Converging Perturbative Solutions of the Schroedinger Equation for a Two-Level System with a Hamiltonian Depending Periodically on Time

We study the Schroedinger equation of a class of two-level systems under the action of a periodic time-dependent external field in the situation where the energy difference 2epsilon between the free energy levels is sufficiently small with respect to the strength of the external interaction. Under suitable conditions we show that this equation has a solution in terms of converging power series expansions in epsilon. In contrast to other expansion methods, like in the Dyson expansion, the method we present is not plagued by the presence of ``secular terms''. Due to this feature we were able to prove absolute and uniform convergence of the Fourier series involved in the computation of the wave functions and to prove absolute convergence of the epsilon-expansions leading to the ``secular frequency'' and to the coefficients of the Fourier expansion of the wave function

Orion Spacecraft MMOD Protection Design and Assessment

The Orion spacecraft will replace the Space Shuttle Orbiter for American and international partner access to the International Space Station by 2015 and, afterwards, for access to the moon for initial sorties and later for extended outpost visits as part of the Constellation Exploration Initiative. This work describes some of the efforts being undertaken to ensure that the Constellation Program, Orion Crew Exploration Vehicle design will meet or exceed the stringent micrometeoroid and orbital debris (MMOD) requirements set out by NASA when exposed to the environments encountered with these missions. This paper will provide a brief overview of the approaches being used to provide MMOD protection to the Orion vehicle and to assess the spacecraft for compliance to the Constellation Program s MMOD requirements

Progress with the Upgrade of the SPS for the HL-LHC Era

The demanding beam performance requirements of the High Luminosity (HL-) LHC project translate into a set of requirements and upgrade paths for the LHC injector complex. In this paper the performance requirements for the SPS and the known limitations are reviewed in the light of the 2012 operational experience. The various SPS upgrades in progress and still under consideration are described, in addition to the machine studies and simulations performed in 2012. The expected machine performance reach is estimated on the basis of the present knowledge, and the remaining decisions that still need to be made concerning upgrade options are detailed.Comment: 3 p. Presented at 4th International Particle Accelerator Conference (IPAC 2013

Identification of target-specific bioisosteric fragments from ligand-protein crystallographic data

Bioisosteres are functional groups or atoms that are structurally different but that can form similar intermolecular interactions. Potential bioisosteres were identified here from analysing the X-ray crystallographic structures for sets of different ligands complexed with a fixed protein. The protein was used to align the ligands with each other, and then pairs of ligands compared to identify substructural features with high volume overlap that occurred in approximately the same region of geometric space. The resulting pairs of substructural features can suggest potential bioisosteric replacements for use in lead-optimisation studies. Experiments with 12 sets of ligand-protein complexes from the Protein Data Bank demonstrate the effectiveness of the procedure

A Metric Discrepancy Result With Given Speed

It is known that the discrepancy DN{ kx} of the sequence { kx} satisfies NDN{ kx} = O((log N) (log log N) 1 + ε) a.e. for all ε> 0 , but not for ε= 0. For nk= θk, θ> 1 we have NDN{ nkx} ≦ (Σ θ+ ε) (2 Nlog log N) 1 / 2 a.e. for some 0 0 , but not for ε 0 , there exists a sequence { nk} of positive integers such that NDN{ nkx} ≦ (Σ + ε) Ψ (N) eventually holds a.e. for ε> 0 , but not for ε< 0. We also consider a similar problem on the growth of trigonometric sums. © 2016, Akadémiai Kiadó, Budapest, Hungary

Oscillatory behaviour on a non-autonomous hybrid SIR-Model

We study the impact of some abstract agent intervention on the disease spread modelled by a SIR-model with linear growth infectivity. The intervention is meant to decrease the infectivity, which are activated by a threshold on the number of infected individuals. The coupled model is represented as a nonlinear non-autonomous hybrid system. Stability and reduction results are obtained using the notions of non-autonomous attractors, Bohl exponents, and dichotomy spectrum. Numerical examples are given where the number of infected individuals can oscillate around a equilibrium point or be a succession of bump functions, which are validated with a tool based on the notion of delta-complete decision procedures for solving satisfiability modulo theories problems over the real numbers and bounded delta-reachability. These findings seem to show that hybrid SIR-models are more flexible than standard models and generate a vast set of solution profiles. It also raises questions regarding the possibility of the agent intervention been somehow responsible for the shape and intensity of future outbreaks.publishe

Energy loss of proton and lead beams in the CERN-SPS

The energy loss of an unbunched beam circulating in the CERN-SPS has been obtained from the observed frequency change of a longitudinal Schottky signal. This experiment was carried out for protons at 14, 120 and 270 GeV/c and for lead ions PB82208 at Z .270 GeV/c momentum. The dominant effects which determine the energy loss are synchrotron radiation, ionization of the residual gas and parasitic mode loss in the resistive longitudinal impedance. Since all the protons in a lead nucleus radiate coherently the synchrotron radiation is proportional to Z2 like the other effects. The experimental results are analyzed and the contributions of the individual effects determined. Using an impedance of | Z/n | ~ 12 W gives the best fit through the experimental data

LEP1 operation, 1989-1995

In October 1995, the last run foreseen for dedicated Z production at CERN was performed in LEP, thereby bringing to a close the first phase of operation of the machine. A total luminosity of 200 pb-1 has been delivered to each of the four experiments, which together have recorded the decays of over 20 millions Zs. Machine performance has increased to the extent that a good weekend in 1995 saw as much luminosity delivered as in the whole of 1989. This improvement has been made possible by a combination of several things. Over and above general operational expertise, special care went into the treatment and stabilisation of the closed orbit in order to obtain reproducible high performances with vertical beam-beam tune shifts exceeding values of xy = 0.04. Both Pretzel and Bunch Train schemes have been introduced to double the number of bunches, and high-tune optics have been developed to produce low transverse emittances which allow operation at the beam-beam limit throughout physics runs. Included in the integrated luminosity are data taken off the peak of the Z resonance, to allow precise determination of the mass and width of this particle. Accurate measurements of the beam energy during these runs have brought to the fore some unusual effects

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request