Wedges, Cones, Cosmic Strings, and the Reality of Vacuum Energy

One of J. Stuart Dowker's most significant achievements has been to observe that the theory of diffraction by wedges developed a century ago by Sommerfeld and others provided the key to solving two problems of great interest in general-relativistic quantum field theory during the last quarter of the twentieth century: the vacuum energy associated with an infinitely thin, straight cosmic string, and (after an interchange of time with a space coordinate) the apparent vacuum energy of empty space as viewed by an accelerating observer. In a sense the string problem is more elementary than the wedge, since Sommerfeld's technique was to relate the wedge problem to that of a conical manifold by the method of images. Indeed, Minkowski space, as well as all cone and wedge problems, are related by images to an infinitely sheeted master manifold, which we call Dowker space. We review the research in this area and exhibit in detail the vacuum expectation values of the energy density and pressure of a scalar field in Dowker space and the cone and wedge spaces that result from it. We point out that the (vanishing) vacuum energy of Minkowski space results, from the point of view of Dowker space, from the quantization of angular modes, in precisely the way that the Casimir energy of a toroidal closed universe results from the quantization of Fourier modes; we hope that this understanding dispels any lingering doubts about the reality of cosmological vacuum energy.Comment: 28 pages, 16 figures. Special volume in honor of J. S. Dowke

Economic optimization of component sizing for residential battery storage systems

Battery energy storage systems (BESS) coupled with rooftop-mounted residential photovoltaic (PV) generation, designated as PV-BESS, draw increasing attention and market penetration as more and more such systems become available. The manifold BESS deployed to date rely on a variety of different battery technologies, show a great variation of battery size, and power electronics dimensioning. However, given today's high investment costs of BESS, a well-matched design and adequate sizing of the storage systems are prerequisites to allow profitability for the end-user. The economic viability of a PV-BESS depends also on the battery operation, storage technology, and aging of the system. In this paper, a general method for comprehensive PV-BESS techno-economic analysis and optimization is presented and applied to the state-of-art PV-BESS to determine its optimal parameters. Using a linear optimization method, a cost-optimal sizing of the battery and power electronics is derived based on solar energy availability and local demand. At the same time, the power flow optimization reveals the best storage operation patterns considering a trade-off between energy purchase, feed-in remuneration, and battery aging. Using up to date technology-specific aging information and the investment cost of battery and inverter systems, three mature battery chemistries are compared; a lead-acid (PbA) system and two lithium-ion systems, one with lithium-iron-phosphate (LFP) and another with lithium-nickel-manganese-cobalt (NMC) cathode. The results show that different storage technology and component sizing provide the best economic performances, depending on the scenario of load demand and PV generation.Web of Science107art. no. 83

A determination of the molar gas constant R by acoustic thermometry in helium

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator maintained near the temperature of the triple point of water and filled with helium with carefully characterized molar mass M = (4.002 6032 ± 0.000 0015) g mol-1, with a relative standard uncertainty ur(M) = 0.37×10-6. From these data and traceable thermometry we estimate the speed of sound in our sample of helium at TTPW = 273.16 K and zero pressure to be u0 2 = (945 710.45 ± 0.85) m2 s-2 and correspondingly deduce the value R = (8.314 4743 ± 0.000 0088) J mol-1 K-1 for the molar gas constant. We estimate the value k = R/NA = (1.380 6508 ± 0.000 0015) × 10-23 J K-1 for the Boltzmann constant using the currently accepted value of the Avogadro constant NA. These estimates of R and k, with a relative standard uncertainty of 1.06 × 10-6, are 1.47 parts in 106 above the values recommended by CODATA in 2010

A parallel VLSI architecture for a digital filter of arbitrary length using Fermat number transforms

A parallel architecture for computation of the linear convolution of two sequences of arbitrary lengths using the Fermat number transform (FNT) is described. In particular a pipeline structure is designed to compute a 128-point FNT. In this FNT, only additions and bit rotations are required. A standard barrel shifter circuit is modified so that it performs the required bit rotation operation. The overlap-save method is generalized for the FNT to compute a linear convolution of arbitrary length. A parallel architecture is developed to realize this type of overlap-save method using one FNT and several inverse FNTs of 128 points. The generalized overlap save method alleviates the usual dynamic range limitation in FNTs of long transform lengths. Its architecture is regular, simple, and expandable, and therefore naturally suitable for VLSI implementation

A Method of Optimal Radio Frequency Assignment for Deep Space Missions

A method for determining optimal radio frequency channels for the Deep Space Network is described. Computer automated routines calculate interference-to-signal ratios over a given mission period and provide a quantitative assessment of the channels which could then be assigned to a new mission. This automated procedure reduces the analysis time considerably and effectively improves upon the accuracy of existing channel assignment techniques