Chaotic behavior of channeling particles

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E(0) and incident angle psi(0), the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles' chaotic motion.     

On the spectrum of the sum of generators for a finitely generated group

Let Γ be a finitely generated group. In the group algebra ℂ[Γ], form the averageh of a finite setS of generators of Γ. Given a unitary representation π of Γ, we relate spectral properties of the operator π(h) to properties of Γ and π. For the universal representationπ _un of Γ, we prove in particular the following results. First, the spectrum Sp(π _un (h)) contains the complex numberz of modulus one iff Sp(π _un (h)) is invariant under multiplication byz, iff there exists a character such that η(S)={z}. Second, forS ⁻¹=S, the group Γ has Kazhdan’s property (T) if and only if 1 is isolated in Sp(π _un (h)); in this case, the distance between 1 and other points of the spectrum gives a lower bound on the Kazhdan constants. Numerous examples illustrate the results.     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

Etude des conditions d'accès au triazino-1,2,4-[4,5-b] indazole

1,2,4-Triazino[4,5-b]indazol-1(2H)one and its derivatives were prepared by transposition of 3-[2-(-1,3,4-oxadiazolyl)]indazole or by ring closure of indazole ethoxymethylidenehydrazides. The synthesis of 1,2,3,4-tetrahydro-l,2,4-triazino[4,5-b]indazole-1,4-dione was achieved by cyclising the N-carbethoxyhydrazide of indazole-3-carboxylic acid and the synthesis of 1,2,4-triazino-[4,5-b]indazol-4(3H)one was made by cyclising the N-carbethoxy-hydrazone of indazole-3-carboxaldehyde. The Oxydation of 1,2,4-triazino[4,5-b]indazole-l(2H)thione gave 1,2,4-triazino-[4,5-b]indazoles. Nmr spectral data are reported.     

Composition and major odorous compounds of the essential oil of Bifora radians,an aldehyde-producing weed

The composition of the essential oil of Bifora radians, an aldehyde-producing weed, has been investigated by capillary gas chromatography, coupled gas chromatography – mass spectrometry, on-line catalytic hydrogenation and coupled gas chromatography – infrared spectrometry. The nineteen compounds identified included eighteen aldehydes: seven alkanals (C6, C9, C10, C11, C12, C13, and C14), ten alkenals, including five (E)-2-alkenals (C12, C13, C14, C15, and C16), and one (E,E)-2,4-alkadienal (C13). Typical Bifora odors were attributed to three major (E)-2-alkenals, C12, C13, and C14.     

Improvement in the synthesis of metallophthalocyanines using microwave irradiation

A successful application of microwave irradiation, in which phthalocyanines were synthesized under solventless conditions from 1,2-phthalonitrile or phthalic anhydride and urea in the presence of metal templates is described. It was found that in comparison with conventional heating, the microwave process is a very useful alternative for cyclotetramerization processes because of reduction of the reaction time, better yield, and easy-to-perform procedure.     

Quantitation of diethylene glycol monoethyl ether in citrus oils

The use of diethylene glycol monoethyl ether as a flavor solvent is restricted. Since existing methods of quantitation are tedious or require sophisticated multi-dimensional GC instrumentation, a simple method has been developed using low cost GC-MS. Monitoring of ions 31 and 45 enables quantitation of DEGEE in essential oils at levels down to 1 μg/g with accuracy equal to or better than 15%.     

13C NMR of indazoles

The carbon-13 chemical shifts and some selected coupling constants of 183 indazoles are reported. The main conclusions of the original references are briefly summarized.Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1159–1179, September, 1995.     

Chemical equilibrium model for the thermodynamic properties of mixed aqueous micellar systems: Application to thermodynamic functions of transfer

Mixed micelles can be formed in water between various pairs of hydrophobic solutes such as surfactants, alcohols and hydrocarbons. These systems can often be studied through the thermodynamic functions of transfer of one of the solutes, usually kept near infinite dilution, from water to an aqueous solution of the other solute. When mixed micelles are formed, these functions change significantly, and often go through extrema, in the region where the binary system micellizes or undergoes some microphase transition.Three main effects are responsible for the observed trends: pair-wise interactions between both solutes in the monomeric form, a distribution of the reference solute between the aqueous and micellar phases and a shift in the monomer-micelle equilibrium in the vicinity of the reference solute. Simple equations can be derived for these three effects which can account for the sign and magnitude of the observed trends using parameters which are derived for the most part from the two binary systems.