Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

Restoration of universality for the rod-to-coil transition scaling in the infinite-dimensionality limit: Exact results for directed walks

We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd.     

Proton-proton correlations at small relative momentum in neon-nucleus collisions at E/A=400 and 800 MeV

Proton-proton small angle correlations have been measured in neon-nucleus collisions, using the 4 pi detector Diogene, at 400 and 800 MeV per nucleon incident energies. Values of the size of the emitting region are obtained by comparison with the Koonin formula, taking into account the biases of the apparatus. The dependence of the density on target mass and incident energy is also analysed.     

Positive muons in bismuth: determination of their sites,detection of a large local lattice contraction and giant associated electric field gradients,evidence for short and long range diffusion

Using a high purity Bi single crystal the temperature and orientation dependence of the zero and transverse field muon spin relaxation rate has been studied in detail. The results imply that the ⁺ occupies one of the two possible interstitial sites in the distorted rhombohedral crystal structure of Bi below 10 K and the other site above 80 K. At both sites the nearest neighbor Bi atoms are found to be shifted towards the ⁺ by 10% of their nominal distance, implying a large local lattice contraction. In concomitance extremely strong electric field gradients are manifest at the nn Bi nuclei. An almost temperature independent reduced relaxation rate in the temperature range from 20 K to 60 K is interpreted in terms of short range diffusion along a limited chain of alternating types of sites. Above 100 K both long range and short range diffusion are indicated.     

Frequency and efficiency measurements on FIR laser lines close to the N+ 3 P 2−3 P 1 transition

FIR laser lines close to the N^{+ 3} P ₂–³ P ₁ transition at 122 m can be used as a local oscillator for heterodyne detectors. The frequencies of some candidate laser lines from CH₂F₂,¹³CH₃OH, CD₃OD, and CD₃OH have been measured and the output power of the most interesting lines has been optimized.     

The influence of substrate material and annealing procedure on the properties of superconducting thin films

Thin layers YBa₂Cu₃O_7–x. are deposited by a laser ablation technique using a pulsed excimer laser operating at 308 nm. The influence of the substrate material and the annealing procedure on the superconducting behaviour of the 123 film and the reactions between the film and the substrate are studied by resistance, X-ray patterns and TEM measurements. The best results are obtained for deposition on (100) SrTiO₃ substrates. The resistance of the 1 m thick film shows a metallic behaviour, an onset in superconductivity at a temperature of 90 K, and has zero resistance at 86 K. The 123 material has a preferential oriented c-axis perpendicular to the surface plane.     

Synthesis of 24-epiteasterone

Starting from ergosterol, the synthesis of the brassinosteroid 24-epiteasterone has been achieved by the use of a new scheme for introducing a 3-hydroxy-6-keto group as the result of the Birch reduction of the corresponding 5-hydroxy-⁷-3,6-dione.Institute of Bioorganic Chemistry, Belorussian Academy of Sciences, Minsk. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 224–227, March–April, 1992.     

Harary-Read numbers for catafusenes: Complete classification according to symmetry

The classical Harary-Read numbers for catafusenes (catacondensed simply connected polyhexes) are reproduced without using generating functions. A complete (mathematical) solution is given for the distribution of these numbers over the different symmetry groups to which the catafusenes belong.     

Study of the dehydration of Portland Cement by Mössbauer spectrometry

Egyptian Portland Cement in the form of one inch cube was hydrated at different times of hydration. Nine cubes of each period of hydration were heated for five minutes 200, 300, 400 up to 1000°C then were quenched in air. The compressive strength was measured for these samples and related to unheated ones. These cubes were ground and measured by Mössbauer spectrometry to correlate the effect of dehydration of cement pastes on the states of iron, with the decrease of compressive strength. It was observed that starting from 400°C the central doublet characteristic of the hydration process decreased as the dehydration temperature was increased. At 1000°C the dehydration process was complete, the central doublet disappeared and the compressive strength vanished. The hydration process was found to be reversible. The application of Mössbauer spectrometry to estimate the degree of fire in concrete building was demonstrated.