89 research outputs found
Thermal vibrational convection in near-critical fluids. Part 2. Weakly non-uniform heating
The governing equations and effective boundary conditions to describe thermal vibrational convection in a near-critical fluid are derived with the help of the multiple-scale method and averaging procedure. In contrast to Part 1, this paper focuses on the effects of density non-homogeneities caused not by external heating but by vibrational and gravity stratifications due to the divergent mechanical compressibility of near-critical media. It is shown that vibrations generate non-homogeneities in the average temperature, which result in the onset of thermal convection even under isothermal boundary conditions. An agreement with the results of previous numerical and asymptotical analyses and with experiments is found.<br/
Thermo-acoustic wave propagation and reflection near the liquid-gas critical point
We study the thermo-acoustic wave propagation and reflection near the
liquid-gas critical point. Specifically, we perform a numerical investigation
of the acoustic responses in a near-critical fluid to thermal perturbations
based on the same setup of a recent ultrasensitive interferometry measurement
in CO2 [Y. Miura et al. Phys. Rev. E 74, 010101(R) (2006)]. The numerical
results agree well with the experimental data. New features regarding the
reflection pattern of thermo-acoustic waves near the critical point under pulse
perturbations are revealed by the proper inclusion of the critically diverging
bulk viscosity.Comment: 14 pages, 4 figures, Accepted by PRE (Rapid Communication
Thermoacoustic effects in supercritical fluids near the critical point: Resonance, piston effect, and acoustic emission and reflection
We present a general theory of thermoacoustic phenomena in supercritical
fluids near the critical point in a one-dimensional cell. We take into account
the effects of the heat conduction in the boundary walls and the bulk viscosity
near the critical point. We introduce a coefficient characterizing
reflection of sound with frequency at the boundary. As applications,
we examine the acoustic eigenmodes in the cell, the response to time-dependent
perturbations, sound emission and reflection at the boundary. Resonance and
rapid adiabatic changes are noteworthy. In these processes, the role of the
thermal diffusion layers is enhanced near the critical point because of the
strong critical divergence of the thermal expansion.Comment: 15 pages, 7 figure
Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising
The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that, according to the fractional exponent s, either vanishes (s 1/2). On the other hand, the normal trace of the solution has the reverse behavior, thus making the Neumann trace analytically well-defined. Nevertheless, the solution develops an increasingly sharp boundary layer in the vicinity of Ω as s decreases. In this work, we extend the technology of automatic hp-adaptivity, originally developed for standard elliptic equations, to the energy setting of a Sobolev space with a Muckenhoupt weight, in order to accommodate for the problem of interest. The numerical evidence confirms that the method maintain exponential convergence. Finally, we discuss image denoising via the fractional Laplacian. In the image processing community, the standard way to apply the fractional Laplacian to a corrupted image is as a filter in Fourier space. This construction is inherently affected by the Gibbs phenomenon, which prevents the direct application to “spliced” images. Since our numerical approximation relies instead on the extension problem, it allows for processing different portions of a noisy image independently and combine them, without complications induced by the Gibbs phenomenon
The Molecular Identification of Organic Compounds in the Atmosphere: State of the Art and Challenges
ON ASYMPTOTIC SOLUTIONS OF DIATOMIC BOLTZMANN'S EQUATION
Matched asymptotic expansion technics is used to derive the equations describing the hydro-dynamical behaviour of a diatomic gas. The vibrational relaxation phenomena appears to correspond to an inner asymptotic description, whereas the frozen and equilibrium cases correspond respectively to what has been called the first and second outer description. To illustrate these features, sound absorption due to vibrational relaxation is shown to correspond to the domain of non uniformity of a-straitforward small frequencies asymptotic expansion of the dispersion relation
Contexte programmatique et budgétaire
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