Wave Functions and Energy Terms of the SCHR\"Odinger Equation with Two-Center Coulomb Plus Harmonic Oscillator Potential

Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form.Comment: 4 pages, no figures, LaTeX, submitted to PR

Damping Rotor Nutation Oscillations in a Gyroscope with Magnetic Suspension

A possibility of an effective damping of rotor nutations by modulating the field of the moment transducers in synchronism with the nutation frequency is considered. The algorithms for forming the control moments are proposed and their application is discussed

Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method I. General Theory

The present paper concerns the derivation of phase-integral quantization conditions for the two-centre Coulomb problem under the assumption that the two Coulomb centres are fixed. With this restriction we treat the general two-centre Coulomb problem according to the phase-integral method, in which one uses an {\it a priori} unspecified {\it base function}. We consider base functions containing three unspecified parameters $C, \tilde C$ and $\Lambda$. When the absolute value of the magnetic quantum number $m$ is not too small, it is most appropriate to choose $\Lambda=|m|\ne 0$. When, on the other hand, $|m|$ is sufficiently small, it is most appropriate to choose $\Lambda = 0$. Arbitrary-order phase-integral quantization conditions are obtained for these choices of $\Lambda$. The parameters $C$ and $\tilde C$ are determined from the requirement that the results of the first and the third order of the phase-integral approximation coincide, which makes the first-order approximation as good as possible. In order to make the paper to some extent self-contained, a short review of the phase-integral method is given in the Appendix.Comment: 23 pages, RevTeX, 4 EPS figures, submitted to J. Math. Phy

Spectra of Doubly Heavy Quark Baryons

Baryons containing two heavy quarks are treated in the Born-Oppenheimer approximation. Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form. Using those formulas, the energy spectra of doubly heavy baryons with various quark compositions are calculated analytically.Comment: 19 pages, latex2e, published at PRC61(2000)04520

Relativistic dynamical polarizability of hydrogen-like atoms

Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The relativistic dynamical polarizability of hydrogen-like atoms is calculated and analysed.Comment: 15 pages, 3 figures (not included, but hard copies are available upon request

Исследование процессов формирования пористых выплавляемых моделей, применяемых для изготовления высокоточного литья

Aerospace, manufacturing, and shipbuilding industries strive to enhance their competitiveness by optimizing material utilization and improving production processes. The investment casting process offers the capability to fabricate intricate and precise components using a diverse range of alloys. However, this method is not without its drawbacks, including high manufacturing costs and a significant rate of defective castings, which can reach up to 30 %. These defects primarily arise from the stresses imposed on the wax patterns and ceramic molds, leading to their distortion. To address this issue, efforts have been made to reduce stress by employing compacted wax powders for the production of investment patterns. However, stress relaxation in the wax patterns remains a concern as it can result in elastic deformation of the compacted material and subsequent alterations in the final product dimensions. To mitigate this issue, a series of tests were conducted with the objective of studying stress relaxation under constant compression strain, as described by the Kohlrausch equation. The obtained results provide valuable insights that enable the prediction of the ultimate dimensions of patterns created using different grades of wax.Конкурентоспособность современных предприятий машино-, судо- и авиастроения во многом определяется материало- и энергоэффективностью технологий, направленных на получение конструкций и узлов деталей ответственного назначения. Применение литья по выплавляемым моделям (ЛВМ) обеспечивает получение заготовок повышенной размерной и геометрической точности, сложной пространственной конфигурации из широкой номенклатуры сплавов. К недостаткам ЛВМ следует отнести многостадийность процесса и высокую стоимость конечного продукта, что предполагает недопустимость брака, доля которого может достигать 30 %. Брак в ЛВМ преимущественно вызван теплофизическими явлениями, сопровождающими ряд технологических операций и обусловливающими наличие напряжений в структуре воскообразных и керамических материалов, что определяет деформационные процессы в выплавляемых моделях и оболочковых формах. Для устранения негативного влияния теплофизического фактора и снижения напряжений в структурах промежуточных изделий процесса, выплавляемые модели формируют прессованием порошков воскообразных модельных композиций. При этом нерешенным остается вопрос релаксации напряжений в прессовках, приводящих к упругому отклику уплотненного материала и, как следствие, изменению размеров получаемого изделия. Поиск вариантов наиболее рационального режима формирования прессовки привел к необходимости проведения серии экспериментов, в результате которых предполагается достижение релаксации напряжений σ в условиях постоянной деформации сжатия, описываемого уравнением Кольрауша. Полученные в ходе эксперимента результаты позволят прогнозировать конечные размеры прессовок и сформировать математическую модель процесса, актуальную для широкой номенклатуры воскообразных модельных материалов, применяемых в ЛВМ

Glass capillary X-ray lens: fabrication technique and ray tracing calculations

A new method for producing a compound refractive X-ray lens is described. The lens is designed as glass capillary "lled by a set of concave individual lenses. The method is appropriate for the preparation of 10}1000 spherical lenses in a glass capillary with a diameter of 0.1}1 mm. Lens aberrations are considered and simple formulas for spot size are derived. Ray-tracing simulations on the focusing experiments using 18 keV X-rays are reported. ( 2000 Elsevier Science B.V. All rights reserved