2,717 research outputs found
The linear and non linear Rayleigh-Taylor instability for the quasi isobaric profile
We study the stability of the system of the Euler equation in the
neighborhood of a stationary profile associated with the quasi isobaric model
in a gravity field. This stationary profile is not bounded below, hence the
operator is not coercive. We use this linear result to deduce a nonlinear
resul
Study of the linear ablation growth rate for the quasi isobaric model of Euler equations with thermal conductivity
In this paper, we study a linear system related to the 2d system of Euler
equations with thermal conduction in the quasi-isobaric approximation of
Kull-Anisimov [14]. This model is used for the study of the ablation front
instability, which appears in the problem of inertial confinement fusion. This
physical system contains a mixing region, in which the density of the gaz
varies quickly, and one denotes by L0 an associated characteristic length. The
system of equations is linearized around a stationary solution, and each
perturbed quantity is written using the normal modes method. The resulting
linear system is not self-adjoint, of order 5, with coefficients depending on x
and on physical parameters . We calculate Evans function
associated with this linear system, using rigorous constructions of decreasing
at solutions of systems of ODE. We prove that for small,
there is no bounded solution of the linearized system.Comment: Indiana University Mathematical Journal (2007) in pres
The band spectrum of the periodic airy-schrodinger operator on the real line
We introduce the periodic Airy-Schr\"odinger operator and we study its band
spectrum. This is an example of an explicitly solvable model with a periodic
potential which is not differentiable at its minima and maxima. We define a
semiclassical regime in which the results are stated for a fixed value of the
semiclassical parameter and are thus estimates instead of asymptotic results.
We prove that there exists a sequence of explicit constants, which are zeroes
of classical functions, giving upper bounds of the semiclassical parameter for
which the spectral bands are in the semiclassical regime. We completely
determine the behaviour of the edges of the first spectral band with respect to
the semiclassical parameter. Then, we investigate the spectral bands and gaps
situated in the range of the potential. We prove precise estimates on the
widths of these spectral bands and these spectral gaps and we determine an
upper bound on the integrated spectral density in this range. Finally, in the
semiclassical regime, we get estimates of the edges of every spectral bands and
thus of the widths of every spectral bands and spectral gaps
Asymptotic behavior of splitting schemes involving time-subcycling techniques
This paper deals with the numerical integration of well-posed multiscale
systems of ODEs or evolutionary PDEs. As these systems appear naturally in
engineering problems, time-subcycling techniques are widely used every day to
improve computational efficiency. These methods rely on a decomposition of the
vector field in a fast part and a slow part and take advantage of that
decomposition. This way, if an unconditionnally stable (semi-)implicit scheme
cannot be easily implemented, one can integrate the fast equations with a much
smaller time step than that of the slow equations, instead of having to
integrate the whole system with a very small time-step to ensure stability.
Then, one can build a numerical integrator using a standard composition method,
such as a Lie or a Strang formula for example. Such methods are primarily
designed to be convergent in short-time to the solution of the original
problems. However, their longtime behavior rises interesting questions, the
answers to which are not very well known. In particular, when the solutions of
the problems converge in time to an asymptotic equilibrium state, the question
of the asymptotic accuracy of the numerical longtime limit of the schemes as
well as that of the rate of convergence is certainly of interest. In this
context, the asymptotic error is defined as the difference between the exact
and numerical asymptotic states. The goal of this paper is to apply that kind
of numerical methods based on splitting schemes with subcycling to some simple
examples of evolutionary ODEs and PDEs that have attractive equilibrium states,
to address the aforementioned questions of asymptotic accuracy, to perform a
rigorous analysis, and to compare them with their counterparts without
subcycling. Our analysis is developed on simple linear ODE and PDE toy-models
and is illustrated with several numerical experiments on these toy-models as
well as on more complex systems. Lie andComment: IMA Journal of Numerical Analysis, Oxford University Press (OUP):
Policy A - Oxford Open Option A, 201
SAFT-γ force field for the simulation of molecular fluids: 4. A single-site coarse-grained model of water applicable over a wide temperature range
In this work, we develop coarse-grained (CG) force fields for water, where the effective CG intermolecular interactions between particles are estimated from an accurate description of the macroscopic experimental vapour-liquid equilibria data by means of a molecular-based equation of state. The statistical associating fluid theory for Mie (generalised Lennard-Jones) potentials of variable range (SAFT-VR Mie) is used to parameterise spherically symmetrical (isotropic) force fields for water. The resulting SAFT-γ CG models are based on the Mie (8-6) form with size and energy parameters that are temperature dependent; the latter dependence is a consequence of the angle averaging of the directional polar interactions present in water. At the simplest level of CG where a water molecule is represented as a single bead, it is well known that an isotropic potential cannot be used to accurately reproduce all of the thermodynamic properties of water simultaneously. In order to address this deficiency, we propose two CG potential models of water based on a faithful description of different target properties over a wide range of temperatures: our CGW1-vle model is parameterised to match the saturated-liquid density and vapour pressure; our other CGW1-ift model is parameterised to match the saturated-liquid density and vapour-liquid interfacial tension. A higher level of CG corresponding to two water molecules per CG bead is also considered: the corresponding CGW2-bio model is developed to reproduce the saturated-liquid density and vapour-liquid interfacial tension in the physiological temperature range, and is particularly suitable for the large-scale simulation of bio-molecular systems. A critical comparison of the phase equilibrium and transport properties of the proposed force fields is made with the more traditional atomistic models
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