Quadratic interaction functional for general systems of conservation laws

For the Glimm scheme approximation u_\e to the solution of the system of conservation laws in one space dimension \begin{equation*} u_t + f(u)_x = 0, \qquad u(0,x) = u_0(x) \in \R^n, \end{equation*} with initial data $u_0$ with small total variation, we prove a quadratic (w.r.t. \TV(u_0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux $f$ are made (apart smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely we obtain the following results: \begin{itemize} \item a new analysis of the interaction estimates of simple waves; \item a Lagrangian representation of the derivative of the solution, i.e. a map $\mathtt x(t,w)$ which follows the trajectory of each wave $w$ from its creation to its cancellation; \item the introduction of the characteristic interval and partition for couples of waves, representing the common history of the two waves; \item a new functional $\mathfrak Q$ controlling the variation in speed of the waves w.r.t. time. \end{itemize} This last functional is the natural extension of the Glimm functional for genuinely nonlinear systems. The main result is that the distribution $D_{tt} \mathtt x(t,w)$ is a measure with total mass \leq \const \TV(u_0)^2

Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

A taxonomic study of Jacquemontia evolvuloides (Moric.) Meisn. and related species (Convolvulaceae).

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Thomson scattering and collisional ionization in the X-ray grating spectra of the recurrent nova U Scorpii

We present a Chandra observation of the recurrent nova U Scorpii, done with the High Resolution camera-S (HRC-S) detector and the Low Energy Transmission Grating (LETG) on day 18 after the observed visual maximum of 2010, and compare it with XMM?Newton observations obtained on days 23 and 35 after maximum. The total absorbed flux was in the range 2.2?2.6 × 10−11 erg cm−2 s−1, corresponding to unabsorbed luminosity 7?8.5 × 1036 ×(d/12 kpc)2 for N(H) = 2?2.7 × 1021 cm−2. On day 18, 70 per cent of the soft X-tray flux was in a continuum typical of a very hot white dwarf (WD) atmosphere, which accounted for about 80 per cent of the flux on days 23 and 35. In addition, all spectra display very broad emission lines, due to higher ionization stages at later times. With Chandra we observed apparent P Cygni profiles. We find that these peculiar profiles are not due to blueshifted absorption and redshifted emission in photoionized ejecta, like the optical P Cyg of novae, but they are rather a superposition of WD atmospheric absorption features reflected by the already discovered Thomson scattering corona, and emission lines due to collisional ionization in condensations in the ejecta. On days 23 and 35, the absorption components were no longer measurable, having lost the initial large blueshift that displaced them from the core of the broad emission lines. We interpret this as an indication that mass-loss ceased between day 18 and day 23. On day 35, the emission line spectrum became very complex, with several different components. Model atmospheres indicate that the WD atmospheric temperature was about 730 000 K on day 18 and reached 900 000?1000 000 K on day 35. This peak temperature is consistent with a WD mass of at least 1.3 M⊙.Fil: Orio, M.. INAF Osservatorio di Padova; Italia. University of Wisconsin; Estados UnidosFil: Behar, E.. Department of Physics, Technion; IsraelFil: Gallagher, J.. University of Wisconsin; Estados UnidosFil: Bianchini, A.. Universita Di Padova; ItaliaFil: Chiosi, E.. INAF Osservatorio di Padova; ItaliaFil: Luna, Gerardo Juan Manuel. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Nelson, T.. University Of Minnesota; Estados UnidosFil: Rauch, T.. Eberhard Karls University; AlemaniaFil: Schaefer, B. E.. State University Of Louisiana; Estados UnidosFil: Tofflemire, B.. University of Wisconsin; Estados Unido

Ultraviolet Emission Line Ratios of Cataclysmic Variables

We present a statistical analysis of the ultraviolet emission lines of cataclysmic variables (CVs) based on $\approx 430$ ultraviolet spectra of 20 sources extracted from the International Ultraviolet Explorer Uniform Low Dispersion Archive. These spectra are used to measure the emission line fluxes of N V, Si IV, C IV, and He II and to construct diagnostic flux ratio diagrams. We investigate the flux ratio parameter space populated by individual CVs and by various CV subclasses (e.g., AM Her stars, DQ Her stars, dwarf novae, nova-like variables). For most systems, these ratios are clustered within a range of $\sim 1$ decade for log Si IV/C IV $\approx -0.5$ and log He II/C IV $\approx -1.0$ and $\sim 1.5$ decades for log N V/C IV $\approx -0.25$. These ratios are compared to photoionization and collisional ionization models to constrain the excitation mechanism and the physical conditions of the line-emitting gas. We find that the collisional models do the poorest job of reproducing the data. The photoionization models reproduce the Si IV/C IV line ratios for some shapes of the ionizing spectrum, but the predicted N V/C IV line ratios are simultaneously too low by typically $\sim 0.5$ decades. Worse, for no parameters are any of the models able to reproduce the observed He II/C IV line ratios; this ratio is far too small in the collisional and scattering models and too large by typically $\sim 0.5$ decades in the photoionization models.Comment: LaTeX format, uses aaspp4.sty, 28 pages, 11 Postscript figures, accepted for publication in The Astrophysical Journal 10/16/9

Global classical solutions for partially dissipative hyperbolic system of balance laws

This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of classical solutions in the framework of Chemin-Lerner's spaces with critical regularity is established. To do this, we first explore the functional space theory and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin-Lerner's spaces. Then this fact allows to prove the local well-posedness for general data and global well-posedness for small data by using the Fourier frequency-localization argument. Finally, we apply the new existence theory to a specific fluid model-the compressible Euler equations with damping, and obtain the corresponding results in critical spaces.Comment: 39 page

Shell model in the complex energy plane and two-particle resonances

An implementation of the shell-model to the complex energy plane is presented. The representation used in the method consists of bound single-particle states, Gamow resonances and scattering waves on the complex energy plane. Two-particle resonances are evaluated and their structure in terms of the single-particle degreees of freedom are analysed. It is found that two-particle resonances are mainly built upon bound states and Gamow resonances, but the contribution of the scattering states is also important.Comment: 20 pages, 9 figures, submitted to Phys.Rev.