9,467 research outputs found
The boundary Riemann solver coming from the real vanishing viscosity approximation
We study a family of initial boundary value problems associated to mixed
hyperbolic-parabolic systems:
v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x =
\epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx}
The conservative case is, in particular, included in the previous
formulation.
We suppose that the solutions to these problems converge to a
unique limit. Also, it is assumed smallness of the total variation and other
technical hypotheses and it is provided a complete characterization of the
limit.
The most interesting points are the following two.
First, the boundary characteristic case is considered, i.e. one eigenvalue of
can be .
Second, we take into account the possibility that is not invertible. To
deal with this case, we take as hypotheses conditions that were introduced by
Kawashima and Shizuta relying on physically meaningful examples. We also
introduce a new condition of block linear degeneracy. We prove that, if it is
not satisfied, then pathological behaviours may occur.Comment: 84 pages, 6 figures. Text changes in Sections 1 and 3.2.3. Added
Section 3.1.2. Minor changes in other section
SBV regularity of Systems of Conservation Laws and Hamilton-Jacobi Equation
We review the SBV regularity for solutions to hyperbolic systems of conservation laws and Hamilton-Jacobi equations. We give an overview of the techniques involved in the proof, and a collection of related problems concludes the paper
Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension
The paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points \u398 and a countable family of Lipschitz curves T{script} such that outside T{script} 2a \u398 the solution is continuous, and for all points in T{script}{set minus}\u398 the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems
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 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 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 which follows the trajectory of each wave 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 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 is a measure with total mass \leq \const \TV(u_0)^2
Constraints on Cosmological Parameters from the 500 degÂČ SPTPOL Lensing Power Spectrum
We present cosmological constraints based on the cosmic microwave background (CMB) lensing potential power spectrum measurement from the recent 500 degÂČ SPTPOL survey, the most precise CMB lensing measurement from the ground to date. We fit a flat ÎCDM model to the reconstructed lensing power spectrum alone and in addition with other data sets: baryon acoustic oscillations (BAO), as well as primary CMB spectra from Planck and SPTPOL. The cosmological constraints based on SPTPOL and Planck lensing band powers are in good agreement when analyzed alone and in combination with Planck full-sky primary CMB data. With weak priors on the baryon density and other parameters, the SPTPOL CMB lensing data alone provide a 4% constraint on ÏâΩ^(0.25)_m = 0.593 ± 0.025. Jointly fitting with BAO data, we find Ïâ = 0.779±0.023, Ω_m = 0.368^(+0.032)_(â0.037), and Hâ = 72.0^(+2.1)_(â2.5)kmsâ»Âč Mpcâ»Âč, up to 2Ï away from the central values preferred by Planck lensing + BAO. However, we recover good agreement between SPTPOL and Planck when restricting the analysis to similar scales. We also consider single-parameter extensions to the flat ÎCDM model. The SPTPOL lensing spectrum constrains the spatial curvature to be Ω_K = â0.0007±0.0025 and the sum of the neutrino masses to be âm_Îœ < 0.23 eV at 95% C.L. (with Planck primary CMB and BAO data), in good agreement with the Planck lensing results. With the differences in the signal-to-noise ratio of the lensing modes and the angular scales covered in the lensing spectra, this analysis represents an important independent check on the full-sky Planck lensing measurement
SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one space dimension
We prove that if is the entropy
solution to a strictly hyperbolic system of conservation laws with
genuinely nonlinear characteristic fields then up to a
countable set of times the function is in
, i.e. its distributional derivative is a measure with no
Cantorian part.
The proof is based on the decomposition of into waves belonging to
the characteristic families and the balance
of the continuous/jump part of the measures in regions bounded by
characteristics. To this aim, a new interaction measure \mu_{i,\jump} is
introduced, controlling the creation of atoms in the measure .
The main argument of the proof is that for all where the Cantorian part
of is not 0, either the Glimm functional has a downward jump, or there is
a cancellation of waves or the measure is positive
On a quadratic functional for scalar conservation laws
We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme. The proof is based on the introduction of a quadratic functional (t), decreasing at every interaction, and such that its total variation in time is bounded. Differently from other interaction potentials present in the literature, the form of this functional is the natural extension of the original Glimm functional, and coincides with it in the genuinely nonlinear case
Quadratic interaction functional for systems of conservation laws: a case study
We prove a quadratic interaction estimate for wavefront approximate solutions to the triangular system of conservation laws
This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme \cite{anc_mar_11_CMP}.
Our aim is to extend the analysis, done for scalar conservation laws \cite{bia_mod_13}, in the presence of transversal interactions among wavefronts of different families.
The proof is based on the introduction of a quadratic functional , decreasing at every interaction, and such that its total variation in time is bounded. %cancellations it variation is controlled by the total variation growths at most of the total variation of the solution multiplied by the amount of cancellation.
The study of this particular system is a key step in the proof of the quadratic interaction estimate for general systems: it requires a deep analysis of the wave structure of the solution and the reconstruction of the past history of each wavefront involved in an interaction
V4743 Sgr, a magnetic nova?
Two XMM Newton observations of Nova V4743 Sgr (Nova Sgr 2002) were performed
shortly after it returned to quiescence, 2 and 3.5 years after the explosion.
The X-ray light curves revealed a modulation with a frequency of ~0.75 mHz,
indicating that V4743 Sgr is most probably an intermediate polar (IP). The
X-ray spectra have characteristics in common with known IPs, with a hard
thermal plasma component that can be fitted only assuming a partially covering
absorber. In 2004 the X-ray spectrum had also a supersoft blackbody-like
component, whose temperature was close to that of the white dwarf (WD) in the
supersoft X-ray phase following the outburst, but with flux by at least two
orders of magnitude lower. In quiescent IPs, a soft X-ray flux component
originates at times in the polar regions irradiated by an accretion column, but
the supersoft component of V4743 Sgr disappeared in 2006, indicating a possible
origin different from accretion. We suggest that it may have been due to an
atmospheric temperature gradient on the WD surface, or to continuing localized
thermonuclear burning at the bottom of the envelope, before complete turn-off.
An optical spectrum obtained with SALT 11.5 years after the outburst showed a
prominent He II 4686A line and the Bowen blend, which reveal a very hot region,
but with peak temperature shifted to the ultraviolet (UV) range. V4743 Sgr is
the third post-outburst nova and IP candidate showing a low-luminosity
supersoft component in the X-ray flux a few years after the outburst.Comment: 9 pages, 5 figures, accepted to MNRA
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