Frequency relationships for ultrasonic activation of free microbubbles, encapsulated microbubbles, and gas-filled micropores.

The ultrasonic activation of free microbubbles, encapsulated microbubbles, and gas-filled micropores was explored using available linear theory. Encapsulated microbubbles, used in contrast agents for diagnostic ultrasound, have relatively high resonance frequencies and damping. At 2 MHz the resonance radii are 1.75 microns for free microbubbles, 4.0 microns for encapsulated microbubbles, and 1.84 microns for gas-filled micropores. Higher-pressure amplitudes are needed to elicit equivalent subharmonic, fundamental, or second-harmonic responses from the encapsulated microbubbles, and this behavior increases for higher frequencies. If an encapsulated microbubble becomes destabilized during exposure,the resulting liberated microbubble would be about twice the linear resonance size, which would be likely to produce subharmonic signals. Scattered signals used for medical imaging purposes may be indicative of bioeffects potential: The second harmonic signal is proportional to local shear stress for a microbubble on a boundary, and a strong subharmonic signal may imply destabilization and nucleation of free-microbubble cavitation activity. The potential for bioeffects from contrast agent gas bodies decreases rapidly with increasing frequency. This information should be valuable for understanding of the etiology of bioeffects related to contrast agents and for developing exposure indices and risk management strategies for their use in diagnostic ultrasound.     

An improved LCAO-MO-SCF π-electron method

Using the method of a previous paper a modified technique is used to calculate the core parameters for carbon, nitrogen and oxygen atoms. The one-center core parameters H _pp ⁰ , are identified with conventional atomic valence state ionization potentials. The two-center core parameters are given by the equation H _pq ⁰ = (H _pp ⁰ + H _qq ⁰ )/2 (H _pq – 0.0855 R _pq + 0.24639) – n _p (S _pq /4)( _pp + _pq ) – n _q (S _pq /4) · ( _qq + _pq ).It is shown that these parameters, along with the electron repulsion integrals adopted earlier allow one to calculate with reasonable accuracy the singlet spectra and ionization potentials (within Koopmans' approximation) of a large number of unsaturated hydrocarbons as well as the heterocycles pyridine, p-benzoquinone (PBQ), pyrrole and furan.

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Zusammenfassung Unter Benutzung einer früheren Methode wird ein modifiziertes Verfahren zur Berechnung der Rumpfparameter von C-, N- und O-Atomen vorgeschlagen. Die Einzentren-Rumpfparameter H _pp ⁰ werden den üblichen Ionisationspotentialen für die atomaren Valenzzustände gleichgesetzt. Die Zweizentren-Rumpfparameter werden nach H _pq ⁰ = (H _pp ⁰ + H _qq ⁰ )/2 (H _pq – 0.0855 R _pq + 0.24639) – n _p (S _pq /4)( _pp + _pq ) – n _q (S _pq /4) · ( _qq + _pq ) berechnet.Auf diese Weise und unter Verwendung der schon früher benützten Coulombintegrale lassen sich die Singulett-Spektren und Ionisationspotentiale einer großen Anzahl ungesättigter Kohlenwasserstoffe sowie der Heterocyclen Pyridin, p-Benzochinon, Pyrrol und Furan mit der üblichen Genauigkeit berechnen.

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Résumé Calcul des paramètres de coeur du carbone, de l'azote et de l'oxygène, en utilisant la méthode d'un article précédent techniquement modifiée. Les paramètres de coeur monocentriques H _pp ⁰ sont identifiés avec les potentiels d'ionisation de l'état atomique de valence conventionnel. Les paramètres de coeur bicentriques sont donnée par l'équation H _pq ⁰ = (H _pp ⁰ + H _qq ⁰ )/2 (H _pq – 0.0855 R _pq + 0.24639) – n _p (S _pq /4)( _pp + _pq ) – n _q (S _pq /4) · ( _qq + _pq ). On montre que ces paramètres utilisés avec les intégrales de répulsion précédemment adoptées permettent de calculer avec une précision raisonnable le spectresingulet et les potentiels d'ionisation (dans l'approxirnation de Koopmans) pour un grand nombre d'hydrocarbures non saturés et des hétérocycles commee la pyridine, la p-benzoquinone (PBQ), le pyrrole et le furane.

     

Direction-direction correlations of oriented polymers

We calculate the direction-direction correlations between the tangent vectors of an oriented self-avoiding walk (SAW). LetJ (x) andJ ^v (0) be components of unit-length tangent vectors of an oriented SAW, at the spatial pointsx and 0, respectively. Then for distances |x| much less than the average distance between the endpoints of the walk, the correlation function ofJ (x) withJ ^v (0) has, ind dimensions, the form . The dimensionless amplitudek(d) is universal, and can be calculated exactly in two dimensions by using Coulomb gas techniques, where it is found to bek(2)=12/25 ². In three dimensions, the -expansion to second order in together with the exact value ofk(2)in two dimensions allows the estimatek(3)=0.0178±0.0005. In dimensionsd4, the universal amplitudek(d) of the direction-direction correlation functions of an oriented SAW is the same as the universal amplitude of the direction-direction correlation functions of an oriented random walk, and is given byk(d)= ²(d/2)/(d–2) ^d .