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Impacts of variable renewable energy on wholesale markets and generating assets in the United States: A review of expectations and evidence
We synthesize available literature, data, and analysis on the degree to which growth in variable renewable energy (VRE) has impacted or might in the future impact bulk power system assets, pricing, and costs in the United States. Most studies of future scenarios indicate that VRE reduces wholesale energy prices and capacity factors of thermal generators. Traditional baseload generators are more exposed to these changing market conditions than low-capital cost and more flexible intermediate and peak-load generators. From analysis of historical data we find that VRE is already influencing the bulk power market through changes in temporal and geographic patterns areas with higher levels of VRE. The most significant observed impacts have concentrated in areas with significant VRE and/or nuclear generation along with limited transmission, with negative pricing also often occurring during periods with lower system-wide load. So far, however, VRE, has had a relatively modest impact on historical average annual wholesale prices across entire market regions, at least in comparison to other drivers. The reduction of natural gas prices is the primary contributor to the decline in wholesale prices since 2008. Similarly, VRE impacts on thermal plant retirements have been limited and there is little relationship between the location of recent retirements and VRE penetration levels. Although impacts on wholesale prices have been modest so far, impacts of VRE on the electricity market will be more significant under higher VRE penetrations
Orbital roulette: a new method of gravity estimation from observed motions
The traditional way of estimating the gravitational field from observed
motions of test objects is based on the virial relation between their kinetic
and potential energy. We find a more efficient method. It is based on the
natural presumption that the objects are observed at a random moment of time
and therefore have random orbital time phases. The proposed estimator, which we
call "orbital roulette", checks the randomness of the phases. The method has
the following advantages: (1) It estimates accurately Keplerian (point-mass)
potentials as well as non-Keplerian potentials where the unknown gravitating
mass is distributed in space. (2) It is a complete statistical estimator: it
checks a trial potential and accepts it or rules it out with a certain
significance level; the best-fit measurement is thus supplemented with error
bars at any confidence level. (3) It needs no a priori assumptions about the
distribution of orbital parameters of the test bodies. We test our estimator
with Monte-Carlo-generated motions and demonstrate its efficiency. Useful
applications include the Galactic Center, dark-matter halo of the Galaxy, and
clusters of stars or galaxies.Comment: 30 pages, accepted to Ap
Mechanism of droplet-formation in a supersonic microfluidic spray device
Spray drying is an approach employed in automotive, food, and pharmaceutical industries as a robust and cost efficient liquid atomization technique offering direct control over droplet dimensions. The majority of commercially available spray nozzles are designed for large throughput spray drying applications or uniform surface coating, but microfluidic nebulizers have recently been developed as small scale alternatives. Here, we explore the physical parameters that define the droplet size and formation under supersonic flow conditions commonly found in microfluidic spray drying systems. We examined the spray nozzle operation using high speed imaging and laser scattering measurements, which allowed us to describe the spray regimes and droplet size distributions. It was determined that by using this spray nozzle device, droplets with diameters of 4–8 μm could be generated. Moreover, we show that the supersonic de Laval nozzle model can be used to predict the average droplet size. Our approach can be used as a platform for interfacing fluid microprocessing with gas phase detection and characterization
Real inequality in Europe since 1500
Introducing a concept of real, as opposed to nominal, inequality of income or wealth suggests some historical reinterpretations, buttressed by a closer look at consumption by the rich. The purchasing powers of different income classes depend on how relative prices move. Relative prices affected real inequality more strongly in earlier centuries than in the twentieth. Between 1500 and about 1800, staple food and fuels became dearer, while luxury goods, especially servants, became cheaper, greatly widening the inequality of lifestyles. Peace, industrialization, and globalization reversed this inegalitarian price effect in the nineteenth century, at least for England
Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation
The mathematical theory of integrable Painleve/Toda type systems sheds new
light on the behavior of solutions to the Poisson-Boltzmann equation for the
potential due to a long rod-like macroion. We investigate here the case of
symmetric electrolytes together with that of 1:2 and 2:1 salts. Short and large
scale features are analyzed, with a particular emphasis on the low salinity
regime. Analytical expansions are derived for several quantities relevant for
polyelectrolytes theory, such as the Manning radius. In addition, accurate and
practical expressions are worked out for the electrostatic potential, which
improve upon previous work and cover the full range of radial distances
Chaos and Order in Models of Black Hole Pairs
Chaos in the orbits of black hole pairs has by now been confirmed by several
independent groups. While the chaotic behavior of binary black hole orbits is
no longer argued, it remains difficult to quantify the importance of chaos to
the evolutionary dynamics of a pair of comparable mass black holes. None of our
existing approximations are robust enough to offer convincing quantitative
conclusions in the most highly nonlinear regime. It is intriguing to note that
in three different approximations to a black hole pair built of a spinning
black hole and a non-spinning companion, two approximations exhibit chaos and
one approximation does not. The fully relativistic scenario of a spinning
test-mass around a Schwarzschild black hole shows chaos, as does the
Post-Newtonian Lagrangian approximation. However, the approximately equivalent
Post-Newtonian Hamiltonian approximation does not show chaos when only one body
spins. It is well known in dynamical systems theory that one system can be
regular while an approximately related system is chaotic, so there is no formal
conflict. However,the physical question remains, Is there chaos for comparable
mass binaries when only one object spins? We are unable to answer this question
given the poor convergence of the Post-Newtonian approximation to the fully
relativistic system. A resolution awaits better approximations that can be
trusted in the highly nonlinear regime
Resolvent convergence of Sturm-Liouville operators with singular potentials
In this paper we consider the Sturm-Liuoville operator in the Hilbert space
with the singular complex potential of and two-point boundary
conditions. For this operator we give sufficient conditions for norm resolvent
approximation by the operators of the same class.Comment: 6 pages, to appear in Math. Note
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