Solving topological defects via fusion

Integrable defects in two-dimensional integrable models are purely transmitting thus topological. By fusing them to integrable boundaries new integrable boundary conditions can be generated, and, from the comparison of the two solved boundary theories, explicit solutions of defect models can be extracted. This idea is used to determine the transmission factors and defect energies of topological defects in sinh-Gordon and Lee–Yang models. The transmission factors are checked in Lagrangian perturbation theory in the sinh-Gordon case, while the defect energies are checked against defect thermodynamic Bethe ansatz equations derived to describe the ground-state energy of diagonal defect systems on a cylinder. Defect bootstrap equations are also analyzed and are closed by determining the spectrum of defect bound-states in the Lee–Yang model.     

Dislocation and disclination loops in the virtual-defect method

A method of virtual circular defect loops is developed for determining the elastic fields produced by defects in a bounded medium in the case of an axially symmetric geometry. In this method, continuously distributed virtual circular Volterra and Somigliana dislocation loops are adjusted in such a way as to satisfy the boundary conditions imposed at free surfaces and interfaces. Original calculations of the elastic fields of circular defect loops of different types are carried out. The elastic fields are found for the case of straight dislocations and disclinations in a plate that are perpendicular to the plate plane and for the case of circular disclination loops parallel to the plate plane or to an interface.     

A computational approach towards modelling dislocation transmission across phase boundaries

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.     

Diffusive fluxes associated with interfacial defeet motion and interaction

The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless.Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.     

Point defect properties in the vicinity of an Al/U interface

The static and dynamic properties of vacancies and interstitials have been studied in the neighbourhood of a (1 1 1)Al/(0 0 1)αU interface using classical atomistic techniques. A suitable interatomic EAM potential for the U–Al system have been used for this purpose. To characterize their properties far from the interface, the same defects have also been studied in bulk Al and αU. We observe that point defect stability depends on both distance and zone on the interface plane where it is created and have their minimum formation energy in the first interface layers. Point defects generated beyond the third plane on each phase recover their corresponding bulk value. Regarding vacancy migration, only jumps in the first few layers around the interface are studied. Results show that the vacancy in αU exchanges faster with Al impurities than with most U atoms while the opposite behaviour is observed in Al. All these results suggest a faster diffusion of Al in αU than vice versa in agreement with the experiments.     

The Formation of Defect Complexes in a ZnO Grain Boundary

The microscopic properties a ZnO grain boundary containing extrinsic point defects are studied using a density functional computational approach. The results show that the grain boundary acts as a sink for native defects, such as the zinc vacancy and the oxygen interstitial, and also for bismuth substitutional impurities. The defects tend to accumulate at under-coordinated sites in the boundary core and prefer to form small clusters. In particular the segregation of Bi promotes the formation of the other native defects by lowering their formation energies in the boundary. Individually, the native defects and the Bi impurity do not produce deep interface states in the band gap which are electrically active. However, when the defects cluster to form a Bi_Zn-V_Zn-O_i complex, new gap states are created of acceptor type. It is suggested that these new states are caused by defect interactions which compensate one another resulting in the depletion of an occupied impurity state and new bond formation. The results are discussed in terms of the Schottky barrier model commonly used to describe the electrical characteristics of ZnO varistors.     

Effect of grain boundary structures on the behavior of He defects in Ni: An atomistic study

We investigated the effect of grain boundary structures on the trapping strength of He_N(N is the number of helium atoms) defects in the grain boundaries of nickel. The results suggest that the binding energy of an interstitial helium atom to the grain boundary plane is the strongest among all sites around the plane. The He_N defect is much more stable in nickel bulk than in the grain boundary plane. Besides, the binding energy of an interstitial helium atom to a vacancy is stronger than that to a grain boundary plane. The binding strength between the grain boundary and the He _N defect increases with the defect size. Moreover, the binding strength of the He_N defect to the Σ3(12)[110] grain boundary becomes much weaker than that to other grain boundaries as the defect size increases.     

Trees at an Interface

A lattice tree at an interface between two solvents of different quality is examined as a model of a branched polymer at an interface. Existence of the free energy is shown, and the existence of critical lines in its phase diagram is proven. In particular, there is a line of first order transitions separating a positive phase from a negative phase (the tree being predominantly on either side of the interface in these phases), and a curve of localization–delocalization transitions which separate the delocalized positive and negative phases from a phase where the tree is localized at the interface. This model is generalized to a branched copolymer which is examined in a certain averaged quenched ensemble. Existence of a thermodynamic limit is shown for this model, and it is also shown that the model is self-averaging. Lastly, a model of branched polymers interacting with one another through a membrane is considered. The existence of a limiting free energy is shown, and it is demonstrated that if the interaction is strong enough, then the two branched polymers will adsorb on one another.     

Total internal reflection of a Gaussian light beam

An approximate theoretical model for calculating the reflected and refracted fields of a Gaussian light beam at a plane interface between two isotropic media is formulated on the basis of a Fourier integral. In the vicinity of the critical angle of incidence (for total internal reflection) the model predicts the presence of two refracted beams, one displaced along the interface by an amount equal to the Goos-Hänchen shift; curvature of the phase fronts and nonalignment of the effective directions of energy and phase propagation occur for each beam, as in an anisotropic medium.     

Theoretical results concerning the influence of non‐random‐field defects

We shall focus on extended defect systems and review their critical behavior. Primarily, with two aims, one of which is to understand phase transitions and how to derive effective dimension of extended defects with various structures, and the other is to propose a new research-method for defect systems, we let extended defects grow on a triangular lattice with frustration in a similar fashion to diffusion-limited aggregation, and discuss the situation. The existence of phase transitions, phase diagram, effective defect dimension, etc. will be shown. Furthermore, we shall summarize theoretical studies of extended defect systems on phase diagrams, critical behavior, tricritical behavior, and crossover behavior as static properties, and on nonconserved systems and conserved systems as dynamic properties.     

First-order depinning transition in two-dimensional abraham model: RG approach

Using a position-space renormalization group (RG) we analyse the competition for an interface between the boundary defect and an additional line of defect bonds in the two-dimensional Abraham model. The RG phase diagram, obtained over the whole range of temperatures and pinning parameters, indicate that beside the continuous wetting transition this model exhibits a finite-temperature interface depinning transition of the first order in agreement with recently obtained exact results.     

一维相位缺陷量子行走的共振传输

从分立时间量子行走理论出发, 分别在包含两个格点相位缺陷和一段格点相位缺陷(方相位势)的一维格点线上研究量子行走的静态共振传输. 利用系统独特的色散关系和边界点上的能量守恒条件, 获得量子行走通过缺陷区域的透射率, 讨论了相位缺陷的强度和宽度不同时透射率随入射动量的变化行为. 在相位缺陷强度π/2两侧, 透射率表现出不同的共振特性, 并给出了强缺陷强度下共振峰和缺陷宽度的关系.     

Delocalization transition of a rough adsorption-reaction interface

We introduce a kinetic interface model suitable for simulating adsorption-reaction processes which take place preferentially at surface defects such as steps and vacancies. As the average interface velocity is taken to zero, the self-affine interface with Kardar-Parisi-Zhang-like scaling behavior undergoes a delocalization transition with critical exponents that fall into a different universality class. As the critical point is approached, the interface becomes a multivalued, multiply connected self-similar fractal set. The scaling behavior and critical exponents of the relevant correlation functions are determined from Monte Carlo simulations and scaling arguments.     

Anderson Localization for a Supersymmetric Sigma Model

We study a lattice sigma model which is expected to reflect the Anderson localization and delocalization transition for real symmetric band matrices in 3D. In this statistical mechanics model, the field takes values in a supermanifold based on the hyperbolic plane. The existence of a diffusive phase in 3 dimensions was proved in Disertori et al. (Commun. Math. Phys., doi:, 2009) [2] for low temperatures. Here we prove localization at high temperatures for any dimension d ≥ 1. Our analysis uses Ward identities coming from internal supersymmetry.     

Surface induced disordering at first-order bulk transitions

Semi-infinite systems may undergo surface induced disordering transitions. These transitions exhibit both critical surface behaviour and interface delocalization phenomena. As a consequence, various surface exponents can be defined although there are no bulk exponents. It is shown that the corresponding power laws can be derived from a scaling form for the surface free energy where two independent surface exponentsΔ ₁ and α _s enter. In addition, global phase diagrams with finite symmetry breaking fields are also briefly discussed.     

相位失配弹性平板复合波导中的缺陷态*

为了在弹性波波导中实现缺陷态的调控,该文基于相位失配原理设计了一种周期性平板波导结构。以正弦边界弹性波导为例,通过连接具有不同相位的两段波导结构,形成了弹性板中不同程度的缺陷,并分析了其谱带特性和能量局域化特征。结果表明,禁带中存在两个不同模式的缺陷态,其以透射峰形式出现并随着相位的改变产生频移。与此同时,两个缺陷态在空间上对应的应力场和位移场分布也具有不同的模态特征。该文提出的复合弹性波导缺陷态调控方法,不仅为研究弹性波与结构之间的内在联系提供了关键的理论支持,也为实际弹性波探测器件的设计提供重要参考。     

Quasi-Diffusion in a 3D Supersymmetric Hyperbolic Sigma Model

We study a lattice field model which qualitatively reflects the phenomenon of Anderson localization and delocalization for real symmetric band matrices. In this statistical mechanics model, the field takes values in a supermanifold based on the hyperbolic plane. Correlations in this model may be described in terms of a random walk in a highly correlated random environment. We prove that in three or more dimensions the model has a ‘diffusive’ phase at low temperatures. Localization is expected at high temperatures. Our analysis uses estimates on non-uniformly elliptic Green’s functions and a family of Ward identities coming from internal supersymmetry.     

Domain wall delocalization,dynamics and fluctuations in an exclusion process with two internal states

We investigate the delocalization transition appearing in an exclusion process with two internal states, respectively on two parallel lanes. At the transition, delocalized domain walls form in the density profiles of both internal states, in agreement with a mean-field approach. Remarkably, the topology of the system’s phase diagram allows for the delocalization of a (localized) domain wall when approaching the transition. We quantify the domain wall’s delocalization close to the transition by analytic results obtained within the framework of the domain wall picture. Power law dependences of the domain wall width on the distance to the delocalization transition as well as on the system size are uncovered, they agree with numerical results.     

Curvature walls and focal conic domains in a lyotropic lamellar phase

In the quasi-ternary CPCl/brine/hexanol lyotropic system, the interface of the lamellar and L₃ sponge phases displays a phenomenon of epitaxy: the layers of the lamellar phase tend to make a constant non-trivial angle with the interface. Thin samples of lamellar phase embedded in the sponge phase are thus submitted to oblique anchoring conditions and defects are created in the lamellar phase in order to satisfy the bulk lamellar ordering and the boundary conditions. We have studied small droplets of lamellar phase in the sponge phase. They do not exhibit the classic defects (focal conic domains) but wall defects, which appear in order to satisfy the smectic elasticity and the boundary conditions. Moreover we show through experiments in controlled geometry that, even in the presence of focal conic domains, wall defects control the size and periodicity of the textures which are observed at the interface. Received 4 November 1998     

Defects in rutile and anatase polymorphs of TiO2: kinetics and thermodynamics near grain boundaries

The direct consequence of irradiation on a material is the creation of point defects-typically interstitials and vacancies, and their aggregates-but it is the ultimate fate of these defects that determines the material's radiation tolerance. Thus, understanding how defects migrate and interact with sinks, such as grain boundaries, is crucial for predicting the evolution of the material. We examine defect properties in two polymorphs of TiO(2)-rutile and anatase-to determine how these materials might respond differently to irradiation. Using molecular statics and temperature accelerated dynamics, we focus on two issues: how point defects interact with a representative grain boundary and how they migrate in the bulk phase. We find that grain boundaries in both polymorphs are strong sinks for all point defects, though somewhat stronger in rutile than anatase. Further, the defect kinetics are very different in the two polymorphs, with interstitial species diffusing quickly in rutile while oxygen defects-both interstitials and vacancies-are fast diffusers in anatase. These results allow us to speculate on how grain boundaries will modify the radiation tolerance of these materials. In particular, grain boundaries in rutile will lead to a space charge layer at the boundary and a vacancy-rich damage structure, while in anatase the damage structure would likely be more stoichiometric, but with larger defects consisting primarily of Ti ions.