Dynamic Energy Management

We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to the case of optimizing dynamic power flows, i.e., power flows that change with time over a horizon. We leverage this to develop a real-time control strategy, model predictive control, which at each time step solves a dynamic power flow optimization problem, using forecasts of future quantities such as demands, capacities, or prices, to choose the current power flow values. Finally, we consider a useful extension of model predictive control that explicitly accounts for uncertainty in the forecasts. We mirror our framework with an object-oriented software implementation, an open-source Python library for planning and controlling power flows at any scale. We demonstrate our method with various examples. Appendices give more detail about the package, and describe some basic but very effective methods for constructing forecasts from historical data.Comment: 63 pages, 15 figures, accompanying open source librar

Precision Spectroscopy at Heavy Ion Ring Accelerator SIS300

Unique spectroscopic possibilities open up if a laser beam interacts with relativistic lithium-like ions stored in the heavy ion ring accelerator SIS300 at the future Facility for Antiproton and Ion Research FAIR in Darmstadt, Germany. At a relativistic factor gamma = 36 the 2P 1/2 level can be excited from the 2S 1/2 ground state for any element with frequency doubled dye-lasers in collinear geometry. Precise transition energy measurements can be performed if the fluorescence photons, boosted in forward direction into the X-ray region, are energetically analyzed with a single crystal monochromator. The hyperfine structure can be investigated at the 2P 1/2 - 2S 1/2 transition for all elements and at the 2P 3/2 - 2S 1/2 transition for elements with Z < 50. Isotope shifts and nuclear moments can be measured with unprecedented precision, in principle even for only a few stored radioactive species with known nuclear spin. A superior relative line width in the order of 5E-7 may be feasible after laser cooling, and even polarized external beams may be prepared by optical pumping

The Standard Model in Strong Fields: Electroweak Radiative Corrections for Highly Charged Ions

Electroweak radiative corrections to the matrix elements $<ns_{1/2}|{\hat H}_{PNC}|n'p_{1/2}>$ are calculated for highly charged hydrogenlike ions. These matrix elements constitute the basis for the description of the most parity nonconserving (PNC) processes in atomic physics. The operator ${\hat H}_{PNC}$ represents the parity nonconserving relativistic effective atomic Hamiltonian at the tree level. The deviation of these calculations from the calculations valid for the momentum transfer $q^{2}=0$ demonstrates the effect of the strong field, characterized by the momentum transfer $q^{2}=m_{e}^{2}$ ($m_{e}$ is the electron mass). This allows for a test of the Standard Model in the presence of strong fields in experiments with highly charged ions.Comment: 27 LaTex page

Adiabatic Pair Creation

We give here the proof that pair creation in a time dependent potentials is possible. It happens with probability one if the potential changes adiabatically in time and becomes overcritical, that is when an eigenvalue enters the upper spectral continuum. The potential may be assumed to be zero at large negative and positive times. The rigorous treatment of this effect has been lacking since the pioneering work of Beck, Steinwedel and Suessmann in 1963 and Gershtein and Zeldovich in 1970.Comment: 53 pages, 1 figure. Editorial changes on page 22 f

Screened self-energy correction to the 2p3/2-2s transition energy in Li-like ions

We present an ab initio calculation of the screened self-energy correction for (1s)^2 2p3/2 and (1s)^2 2s states of Li-like ions with nuclear charge numbers in the range Z = 12-100. The evaluation is carried out to all orders in the nuclear-strength parameter Z \alpha. This investigation concludes our calculations of all two-electron QED corrections for the 2p3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions

Evaluation of the low-lying energy levels of two- and three-electron configurations for multi-charged ions

Accurate QED evaluations of the one- and two-photon interelectron interaction for low lying two- and three-electron configurations for ions with nuclear charge numbers $60\le Z \le 93$ are performed. The three-photon interaction is also partly taken into account. The Coulomb gauge is employed. The results are compared with available experimental data and with different calculations. A detailed investigation of the behaviour of the energy levels of the configurations $1s_{1/2}2s_{1/2} {}^1 S_0$, $1s_{1/2}2p_{1/2} {}^3 P_0$ near the crossing points Z=64 and Z=92 is carried out. The crossing points are important for the future experimental search for parity nonconserving (PNC) effects in highly charged ions

Relativistic nuclear recoil corrections to the energy levels of hydrogen-like and high ZZ lithium like atoms in all orders in αZ\alpha Z

The relativistic nuclear recoil corrections to the energy levels of low-laying states of hydrogen-like and high $Z$ lithium-like atoms in all orders in $\alpha Z$ are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low $Z$ the results of the calculation are in good agreement with the $\alpha Z$ -expansion results. It is found that the nuclear recoil contribution, additional to the Salpeter's one, to the Lamb shift ($n=2$) of hydrogen is $-1.32(6)\,kHz$. The total nuclear recoil correction to the energy of the $(1s)^{2}2p_{\frac{1}{2}}-(1s)^{2}2s$ transition in lithium-like uranium constitutes $-0.07\,eV$ and is largely made up of QED contributions.Comment: 19 pages, latex, accepted for publication in Phys. Rev.

Constructing seasonally adjusted data with time-varying confidence intervals

Seasonal adjustment methods transform observed time series data into estimated data, where these estimated data are constructed such that they show no or almost no seasonal variation. An advantage of model-based methods is that these can provide confidence intervals around the seasonally adjusted data. One particularly useful time series model for seasonal adjustment is the basic structural time series [BSM] model. The usual premise of the BSM is that the variance of each of the components is constant. In this paper we address the possibility that the variance of the trend component in a macro-economic time series in some way depends on the business cycle. One reason for doing so is that one can expect that there is more uncertainty in recession periods. We extend the BSM by allowing for a business-cycle dependent variance in the level equation. Next we show how this affects the confidence intervals of seasonally adjusted data. We apply our extended BSM to monthly US unemployment and we show that the estimated confidence intervals for seasonally adjusted unemployment change with past changes in the oil price

Relativistic quantum dynamics in strong fields: Photon emission from heavy, few-electron ions

Recent progress in the study of the photon emission from highly-charged heavy ions is reviewed. These investigations show that high-$Z$ ions provide a unique tool for improving the understanding of the electron-electron and electron-photon interaction in the presence of strong fields. Apart from the bound-state transitions, which are accurately described in the framework of Quantum Electrodynamics, much information has been obtained also from the radiative capture of (quasi-) free electrons by high-$Z$ ions. Many features in the observed spectra hereby confirm the inherently relativistic behavior of even the simplest compound quantum systems in Nature.Comment: Version 18/11/0