Stability analysis of anisotropic universe in nonlinear electrodynamics

This paper is devoted to analyze the stability of locally rotationally symmetric Bianchi type I model through phase space portrait in the presence of nonlinear electrodynamics. The normalized dimensionless quantities are introduced to construct an autonomous system of equations. The critical points and respective eigenvalues are evaluated for different linear forms of coupling between scalar field models and dark matter to discuss the stability of the cosmos. We conclude that the increase/decrease of stability in the presence of nonlinear electrodynamics completely depends on the choice of interaction terms between matter and dark energy models.

Stability analysis of coupled phantom and tachyon field models in nonlinear electrodynamics

This paper is devoted to studying the phase space portrait of FRW universe by taking different linear forms of coupling between scalar field models and dark matter with nonlinear electromagnetic effects. We introduce normalized dimensionless quantities to construct an autonomous system of equations. We evaluate critical points and respective eigenvalues for different parameters to analyze the stability of the cosmos. These points show saddle/unstable behavior for tachyon coupled field with the nonaccelerating universe. In the case of phantom energy, the stability decreases for some critical points which also represent the nonaccelerating universe. We conclude that the dynamical stability of the isotropic and homogeneous universe model reduces in the presence of nonlinear electrodynamics for tachyon as well as the phantom field.

Width dependent collisionless electron dynamics in the static fields of the shock ramp, 2, Phase space portrait

We study numerically in detail the behaviour of electrons in the strongly inhomogeneous static magnetic and electric fields, which are typical for thin quasiperpendicular collisionless shocks. We pay particular attention to the dependence of the final electron velocities on their initial velocities, for different shock widths. Electrons are completely magnetized when the shock is wide, but become demagnetized, and the energies that they acquire rapidly increase with the steepening of the field structure. One of the clear manifestations of the electron demagnetization is the loss of even approximate one-to-one correspondence of the downstream perpendicular velocity to the upstream perpendicular velocity. Electron reflection occurs despite the large cross-shock potential which accelerates electrons along the magnetic field (the regime of complete magnetization) or across the shock (strong demagnetization). The reflected ion fraction is sensitive to the potential, magnetic field jump, and ramp width.

Stochasticity in the Josephson map

The Josephson map describes the nonlinear dynamics of systems characterized by the standard map with a uniform external bias superposed. The intricate structures of the phase-space portrait of the Josephson map are examined here on the basis of the associated tangent map. A numerical investigation of stochastic diffusion in the Josephson map is compared with the renormalized diffusion coefficient calculated using the characteristic function. The global stochasticity of the Josephson map occurs at far smaller values of the stochastic parameter than is the case of the standard map.

THE PHASE-SPACE VIEW OF INFLATION II: FOURTH-ORDER MODELS

The phase space portrait of the cosmological models deduced from fourth-order gravity theories is discussed with the analytical and numerical methods of our previous paper. A comparison is carried out between models inferred from Lagrangian densities containing powers higher than two in the Ricci scalar of curvature, and the Starobinsky model. Some peculiar structures, such as attractors and singular points, emerging neatly from both theories, have a close physical affinity, in addition to the mathematical one. Trajectories of interest in both scenarios are those undergoing an inflationary expansion and then reaching a Friedmannian asymptotic stable phase. These features are moreover discussed through a potential U(R) in RN-models. Three kinds of potential regions are recognized. They are the allowed regions (a-regions), in which trajectories can reach the Friedmannian phase after possibly undergoing an inflationary period, the disconnected regions (d-regions), in which trajectories, although physical, never reach the Friedmannian stage and the forbidden regions (f-regions), in which there are no physical solutions. A general survey of the global phase space for Starobinsky and RN-models is given via Poincaré projections of suitable variables. a-, d-, and f-regions are represented.

THE PHASE-SPACE VIEW OF INFLATION I: THE NON-MINIMALLY COUPLED SCALAR FIELD

The Phase Space portrait of a cosmological model with a scalar field coupled to curvature is discussed in detail, analytically and numerically, for any value of the coupling constant ξ and any power law (ϕ2n) potential. The results, particularly intuitive from the graphical point of view, generalize previous studies on the phase space with minimal coupling (ξ = 0) and quadratic or quartic potentials to the entire parameter space (ξ, n). We find global inflationary attractors, often in analytical form, with or without the correct Friedmannian limit. If the coupling constant is negative, escaping regions may occur, while, if it is positive, a forbidden region cuts out a large part of the phase space. Semiclassical instability of vacuum states and singularity-free trajectories are also discussed.

Generic Classes of Iterative Behavior in Engineering Design Optimization

The iterative dynamics of engineering design optimization processes are considered and generic features are identified. Two optimization methods are applied to the design of an elastic grillage structure and basins of attraction are produced to locate both simple and cyclic attractors. A phase-space portrait is constructed to visualize a complex non-cyclic attractor.