Ultracold collisions between two light indistinguishable diatomic molecules: elastic and rotational energy transfer in HD+HD

A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T \sim 10^{-8}$ K. A global six-dimensional H$_2$-H$_2$ potential energy surface is adopted from a previous work [Boothroyd {\it et al.}, J. Chem. Phys., {\bf 116}, 666 (2002).] State-resolved integral cross sections $\sigma_{ij\rightarrow i'j'}(\varepsilon_{kin})$ of different quantum-mechanical rotational transitions $ij\rightarrow i'j'$ in the HD molecules and corresponding state-resolved thermal rate coefficients $k_{ij\rightarrow i'j'}(T)$ have been computed. Additionally, for comparison, H$_2$+H$_2$ calculations for a few selected rotational transitions have also been performed. The hydrogen and deuterated hydrogen molecules are treated as rigid rotors in this work. A pronounced isotope effect is identified in the cross sections of these collisions at low and ultracold temperatures.Comment: 9 pages, 9 figures. Accepted for publication in Physical Review

Low-energy three-body charge transfer reactions with Coulomb interaction in the final state

Three-body charge transfer reactions with Coulomb interaction in the final state are considered in the framework of coordinate-space integro-differential Faddeev-Hahn-type equations within two- and six-state close coupling approximations. The method is employed to study direct muon transfer in low-energy collisions of the muonic hydrogen H$_\mu$ by helium (He$^{++}$) and lithium (Li$^{+++}$) nuclei. The experimentally observed isotopic dependence is reproduced.Comment: 14 pages REVTeX, accepted for publication in Journal of Physics

Low-energy direct muon transfer from H to Ne10+^{10+}, S16+^{16+} and Ar18+^{18+} using two-state close-coupling approximation to Faddeev-Hahn-type equation

We perform three-body calculation of direct muon-transfer rates from thermalized muonic hydrogen isotopes to bare nuclei Ne$^{10+}$, S$^{16+}$, and Ar$^{18+}$ employing integro-differential Faddeev-Hahn-type equations in configuration space with two-state close-coupling approximation scheme. All Coulomb potentials including the strong final-state Coulomb repulsion are treated exactly. A long-range polarization potential is included in the elastic channel to take into account the high polarizability of the muonic hydrogen. The transfer rates so calculated are in good agreement with recent experiments. We find that the muon is captured predominantly in the $n=6$, 9, and 10 states of muonic Ne$^{10+}$, S$^{16+}$, and Ar$^{18+}$, respectively

Dynamical calculation of direct muon-transfer rates from thermalized muonic hydrogen to C^{6+} and O^{8+}

We perform dynamical calculations of direct muon-transfer rates from thermalized muonic hydrogen isotopes to bare nuclei C$^{6+}$ and O$^{8+}$. For these three-body charge-transfer reactions with Coulomb interaction in the final state we use two-component integro-differential Faddeev-Hahn-type equations in configuration space using close-coupling approximation. To take into account the high polarizability of the muonic hydrogen due to the large charge of the incident nuclei, a polarization potential is included in the elastic channel. The large final-state Coulomb interaction is explicitly included in the transfer channel. The transfer rates so calculated are in good agreement with recent experiments

Mathematical modeling of large elastic-plastic deformations

© 2014 L. U. Sultanov and R. L. Davydov. The paper is devoted to development and numerical implementation for a method for investigation of stress-strain state of the solids with large elastic-plastic deformations. Calculation algorithm is based on the linearized equation of virtual work, defined to actual state. The arc-length method is used. A spatial discretization is based on the finite element method. The developed algorithm of investigation of large elastic-plastic deformations is tested on the solution of the necking of circular bar

Application of confidential intervals for verification of reservoir model at interpretation of well test data

The information on arguments of an oil reservoir to a well test from the point of view of the Bayesian inference are express through even allocation of odds in room of arguments. In article application of confidential spacing for a quantitative appraisal of the information receive from the analysis of results of well test which one are us for upgrading of allocations of odds are offered. Use of confidential spacing for an appraisal of a correctness of a choice of a laboratory formation are show

STRAIN CHARACTERISTICS OF SOILS AND THE METHODS OF THEIR DETERMINATIO

A method is proposed for determining the strain characteristics of soils under dynamic loads, based on the results of experiments on dynamic compression of soils in laboratory conditions on a device of dynamic loading and for solving a wave problem, the statement of which is identical to the statement of the experiment. With the proposed method, the dynamic and static compression moduli, the unloading modulus, the viscosity coefficient of loess soil in the range of seismic loads were determined in accordance with the elastic-viscoelastic soil model developed by G.M. Lyakhov

Numerical Algorithm for Investigating Large Elasto-Plastic Deformations

© 2015, Springer Science+Business Media New York. A method of investigating the stressed-strained state of elasto-plastic bodies subjected to large deformations is presented

Numerical algorithm of solving the problem of large elastic-plastic deformation by fem

A numerical algorithm of the investigation of stress-strain state of the elastic-plastic solids with large deformations is described. The left Cauchy-Green tensor and velocity gradient tensor are used as the tensors describing the deformation and deformation rate. The potential of the elastic strain the specific strain energy, which depends on the left Cauchy-Green tensor is introduced. An isotropic material is considered. The state of stress is described by the Cauchy stress tensor. The linearized constitutive equations of elastic deformation are obtained as a function of the derivative of the Truesdell stress rate on the strain rate. The theory of flow and an additive representation of the total deformation rate are used. The von Mises yield criterion is applied. The research algorithm is based on the incremental method. The principle of virtual work in terms of the virtual velocity is used. After linearization the system of linear equations is obtained, where the unknown is the increment of displacement in the current state. The radial return method with an iterative refinement of the current mode of deformation, based on the introduction to the governing equations of additional power voltages is applied. As an example the potential of elastic deformation is considered. The von Mises yield criterion with isotropic hardening is used. The linearized constitutive relations is obtained. The numerical implementation is based on the finite element method. An 8-node brick element is used. Developed algorithm of investigation of large elastoplastic deformations is tested on the solution of the necking of circular bar problem. The results of solutions and comparison with results obtained by other authors is reduced. Also the deformation of a square plate under internal pressure is investigated

Memory efficient algorithm for solving the inverse gravimetry problem of finding several boundary surfaces in multilayered medium

For solving the inverse gravimetry problem of finding several boundary surfaces in a multilayered medium, the parallel algorithm was constructed and implemented for multicore CPU using OpenMP technology. The algorithm is based on the modified nonlinear conjugate gradient method with weighting factors previously proposed by authors. To reduce the memory requirements and computation time, the modification was constructed on the basis of utilizing the Toeplitz-block-Toeplitz structure of the Jacobian matrix of the integral operator. The model problem of reconstructing three surfaces using the quasi-real gravitational data was solved on a large grid. It was shown that the proposed implementation reduces the computation time by 80% in comparison with the earlier algorithm based on calculating the entire matrix. The parallel algorithm shows good scaling of 94% on 8-core processor. © 2019 Author(s).Ministry of Education and Science of the Republic of Kazakhstan: AP 05133873This work was financially supported by the Ministry of Education and Science of the Republic of Kazakhstan (project AP 05133873)