Doppler Effect of Nonlinear Waves and Superspirals in Oscillatory Media

Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example, where waves originate from a source exhibiting a back-and-forth movement in radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves (``superspiral''). Using the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonous growth or decay as well as saturation of these modulations away from the source depending on the perturbation frequency. Our findings allow a consistent interpretation of recent experimental observations concerning superspirals and their decay to spatio-temporal chaos.Comment: 4 pages, 4 figure

Hyperpolarizability effects in a Sr optical lattice clock

We report the observation of the higher order frequency shift due to the trapping field in a $^{87}$Sr optical lattice clock. We show that at the magic wavelength of the lattice, where the first order term cancels, the higher order shift will not constitute a limitation to the fractional accuracy of the clock at a level of $10^{-18}$. This result is achieved by operating the clock at very high trapping intensity up to $400$kW/cm$^2$ and by a specific study of the effect of the two two-photon transitions near the magic wavelength

Accurate spectroscopy of Sr atoms

We report the frequency measurement with an accuracy in the 100 kHz range of several optical transitions of atomic Sr : $^1S_0- ^3P_1$ at 689 nm, $^3P_1- ^3S_1$ at 688 nm and $^3P_0- ^3S_1$ at 679 nm. Measurements are performed with a frequency chain based on a femtosecond laser referenced to primary frequency standards. They allowed the indirect determination with a 70 kHz uncertainty of the frequency of the doubly forbidden 5s^2^1S_0- 5s5p^3P_0 transition of $^{87}$Sr at 698 nm and in a second step its direct observation. Frequency measurements are performed for $^{88}$Sr and $^{87}$Sr, allowing the determination of $^3P_0$, $^3P_1$ and $^3S_1$ isotope shifts, as well as the $^3S_1$ hyperfine constants.Comment: 12 pages, 16 figure

Measurement of the 3s3p 3P1 lifetime in magnesium using a magneto-optical trap

We demonstrate an accurate method for measuring the lifetime of long-lived metastable magnetic states using a magneto-optical trap (MOT). Through optical pumping, the metastable (3s3p) (3)P(1) level is populated in a standard MOT. During the optical pumping process, a fraction of the population is captured in the magnetic quadrupole field of the MOT. When the metastable atoms decay to the (3s(2)) (1)S(0) ground state they are recaptured into the MOT. In this system no alternative cascading transition is possible. The lifetime of the metastable level is measured directly as an exponential load time of the MOT. We have experimentally tested our method by measuring the lifetime of the (3s3p) (3)P(1) of (24)Mg. This lifetime has been measured numerous times previously, but with quite different results. Using our method we find the (3s3p) (3)P(1) lifetime to be (4.4 +/- 0.2) ms. Theoretical values point toward a lower value for the lifetime

Forecasting the SST space-time variability of the Alboran Sea with genetic algorithms

We propose a nonlinear ocean forecasting technique based on a combination of genetic algorithms and empirical orthogonal function (EOF) analysis. The method is used to forecast the space-time variability of the sea surface temperature (SST) in the Alboran Sea. The genetic algorithm finds the equations that best describe the behaviour of the different temporal amplitude functions in the EOF decomposition and, therefore, enables global forecasting of the future time-variability.Comment: 15 pages, 3 figures; latex compiled with agums.st

On elliptic solutions of the cubic complex one-dimensional Ginzburg-Landau equation

The cubic complex one-dimensional Ginzburg-Landau equation is considered. Using the Hone's method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing wave nor elliptic travelling wave solutions. This result amplifies the Hone's result, that this equation has no elliptic travelling wave solutions.Comment: LaTeX, 12 page

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

Spatial Modeling of Vesicle Transport and the Cytoskeleton: The Challenge of Hitting the Right Road

The membrane trafficking machinery provides a transport and sorting system for many cellular proteins. We propose a mechanistic agent-based computer simulation to integrate and test the hypothesis of vesicle transport embedded into a detailed model cell. The method tracks both the number and location of the vesicles. Thus both the stochastic properties due to the low numbers and the spatial aspects are preserved. The underlying molecular interactions that control the vesicle actions are included in a multi-scale manner based on the model of Heinrich and Rapoport (2005). By adding motor proteins we can improve the recycling process of SNAREs and model cell polarization. Our model also predicts that coat molecules should have a high turnover at the compartment membranes, while the turnover of motor proteins has to be slow. The modular structure of the underlying model keeps it tractable despite the overall complexity of the vesicle system. We apply our model to receptor-mediated endocytosis and show how a polarized cytoskeleton structure leads to polarized distributions in the plasma membrane both of SNAREs and the Ste2p receptor in yeast. In addition, we can couple signal transduction and membrane trafficking steps in one simulation, which enables analyzing the effect of receptor-mediated endocytosis on signaling

BioSimulators: a central registry of simulation engines and services for recommending specific tools

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed through a distinct interface. To help investigators find and use simulation tools, we developed BioSimulators (https://biosimulators.org), a central registry of the capabilities of simulation tools and consistent Python, command-line and containerized interfaces to each version of each tool. The foundation of BioSimulators is standards, such as CellML, SBML, SED-ML and the COMBINE archive format, and validation tools for simulation projects and simulation tools that ensure these standards are used consistently. To help modelers find tools for particular projects, we have also used the registry to develop recommendation services. We anticipate that BioSimulators will help modelers exchange, reproduce, and combine simulations