Integral geometry on families of surfaces in the space

A complex {B_ξ} of submanifolds is called admissible in the sense of integral geometry if there are such densities μ_ξ on B_ξ, that the integral transformation

has a local inversion formula. We prove that compact smooth surfaces of an admissible complex in P³ has degree 3 and obtain complete classification of admissible complexes of quadrics. Several general theorems and conjectures about admissible complex of k-dimensional submanifolds are stated.     

(Q) corrections to particle multiplicity ratios in gluon and quark jets

The order (Q²) correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. Through (Q²) we find

, with r = <n>_{gluon jet}/<n>_{quark jet}. This ratio is independent of the opening angle chosen to define the jets.     

Differential operators on a Riemann surface with projective structure

Let X be a Riemann surface equipped with a projective structure and a theta characteristic on X, or in other words, is a holomorphic line bundle equipped with a holomorphic isomorphism with the holomorphic cotangent bundle Ω_X. The complement of the zero section in the total space of the line bundle has a natural holomorphic symplectic structure, and using , this symplectic structure has a canonical quantization. Using this quantization, holomorphic differential operators on X are constructed. The main result is the construction of a canonical isomorphism

, n≥0, provided i[−2(k−1),0].     

Nonlinear and nonlocal dynamics of spatially extended systems: Stationary states, bifurcations and stability

Spatially extended systems with nonlocal dynamics (e.g. ferromagnetic resonance or current instability) of the type

with uε ⁿ will be studied near the soft-mode instability (wave number k_c ≠ 0) of a stationary and uniform state. An amplitude equation is derived within the framework of a multiple-scale perturbation theory. A particular example of this class of nonlocal dynamics is also treated numerically. As the main result we find that in contrast to the well-known supercritical bifurcation into a stable periodic state, the uniform state can bifurcate supercritically into a stationary state of an amplitude-modulated fast oscillation in space.     

Distance functions and statistics

This paper proves that the Riemannian distance function is maximal in the class of distance functions associated with the Riemannian metric tensor.

Secondly, it is proven that there exists a unique minimum of

on a complete Riemannian surface (M,g) with small curvature, small curvature change and injectivity radius +∞. Here p_iM and γ_v is the maximal geodesic with initial velocity v and 0<t₁<<t_m.     

Simulation of the track growth and determining the track parameters

We have found the equation of the etch pit wall in solid state nuclear track detectors, as follows:

where: x is the distance along a track from the point where the particle entered the detector; V(x) is the ratio of the track etch rate to the bulk etch rate; C is the integration constant that can be determined from particle penetration depth, and y is the normal distance from the particle trajectory to the etch pit wall. The equation is derived assuming the increasing track etch rate V_t along the particle trajectory.

The above equation can be used for the simulation of the track growth and calculating the major and the minor axis of the etch pit opening. The corresponding computer program was set up. The input parameters of this program are: alpha particle energy, incidence angle and removed layer: the output are track parameters. The results obtained by this method are compared with another approach given by Somogyi and Szalay (1973) and reasonably good agreement is found.     

From Planck to GUT via dimensional transmutation

Consider a gauge singlet superfield S coupled to a pair of adjoint fields in a SUSY-GUT. If the tree-level vacuum is flat in S, the vev S which defines the GUT scale will be determined via dimensional transmutation at a scale M where the soft-breaking (mass)² vanishes as a result of running from M_P = (8πG_N)^−1/2. Because of the large number of adjoint fields N_A coupled to S, one finds that M can be generically close to M_GUT = 2 × 10¹⁶GeV:

, where λ is a Yukawa 0.7. This work examines the symmetries and dynamical constraints required in a SUSY-GUT in order that the desired flatness in S is achieved, and that this flatness may survive in a supergravity framework.     

Relative production of vector and pseudoscalar states for light- and heavy-flavour mesons

The relative fractions of vector, V, and pseudoscalar, P, primary mesons produced in and decays, and primary light-flavour mesons produced in fragmentation processes are explained by the hyperfine mass splitting. The difference in corresponding fractions arises from the difference in the constituent quark masses , m_s, m_c and m_b:

The production ratios for strange, charm and beauty mesons evaluated from the ρ/(3π) ratio, measured at LEP for primary produced ρ and π, agree with the results of LEP and lower energy e⁺e⁻ experiments.     

Formation of cementite in tempered Fe–Co–C alloys

In Fe–Co–C alloys, undesirable grain coarsening results from the specific austenite orientation variants that form after the γ→→γ transformations. Tempering of martensite before reheating prevents austenite returning to its original orientation and also limits grain coarsening. However, the reasons for this are unclear. It may be assumed that some differences between cementite formed in tempered and rapidly heated alloys may cause the variation in the final austenite structure. In the present work the orientation relationships between cementite and martensite in two tempered Fe–Co–C alloys have been studied using microbeam electron diffraction in a transmission electron microscope. In both alloys after short-term (rapid heating at 100°C s⁻¹ followed by quench) and long-term (1 and 3 h) tempering treatments the orientation relationships were shown to obey the Isaichev orientation relationships:

However, after rapid tempering, only one carbide variant was found in each crystal, while after long-term tempering, up to three variants were present. This might account for the observed crystallographic reversibility in rapidly heated alloys, contrary to the multiplication of γ variants formed from the long-term tempered martensite.     

Experimental verification of the GDH sum rule

Sum rules involving the spin structure of the nucleon like those due to Bjorken, Ellis and Jaffe and the one due to Gerasimov, Drell and Hearn offer the opportunity to study the structure of strong interactions. At long distance scales in the confinement regime the Gerasimov-Drell-Hearn (GDH) Sum Rule connects static properties of the nucleon like the anomalous magnetic moment κ and the nucleon mass m, with the spin dependent absorption of real photons with total cross sections 0gs_3/2 and σ_1/2:

Here 3/2 and 1/2 identify relative spin orientation of the photon and the nucleon parallel or anti-parallel respectively in the nucleon rest frame; denotes the fine-structure constant and ν the energy of the photon. Hence the full spin-dependent excitation spectrum of the nucleon is related to its static properties. The sum rule has not been investigated experimentally until recently. For the first time this fundamental sum rule is verified by the GDH-Collaboration with circularly polarized real photons and longitudinally polarized nucleons at the two accelerators and . The investigation of the response of the proton as well as of the neutron allows to perform an isospin decomposition. Data from the resonance region up to the onset of the Regge regime are shown. The “sum” on the left hand side of the GDH Sum Rule can be generalized to the case of virtual photons. This allows to establish a Q² dependency and to study the transition to the perturbative regime of QCD. This is the subject of several experiments e.g. at for the resonance region and of the experiment at for higher Q². Moreover, this paper covers the status of theory concerning the GDH Sum Rule, the different experimental approaches and the results for the absorption of real and virtual photons will be reviewed.     

Chemical diffusion in non-stoichiometric cuprous oxide

The kinetics and thermodynamics of point defect diffusion in non-stoichiometric cuprous oxide, Cu_2−yO, has been studied as a function of temperature (1173–1373 K) and oxygen pressure (10²–7×10⁴ Pa) using microthermogravimetric reequilibration technique. It has been shown that the defect diffusion coefficient of cation vacancies, constituting the predominant point defects in this oxide does not change with their concentration, clearly indicating that these defects do not interact and are randomly distributed in the crystal lattice. Consequently, cation vacancy diffusion coefficient, D_V, being the direct measure of defect mobility, can be described by the following empirical equation:

     

Kinetic model for the relationship between mean diameter shortening and age reduction in glass samples

Fission tracks in glass samples are shortened when they experience thermal treatment. Consequently, the observable dimensions associated with track length also diminish. The dimension normally used to characterize track size is the mean diameter of the etched track at the surface, D. Another consequence of length shortening is the reduction of surface density, ρ, implying a reduction of the fission-track age. In this work, a kinetic model is developed to describe the relationship between fission-track mean diameter shortening and surface fission-track density reduction in glass samples, based on geometrical and etching hypotheses. The result is a two-parameter equation given by

(1)

in which h is the thickness of the layer removed during etching and n is a parameter related to the latent track geometry and etching reaction rate. The equation was compared with experimental data on Australite glass found in the literature and with fresh data on Macusanite glass presented in this work. The model fits the experimental curves quite well, showing that it describes the etching effects correctly (within its limitations). In addition, the model equation derived in this work can be very useful in age correction of partially annealed glass samples.     

Thermal characterization of a liquid resin for 3D printing using photothermal techniques

Thermal properties of a liquid resin were studied by thermal lens spectrometry (TLS) and open photoacoustic cell (OPC), respectively. In the case of the TLS technique, the two mismatched mode experimental configuration was used with a He–Ne laser, as a probe beam and an Argon laser was used as the excitation source. The characteristic time constant of the transient thermal lens was obtained by fitting the theoretical expression to the experimental data in order to obtain the thermal diffusivity (α) of the resin. On the other hand, the sample thermal effusivity (e) was obtained by using the OPC technique. In this technique, an Argon laser was used as the excitation source and was operated at 514 nm with an output power of 30 mW. From the obtained thermal diffusivity (α) and thermal effusivity (e) values, the thermal conductivity (k) and specific heat capacity per unit volume (ρc) of resin were calculated through the relationships k = e(α)^1/2 and ρc = e/(α)^1/2. The obtained thermal parameters were compared with the thermal parameters of the literature. To our knowledge, the thermal characterization of resin has not been reported until now. The present study has applications in laser stereo-lithography to manufacture 3D printing pieces.     

Mesure de la diffusivité longitudinale de matériaux anisotropes

Measurement of in-plane diffusivity of anisotropic solid samples. Survey of the techniques developed at LEMTA. Three techniques for the measurement of in-plane diffusivity of anisotropic solid samples have been developed at the Laboratory and are presented here :

• •the two directional heat pulse (flash) method with local contact measurement of two temperatures;
• •the fin method with local contact or contactless measurement of two temperatures;
• •the two directional heat pulse method with measurement of the temperature field by an infrared camera and data processing through integral transformations.

     

接触角与液固界面热阻关系的分子动力学模拟

本文利用分子动力学方法模拟了液体在固体表面的 接触角及液固界面热阻, 并探讨了二者之间的关系. 通过分别改变液固结合强度和固体的原子性质来分析接触角和界面热阻的关系及变化趋势. 模拟结果显示增强液固间相互作用时, 接触角减小的同时界面热阻也随之单调减小; 而改变固体原子间结合强度和原子质量时, 接触角几乎保持不变, 但界面热阻显著改变. 固体原子间结合强度和原子质量影响界面热阻的原因是其改变了固体的振动频率分布, 导致液固原子间的振动耦合程度发生变化. 本文的结果表明界面热阻不仅与由接触角所表征的液固结合强度有关, 还与液固原子间的振动耦合程度有关. 接触角与界面热阻间不存在单值的对应关系, 不能单一地将接触角作为液固界面热阻的评价标准. 关键词： 液固界面 接触角 界面热阻 分子动力学模拟     

Temperature dependence of intensities and widths of N2-broadened lines in the 15 μm CO2 band from tunable laser measurements

Intensities and nitrogen-broadened widths of several low-J lines in the Q-branch of the 15 μm band of CO₂ have been determined over the temperature range 200–300 K. Measurements were made with a tunable infra-red diode laser spectrometer having a spectral resolution 10^-4 cm^-1. Measured intensities are uniformly about 7% lower than available calculations which were based on previous measurements of band intensity. Measured line widths are higher than available calculations and generally followed the relation

b_L⁰(T)=b_L⁰(T₀)(T₀|T)ⁿ

with n = 0.74 (standard deviation 0.08).     

Characteristics of heavy ion tracks in bubble detectors

Characteristics of tracks created by heavy ions in bubble detectors have been studied in detail by using four types of super long (23 cm), self-made bubble detectors and six species of high energy heavy ions: ¹²C, ²⁸Si, ⁴⁰Ar, ⁵⁶Fe, ⁸⁴Kr and ¹³²Xe. The following characteristics of heavy ion tracks in bubble detectors have been recognized:

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On the normalization of Gamow functions

It is proved that the definitions of the norm given by Berggren and Romo are identical. Regularization in ref. ¹) with any convergence factor of the form

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leads to the same result. The existence of the norm is also established for the proton. The norm for neutrons is analytically given.     

Generalized holonomy of supergravities with 8 real supercharges

We show that the generalized holonomy groups of ungauged supergravity theories with 8 real supercharges must be contained in

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, where is the generalized structure group. Here n=4ν is the number of preserved supersymmetries, so the allowed values are limited to n=0,4,8. In particular, solutions of ungauged supergravities in four, five and six dimensions are examined and found to explicitly follow this pattern. We also argue that the G-structure has to be a subgroup of this generalized holonomy group, which may provide a possible classification for supergravity vacua with respect to the number of supercharges.     

Electrochemical behaviour of oxygen at nickel nest cathodic material with catalyst La1−xSrxCoO3

The reduction of oxygen in the three phases gas–liquid–solid using a nickel nest as electrode with a La_1−xSr_xCoO₃ (x=0, 0.3, 0.5, 0.7, 1) series of combined oxides as a catalyst in different electrolytes of acidic H₃PO₄ or alkaline KOH, NaOH or LiOH solution at a fixed optimum oxygen flow-rate at room temperature was studied by the electrochemical method. The electrochemical parameters, such as electron transfer coefficient and exchange current density, were also determined. The La_1−xSr_xCoO₃ series of catalysts was synthesized by a solid-state reaction. XRD was used to confirm the structure of the catalyst. BET, EDS and resistivity measurements were used to investigated the electrochemical behaviour of the cathodic reduction of oxygen in the presence of the catalyst. SEM was also used to inspect the change before and after the reaction with the catalyst. The electron transfer coefficients, β, from the experiments with the various catalysts in the different alkaline electrolytes were determined as follows:

β(in KOH)>β(in NaOH)>β(in LiOH).

It was discovered that La_0.7Sr_0.3CoO₃ as a catalyst has a higher catalytic activity, a higher specific surface area, lower electrical resistivity, better stability and less agglomeration. Therefore, the above catalyst is the best catalyst for oxygen reduction of those studied.