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 $\mu(x)$

Simultaneous determination of the drift and diffusion coefficients in stochastic differential equations

In this work, we consider a one-dimensional It{\^o} diffusion process X t with possibly nonlinear drift and diffusion coefficients. We show that, when the diffusion coefficient is known, the drift coefficient is uniquely determined by an observation of the expectation of the process during a small time interval, and starting from values X 0 in a given subset of R. With the same type of observation, and given the drift coefficient, we also show that the diffusion coefficient is uniquely determined. When both coefficients are unknown, we show that they are simultaneously uniquely determined by the observation of the expectation and variance of the process, during a small time interval, and starting again from values X 0 in a given subset of R. To derive these results, we apply the Feynman-Kac theorem which leads to a linear parabolic equation with unknown coefficients in front of the first and second order terms. We then solve the corresponding inverse problem with PDE technics which are mainly based on the strong parabolic maximum principle