Lie symmetries and exact solutions of nonlinear equations of heat conductivity with convection term

The Lie symmetries of nonlinear diffusion equations with convection term are completely described. The Lie ansatzes and exact solutions of a certain nonlinear generalization of the Murray equation are constructed. An example of the family of non-Lie solutions of the Murray equation is given.     

Parametric study of high energy plasmas for electrothermal-chemicalpropulsion applications

Theoretical calculations are performed with a one-dimensional (1-D), steady state, isothermal computer plasma model to define plasma output parameters for various input electrical energies and capillary radii of relevance to the electrothermal-chemical (ETC) propulsion concept. Three capillaries of 1.92, 4.75, and 7.0 mm radius, and a fixed length of 11.84 cm, were chosen for this study with input currents between 30 and 350 kA. Plasmas are categorized according to their total power and energy levels (based on a 3-ms pulse width) and are compared with respect to their resistance, exit pressure, and core plasma temperature. The input power ranges from 0.17 to 1.89 GW, for input energies from 0.49 to 5.80 MJ, which is considered suitable coverage for ETC ignition through ETC enhanced propulsion concepts. The study shows that the range of resistance, pressure, and temperature are 12.8-195 mΩ, 19.8-2000 MPa, and 2.9-13.5 eV, respectively, for the chosen capillary geometry. Flow conditions for plasma calculations include choked (no pressure boundary) and unchoked (450-MPa pressure boundary) for some calculations. Results from the computational model and interpretations from the perspective of capillary implementation into ETC propulsion concepts are also included     

Excimer Laser Processing of Grey Cast Iron: Microstructural and Tribological Characterization

Pearlitic grey iron was treated by means of a XeCl laser to remelt only a shallow layer. This process allows to modify the heteregeneous surfaces of cast irons in order to improve their tribological behaviour. The energy density ranged from 0.3 to 3 J/cm² and the number of shots from 4 to 40. It is shown that after laser irradiation austenite is formed in the melted layer; compressive stresses at the surface were exhibited as well as the deposition of graphite and the formation of carbides. It is shown that excimer laser processing highly decreases the coefficient of friction and the wear rate. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ferromagnetic resonance in multilayer [Fe/Cr]n structures with noncollinear magnetic ordering

The excitation spectrum in an [Fe/Cr]n multilayer structure with non-collinear magnetic ordering was studied by the ferromagnetic resonance (FMR) method in the frequency interval 9.5–37 GHz at room temperature. Besides an acoustic branch, several additional modes were observed under parallel excitation of resonance. The FMR spectrum was calculated analytically in a biquadratic exchange model, neglecting in-plane anisotropy, for an infinite number of layers in the structure and numerically for a finite number of layers contained in real samples. It was shown that the observed modes correspond to excitation of standing spin waves with wave vectors perpendicular to the film plane. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 690–695 (10 May 1998)     

On the nature of the γ-α transition in cerium

In 1964 Davis and Adams established that the large increase of the thermal expansion and compressibility in the critical region of the γ-to α-Ce phase transition occurs predominantly in the α phase. This provides strong evidence that a tricritical point is realized in Ce. This also means that the aforementioned transition is not isomorphic and that α-Ce should have a distorted fcc structure. A careful examination of Jayaraman’s data (1965) shows that a second-order transition line continues beyond the tricritical point to the vicinity of a triple point on the melting curve. The phase boundary with the tricritical point and the minimum of the melting curve are reconstructed within the framework of Landau theory. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 111–117 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Nuclear fusion in the mesic molecule d μ 3He

A new scheme is presented for the physical processes leading to the nuclear fusion reaction d(³He, ⁴He)p catalyzed by a negatively charged muon μ⁻. It is shown that the observable rate and yield of the nuclear reaction depend on a chain of ion-molecular reactions involving the participation of the dμ ³He molecule. New calculations of the nuclear fusion rates in the dμ³He molecule are presented. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 89–94 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The stress-strain state of anisotropic rock

We use integrals of Cauchy type and the complex potentials of S. G. Lekhnitskii to solve the problem of the stress-strain state of a piecewise-homogeneous anisotropic rock during the working of a horizontal seam of mineral. We study the stress distribution in the deloaded zones. Three figures, 1 table. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 81–86.     

Statistical hydrodynamics of magnetic fluids. I. the nonequilibrium statistical operator method

The Zubarev nonequilibrium statistical operator is used to describe the generalized hydrodynamic state of a magnetic fluid in an external magnetic field. The magnetic fluid is modeled with “liquid-state” and “magnetic” subsystems described using the classical and quantum statistics methods respectively. Equations of the generalized statistical hydrodynamics for a magnetic fluid in a nonhomogeneous external magnetic field with the Heisenberg spin interaction are derived for “liquid-state” and “magnetic” subsystems characterized by different nonequilibrium temperatures. These equations can be used to describe both the weakly and strongly nonequilibrium states. Some limiting cases are analyzed in which the variables of one of the subsystems can be formally neglected. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 115, No. 1, pp. 132–153, April, 1998.     

Kinetics of the reactions of the IO radical with dimethyl sulfide,methanethiol, ethylene,and propylene

The reactions of IO radicals with CH₃SCH₃, CH₃SH, C₂H₄, and C₃H₆ have been studied using the discharge flow method with direct detection of IO radicals by mass spectrometry. The absolute rate constants obtained at 298 K are the following: IO + CH₃SCH₃ → products (1): k₁ = (1.5 ± 0.2) × 10^?14; IO + CH₃SH → products (2): k₂ = (6.6 ± 1.3) × 10^?16; IO + C₂H₄ →products (3): k₃ < 2 × 10^?16; IO + C₃H₆ → products (4): k₄ < 2 × 10^?16 (units are cm³ molecule^?1 s^?1). CH₃S(O)CH₃ and HOI were found as products of reactions (1) and (2), respectively. The present lower value of k₁ compared to our previous determination is discussed.