Dielectric,structural and specific heat properties of lead-free [(1−x)(Na0.5Bi0.5)−xBa]Zr1−yTiyO3 ceramics (x = 0.06, 0.085, 0.09, 0.1 and y = 0.97)

Lead-free [(1?x)(Na_0.5Bi_0.5)?xBa]Zr_1?yTi_yO₃ ceramics (x = 0.06, 0.085, 0.09, 0.1 and y = 0.97) have been prepared by solid-state hot-pressing sintering process. The obtained samples reveal perovskite structure. Structural, thermal expansion, heat capacity, ferroelectric and dielectric measurements have been carried out on these samples in a wide temperature range. The broad anomalies were observed in thermal expansion and heat capacity, which approximately correspond to a structural, ferroelectric and dielectric properties anomaly. These anomalies can be related to temperature features of polar regions and a formation of long-range-order ferroelectric phase. The determined Burns temperature was found to increase with increasing Ba content. The obtained results are discussed in terms of local electric and strain fields caused by a difference in the ionic radii of (Na,Bi) and Ba, and Ti and Zr ions. The NBT–BTZ system is expected to be a new promising candidate for lead-free electronic ceramics.     

In situ study of self-ion irradiation damage in W and W–5Re at 500 °C

In situ self-ion irradiations (150?keV?W⁺) have been carried out on W and W–5Re at 500?°C, with doses ranging from 10¹⁶ to 10¹⁸ W⁺m^?2 (～1.0?dpa). Early damage formation (10¹⁶W⁺m^?2) was observed in both materials. Black–white contrast experiments and image simulations using the TEMACI software suggested that vacancy loops were formed within individual cascades, and thus, the loop nucleation mechanism is likely to be ‘cascade collapse’. Dynamic observations showed the nucleation and growth of interstitial loops at higher doses, and that elastic loop interactions may involve changes in loop Burgers vector. Elastic interactions may also promote loop reactions such as absorption or coalescence or loop string formation. Loops in both W and W–5Re remained stable after annealing at 500?°C. One-dimensional hopping of loops (b?=?1/2 ?111>) was only seen in W. At the final dose (10¹⁸W⁺m^?2), a slightly denser damage microstructure was seen in W–5Re. Both materials had about 3–4?×?10¹⁵ loops m^?2. Detailed post-irradiation analyses were carried out for loops of size???4?nm. Both b?=?1/2 ?111? (～75%) and b?= ?100> (～25%) loops were present. Inside–outside contrast experiments were performed under safe orientations to determine the nature of loops. The interstitial-to-vacancy loop ratio turned out close to unity for 1/2 ?111? loops in W, and for both 1/2 ?111? and ?100? loops in W–5Re. However, interstitial loops were dominant for ?100? loops in W. Re seemed to restrict loop mobility, leading to a smaller average loop size and a higher number density in the W-Re alloy.     

Surface/interface effects on the formation of misfit dislocation in a core–shell nanowire

The misfit strain within the core of a two-phase free-standing core–shell nanowire resulting in the generation of an edge misfit dislocation or an edge misfit dislocation dipole at the core–shell interface is considered theoretically within both the classical and surface/interface elasticity approaches. The critical conditions for the misfit dislocation generation are studied and discussed in detail with special attention to the non-classical surface/interface effect. It is shown that this effect is significant for fine cores of radius smaller than roughly 20 interatomic distances. The positive and negative surface/interface Lamé constants mostly make the generation of the misfit dislocation easier and harder, respectively. Moreover, the positive (negative) residual surface/interface tensions mostly make the generation of the misfit dislocation harder (easier). The formation of individual misfit dislocation is energetically more preferential in finer two-phase nanowires, while the formation of misfit dislocation dipole is more expectable in the coarser ones.     

Expected utility approximation and portfolio optimisation

Classical portfolio selection problems that optimise expected utility can usually not be solved in closed form. It is natural to approximate the utility function, and we investigate the accuracy of this approximation when using Taylor polynomials. In the important case of a Merton market and power utility we show analytically that increasing the order of the polynomial does not necessarily improve the approximation of the expected utility. The proofs use methods from the theory of parabolic second-order partial differential equations. All results are illustrated by numerical examples.     

Helical solitons in vector modified Korteweg–de Vries equations

We study existence of helical solitons in the vector modified Korteweg–de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems, including plasma and chains of particles connected by elastic springs. By using the dynamical system methods such as the blow-up near singular points and the construction of invariant manifolds, we construct helical solitons by the efficient shooting method. The helical solitons arise as the result of co-dimension one bifurcation and exist along a curve in the velocity-frequency parameter plane. Examples of helical solitons are constructed numerically for the non-integrable equation and compared with exact solutions in the integrable vector mKdV equation. The stability of helical solitons with respect to small perturbations is confirmed by direct numerical simulations.     

Stochastic delay foraging arena predator–prey system with Markov switching

Abstract

In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.