The conformal mapping of the interior of the unit circle onto the interior of a class of smooth curves

Outer and inner curved plates and shell shapes optimized by conformal mappin

Low-profile and wearable energy harvester based on plucked piezoelectric cantilevers

The Pizzicato Energy Harvester (EH) introduced the technique of frequency up-conversion to piezoelectric EHs wearable on the lateral side of the knee-joint. The operation principle is to pluck the piezoelectric bimorphs with plectra so that they produce electrical energy during the ensuing mechanical vibrations. The device presented in this work is, in some ways, an evolution of the earlier Pizzicato: it is a significantly more compact and lighter device; the central hub holds 16 piezoelectric bimorphs shaped as trapezoids, which permits a sleek design and potentially increased energy output for the same bimorph area. Plectra were formed by Photochemical Machining of a 100-μm-thick steel sheet. To avoid the risk of short-circuiting, the plectra were electrically passivated by sputtering a 100 nm layer of ZrO2. Bench tests with the steel plectra showed a very large energy generation. Polyimide plectra were also manufactured with a cutting plotter from a 125μm-thick film. Besides bench tests, a volunteer wore the device while walking on flat ground or climbing stairs, with a measured energy output of approximately 0.8 mJ per step. Whereas most of the tests were performed by the traditional method of discharging the rectified output from the EH onto a resistive load, tests were performed also with a circuit offering a stabilised 3.3 V supply. The circuit produced a stable 0.1 mA supply during running gait with kapton plectra

A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs

In this paper we provide a complete theoretical analysis of a two-dimensional degenerate nonconvex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control, and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there

Large Fluctuations in Locational Marginal Prices

This paper investigates large fluctuations of Locational Marginal Prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form ℙ(LMP∉∏ni=1[α−i,α+i]), where LMP is the vector of LMPs at the n power grid nodes, and α−,α+∈ℝn are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply-demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modeling uncontrollable renewable generation. We utilize techniques from large deviations theory to identify the most likely ways for extreme price spikes to happen, and to rank the nodes of the power grid in terms of their likelihood of experiencing a price spike. Our results are derived in the case of Gaussian fluctuations and are validated numerically on the IEEE 14-bus test case

Contributors of the Summer Issue/Notes

Notes by William G. Greif, Louis Albert Hafner, William T. Huston, Maurice J. Moriarty, F. Richard Kramer, and George J. Murphy, Jr

Numerical simulations of string networks in the Abelian-Higgs model

We present the results of a field theory simulation of networks of strings in the Abelian Higgs model. Starting from a random initial configuration we show that the resulting vortex tangle approaches a self-similar regime in which the length density of lines of zeros of $\phi$ reduces as $t^{-2}$. We demonstrate that the network loses energy directly into scalar and gauge radiation. These results support a recent claim that particle production, and not gravitational radiation, is the dominant energy loss mechanism for cosmic strings. This means that cosmic strings in Grand Unified Theories are severely constrained by high energy cosmic ray fluxes: either they are ruled out, or an implausibly small fraction of their energy ends up in quarks and leptons.Comment: 4pp RevTeX, 3 eps figures, clarifications and new results included, to be published in Phys. Rev. Let