A Dynamic Ion-Atom Hybrid Trap for High-Resolution Cold-Collision Studies

We present a dynamic ion-atom hybrid trap for studies of cold ion-neutral collisions and reactions with a significantly improved energy resolution compared with previous experiments. Our approach is based on pushing a cloud of laser-cooled Rb atoms through a stationary Coulomb crystal of cold ions by using precisely controlled, tunable radiation pressure forces. We demonstrate the tuning of the atom kinetic energies over an interval ranging from 30 mK up to 350 mK with energy spreads as low as 24 mK, inferred from the comparison of experimental time-of-flight measurements with Monte Carlo trajectory simulations. We also demonstrate the first applications of our method to the investigation of chemical reactions. Our development opens up perspectives for accurate studies of the energy dependence of the reaction rates, the dynamics, and the reaction-product ratios of the ion-neutral processes in the cold regime. It also paves the way for the realization of fully energy- and state-controlled cold-collision experiments

Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

Cascade Failure in a Phase Model of Power Grids

We propose a phase model to study cascade failure in power grids composed of generators and loads. If the power demand is below a critical value, the model system of power grids maintains the standard frequency by feedback control. On the other hand, if the power demand exceeds the critical value, an electric failure occurs via step out (loss of synchronization) or voltage collapse. The two failures are incorporated as two removal rules of generator nodes and load nodes. We perform direct numerical simulation of the phase model on a scale-free network and compare the results with a mean-field approximation.Comment: 7 pages, 2 figure

Neuroanatomic Correlates of Female Sexual Dysfunction in Multiple Sclerosis

OBJECTIVE: This study intended to determine associations between alterations of female sexual arousal as well as vaginal lubrication and the site of cerebral multiple sclerosis (MS) lesions. METHODS: In 44 women with MS (mean age: 36.5 ± 9.9 years), we assessed their medical history and evaluated sexual function using the Female Sexual Function Index scores for arousal and vaginal lubrication. We determined potential confounding factors of sexual dysfunction: age; disease duration; physical disability; depression; bladder or urinary dysfunction; and total volume of cerebral lesions. Arousal and lubrication scores were correlated with one another and with potential confounding factors. Cerebral MS lesions were recorded on imaging scans. A voxel-based lesion symptom mapping (VLSM) analysis adjusted for confounding variables was performed correlating cerebral sites of MS lesions with arousal and lubrication scores. RESULTS: Decreased arousal scores correlated with decreased lubrication scores; decreased lubrication scores were associated with bladder or urinary symptoms. Arousal and lubrication scores were not associated with any other variables. Multivariate VLSM analysis, including arousal and lubrication scores as covariables of interest, showed right occipital lesions associated with impaired arousal and left insular lesions associated with decreased lubrication. Impaired lubrication remained associated with left insular lesions after adjustment for bladder or urinary dysfunction. INTERPRETATION: Our data indicate that impaired female sexual arousal is associated with MS lesions in the occipital region, integrating visual information and modulating attention toward visual input. Impaired lubrication correlated with lesions in the left insular region, contributing to mapping and generating visceral arousal states

Dynamics of fully coupled rotators with unimodal and bimodal frequency distribution

We analyze the synchronization transition of a globally coupled network of N phase oscillators with inertia (rotators) whose natural frequencies are unimodally or bimodally distributed. In the unimodal case, the system exhibits a discontinuous hysteretic transition from an incoherent to a partially synchronized (PS) state. For sufficiently large inertia, the system reveals the coexistence of a PS state and of a standing wave (SW) solution. In the bimodal case, the hysteretic synchronization transition involves several states. Namely, the system becomes coherent passing through traveling waves (TWs), SWs and finally arriving to a PS regime. The transition to the PS state from the SW occurs always at the same coupling, independently of the system size, while its value increases linearly with the inertia. On the other hand the critical coupling required to observe TWs and SWs increases with N suggesting that in the thermodynamic limit the transition from incoherence to PS will occur without any intermediate states. Finally a linear stability analysis reveals that the system is hysteretic not only at the level of macroscopic indicators, but also microscopically as verified by measuring the maximal Lyapunov exponent.Comment: 22 pages, 11 figures, contribution for the book: Control of Self-Organizing Nonlinear Systems, Springer Series in Energetics, eds E. Schoell, S.H.L. Klapp, P. Hoeve

Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

Experimental study of the robust global synchronization of Brockett oscillators

International audienceThis article studies the experimental synchronization of a family of a recently proposed oscillator model, i.e. the Brockett oscillator [Brockett, 2013]. Due to its structural property, Brockett oscillator can be considered as a promising benchmark nonlinear model for investigating synchronization and the consensus phenomena. Our experimental setup consists of analog circuit realizations of a network of Brockett oscillators. Experimental results obtained in this work correspond to the prior theoretical findings

Distributed and Constrained H2 \mathcal{H}_2 Control Design via System Level Synthesis and Dual Consensus ADMM

Design of optimal distributed linear feedback controllers to achieve a desired aggregate behavior, while simultaneously satisfying state and input constraints, is a challenging but important problem in many applications, including future power systems with weather-dependent renewable generation. System level synthesis is a recent technique which has been used to reparametrize the optimal control problem as a convex program. However, prior work is restricted to a centralized control design, which lacks robustness to communication failures and disturbances, has high computational cost and does not preserve data privacy of local controllers. The main contribution of this work is to develop a distributed solution to the previous optimal control problem, while incorporating agent-specific and globally coupled constraints in a non-conservative manner. To achieve this, it is first shown that the dual of this problem is a distributed consensus problem. Then, an algorithm is developed based on the alternating direction method of multipliers to solve the dual while recovering a primal solution, and a convergence certificate is provided. Finally, the method's performance is demonstrated on a test case of control design for distributed energy resources that collectively provide stability services to the power grid

The emergence of waves in random discrete systems

Essential criteria for the emergence of wave-like manifestations occurring in an entirely discrete system are identified using a simple model for the movement of particles through a network. The dynamics are entirely stochastic and memoryless involving a birth-death-migration process. The requirements are that the network should have at least three nodes, that migration should have a directional bias, and that the particle dynamics have a non-local dependence. Well defined bifurcations mark transitions between amorphous, wave-like and collapsed states with an intermittent regime between the latter two