Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

On some properties of linear and nonlinear waves in pair-ion plasmas

It is pointed out that the observation of the electrostatic ion acoustic wave frequency can be a suitable check to determine whether the produced plasma is a pure pair-ion plasma or whether it comprises some concentration of electrons. A theoretical model for the pair-ion plasma dynamics is presented along with a new electrostatic mode which can exist only in such systems. It can become unstable in the presence of shear flow and it can give rise to vortex structures in the nonlinear regime. The possibility of shocks and solitons, due to nonlinear drift waves in a pair-ion plasma comprising electrons, is also discussed. The relevance of this investigation to both laboratory and astrophysical plasmas is pointed out.     

A novel capacitive pressure sensor structure with high sensitivity and quasi-linear responseUne nouvelle structure de capteur de pression capacitif avec haute sensibilitée et réponse quasi-linéaire

This paper describes a new capacitive structure of pressure sensor to increase simultaneously the sensitivity and the linearity of the transducer. This structure contains two capacitors which change in response to pressure, but in opposite senses. To increase even more the sensitivity of each capacitor, the pressure sensitive diaphragm carries a central boss. The optimal position and the length of the boss are also calculated. To cite this article: A. Ettouhami et al., C. R. Mecanique 332 (2004).     

Synthesis and structure of fluorotricyanomethane

Fluorotricyanomethane is prepared from potassium tricyanomethanide and perchlorylfluoride. The crystal structure of this compound (orthorhombic, space group P2₁2₁2₁, with a=6.270, b=6.734, c=11.776 Å) has been determined by X-ray analysis. The results are discussed in relation to those of (NC)₃C? X (X=? CH₃, ? Cl, ? Br or ? CN).     

A theoretical study of electronic spectra of radical cations of some dihydroxynaphthalenes

Electronic transition energies of radical cations of 1.2-, 1.3-, 1.6-, and 1.7?dihydroxynaphthalenes are calculated using an open-shell SCF method with configuration interaction. The results are critically analyzed and a correlation diagram is given that shows the energy-shift and intensity variation in the electronic transitions when moving from one system to another, thus revealing the characteristic behavior of the transitions depending on the positions of the hydroxyl substituents. An interesting relation connecting the electronic spectroscopy with the UV photoelectron spectroscopy is suggested on the basis of which the first ionization potentials (IPS ) of the substituted aromatic systems can be inferred from the calculated energy of the A-type (HOMO → LUMO ) transitions for their radical cations. Furthermore, the predictability of the IP s is found to be considerably increased with the incorporation of “molecular size” in the regression.     

Characterization of the short-chain branches in poly(vinyl chloride)s by γ irradiation of the reduced polymers

The volatile products from the γ irradiation of samples of poly(vinyl chloride) prepared under different conditions and reduced to the corresponding polyethylenes have been measured quantitatively and compared with those for low- and high-density polyethylenes and copolymers of ethylene with small amounts of α-olefins. The presence of methyl branches is clearly demonstrated and there is also evidence for ethyl and butyl branches, although these had not been considered significant in previous [¹³C] NMR studies. The method is shown to be extremely sensitive to small quantities of residual trialkyl tin hydride reductant occluded in, and possibly also reacted with, the polymer, and to residual chlorine (<0.5%). The yields of alkanes are higher than expected from the branch frequencies determined by i.r. and [¹³C] NMR and results for ethylene-α-olefin copolymers. This difference is apparently due to sensitisation of the radiation degradation by residual chlorine and reductant. Quantitative determinations of branch frequencies by the radiolytic method are unlikely to be obtained until these problems are overcome.     

Dichotenone-a and -b: two new enones from the marine brown alga Dictyota dichotoma (Hudson) Lamour

Marine brown alga Dictyota dichotoma (Dictyotaceae) collected from Karachi coast of Arabian Sea yielded two new (1 and 2) enones (dolastane-diterpenoids) named: dichotenone-A and -B along with an olide (loliolide, 3) as a new source. Their structures have been characterized with the aid of 2D-NMR spectroscopic techniques.     

Dynamics of kink-soliton solutions of the $$(2+1)$$ -dimensional sine-Gordon equation

Theoretical and Mathematical Physics - We study the dynamics of explicit solutions of the $$(2+1)$$ -dimensional (2D) sine-Gordon equation. The Darboux transformation is applied to the associated...