Excitation of K-shell electrons by electron impact

The universal scaling behavior for the electron-impact excitation cross sections of the $2s$ states of hydrogen- and helium-like multicharged ions is deduced. The study is performed within the framework of non-relativistic perturbation theory, taking into account the one-photon exchange diagrams. Special emphasis is laid on the near-threshold energy domain. The parametrical relationship between the cross sections for excitation of multicharged ions with different number of electrons is established.Comment: to be published in Physics Letters

Monte Carlo calculations of diatomic molecule gas flows including rotational mode excitation

The direct simulation Monte Carlo method was used to solve the Boltzmann equation for flows of an internally excited nonequilibrium gas, namely, of rotationally excited homonuclear diatomic nitrogen. The semi-classical transition probability model of Itikawa was investigated for its ability to simulate flow fields far from equilibrium. The behavior of diatomic nitrogen was examined for several different nonequilibrium initial states that are subjected to uniform mean flow without boundary interactions. A sample of 1000 model molecules was observed as the gas relaxed to a steady state starting from three specified initial states. The initial states considered are: (1) complete equilibrium, (2) nonequilibrium, equipartition (all rotational energy states are assigned the mean energy level obtained at equilibrium with a Boltzmann distribution at the translational temperature), and (3) nonequipartition (the mean rotational energy is different from the equilibrium mean value with respect to the translational energy states). In all cases investigated the present model satisfactorily simulated the principal features of the relaxation effects in nonequilibrium flow of diatomic molecules

Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities

Agraïments: The first author is is supported by a Ciência sem Fronteiras-CNPq grant number 201002/ 2012-4. A CAPES grant number 88881.030454/2013-01 from the program CSF-PVEWe classify the global phase portraits in the Poincar\'e disc of the differential systems =-y xf(x,y), =x yf(x,y), where f(x,y) is a homogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. This paper together with the results presented in IL2 completes the classification of the global phase portraits in the Poincar\'e disc of all quartic polynomial differential systems with a uniform isochronous center at the origin

New classes of polynomial maps satisfying the real Jacobian conjecture in R2

We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ2. The first class is formed by the polynomials maps of the form (q(x) - p(y),q(y) + p(x)): ℝ2 → ℝ2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f,g): ℝ2 → ℝ2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions