Notes on the products of the lower topology and Lawson topology on posets

In this paper, we investigate the relation between the lower topology respectively the Lawson topology on a product of posets and their corresponding topological product. We show that (1) if S and T are nonsingleton posets, then Ω(S×T)=Ω(S)×Ω(T) iff both S and T are finitely generated upper sets; (2) if S and T are nontrivial posets with σ(S) or σ(T) being continuous, then Λ(S×T)=Λ(S)×Λ(T) iff S and T satisfy property K, where for a poset L, Ω(L) means the lower topological space, Λ(L) means the Lawson topological space, and L is said to satisfy property K if for any x∈L, there exist a Scott open U and a finite F⊆L with x∈U⊆↑F.     

Rearrangement of Rare Earth Defects Under Domain Inversion in LiNbO3

Using high resolution excitation-emission spectroscopy we investigated the changes occurring in the optical transition of Er^3? ions in LiNbO₃ during inversion of the ferroelectric axis. In stoichiometric LiNbO₃ we find that a drastic reconfiguration among the different defect sites takes places favoring those centers which have already been dominant in the as-grown sample. The reconfiguration is attributed to changes in the arrangement of the local charge compensators. Furthermore, we find a small shift of the emission transition energy, which is consistent with an increase of the intrinsic electric field. These findings make the Er^3? ions very suitable probes for 3D imaging of domain structures and for in-situ studies of the dynamics of the domain inversion processes and the defect/domain wall interaction.     

Analysis of Iterative Sub-structuring Techniques for Boundary Element Approximation of the Hypersingular Operator in Three Dimensions

The article deals with the analysis of Additive Schwarz preconditioners for the h -version of the boundary element method for the hypersingular integral equation on surfaces in three dimensions. The first preconditioner consists of decomposing into local spaces associated with the subdomain interiors, supplemented with a wirebasket space associated with the subdomain interfaces. The wirebasket correction only involves the inversion of a diagonal matrix, while the interior correction consists of inverting the sub-blocks of the stiffness matrix corresponding to the interior degrees of freedom on each subdomain. It is shown that the condition number of the preconditioned system grows at most as max K H m 1 (1 + log H / h K ) 2 where H is the size of the quasi-uniform subdomains and h K is the size of the elements in subdomain K . A second preconditioner is given that incorporates a coarse space associated with the subdomains. This improves the robustness of the method with respect to the number of subdomains: theoretical analysis shows that growth of the condition number of the preconditioned system is now bounded by max K (1 + log H / h K ) 2 .     

Piezoelectric activities and domain patterns of orthorhombic Ba(Zr,Ti)O3 ceramics

Ba(Zr_xTi_1?x)O₃ (0.025 ≤ x ≤ 0.065) ceramics were prepared by conventional solid-state reaction method. Crystalline structures were analyzed by X-ray diffraction. It was shown that all the Ba(Zr_xTi_1?x)O₃ (0.025 ≤ x ≤ 0.065) ceramics were of orthorhombic phase at room temperature. Piezoelectric activities and domain patterns were investigated and compared with those of BaTiO₃ ceramic. All the Ba(Zr_xTi_1?x)O₃ ceramics showed nearly the same d₃₃ values of about 265 pC/N and the same domain width of about 220 nm. By comparing the grain sizes and domain width of the Ba(Zr_xTi_1?x)O₃ ceramics with those of BaTiO₃ ceramic, it is speculated that the variation of domain width with grain sizes in orthorhombic Ba(Zr_xTi_1?x)O₃ ceramics may be different with that in tetragonal BaTiO₃ ceramic. Besides domain width, the effective inertia mass of domain wall is also considered to be a very important factor that impacts the piezoelectric activities of the Ba(Zr_xTi_1?x)O₃ ceramics.     

In situ hot-stage transmission electron microscopy of Pb(Zr0.52Ti0.48)O3

The domain structure of Pb(Zr_0.52Ti_0.48)O₃ before and after hot-stage experiment has been studied. The influence of maximum temperature, heating and cooling rate on the domain configuration of Pb(Zr_{1? x} , Ti _x )O₃ with x = 0.40, 0.45, 0.48 and 0.55 was analysed. A reliable basis for further hot-stage experiments of Pb(Zr_1?x, Ti_x)O₃ has been established. The investigations revealed a temperature dependent appearance and disappearance of nano- and microdomains. The appearance of microdomains in the nano scale range during cooling, denoted as domain miniaturisation, and the time dependent recovering of the former domain structure, revealed that under specific experimental conditions the domain configuration is reversible.     

Ultrafast Primary Process of Photo-induced N-I Transition and Macroscopic Oscillation of Domain Boundary in TTF-CA

Initial dynamics of photo-induced ionic (I) to neutral (N) phase transition in tetrathiafulvalene- p -chloranil (TTF-CA) was investigated by femtosecond reflection spectroscopy with various excitation intensities. A charge transfer excitation in the I phase produces N donor (D 0 )-acceptor (A 0 ) strings within 2 ps. For a weak excitation intensity, these initial N states decay with a life time of 300 ps at 4 K, but rather multiply leading to macroscopic I-N conversion within 20 ps at 77 K just below the N-I transition temperature T NI . Near T NI , we also found the coherent motion of the macroscopic N-I domain boundary with a period of 85 ps.     

Analysis of the ferroelastic domains and phase transition in the K2SO4 crystal

Abstract

The domain structures of the β-K₂SO₄ crystal were analyzed by group theory. We obtained the permissible kinds of domain association and domain walls from the results of the group theory. It is suggested from the analysis that the (110) and (130) planes are W_mb walls. The value of the spontaneous strain of K₂SO₄ wast = 6.32 × 10^?3 at room temperature and also its temperature dependence was observed.     

Global Stability and Bounds for Coarsening Rates Within the Mean-Field Theory for Domain Coarsening

We investigate the long-time behavior of solutions to the classical mean-field model for coarsening by Lifshitz–Slyozov and Wagner (LSW). In the original work (Lifshitz and Slyozov, 1961 Lifshitz , I. M. , Slyozov , V. V. ( 1961 ). The kinetics of precipitation from supersaturated solid solutions . J. Phys. Chem. Solids 19 : 35 – 50 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]; Wagner 1961 Wagner , C. ( 1961 ). Theorie der Alterung von Niederschlägen durch Umlösen . Z. Elektrochemie 65 : 581 – 594 . [CSA]  [Google Scholar]) convergence of solutions to a uniquely determined self-similar solution was predicted. However, it is by now well known (Giron et al., 1998 Giron , B. , Meerson , B. , Sasorov , V. P. ( 1998 ). Weak selection and stability of localized distributions in Ostwald ripening . Phys. Rev. E 58 : 4213 – 4216 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]; Niethammer and Pego 1999 Niethammer , B. , Pego , R. L. ( 1999 ). Non-self-similar behavior in the LSW theory of Ostwald ripening . J. Stat. Phys. 95 ( 5/6 ): 867 – 902 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar] 2001 Niethammer , B. , Pego , R. L. ( 2001 ). The LSW model for domain coarsening: Asymptotic behavior for total conserved mass . J. Stat. Phys. 104 ( 5/6 ): 1113 – 1144 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) that the long-time behavior of solutions depends sensitively on the initial data. In Niethammer and Pego (1999 Niethammer , B. , Pego , R. L. ( 1999 ). Non-self-similar behavior in the LSW theory of Ostwald ripening . J. Stat. Phys. 95 ( 5/6 ): 867 – 902 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar] 2001 Niethammer , B. , Pego , R. L. ( 2001 ). The LSW model for domain coarsening: Asymptotic behavior for total conserved mass . J. Stat. Phys. 104 ( 5/6 ): 1113 – 1144 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) a necessary criterion for convergence to any self-similar solution which behaves like a finite power at the end of its (compact) support is given. It says that the data have to be regularly varying at the end of their support with the same power. This criterion is also shown to be sufficient if the power is sufficiently small and for data which are close to self-similar.

In this article we extend the local stability result to the whole range of self-similar solutions with compact support. Our first main result establishes global stability of self-similar solutions with not too large power. The proof relies on a global contraction argument for the spreading of characteristics. In addition, we also establish upper and lower bounds for the coarsening rates of the system for a suitable class of initial data whose variation is bounded at the end of the support but not necessarily regular.     

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO₃ ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.     

On Axially Symmetric Domain Walls and Cosmic Strings in Bimetric Theory

It is shown that the axially symmetric thick domain walls and cosmic strings do not survive in the frame work of bimetric theory of gravitation proposed by Rosen (Gen. Relativ. Gravit. 4:435, 1973). Hence vacuum models are presented and studied.