10,276 research outputs found
Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations
In this article, we study the self-similar solutions of the 2-component
Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}%
\rho_{t}+u\rho_{x}+\rho u_{x}=0
m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation}
with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation
method, we can obtain a class of blowup or global solutions for or
. In particular, for the integrable system with , we have the
global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}%
\rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right)
}{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi}
0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right.
,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x
\overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}%
>0,\text{ }\overset{\cdot}{a}(0)=a_{1}
f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right)
^{2}}% \end{array} \right. \end{equation}
where with and are
arbitrary constants.\newline Our analytical solutions could provide concrete
examples for testing the validation and stabilities of numerical methods for
the systems.Comment: 5 more figures can be found in the corresponding journal paper (J.
Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm
Equations, Shallow Water System, Analytical Solutions, Blowup, Global,
Self-Similar, Separation Method, Construction of Solutions, Moving Boundar
The formation of high-field magnetic white dwarfs from common envelopes
The origin of highly-magnetized white dwarfs has remained a mystery since
their initial discovery. Recent observations indicate that the formation of
high-field magnetic white dwarfs is intimately related to strong binary
interactions during post-main-sequence phases of stellar evolution. If a
low-mass companion, such as a planet, brown dwarf, or low-mass star is engulfed
by a post-main-sequence giant, the hydrodynamic drag in the envelope of the
giant leads to a reduction of the companion's orbit. Sufficiently low-mass
companions in-spiral until they are shredded by the strong gravitational tides
near the white dwarf core. Subsequent formation of a super-Eddington accretion
disk from the disrupted companion inside a common envelope can dramatically
amplify magnetic fields via a dynamo. Here, we show that these disk-generated
fields are sufficiently strong to explain the observed range of magnetic field
strengths for isolated, high-field magnetic white dwarfs. A higher-mass binary
analogue may also contribute to the origin of magnetar fields.Comment: Accepted to Proceedings of the National Academy of Sciences. Under
PNAS embargo until time of publicatio
Definition of large components assembled on-orbit and robot compatible mechanical joints
One of four major areas of project Pathfinder is in-space assembly and construction. The task of in-space assembly and construction is to develop the requirements and the technology needed to build elements in space. A 120-ft diameter tetrahedral aerobrake truss is identified as the focus element. A heavily loaded mechanical joint is designed to robotically assemble the defined aerobrake element. Also, typical large components such as habitation modules, storage tanks, etc., are defined, and attachment concepts of these components to the tetrahedral truss are developed
Astrophysical Fluid Dynamics via Direct Statistical Simulation
In this paper we introduce the concept of Direct Statistical Simulation (DSS)
for astrophysical flows. This technique may be appropriate for problems in
astrophysical fluids where the instantaneous dynamics of the flows are of
secondary importance to their statistical properties. We give examples of such
problems including mixing and transport in planets, stars and disks. The method
is described for a general set of evolution equations, before we consider the
specific case of a spectral method optimised for problems on a spherical
surface. The method is illustrated for the simplest non-trivial example of
hydrodynamics and MHD on a rotating spherical surface. We then discuss possible
extensions of the method both in terms of computational methods and the range
of astrophysical problems that are of interest.Comment: 26 pages, 11 figures, added clarifying remarks and references, and
corrected typos. This version is accepted for publication in The
Astrophysical Journa
Standard Solar models in the Light of New Helioseismic Constraints II. Mixing Below the Convective Zone
In previous work, we have shown that recent updated standard solar models
cannot reproduce the radial profile of the sound speed at the base of the
convective zone (CZ) and fail to predict the Li7 depletion. In parallel,
helioseismology has shown that the transition from differential rotation in the
CZ to almost uniform rotation in the radiative solar interior occurs in a
shallow layer called the tachocline. This layer is presumably the seat of large
scale circulation and of turbulent motions. Here, we introduce a macroscopic
transport term in the structure equations, which is based on a hydrodynamical
description of the tachocline proposed by Spiegel and Zahn, and we calculate
the mixing induced within this layer. We discuss the influence of different
parameters that represent the tachocline thickness, the Brunt-Vaissala
frequency at the base of the CZ, and the time dependence of this mixing process
along the Sun's evolution. We show that the introduction of such a process
inhibits the microscopic diffusion by about 25%. Starting from models including
a pre-main sequence evolution, we obtain: a) a good agreement with the observed
photospheric chemical abundance of light elements such as He3, He4, Li7 and
Be9, b) a smooth composition gradient at the base of the CZ, and c) a
significant improvement of the sound speed square difference between the
seismic sun and the models in this transition region, when we allow the
phostospheric heavy element abundance to adjust, within the observational
incertitude, due to the action of this mixing process. The impact on neutrino
predictions is also discussed.Comment: 15 pages, 7 figures, to be published in ApJ (used emulateapj style
for latex2e). New email for A. S. Brun: [email protected]
Coarse-grained model of entropic allostery
Many signaling functions in molecular biology require proteins to bind to substrates such as DNA in response to environmental signals such as the simultaneous binding to a small molecule. Examples are repressor proteins which may transmit information via a conformational change in response to the ligand binding. An alternative entropic mechanism of "allostery" suggests that the inducer ligand changes the intramolecular vibrational entropy, not just the mean static structure. We present a quantitative, coarse-grained model of entropic allostery, which suggests design rules for internal cohesive potentials in proteins employing this effect. It also addresses the issue of how the signal information to bind or unbind is transmitted through the protein. The model may be applicable to a wide range of repressors and also to signaling in trans-membrane proteins
Instabilities in the Envelopes and Winds of Very Massive Stars
The high luminosity of Very Massive Stars (VMS) means that radiative forces
play an important, dynamical role both in the structure and stability of their
stellar envelope, and in driving strong stellar-wind mass loss. Focusing on the
interplay of radiative flux and opacity, with emphasis on key distinctions
between continuum vs. line opacity, this chapter reviews instabilities in the
envelopes and winds of VMS. Specifically, we discuss how: 1) the iron opacity
bump can induce an extensive inflation of the stellar envelope; 2) the density
dependence of mean opacity leads to strange mode instabilities in the outer
envelope; 3) desaturation of line-opacity by acceleration of near-surface
layers initiates and sustains a line-driven stellar wind outflow; 4) an
associated line-deshadowing instability leads to extensive small-scale
structure in the outer regions of such line-driven winds; 5) a star with
super-Eddington luminosity can develop extensive atmospheric structure from
photon bubble instabilities, or from stagnation of flow that exceeds the
"photon tiring" limit; 6) the associated porosity leads to a reduction in
opacity that can regulate the extreme mass loss of such continuum-driven winds.
Two overall themes are the potential links of such instabilities to Luminous
Blue Variable (LBV) stars, and the potential role of radiation forces in
establishing the upper mass limit of VMS.Comment: 44 pages, 13 figures. Chapter to appear in the book "Very Massive
Stars in the Local Universe", Springer, J.S. Vink, e
{The Noise Handling Properties of the Talbot Algorithm for Numerically Inverting the Laplace Transform}
This paper examines the noise handling properties of three of the most widely used algorithms for numerically inverting the Laplace Transform. After examining the genesis of the algorithms, the regularization properties are evaluated through a series of standard test functions in which noise is added to the inverse transform. Comparisons are then made with the exact data. Our main finding is that the Talbot inversion algorithm is very good at handling noisy data and is more accurate than the Fourier Series and Stehfest numerical inversion schemes as they are outlined in this paper. This offers a considerable advantage for it's use in inverting the Laplace Transform when seeking numerical solutions to time dependent differential equations.Peer reviewedFinal Published versio
Sonoluminescence as a QED vacuum effect. II: Finite Volume Effects
In a companion paper [quant-ph/9904013] we have investigated several
variations of Schwinger's proposed mechanism for sonoluminescence. We
demonstrated that any realistic version of Schwinger's mechanism must depend on
extremely rapid (femtosecond) changes in refractive index, and discussed ways
in which this might be physically plausible. To keep that discussion tractable,
the technical computations in that paper were limited to the case of a
homogeneous dielectric medium. In this paper we investigate the additional
complications introduced by finite-volume effects. The basic physical scenario
remains the same, but we now deal with finite spherical bubbles, and so must
decompose the electromagnetic field into Spherical Harmonics and Bessel
functions. We demonstrate how to set up the formalism for calculating Bogolubov
coefficients in the sudden approximation, and show that we qualitatively retain
the results previously obtained using the homogeneous-dielectric (infinite
volume) approximation.Comment: 23 pages, LaTeX 209, ReV-TeX 3.2, five figure
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