Diffractive Microlensing I: Flickering Planetesimals at the Edge of the Solar System

Microlensing and occultation are generally studied in the geometric optics limit. However, diffraction may be important when recently discovered Kuiper-Belt objects (KBOs) occult distant stars. In particular the effects of diffraction become more important as the wavelength of the observation and the distance to the KBO increase. For sufficiently distant and massive KBOs or Oort cloud objects not only is diffraction important but so is gravitational lensing. For an object similar to Eris but located in the Oort cloud, the signature of gravitational lensing would be detected easily during an occultation and would give constraints on the mass and radius of the object.Comment: 5 pages, 4 figures, changes to reflect the version accepted by MN Letter

Market Design for Generation Adequacy: Healing Causes rather than Symptoms

Keywords JEL Classification This paper argues that electricity market reform – particularly the need for complementary mechanisms to remunerate capacity – need to be analysed in the light of the local regulatory and institutional environment. If there is a lack of investment, the priority should be to identify the roots of the problem. The lack of demand side response, short-term reliability management procedures and uncompetitive ancillary services procurement often undermine market reflective scarcity pricing and distort long-term investment incentives. The introduction of a capacity mechanism should come as an optional supplement to wholesale and ancillary markets improvements. Priority reforms should focus on encouraging demand side responsiveness and reducing scarcity price distortions introduced by balancing and congestion management through better dialog between network engineers and market operators. electricity market, generation adequacy, market design, capacity mechanis

On the determination of the nonlinearity from localized measurements in a reaction-diffusion equation

This paper is devoted to the analysis of some uniqueness properties of a classical reaction-diffusion equation of Fisher-KPP type, coming from population dynamics in heterogeneous environments. We work in a one-dimensional interval $(a,b)$ and we assume a nonlinear term of the form $u \, (\mu(x)-\gamma u)$ where $\mu$ belongs to a fixed subset of $C^{0}([a,b])$. We prove that the knowledge of $u$ at $t=0$ and of $u$, $u_x$ at a single point $x_0$ and for small times $t\in (0,\varepsilon)$ is sufficient to completely determine the couple $(u(t,x),\mu(x))$ provided $\gamma$ is known. Additionally, if $u_{xx}(t,x_0)$ is also measured for $t\in (0,\varepsilon)$, the triplet $(u(t,x),\mu(x),\gamma)$ is also completely determined. Those analytical results are completed with numerical simulations which show that, in practice, measurements of $u$ and $u_x$ at a single point $x_0$ (and for $t\in (0,\varepsilon)$) are sufficient to obtain a good approximation of the coefficient $\mu(x).$ These numerical simulations also show that the measurement of the derivative $u_x$ is essential in order to accurately determine $\mu(x)$

Absolute timing of the Crab pulsar with the INTEGRAL/SPI telescope

We have investigated the pulse shape evolution of the Crab pulsar emission in the hard X-ray domain of the electromagnetic spectrum. In particular, we have studied the alignment of the Crab pulsar phase profiles measured in the hard X-rays and in other wavebands. To obtain the hard X-ray pulse profiles, we have used six year (2003-2009, with a total exposure of about 4 Ms) of publicly available data of the SPI telescope on-board of the INTEGRAL observatory, folded with the pulsar time solution derived from the Jodrell Bank Crab Pulsar Monthly Ephemeris. We found that the main pulse in the hard X-ray 20-100 keV energy band is leading the radio one by $8.18\pm0.46$ milliperiods in phase, or $275\pm15 \mu s$ in time. Quoted errors represent only statistical uncertainties.Our systematic error is estimated to be $\sim 40 \mu s$ and is mainly caused by the radio measurement uncertainties. In hard X-rays, the average distance between the main pulse and interpulse on the phase plane is $0.3989\pm0.0009$. To compare our findings in hard X-rays with the soft 2-20 keV X-ray band, we have used data of quasi-simultaneous Crab observations with the PCA monitor on-board the Rossi X-Ray Timing Explorer (RXTE) mission. The time lag and the pulses separation values measured in the 3-20 keV band are $0.00933\pm0.00016$ (corresponding to $310\pm6 \mu s$) and $0.40016\pm0.00028$ parts of the cycle, respectively. While the pulse separation values measured in soft X-rays and hard X-rays agree, the time lags are statistically different. Additional analysis show that the delay between the radio and X-ray signals varies with energy in the 2 - 300 keV energy range. We explain such a behaviour as due to the superposition of two independent components responsible for the Crab pulsed emission in this energy band