An exact solution for polaron in the nonlinear lattice in the Su–Schrieffer–Heeger approximation

The exact solution for a polaron in a lattice with cubic nonlinearity is obtained. The electron–phonon interaction is taken into account in the Su–Schrieffer–Heeger approximation. The system of nonlinear differential equations in partial derivatives, obtained in the continuum approximation, is exactly integrable at a certain ratio between the parameters of nonlinearity, α, and the electron–phonon interaction, χ. An approximate solution is obtained for arbitrary values of α and χ. A good agreement between the analytical results with the numerical simulation is observed at not too large values of parameters α and χ, where the continuum approximation is valid. Stable solutions also exist at higher values of these parameters.     

Numerical approximation of the Euler–Maxwell model in the quasineutral limit

We derive and analyze an Asymptotic-Preserving scheme for the Euler–Maxwell system in the quasi-neutral limit. We prove that the linear stability condition on the time-step is independent of the scaled Debye length λ when λ → 0. Numerical validation performed on Riemann initial data and for a model plasma opening switch device show that the AP-scheme is convergent to the Euler–Maxwell solution when Δx/λ → 0 where Δx is the spatial discretization. But, when λ/Δx → 0, the AP-scheme is consistent with the quasi-neutral Euler–Maxwell system. The scheme is also perfectly consistent with the Gauss equation. The possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage.     

Calculation of open p-shell atoms in the algebraic approach of the Hartree–Fock method

Highly precise calculations of analytical Hartree–Fock orbitals and energies have been performed within the limits of the Roothaan–Hartree–Fock atomic theory (Roothaan–Bagus method) for all open p-shell atoms of the Periodic Table. They were calculated in an algebraic approach using Slater-type atomic orbitals (AOs) as basis functions. Nonlinear parameters (orbital exponents) of AOs were optimized with exceptional accuracy by second-order methods. As a result, it was possible to satisfy exactly the virial relation (10^–14–10^–17) with calculated atomic term energies being close to the Hartree–Fock limit.     

On the algebraic types of the Bel–Robinson tensor

The Bel–Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov–Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov–Bel types and the additional ones are intrinsically characterized in terms of the sole Bel–Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel–Robinson tensor in regular cases.     

Numerical approximation of the Vlasov–Poisson–Fokker–Planck system in two dimensions

A numerical method is developed for approximating the solution to the Vlasov–Poisson–Fokker–Planck system in two spatial dimensions. The method generalizes the approximation for the system in one dimension given in [S. Wollman, E. Ozizmir, Numerical approximation of the Vlasov–Poisson–Fokker–Planck system in one dimension, J. Comput. Phys. 202 (2005) 602–644]. The numerical procedure is based on a change of variables that puts the convection–diffusion equation into a form so that finite difference methods for parabolic type partial differential equations can be applied. The computational cycle combines a type of deterministic particle method with a periodic interpolation of the solution along particle trajectories onto a fixed grid. computational work is done to demonstrate the accuracy and effectiveness of the approximation method. Parts of the numerical procedure are adapted to run on a parallel computer.     

Numerical approximation of the Vlasov–Maxwell–Fokker–Planck system in two dimensions

A numerical method is developed for solving the Vlasov–Maxwell–Fokker–Planck system in two spatial dimensions. This system of equations is a model for a collisional plasma in the presence of a self consistent electromagnetic field. The numerical procedure is a type of deterministic particle method and is an extension to include the full electromagnetic field of the approximation method of Wollman and Ozizmir [S. Wollman, E. Ozizmir, Numerical approximation of the Vlasov–Poisson–Fokker–Planck system in two dimensions, J. Comput. Phys. 228 (2009) 6629–6669]. In addition, the long time asymptotic behavior of solutions is studied. It is determined that the solution to the Vlasov–Maxwell–Fokker–Planck system converges to the same steady state solution as that for the Vlasov–Poisson–Fokker–Planck system.     

On the accuracy of the IWM–CFC approximation in differentially rotating relativistic stars

A circular restricted three-body problem describes the motion of a test particle around two massive bodies in circular orbits. In this system, orbital decay caused by a gravitational radiation reaction between the two primary bodies is considered but the direct effect of gravitational radiation on the test particle is neglected. We adopt distance- and time-scale transformations to Newtonian problems so that systems without orbital decay will not depend on separation between the primaries but systems with orbital decay will depend on this separation. If a regular or chaotic orbit is given in a Newtonian system, the starting separation of the primaries varies according to the corresponding decay system. Thus, insights into the chaotic behaviour of a third body in a decay case are provided. For a large initial separation between the primaries, the chaos that exists in a Newtonian problem may be retained for a long enough time scale of dissipative evolution before the primaries coalesce. The final state of a third body is escape attributed to orbital decay.     

An updated description of heavy-hadron interactions in Geant-4

Exotic stable massive particles (SMP) are proposed in a number of scenarios of physics beyond the Standard Model. LHC experiments are expected to be able both to detect and extract the quantum numbers of any SMP with masses around the TeV scale. An understanding of the interactions of SMPs in matter is required to optimise the detection methods and calculate acceptances in an SMP search. In this paper a regge-based model of R-hadron scattering is extended and implemented in Geant-4. In addition, the implications of R-hadron scattering for collider searches are discussed.     

Diamagnetic length scales of the Condon domain phase in Lifschitz–Kosevich–Shoenberg approximation

Equilibrium properties of the non-uniform diamagnetic phase in normal metals (Condon domains) are studied theoretically in the framework of Lifschitz–Kosevich–Shoenberg (LKS) approximation. It is found that characteristic diamagnetic lengths of the phase, e.g. a period of the domain structure and width of interface boundary between domains, as well as specific surface energy of domain wall, are strongly affected by electron correlations and depend on temperature, magnetic field and purity of the sample. The developed theory is in a good agreement with existent experiment data.     

Excitation of strontium atom in electron–atom collisions

The excitation of ³D levels of strontium atom by slow monoenergetic electrons has been studied experimentally. Thirty six excitation cross-sections were measured at 30-eV electron energy. Optical excitation functions for most of the transitions were recorded in the 0–200-eV electron-energy range. The excitation cross-section as a function of the principal quantum number has been found to correspond to a power law for all ³D series.     

An alternative mechanism of Jψ suppression in heavy ion collisions

We argue that $\text{J}\text{ψ}$ suppression observed recently in high energy oxygen-uranium collisions by the NA38 Collaboration at CERN need not imply that the quark-gluon plasma was produced. A considerable part of the effect may be caused by the disintegration of $\text{J}\text{ψ}$'s in collisions with dense hadronic matter (below the phase transition into quark-gluon plasma) produced simultaneously with $\text{J}\text{ψ}$ in heavy ion interactions.     

Self–similar and charged spheres in the free–streaming approximation

We evolve nonadiabatic charged spherical distributions of matter. Dissipation is described by the free–streaming approximation. We match a self–similar interior solution with the Reissner–Nordstr?m–Vaidya exterior solution. The transport mechanism is decisive to the fate of the gravitational collapse. Almost a half of the total initial mass is radiated away. The transport mechanism determines the way in which the electric charge is redistributed.     

Beyond the Monchick–Mason approximation: the mobility of Li+ Ions in H2

The Monchick–Mason approximation for the calculation of the transport coefficients of atomic ions in diatomic gases is extended in a manner that allows comparison of theoretical and experimental mobilities of gaseous ions to serve as quantitative tests of the accuracy of the ab initio, angle- and position-dependent interaction potentials used in the calculations. The feasibility of this procedure is demonstrated with Li⁺ in H₂.     

Study of strange charmed baryons in electron–positron collisions

A modern classification of charmed baryons is presented, and the quark model is briefly described for the ground states and energy levels of excited states. In addition, a survey of experimentally observed states of strange charmed baryons is given.     

On the role of theΔ -isobar in deep inelastic scattering on the deuteron

The role of the nuclear structure effects, viz. the boundness of nucleons and-isobar components, in the deep inelastic scattering of leptons on the deuteron is considered. It is shown that small admixture of the-isobar configurations to the deuteron wave function may lead to significant effects in the spin structure functions of the deuteronb ₁ ^D andg ₁ ^D (x): up to 4% in g ₁ ^D (x) dx and up to 10% ing ₁ ^D (x) at smallx.One of the authors (A.U.) thanks Prof. F.C. Khanna for helpful discussions and for kind offering the information used in our calculations.