A method for establishing upper bounds for singular perturbation problems

We present two applications of a new method for proving upper bounds for singular perturbation problems involving maps of bounded variation. The two problems are of first and second order, respectively. The first is a minimization problem, related to the question of optimal lifting for BV-maps with values in $S^1$, for which we prove a Γ-convergence result. The second problem involves the Aviles–Giga functional, $?{\int }_{\Omega }{|{\mathrm{?}}^{2}v|}^2\mathrm{d}x+\frac{1}{?}{\int }_{\Omega }{(1?{|\mathrm{?}v|}^2)}^2\mathrm{d}x$, for which we construct upper bounds via a sequence of functions whose limit has gradient in BV. To cite this article: A. Poliakovsky, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Asymmetric bound states of spiral pairs in excitable media

We present a stable regime of asymmetric bound states for spiral pairs in a generic numerical model of a homogeneous excitable medium. In this regime, one spiral tip (slave) rotates around the other (master). Master-slave dynamics occur for both same-chirality and opposite-chirality spiral pairs in a range of parameters and initial conditions. We study the dependency of master-slave characteristics on the medium's excitation threshold and present a phenomenological model that accounts for the qualitative properties of master-slave dynamics.     

Intermittent self-organization of scroll wave turbulence in three-dimensional excitable media

We study the asymptotic behavior of scroll wave turbulence in large three-dimensional excitable media modeled by FitzHugh-Nagumo equations. The focus is on the type of turbulence caused by negative tension of scroll wave filaments, which is considered to be one of the mechanisms of cardiac fibrillation. We discovered that the initial increase in turbulence complexity can be followed by intermittent self-organization, when complex filament tangles are replaced by a small number of relatively stable triple filament strands. The intermittency is the result of a competition between the destabilizing effect of negative tension and mutual attraction of filaments with similar orientation.     

Induced emission from Cd<Subscript>x</Subscript>Hg<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Te at a wavelength of 3400 nm at 77 K

The results are reported on the observation of the induced emission from Cd_xHg_1?x Te samples optically pumped by a pulsed Nd:YAG laser at temperatures T<77 K. In the wave range λ～ 3300–3600 nm, both stimulated and spontaneous emission were observed. The experimentally measured emission spectra are analyzed. The properties of the spectra from the samples are discussed and the possible applications are considered.     

Energy spectrum and quantum magnetotransport in type-II heterojunctions

Specific features of the energy spectrum of a separated type-II heterojunction in an external magnetic field are studied theoretically and experimentally. It is shown that, due to hybridization of the states of the valence band of one semiconductor and the conduction band of the other semiconductor at the heterointerface, there are level anticrossings, which produce quasigaps in the density of states in a nonzero magnetic field. The experimental results of magnetotransport studies for the GaInAsSb/p-InAs quaternary solid solutions with different doping levels are shown to agree well with the results of simulation, and specific features of the energy spectrum of separated type-II heterojunctions are established.     

CpRu(CO)2(BF4) and [CpFe(CO)2(THF)]+ on mesoporous silica as adsorbents for the removal of dibenzothiophenes from hydrocarbon solutions

The complexes, CpRu(CO)2(BF4) and [CpFe(CO)2(eta2-2-methylpropene)][BF4], react with dibenzothiophene (DBT) and 4,6-dimethyldibenzothiophene (4,6-Me2DBT) to give [CpRu(CO)2(DBT)][BF4] and [CpFe(CO)2(4,6-Me2DBT)][BF4], whose structures were established by X-ray diffraction studies. The same types of products are obtained when dibenzothiophenes react with CpRu(CO)2(BF4) and [CpFe(CO)2(THF)][BF4] that are adsorbed on the mesoporous silica SBA-15. DRIFT and XPS studies indicate that CpRu(CO)2(BF4) and [CpRu(CO)2(DBT)][BF4] are adsorbed on the SBA-15 by hydrogen-bonding of the BF4- anions to surface Si-O-H groups. CpRu(CO)2(BF4)/SBA-15 removes 99% of the DBT in a 45% toluene/55% hexanes simulated petroleum feedstock. This solid phase extractant is less successful for sterically-hindered 4,6-Me2DBT, as only 72% of it is removed. The results show that CpRu(CO)2(BF4) can be immobilized by adsorption on mesoporous silica and that it reacts with dibenzothiophenes in the adsorbed form, CpRu(CO)2(BF4)/SBA-15, in much the same way that it reacts in solution.     

Dispersion of the nonlinear refractive index in sapphire

The nonlinear refractive index, n2, of sapphire was experimentally measured in the 550-1550-nm wavelength range by use of a picosecond Z-scan technique. It was found that in this spectral region the value of n2 decreases monotonically from approximately 3.3 x 10(-16) to approximately 2.8 x 10(-16) cm2/W. An empirical expression for the wavelength dependence of the nonlinear refractive index in the 270-1550-nm range was obtained.     

The Role of Singlet and Triplet Dioxygen Molecules in the EPR and 1H NMR Spectrum Line Broadening

In the Mo^(VI)/H₂O₂/H₂O system, the relaxation time (T ₁) of protons in a water molecule and in a CH₃ group decreases 10 to 30 times under conditions of dismutation of H₂O₂ with the formation of ¹O₂(¹_g). It is experimentally found that the overequilibrium concentration of triplet dioxygen cannot be the reason behind a decrease in T ₁ in the ¹H NMR spectra. Neither can it explain the anomalous line broadening in ESR spectra under conditions of ¹O₂(¹_g) formation in the systems V^(V)/H₂O₂/AcOH and Mo^(VI)/H₂O₂/H₂O. Ab initio calculations showed that it is principle possible that the ³O₄(³·^- _g-¹_g) molecule exists in a snake-like form and is formed by the reaction between ³O₂(³·^- _g) and ¹O₂(¹_g), which is the product of H₂O₂ decomposition in the systems V^(V)/H₂O₂/AcOH and Mo^(IV)/H₂O₂/H₂O. The interaction of ¹O₂ with the ·OOH radical is exothermic (Q = 2.30 kcal/mol) and leads to the formation of ·OOOOH. It is assumed that the paramagnetic species of type ·OOOOH or ³O₄(³ A ₁) that is formed in the reaction might be responsible for the spectral effects observed.     

Synthesis of Aminoalcohols of the Adamantane Series

The reduction of - and -aminoketones and enaminoketones of the adamantane series with sodium borohydride in methanol at room temperature gives the corresponding adamantylaminoalkanols.