The Fukushima Inverse Problem

Knowing what amount of radioactive material was released from Fukushima in March 2011 and at what time instants is crucial to assess the risk, the pollution, and to understand the scope of the consequences. Moreover, it could be used in forward simulations to obtain accurate maps of deposition. But these data are often not publicly available. We propose to estimate the emission waveforms by solving an inverse problem. Previous approaches have relied on a detailed expert guess of how the releases appeared, and they produce a solution strongly biased by this guess. If we plant a nonexistent peak in the guess, the solution also exhibits a nonexistent peak. We pro- pose a method that solves the Fukushima inverse problem blindly. Using atmospheric dispersion models and worldwide radioactivity measurements together with sparse regularization, the method correctly reconstructs the times of major events during the accident, and gives plausible estimates of the released quantities of Xenon

Chiral and deconfinement transitions in a magnetic background using the functional renormalization group with the Polyakov loop

We use the Polyakov loop coupled quark-meson model to approximate low energy QCD and present results for the chiral and deconfinement transitions in the presence of a constant magnetic background $B$ at finite temperature $T$ and baryon chemical potential $\mu_B$. We investigate effects of various gluoni potentials on the deconfinement transition with and without a fermionic backreaction at finite $B$. Additionally we investigate the effect of the Polyakov loop on the chiral phase transition, finding that magnetic catalysis at low $\mu_B$ is present, but weakened by the Polyakov loop.Comment: 17 pages and 8 figs. v2: added ref

Functional renormalization group study of the Nambu--Jona-Lasinio model at finite temperature and density in an external magnetic field

In this study, we investigate the Nambu--Jona-Lasinio (NJL) model at finite temperature and finite density in an external magnetic field using the functional renormalization group. We investigate the dependence of the position of the ultraviolet fixed point (UVFP) of the four-Fermi coupling constant on the temperature, density, and external magnetic field, and we obtain the chiral phase structure. The UVFP at low temperature and finite chemical potential oscillates in a small external magnetic field, which can be interpreted as the de Haas--van Alphen effect. We also obtain phase diagrams with complex structures, where the phase boundary moves back and forth as the external magnetic field increases in the low temperature and high density region.Comment: 6 pages, 6 figures, published versio

Outlier removal for improved source estimation in atmospheric inverse problems

Estimation of the quantities of harmful substances emitted into the atmosphere is one of the main challenges in modern environmen- tal sciences. In most of the cases, this estimation requires solving a linear inverse problem. A key difficulty in evaluating the performance of any algorithm to solve this linear inverse problem is that the ground truth is typically unknown. In this paper we show that the noise encountered in this linear inverse problem is non-Gaussian. Next, we develop an algorithm to deal with the strong outliers present in the measurements. Finally, we test our approach on three different experiments: a simple synthetic experiment, a controlled real-world experiment, and real data from the Fukushima nuclear accident

Progress on Hardy-type Inequalities

This paper surveys some of our recent progress on Hardy-type inequa\-lities which consist of a well-known topic in Harmonic Analysis. In the first section, we recall the original probabilistic motivation dealing with the stability speed in terms of the $L^2$-theory. A crucial application of a result by Fukushima and Uemura (2003) is included. In the second section, the non-linear case (a general Hardy-type inequality) is handled with a direct and analytic proof. In the last section, it is illustrated that the basic estimates presented in the first two sections can still be improved considerably.Comment: 13 pages, 5 figures, Festschrift Masatoshi Fukushima: In Honor of Masatoshi Fukushima's Sanju. World Scientific, 201