Sulla stabilità di un fluido politropico, viscoso e pesante in un contenitore limitato da pareti perfette conduttrici di calore

Sunto In questa Nota, si affronta il problema del comportamento asintotico nel tempo di perturbazioni alla quiete per il sistema di equazioni per un fluido comprimibile, viscoso e politropico. Ammesso che esista una soluzione regolare globale, si dimostra, sotto l’ipotesi che il gradiente della temperatura assegnata al bordo sia piccolo, che la differenza tra la soluzione corrispondente a dati iniziali arbitrari e la quiete decade a zero pert che tende ad infinito nella normal diL ².

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We consider the equation system for a compressible viscous polytropic fluid in a regualar bounded domain and we study the asymptotic behavior as time goes to infinity of perturbations with respect to the basic rest state. Under the assumption of the smallness of the gradient of the given temperature on the boundary, we prove the exponential decay of theL ²-norm of the difference between the solution corresponding to arbitrary initial data and the rest state.

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The second author thanks the 60% contract MURST, also she acknowledges the GNFM of italian CNR-INDAM for financial supports.     

Packed Column SFC of Gas Oils. Part II: Experimental Design Optimization of the Group-Type Analysis using CO2-SF6 as the Mobile Phase

An optimization procedure is presented for group-type analysis of diesel fuel by supercritical fluid chromatography using packed silica column and a mixed mobile phase. A set of five responses, four values of resolution of a performance mixture and analysis time, was modeled using a Doehlert matrix for experimental design. Optimized experimental conditions for the five responses were obtained from a response surfaces optimization, taking into account various constraints on SF₆ content in mobile phase and analysis time. The predicted and experimental resolutions were in good agreement for the different optimized conditions and one of them was selected to for application to a given diesel fuel for comparison with the results obtained by SFC using pure CO₂ and by HPLC. The conditions found in this study provide an alternative method for the determination of mono-, di-, and polyaromatic compounds in middle distillates.     

Modelling of pipeline integrity taking into account the fluid–structure interaction

Two mechanical models have been presented in this paper for structural failure prediction of piping systems conveying liquids subjected to pressure transients. One model takes into account the axial fluid–structure interaction (FSI) phenomenon between fluid and pipe motion, whereas the other refers to an extension of the well-known waterhammer formulation. Both models are described by a system of non-linear hyperbolic equations which are solved by using a numerical procedure based upon the operator splitting technique and Glimm's scheme. To implement Glimm's method, it is presented the solution of a 4×4 Riemann problem with discontinuous coefficients. Numerical predictions of both models are presented and compared, so that the influence of the FSI term on the failure analysis is focused on. © 1998 John Wiley & Sons, Ltd.     

Thermal system identification using fractional models for high temperature levels around different operating points

This work aims at the preparation of an experiment for the thermal modeling of an ARMCO iron sample (iron of the American Rolling Mill COmpany) for small temperature variations around different operating points. Fractional models have proven their efficacy for modeling thermal diffusion around the ambient temperature and for small variations. Due to their compactness, as compared to rational models and to finite element models, they are suitable for modeling such diffusive phenomena. However, for large temperature variations, thermal characteristics such as thermal conductivity and specific heat vary along with the temperature. In this context, the thermal diffusion obeys a nonlinear partial differential equation and cannot be modeled by a single linear model. In this paper, thermal diffusion of the iron sample is modeled around different operating points for temperatures ranging from 400 to 1070?K, which is above the Curie point (In physics and materials science, the Curie temperature (T _C), or Curie point, is the temperature at which a ferromagnetic or a ferrimagnetic material becomes paramagnetic.) showing that for a large range of temperature variations, a nonlinear model is required. Identification and validation data are generated by finite element methods using COMSOL Software.     

A one-dimensional plume plasma expansion: Self-similar approach

The expansion of a plasma induced by laser ablation is investigated using a single-fluid model combined with Saha?s equation. The space coordinates x and time t are combined to a one self-similar variable ξ=x/(ct). To obtain ordinary differential equations, two different transformations for the density are used. The density profiles during the expansion are found to be completely different, one corresponds to the common results i.e., the density decreases monotonically with ξ, while with the second transformation, the profile shows a density increasing for certain interval of the self-similar variable. This effect is enhanced with higher initial ionization fraction. The role of the initial velocity which corresponds to the start of the expansion from an unperturbed plasma or from an expansion already going on is pointed out.     

A nonstandard finite difference method for solving a mathematical model of HIV-TB co-infection

We design and analyze an unconditionally convergent nonstandard finite-difference method to study transmission dynamics of a mathematical model of HIV-TB co-infection. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves positivity of the solution which is one of the essential requirements when modelling epidemic diseases. Furthermore, we show that the numerical method is unconditionally stable. Competitive numerical results confirming theoretical investigations are provided. Comparisons are also made with other conventional approaches that are routinely used to solve these types of problems.     

Quasistatic frictional thermo‐piezoelectric contact problem

We consider here a mathematical model describing the bilateral frictional contact between a thermo‐piezoelectric body and a thermally conductive foundation. We model the behavior of the material with a linear thermo‐electro‐elastic constitutive law. The process is assumed to be quasistatic and the contact is modeled with a nonlocal version of Coulomb's dry friction law, in which the frictional heat generated in the process, is taken into account. We drive a variational formulation of the problem and establish the existence of its weak solution.