Bifurcation problems in fluid-mechanics

Summary A general perturbation technique for dealing with nonlinear problems in the neighborhood of branching points is presented. The general method is then applied to the treatment of several problems in fluid mechanics, i. e. shock waves in an inviscid and a viscous gas, shock structure in kinetic theory, shock waves in mixtures and ionized gases, onset of instabilities in a fluid.

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Sommario Si espone un metodo perturbativo di carattere generale che permette di trattare problemi nonlineari nell'intorno dei punti di biforcazione. Si applica poi il metodo generale alla trattazione di diversi problemi di meccanica dei fluidi e precisamente alle onde d'urto in gas ideali e viscosi, alla struttura delle onde d'urto secondo la teoria cinetica dei gas, alle onde d'urto in gas ionizzati e miscele e all'insorgere di instabilità in un fluido.

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This work was done in the sphere of activity of the C.N.R. Group for mathematical research.     

Color-specific conditioning effects due to both orange and blue stimuli are observed in a Halobacterium salinarum strain devoid of putative methylatable sites on HtrI

Behavioral responses of Halobacterium salinarum appear as changes in the frequency of motion reversals. Turning on orange light decreases the reversal frequency, whereas blue light induces reversals. Light pulses normally induce the same response as step-up stimuli. However, anomalous behavioral reactions, including inverse responses, are seen when stimuli are applied in sequence. The occurrence of a prior stimulus is conditioning for successive stimulation on a time scale of the same order of adaptational processes. These prolonged conditioning effects are color-specific. The only adaptation process identified so far is methylation of the transducers, and this could be somehow color-specific. Therefore we tested for the behavioral anomalies in a mutant in which all methylation sites on the transducer have been eliminated. The results show that behavioral anomalies are unaffected by the absence of methylation processes on the transducer.     

Validation of a Monte Carlo simulation of the plane Couette flow of a rarefied gas

We report and discuss the results of a direct Monte Carlo simulation of the flow of a rarefied gas flowing between two parallel plates when one of them moves in its own plane. The boundary conditions are assumed to be of the bounceback type and the molecules to be Maxwell's. Under this condition the moments can be computed exactly, following a method used by Ikenberry and Truesdell in the unbounded case. This allows a comparison of the Monte Carlo methods with the exact solution and an evaluation of its accuracy.     

Rarefied gas flow through long slots

The transition flow of a gas between two reservoirs through a two-dimensional slot is studied. The width of the slot is much smaller than the length but finite. The ratio of the equilibrium number densities in the reservoirs is near 1 and the equilibrium temperatures are the same. Galerkin's method of solution is applied to the linearized BGK equation and the total mass flow is evaluated as a function of the inverse Knudsen number and the length-to-half width ratioL. Limits 1, 1 andL 1 are investigated and good agreement with other authors is found. Simple analytical expressions are obtained for these cases.

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Riassunto Si studia la corrente gassosa tra due serbatoi uniti da un canale bi-dimensionale nel regime di transizione. La larghezza del canale è molto più piccola della sua lunghezza ma è finita. II rapporto tra le densità di molecole nei serbatoi è prossimo a 1 e le temperature d'equilibrio sono le stesse. II metodo di soluzione di Galerkin viene applicato all'equazione di Bhatnagar, Gross e Krook linearizzata e si valuta la protata in funzione del numero inverso di Knudsen e del rapportoL tra lunghezza e semi-larghezza. Si studiano i limiti 1, 1 eL1 e si trova un boun accordo con precedenti lavori. Per questi casi si trovano semplici espressioni analitiche.

     

On a Nonquantum Derivation of Planck’s Distribution Law

We prove that a correct nonquantum treatment of electromagnetic radiation leads to Planck's distribution (including zero-point energy). The only principles that we invoke are general invariance principles or, alternatively, the impossibility of violating the second law at a macroscopic level.     

The grad limit for a system of soft spheres

A model describing the dynamics of a system of soft spheres is introduced. The model contains a random mechanism which mollifies the deterministic model of hard sphere molecules. It allows a rigorous deduction of the corresponding Boltzmann equation for a wide class of initial data and arbitrarily long times.     

Heat transfer in a Knudsen gas

The behavior of a Knudsen gas between two plates at unequal temperatures is discussed. A general formulation is given for the case of small temperature difference. The use of perturbation theory is then demonstrated and applied to the case of a nonspherical interaction of a polyatomic gas with the solid walls in the presence of a magnetic field.     

Shear Flow of a Granular Material

The shear flow of a granular material between parallel plates is treated by means of the Boltzmann equation with pseudo-Maxwellian grains. The moments for reverse reflection boundary conditions are found explicitly. The shearing stress is found to depend quadratically on the shear rate.     

Half-range completeness for the Fokker-Planck equation with an external force

This paper deals with a generalization of a classical result obtained by R. Beals and V. Protopopescu for the Fokker-Planck equations to the case in which a constant external force is present.