8,615 research outputs found
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 â particularly the need for complementary mechanisms to remunerate capacity â 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
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
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 and we assume a nonlinear term of the form where belongs to a fixed subset of . We
prove that the knowledge of at and of , at a single point
and for small times is sufficient to completely
determine the couple provided is known.
Additionally, if is also measured for ,
the triplet is also completely determined. Those
analytical results are completed with numerical simulations which show that, in
practice, measurements of and at a single point (and for ) are sufficient to obtain a good approximation of the
coefficient These numerical simulations also show that the
measurement of the derivative is essential in order to accurately
determine
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