A mathematical model of the ring-spinning process

This paper develops a mathematical model of the ring-spinning process that takes into account its non-stationary nature. A complex system of differential equations is obtained, which from a mathematical point of view constitutes a ‘free-boundary’ problem. Its solution involves definition of suitable boundary conditions related to the mechanical characteristics of the process and of the spinning machine itself. The boundary conditions which determine the solution are pointed out. A numerical solution of the system of differential equations can be obtained by the Finite-Segments method, as shown in an example.     

Sul problema generale dell'equilibrio spontaneo di una massa fluida gravitante e ruotante

Sunto Si studia, da un punto di vista generale, l'equilibrio relativo di una massa fluida gravitante isolata nello spazio e in rotazione stazionaria rigida intorno ad un asse e si determinano, in queste ipotesi, le condizioni alle quali devono soddisfare la velocita di rotazione ω, la pressione p e la densità ρ. Si fanno infine alcune applicazioni dei risultati ottenuti e si ritrovano, come casi particolari, alcuni classici risultati noti. A Giovanni Sansone nel suo 70^mo compleanno     

Fluorescence and Mass Spectrometry Studies of Meta-tetra(hydroxyphenyl)chlorin Photoproducts

The meta-tetra(hydroxyphenyl)chlorin (m-THPC), a second-generation sensitizer used in photodynamic therapy (PDT), is currently under clinical trial. In vivo fluorometry provides direct evidence that photobleaching processes are induced at the tumor site during PDT. Photoproduct formation has thus to be taken into account to fully understand PDT treatment. A preliminary step is to determine the fluorescence characteristics of photoproducts formed in solution. Solutions of m-THPC irradiated at 514 nm have been separated by HPLC using absorption and fluorescence detection. Six main photoproducts have been isolated. According to matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOFMS) results, five fluorescent photoproducts emitting at 652 nm have been attributed to three mono-, one di- and one tri-hydroxy derivatives (m/z 697, 713 and 729, respectively). Fluorescence characteristics of mono-hydroxy forms were found to be similar to those of m-THPC, whereas fluorescence yields in di- and tri-hydroxy derivatives were very low. Another product, corresponding to a MALDI-TOF MS main signal at m/z 542, showed an absorption spectrum maximum at 522 nm while a weak fluorescence was detected at 480 nm. The loss of the Soret band suggests that this photoproduct results from the opening of the reduced pyrrole ring. The part played by each of these products in the photobleaching phenomenon of m-THPC is discussed.     

Rate constant for the OH + CO reaction: Pressure dependence and the effect of oxygen

The effect of pressure on the rate constant of the OH + CO reaction has been measured for Ar, N₂, and SF₆ over the pressure range 200–730 torr. All experiments were at room temperature. The method involved laser-induced fluorescence to measure steady-state OH concentrations in the 184.9 nm photolysis of H₂O-CO mixtures in the three carrier gases, combined with supplementary measurements of the CO depletion in these same carrier gases in the presence and absence of competing reference reactants. The effect of O₂ on the pressure effect was determined. A pressure enhancement of the rate constant was observed for N₂ and SF₆, but not for Ar, within an experimental error of about 10%. The pressure effect for N₂ was somewhat lower than previous literature reports, being about 40% at 730 torr. For SF₆ a factor of two enhancement was seen at 730 torr. In each case it was found that O₂ had no effect on the pressure enhancement. The roles of the radical species HCO and HOCO were evaluated.     

Rates and mechanism of alkyne ozonation

The rates and products of the reactions of ozone with acetylene, methylacetylene, dimethylacetylene, and ethylacetylene have been studied in a long-path infrared cell at 21 ± 1°C. The gas phase reaction gives products formed by cleavage of the carbon–carbon triple bond. A mechanism is proposed that involves formation of a short-lived acid anhydride intermediate, which is energized by virtue of the reaction exothermicity and undergoes unimolecular decomposition. Formation of an α-dicarbonyl was observed in every case, but there is evidence that a side reaction on the walls accounted for that product. The general relationship between alkyne and alkene ozonation is discussed. The rate measurements showed that, unlike the alkenes, the rate of alkyne ozonation is not greatly affected by substitution with simple alkyl groups. The rate constant for C₂H₂ agrees with earlier work and thus provides additional support for the previously derived high A-factor for acetylene ozonation relative to alkenes.     

Su di un nuovo problema del tipo di Stefan

Summary We study a problem of Stefan in a semi-infinite, homogeneous, thermically isotropic medium, whose initial temperature is position indipendent. Our semi-infinite medium is initially in a well defined state and its surface is maintained at a constant temperature. It is remarkable that an hypothesis is made, which is new in connection with Stefan problems: we suppose in fact the change of state temperature is a function of the position at which the change happens. Finally we study the asymptotic behaviour for t → ∞ of the solution of our problem.

---

---

Lavoro eseguito nell'ambito dell'attività del VI^o Gruppo di Ricerca Matematica del C. N. R. presso l'Istituto Matematico ? U. Dini ? della Università di Firenze.     

Manipulation of microparticles using phase-controllable ultrasonic standing waves

A method of manipulating microparticles in a liquid using ultrasound is proposed and demonstrated. An ultrasonic standing wave with nodal planes whose positions are controllable by varying the relative phase of two applied sinusoidal signals is generated using a pair of acoustically matched piezoelectric transducers. The resulting acoustic radiation force is used to trap micron scale particles at a series of arbitrary positions (determined by the relative phase) and then move them in a controlled manner. This method is demonstrated experimentally and 5 μm polystyrene particles are trapped and moved in one dimension through 140 μm.     

Rate constant for the reaction of atomic bromine with ozone

The rate constant for the reaction Br + O₃ → BrO + O₂ has been measured over the temperature range 224 to 422 K in a discharge flow system using a mass spectrometer as a detector. Results, expressed in the form k₁ = (3.34 ± 0.40) × 10^?11 X exp[?(978 ± 36)/T] cm³ s^?1, are compared with previous measurements.     

Un problema di controllo ottimale nel cambiamento di stato in uno strato

Summary In this paper we studied a minimum property for a Stefan-like problem in a slab S. We considered all possible processes of change of state which occur under security conditions in an assigned time interval t_o. We proved that, among these processes the particular one for which the cooling (or warming) temperature f=f(t) is time-independent minimizes the integral . As a consequence, such a process, which occurs in an asigned time interval, minimi zes the external work.

---

---

A Bruno Finzi nel suo 70^mo compleanno

---

Lavoro eseguito nell'ambito dell'attività del contratto di ricerca matematica del C.N.R n^o 115.2210.2 (amm. Prof. R. Einaudi) presso l'Istituto Matematico ? U. Dini ? della Università di Firenze, viale Morgagni 67^a.

---

Entrata in Redazione il 27 febbraio 1970.