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 $Z(\omega)$ characterizing reflection of sound with frequency $\omega$ 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

Curative and organ-preserving treatment with intra-arterial carboplatin induction followed by surgery and/or radiotherapy for advanced head and neck cancer: single-center five-year results

BACKGROUND: This study evaluated the feasibility, toxicity, response rate and survival of neoadjuvant superselective intra-arterial infusion of high dose carboplatin in advanced head and neck cancer. METHODS: Forty-six patients with primary head and neck squamous cell carcinoma received 3 cycles of intra-arterial carboplatin (300 to 350 mg/m(2 )per cycle every 2 weeks), followed by radiotherapy or surgery plus radiotherapy. RESULTS: No complications or severe toxicity occurred. Sixteen patients (35%) were complete responders, 20 (43%) partial responders while 10 (22%) did not respond to treatment. After completion of the multimodality treatment, 38/46 patients (83%) were complete responders. After a 5-year follow-up period, 18/46 patients (39%) are alive and disease-free, 3 (6,5%) have died of a second primary tumor and 25 (54,5%) have died of the disease. CONCLUSION: Intra-arterial carboplatin induction chemotherapy is a safe, well-tolerated technique that discriminates between responders and non-responders and so may have prognostic significance in planning further integrated treatments aimed to organ preservation for advanced head and neck carcinomas