Reaction path as a gradient line on a potential energy surface

The reaction path is shown to be always a gradient line on a potential energy surface (PES ) of a molecule. The properties of gradient lines on the PES are elucidated. Correct symmetry conservation rules along the gradient line are derived. The behavior of the gradient line on a PES with different topologies are considered. © 1994 John Wiley & Sons, Inc.     

A gas pendulum

It is shown that a periodic two-dimensional isentropic motion of a gas exists and it is described by an exact solution of the equations of gas dynamics. A polytropic gas that fills a circular cylinder rotates and oscillates (in the radial direction) simultaneously under the action of periodically changing external pressure. The solution obtained belongs to the class of solutions with a velocity field that is linear in the coordinates (with homogeneous deformation). Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 115–119, September–October, 2000.     

Thermoelectric properties of p-Bi2 ? xSbxTe3 solid solutions under pressure

This paper reports on a study of the Seebeck coefficient and power factor κ of p-Bi_{2 − x} Sb _x Te₃ solid solutions with different contents of antimony atoms in the bismuth sublattice for x = 0, 1.4, 1.5, and 1.6 under variation of pressure of up to 15 GPa. The magnitude of κ has been found to grow nonmonotonically within the pressure region of 2–4 GPa. The effective mass of the density of states m/m ₀ and the mobility μ₀ have been calculated with due account of degeneracy within the parabolic model of the energy spectrum assuming isotropic charge carrier scattering. It has been shown that application of pressure brings about a decrease of the effective mass m/m ₀ and an increase of carrier mobility. The power factor κ of the p-Bi_0.6Sb_1.4Te₃ composition exhibits at the pressure P ≈ 4 GPa the largest increase of the power factor κ as a result of a weak decrease of the effective mass m/m ₀ and an increase of carrier mobility as compared to the other solid solution compositions. The specific feature of the variation of the power factor κ with a change of the pressure in bismuth telluride near P ≈ 3 GPa, which is accompanied by formation of a knee in the m/m ₀ vs. P dependence, can be assigned to an electronic topological transition.     

Optimization of matching section of an accelerator with a spatially uniform quadrupole focusing

A new approach is proposed for determining the matching section profile in an accelerator with spatially uniform quadrupole focusing. The approach based on mathematically formalized optimization problem and considerably extends the class of possible profiles since it is primarily independent of specific laws of variation of rigidity in the matching section and makes it possible to find the values of the aperture at the boundaries and in the cells directly as a solution.     

A method of calculating the radiation flux and its divergence in regions with stepped temperature and chemical composition distribution

An approximate method is proposed which makes it possible to compute the radiation flux and its divergence when the absorption cross section depends in a complex manner on the wavelength. Radiation scattering is ignored. The method is described for the case when the region occupied by the radiating and absorbing gas can be divided into finite number of subregions in which the temperature and the chemical composition are constant. Examples are given of the numerical calculations of the radiation flux.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 54–62, March–April, 1971.The author wishes to express his gratitude to É. Filippova for help in the computations.     

On inner dilatations of the mappings with unbounded characteristic

For the mappings f:D ? D￠,  D,  D￠ ì \mathbbRⁿ f:D \to D',\,\,D,\,\,D' \subset {\mathbb{R}^n} , n ≥ 2, satisfying certain geometric conditions in the fixed domain D, we have proved estimates of the form K _I (x, f) ≤ Q(x) almost everywhere, where K _I (x, f) is the inner dilatation of f at a point x, and Q(x) is a fixed real-valued function responsible for the “control” over a distortion of the families of curves in D at a mapping f.