gain more insight into the coupling process. In this work, we consider commonly used polynomial extrapolation techniques and analyse them in the frequency domain. Based on this system-oriented point of view of the coupling process, a relation between the coupling signals and the macro-step size is available. In accordance to the dynamics of the interconnected subsystems, the model-based relation is used to select the most critical parameter, i.e. the macro-step size. Besides a ‘rule of thumb’ for meaningful step-size selection, a co-simulation benchmark example describing a two degree of freedom (2-DOF) mechanical system is used to demonstrate the advantages of modelling and the efficiency of the proposed method.     

Neutron bound beta-decay: BOB

Frozen solution samples were made from gold chloride and KAu(CN)₂ solvated with TBP/xylene. The ¹⁹⁷Au M?ssbauer parameters were similar to those same species as frozen solutions or adsorbed onto activated carbon. Solvated samples from EuO dissolved in HCl or H₂SO₄ and frozen gave characteristic Eu(III) spectra. All the spectra were consistent with bonding to the TBP being through hydronium ions or water molecules.     

Mössbauer studies of subfossil oak

With the PANDA experiment at the FAIR facility in Darmstadt, Germany it will be possible to investigate antiproton-nucleus reactions in an energy range not explored so far. This provides opportunities for unique measurements of which some are outlined in this article. Possible modifications of hadron properties in nuclear matter is subject of extensive theoretical and experimental studies. With PANDA it will be possible to extend this kind of studies to the charm sector. A study of particular interest will be to measure the J/Ψ-nucleon dissociation cross-section. This cross-section is relevant for the interpretation of the J/Ψ suppression observed in high energy heavy ion reactions. Further topics include the study of antibaryons in nuclei and short-range nucleon-nucleon correlations.     

Design and simulation of self-biased circulators in the ultra high frequency band

Theoretical models were developed to design self-biased Y-junction circulators operating at ultra high frequency (UHF). The proposed circulator designs consist of insulating nanowires of yttrium iron garnet (YIG) embedded in high permittivity barium-strontium titanate (BSTO) substrates. A design with as many as 10⁵ or greater wires may be considered in its entirety to determine the electromagnetic scattering S-parameters of a circulator design, thus helping to mitigate the computational limitations of the available finite element method (FEM) tools. The approach seeks to represent the nanowires and the BSTO substrate by an equivalent medium with effective properties inclusive of the average saturation magnetization, dynamic demagnetizing fields, and permittivity. The effective medium approach was validated in comparison with the FEM models. Using the proposed approach, a self-biased junction circulator consisting of YIG nanowires embedded in a BSTO substrate was designed and simulated in which the center frequency insertion loss was calculated to be as low as 0.16 dB with isolation of −42.3 dB at 1 GHz. The 20 dB bandwidth was calculated to be 50 MHz. These results suggest that practical self-biased circulators at the UHF band are feasible.     

Biorthogonal systems of functionals and decomposition matrices for minimal splines

For the minimal splines of arbitrary order on a nonuniform grid, a system of linear functionals biorthogonal to the system of coordinate splines is constructed. The matrices of refining and sparsing decompositions are obtained for the spaces of splines of arbitrary order associated with infinite and finite nonuniform grids on an interval and on a segment, respectively.     

On Stochastic Sea of the Standard Map

Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set Ω of full Hausdorff dimension. The set Ω is a topological limit of hyperbolic sets and is accumulated by elliptic islands.