Mechanism of adsorption,electroreduction and hydrogenation of compounds with ethylenic bonds on platinum and rhodium: Part II. Comparison of the electroreduction and catalytic hydrogenation processes

The catalytic liquid-phase hydrogenation of maleic acid on platinum and rhodium has been investigated. It is shown that the rate-determining step of this process as well as of the electroreduction process of maleic acid is the interaction of the chemisorbed particle of maleic acid with the adsorbed hydrogen which is formed at the preceding rapid stage of either the dissociative adsorption of molecular hydrogen, or the electrochemical stage of hydrogen ion discharge. The rate of the process with the same degree of surface coverage with hydrogen and chemisorbed particles of maleic acid does not depend on whether the process is carried out catalytically or electrochemically, on whether maleic acid and hydrogen were preliminarily adsorbed on the surface of the electrode-catalyst or not. With due regard for the mutual influence of chemisorbed particles participating in the rate-determining stage, the main kinetic equations for the electroreduction and catalytic hydrogenation processes have been derived. The difference in the rates of electroreduction of maleic acid on platinum and rhodium, with the same degree of electrode surface coverage with reactants, is shown to be the result of differences in the adsorption heats (or bonding strength with the surface) of hydrogen and maleic acid on these two metals. Experimental procedures are described in Part I [1].     

Small-angle scattering from the deterministic fractal systems<Superscript>1</Superscript>

The intensity profile of small-angle neutron sc attering from three-dimensional triadic Cantor and Vicsek fractals is calculated when the fractal sets are monodisperse and their positions are uncorrelated. It is shown that the scattering intensities present minima and maxima superimposed on a power-law decay with the exponent coinciding with the fractal dimension of the scatterer. This is in accordance with the scattering from similar systems like Menger sponge or fractal jacks, which all exhibit the same behavior. For a finite iteration, the Porod power decay of the intensity is displayed at large values of momenta beyond the fractal region.     

Friction and diffusion of matter-wave bright solitons

We consider the motion of a matter-wave bright soliton under the influence of a cloud of thermal particles. In the ideal one-dimensional system, the scattering process of the quasiparticles with the soliton is reflectionless; however, the quasiparticles acquire a phase shift. In the realistic system of a Bose-Einstein condensate confined in a tight waveguide trap, the transverse degrees of freedom generate an extra nonlinearity in the system which gives rise to finite reflection and leads to dissipative motion of the soliton. We calculate the velocity and temperature-dependent frictional force and diffusion coefficient of a matter-wave bright soliton immersed in a thermal cloud.     

Bound states in gauge theories as the Poincaré group representations

The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincaré group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of γ + γ → π ₀ +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.     

Numerical investigation of the air injection effect on the cavitating flow in Francis hydro turbine

At full and over load operating points, some Francis turbines experience strong self-excited pressure and power oscillations. These oscillations are occuring due to the hydrodynamic instability of the cavitating fluid flow. In many cases, the amplitude of such pulsations may be reduced substantially during the turbine operation by the air injection/ admission below the runner. Such an effect is investigated numerically in the present work. To this end, the hybrid one-three-dimensional model of the flow of the mixture “liquid?vapor” in the duct of a hydroelectric power station, which was proposed previously by the present authors, is augmented by the second gaseous component — the noncondensable air. The boundary conditions and the numerical method for solving the equations of the model are described. To check the accuracy of computing the interface “liquid?gas”, the numerical method was applied at first for solving the dam break problem. The algorithm was then used for modeling the flow in a hydraulic turbine with air injection below the runner. It is shown that with increasing flow rate of the injected air, the amplitude of pressure pulsations decreases. The mechanism of the flow structure alteration in the draft tube cone has been elucidated, which leads to flow stabilization at air injection.     

Numerical simulation of steady cavitating flow of viscous fluid in a Francis hydroturbine

Numerical technique was developed for simulation of cavitating flows through the flow passage of a hydraulic turbine. The technique is based on solution of steady 3D Navier—Stokes equations with a liquid phase transfer equation. The approch for setting boundary conditions meeting the requirements of cavitation testing standard was suggested. Four different models of evaporation and condensation were compared. Numerical simulations for turbines of different specific speed were compared with experiment.     

Dilute Bose gas: short-range particle correlations and ultraviolet divergence

The modified Bogoliubov model where the primordial interaction is replaced by the t matrix is reinvestigated. It is shown to provide a negative value of the kinetic energy for a strongly interacting dilute Bose gas, contrary to the original Bogoliubov model. To clear up the origin of this failure, the correct values of the kinetic and interaction energies of a dilute Bose gas are calculated. It is demonstrated that both the problem of the negative kinetic energy and the ultraviolet divergence, dating back to the well-known paper of Lee, Yang and Huang, is connected with an inadequate picture of the short-range boson correlations. These correlations are reconsidered within the thermodynamically consistent model proposed earlier by the present authors. Found results are in absolute agreement with the data of the Monte-Carlo calculations for the hard-sphere Bose gas. Received 10 February 2000 and Received in final form 28 November 2000     

Dilute Bose gas revised

The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject. The aim of our paper is to propose another way of treating the dilute Bose gas with an arbitrary strong interaction. Using the reduced density matrix of the second order and a variational procedure, this way allows us to escape the inconsistency mentioned and operate with singular potentials of the Lennard-Jones type. The derived expansion of the condensate depletion in powers of the boson density n=N/V reproduces the familiar result, while the expansion for the mean energy per particle is of the form epsilon=2 pi planck(2)an/m[1+128/(15 square root of [pi]) square root of [na(3)](1-5b/8a)+...], where a is the scattering length and b> or =0 stands for one more characteristic length depending on the shape of the interaction potential (in particular, for the hard spheres a=b). All the consideration concerns the zero temperature.