Cartesian currents,weak diffeomorphisms and existence theorems in nonlinear elasticity

Summary In this paper we introduce some new classes of functions, among these a class of weak diffeomorphisms. In these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals. In particular, we prove the existence of one-to-one orientation-preserving maps that minimize suitable energies associated with hyperelastic materials. The minimizers are also proved to satisfy equilibrium equations. Finally radial deformations are discussed in connection with cavitation.     

Kinetics of the photodissociation iodine laser with slow pumping

Systematic calculations of maximum inversion were performed for iodine photodissociation laser in dependence on the mixture composition. The flash-lamp radiation was modelled as emanating from an optically thin Xe plasma. Duration of the pumping pulse is about 300 s. The sensitivity of the model to the values of kinetic constants was also tested.     

Laser properties of coactivated YAP: Nd free of colour centres

YAP:Nd, Cr grown under Ar-H₂ or Ar-He-H₂ atmosphere possesses good energy transfer from Cr³⁺ to Nd³⁺ but suffers from the colour centre formation. The centre formation was completely prevented using further admixture of Ce³⁺ and 10^–4–10^–3 wt. % Fe. Small luminescence quenching of Cr³⁺ or Nd³⁺ due to iron ions is negligible in the presence of Ce³⁺. The crystals may be also heavily doped with Nd³⁺ because the increased pumping efficiency compensates the shortening of the luminescence lifetime. YAP: Nd, Ce, Cr, Fe is advisible active laser material particularly for all the types of pulsed lasers.     

Cyclic deformation of aluminium and its alloys

The formation of slip bands is the main mechanism of cyclic deformation in pure Al. Their density, orientation and heights in polycrystalline Al were investigated during cycling. Types, sizes and densities of precipitates are responsible for the mode of cyclic deformation in AlCu4 pure alloy. In technical Al alloys intermetallic phases have detrimental effects on deformation homogeneity and largely govern the fatigue mechanism of the material and especially microcrack initiation.     

Influence of metastable-metastable collisions on electron distribution function in afterglow

The time dependence of the electron distribution function in helium afterglow, for pressures of 60–260 Pa, is calculated for the case in which metastable-metastable reactions are present. The time variation of the shape of the distribution function shows that careful consideration must be made of the time derivative of the distribution function in the Boltzmann equation for the calculation of the rate constant of such reactions from experimentally determined distribution function.     

Large-area boron carbide protective coatings for controlled thermonuclear research prepared byin situ plasma CVD

Impurity release from the first wall and components facing the hot plasma in Tokamak devices for controlled fusion research and the concomitant pollution of the plasma lead to enhanced energy losses and deuterium-tritium luel dilution. Both these effects can prevent reaching the ignition conditions. The recently developed technique for large areain situ deposition of boron carbide protective coatings by means of plasma-induced chemical vapor deposition enables one to significantly improve the purity of the fusion plasma. The prospects of approaching the scientific break-even in the large machines of the Tokarnak type has been increased.Extended version of an invited paper presented at the 10th International Symposium on Boron, Borides, and Related Compounds, Albuquerque, New Mexico, August 1990.The term Tokarnak is an abbreviation of the Russian name toroidal magnetic chamber.     

Scalar gluonium candidates and the radiativeJ/ψ decays

We discuss productions of scalar gluonium candidates in the radiativeJ/ decays. The branching ratios of such productions are estimated on the basis of the Euler-Heisenberg effective Lagrangian for gluon-photon couplings. We mention that these estimates cannot be expected to be accurate to better than within a factor 2. We show that the radiativeJ/ decays probably invalidate gluoniumgg interpretation of the GAMS meson F₀(1590) and a narrow 0⁺⁺ stateS lying below 1 GeV. However, a possible wide scalar effective gluonium candidate(920) is shown not to be excluded by the data on the decayJ/. We also find that the experimental data about radiativeJ/ decays presumably agree with a recently suggested interpretation of F₀(1590) as being approximately a half-and-half mixture of pure 0⁺⁺ gluoniumgg andSU(3)_f singlet quarkoniumq¯q states.     

On the tensor product of supersingleton representations ofosp(1, 2n)

The tensor product of two supersingleton representations _n of the Lie superalgebraosp (1, 2n) is studied forn2. The main results are as follows: (a) anticommutators and commutators of the odd generators in _{n n} form a skew-symmetric representation of the Lie algebrau(n, n); (b) simple explicit form of all irreducible components of _{n n}, which are labelled by a single parameterJ=0, 1, ..., has been found. Each of them is a^*-representation ofosp (1, 2n) for which assertion (a) is valid. The dimension of its vacuum subspace equals , i.e., the nondegenerate vacuum occurs for J=0 only. Basic property of this family of irreducible^*-representations of osp(1, 2n) are analogous to those of massless representations of osp(1, 4).Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.