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Jun Kitagawa

Publications and source records attributed to Jun Kitagawa.

31 records · Page 2Linked to original sources
arXiv2017

Characteristics that Produce White-Light Enhancements in Solar Flares Observed by Hinode/SOT

To understand the conditions that produce white-light (WL) enhancements in solar flares, a statistical analysis of visible continuum data as observed by Hinode/Solar Optical Telescope (SOT) was performed. In this study, approximately 100 flare events from M- and X-class flares were selected. The time period during which the data were recorded spans from January 2011 to February 2016. Of these events, approximately half are classified as white-light flares (WLFs), whereas the remaining events do not show any enhancements of the visible continuum (non-WLF; NWL). In order to determine the existence of WL emission, running difference images of not only the Hinode/SOT WL (G-band, blue, green, and red filter) data but also the Solar Dynamics Observatory/Helioseismic and Magnetic Imager continuum data are used. A comparison between these two groups of WL data in terms of duration, temperature, emission measure of GOES soft X-rays, distance between EUV flare ribbons, strength of hard X-rays, and photospheric magnetic field strength was undertaken. In this statistical study, WLF events are characterized by a shorter time-scale and shorter ribbon distance compared with NWL events. From the scatter plots of the duration of soft X-rays and the energy of non-thermal electrons, a clear distinction between WLF and NWL events can be made. It is found that the precipitation of large amounts of accelerated electrons within a short time period plays a key role in generating WL enhancements. Finally, it was demonstrated that the coronal magnetic field strength in the flare region is one of the most important factors that allow the individual identification of WLF events from NWL events.

astro-ph.SR↗
arXiv2017

Estimates for Dirichlet-to-Neumann maps as integro-differential operators

Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or the generator of the boundary process of a reflected diffusion. In this work, we make some extensions of this theory to the case of a \emph{nonlinear} Dirichlet-to-Neumann mapping that is constructed using a solution to a \emph{fully nonlinear} elliptic equation in a given domain, mapping Dirichlet data to its normal derivative of the resulting solution. Here we begin the process of giving detailed information about the Lévy measures that will result from the integro-differential representation of the Dirichlet-to-Neumann mapping. We provide new results about both linear and nonlinear Dirichlet-to-Neumann mappings. Information about the Lévy measures is important if one hopes to use recent advancements of the integro-differential theory to study problems involving Dirichlet-to-Neumann mappings.

math.AP↗
arXiv2017

Free discontinuities in optimal transport

We prove a nonsmooth implicit function theorem applicable to the zero set of the difference of convex functions. This theorem is explicit and global: it gives a formula representing this zero set as a difference of convex functions which holds throughout the entire domain of the original functions. As applications, we prove results on the stability of singularities of envelopes of semi-convex functions, and solutions to optimal transport problems under appropriate perturbations, along with global structure theorems on certain discontinuities arising in optimal transport maps for Ma-Trudinger-Wang costs. For targets whose components satisfy additional convexity, separation, multiplicity and affine independence assumptions we show these discontinuities occur on submanifolds of the appropriate codimension which are parameterized locally as differences of convex functions (DC, hence $C^2$ rectifiable), and --- depending on the precise assumptions --- $C^{1,α}$ smooth. In this case the highest codimension submanifolds consists of isolated points, each uniquely identified by the (affinely independent) components of the target to which it is transported.

math.AP↗
arXiv2017

Convergence of a Newton algorithm for semi-discrete optimal transport

Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems numerically is to assume that the source probability measure is absolutely continuous while the target measure is finitely supported. We refer to this setting as semi-discrete optimal transport. Among the several algorithms proposed to solve semi-discrete optimal transport problems, one currently needs to choose between algorithms that are slow but come with a convergence speed analysis (e.g. Oliker-Prussner) or algorithms that are much faster in practice but which come with no convergence guarantees Algorithms of the first kind rely on coordinate-wise increments and the number of iterations required to reach the solution up to an error of $ε$ is of order $N^3/ε$, where $N$ is the number of Dirac masses in the target measure. On the other hand, algorithms of the second kind typically rely on the formulation of the semi-discrete optimal transport problem as an unconstrained convex optimization problem which is solved using a Newton or quasi-Newton method. The purpose of this article is to bridge this gap between theory and practice by introducing a damped Newton's algorithm which is experimentally efficient and by proving the global convergence of this algorithm with optimal rates. The main assumptions is that the cost function satisfies a condition that appears in the regularity theory for optimal transport (the Ma-Trudinger-Wang condition) and that the support of the source density is connected in a quantitative way (it must satisfy a weighted Poincaré-Wirtinger inequality).

math.NA↗
arXiv2016

Pointwise estimates and regularity in geometric optics and other Generated Jacobian Equations

The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Ampère type known as generated Jacobian equations. These equations, whose general existence theory has been recently developed by Trudinger go beyond the framework of optimal transport. We obtain pointwise estimates for weak solutions of such equations under a condition analogous to the A3w condition of Ma, Trudinger and Wang. Estimates of this type have played an important role in the regularity theory for optimal transport maps and were previously unknown in this context, including the important case of the near field reflector problem.

math.AP↗
arXiv2015

The multi-marginal optimal partial transport problem

We introduce and study a multi-marginal optimal partial transport problem. Under a natural and sharp condition on the dominating marginals, we establish uniqueness of the optimal plan. Our strategy of proof establishes and exploits a connection with another novel problem, which we call the Monge-Kantorovich partial barycenter problem (with quadratic cost). This latter problem has a natural interpretation as a variant of the mines and factories description of optimal transport. We then turn our attention to various analytic properties of these two problems. Of particular interest, we show that monotonicity of the active marginals can fail, a surprising difference from the two marginal case.

math.AP↗
arXiv2014

Coronal magnetic field and the plasma beta determined from radio and multiple satellite observations

We derived the coronal magnetic field, plasma density, and temperature from the observation of polarization and intensity of radio thermal free-free emission using the Nobeyama Radioheliograph (NoRH) and extreme ultraviolet (EUV) observations. We observed a post-flare loop on the west limb 11 April 2013. The line-of-sight magnetic field was derived from the circularly polarized free-free emission observed by NoRH. The emission measure and temperature were derived from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO). The derived temperature was used to estimate the emission measure from the NoRH radio free-free emission observations. The derived density from NoRH was larger than that determined using AIA, which can be explained by the fact that the low temperature plasma is not within the temperature coverage of the AIA filters used in this study. We also discuss the other observation of the post-flare loops by the EUV Imager onboard the Solar Terrestrial Relations Observatory (STEREO), which can be used in future studies to reconstruct the coronal magnetic field strength. The derived plasma parameters and magnetic field were used to derive the plasma beta, which is a ratio between the magnetic pressure and the plasma pressure. The derived plasma beta is about 5.7*10^(-4) to 7.6*10^(-4) at the loop top region.

astro-ph.SR↗
arXiv2014

Prohibiting isolated singularities in optimal transport

We give natural topological conditions on the support of the target measure under which solutions to the optimal transport problem with cost function satisfying the (weak) Ma, Trudinger, and Wang condition cannot have any isolated singular points.

math.AP↗
arXiv2013

The local geometry of maps with c-convex potentials

We identify a condition for regularity of optimal transport maps that requires only three derivatives of the cost function, for measures given by densities that are only bounded above and below. This new condition is equivalent to the weak Ma-Trudinger-Wang condition when the cost is $C^4$. Moreover, we only require (non-strict) c-convexity of the support of the target measure, removing the hypothesis of strong c-convexity in a previous result of Figalli, Kim, and McCann, but at the added cost of assuming compact containment of the supports of both the source and target measures.

math.AP↗
arXiv2012

On the degeneracy of optimal transportation

We extend a dimensional upper bound on how much an optimal transport map can degenerate for the quadratic transportation cost, originally due to Caffarelli, to cost functions that satisfy the curvature condition of Ma, Trudinger, and Wang.

math.AP↗
arXiv2012

An iterative scheme for solving the optimal transportation problem

We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of iterations necessary for the scheme to terminate, in terms of the error tolerance and number of points in the support of the discrete target measure.

math.OC↗