A New Formulation of a Hénon–Heiles Potential with Additional Singular Gravitational Terms

We examine the orbital dynamics in a new Hénon–Heiles system with an additional gravitational potential, by classifying sets of starting conditions of trajectories. Specifically, we obtain the results on how the total orbital energy along with the transition parameter influence the overall dynamics of the massless test particle, as well as the respective time of escape/collision. By using modern diagrams with color codes we manage to present the different types of basins of the system. We show that the character of the orbits is highly dependent on the energy and the transition parameter.

Experimental Observation of Temperature-Driven Topological Phase Transition in HgTe/CdHgTe Quantum Wells

We report on the comparison between temperature-dependent magneto-absorption and magnetotransport spectroscopy of HgTe/CdHgTe quantum wells in terms of the detection of the phase transition between the topological insulator and band insulator states. Our results demonstrate that temperature-dependent magnetospectroscopy is a powerful tool to discriminate trivial and topological insulator phases, yet the magnetotransport method is shown to have advantages for the clear manifestation of the phase transition with accurate quantitative values of the transition parameter (i.e., critical magnetic field Bc).

Experimental Observation of Temperature-Driven Topological Phase Transition in HgTe/CdHgTe Quantum Wells

We report on comparison between temperature-dependent magneto¬absorption and magnetotransport spectroscopy of HgTe/CdHgTe quantum wells in terms of detection of phase transition between topological insulator and band insulator states. Our results demonstrate that temperature-dependent magnetospectroscopy is a powerful tool to discriminate trivial and topological insulator phases, yet magnetotransport method is shown to have advantages for clear manifestation of the phase transition with accurate quantitative values of transition parameter (i.e. critical magnetic field Bc).

LBB Nozzle Transition Parameter Variation and Plasticity Influence

In the framework of the R6 development programme on leak before break NRG investigated a circumferential through wall crack in a pipe with nozzle. A range of crack angles (3–180°), radius over wall thickness ratios (Ri/t = 5, 10, 20, 50 and 100) and nozzle divergence angles (0, 5, 10, 20, 30 and 40°) have been investigated in order to investigate parameter sensitivity. The stress intensity factor (KI) and the Crack Opening Area (COA) are compared for the nozzle and pipe models. The nozzle investigation is performed using a longitudinal force (100 MPa). It can be concluded that with larger nozzle divergence angles, the resulting maximum KI nozzle factors are higher. The larger nozzle divergence angles have a suppressive effect on the crack opening resulting in a lowered COA nozzle factor. The influence of plasticity has been investigated by a number of analyses including plastic behaviour. The geometry variations are five Ri/t ratios (5, 10, 20, 50 and 100) and eight different crack angles (3, 10, 30, 50, 75, 100, 140 and 180°). A 30° nozzle angle was selected for plastic analyses. The plasticity investigation is performed using longitudinal force (100 MPa). In general the results for KI are higher with the inclusion of plasticity. However, since the inclusion of plasticity has a stress relieving effect on the pipe/nozzle transition, the resulting maximum KI nozzle factor is lowered. The COA results for the individual analyses are overall higher due to the inclusion of plasticity. The COA nozzle factor is lowered, because the relative influence of plasticity is lower on the stiffer nozzle.

Hyperbolic traveling waves driven by growth

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed ϵ-1 (ϵ > 0), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter ϵ: for small ϵ the behavior is essentially the same as for the diffusive Fisher-KPP equation. However, for large ϵ the traveling front with minimal speed is discontinuous and travels at the maximal speed ϵ-1. The traveling fronts with minimal speed are linearly stable in weighted L2 spaces. We also prove local nonlinear stability of the traveling front with minimal speed when ϵ is smaller than the transition parameter.