Effects of boundary inclination and boundary type on shear-driven grain boundary migration

A series of molecular dynamics simulations was performed on a bicrystal to which a fixed shear rate was applied parallel to the boundary plane. Under some conditions, grain boundary motion is coupled to the relative tangential motion of the two grains. In order to investigate the generality of this type of coupled shear/boundary motion, simulations were performed for both special (low Σ) and general (non-Σ) [010] tilt boundaries over a wide range of grain boundary inclinations. The data point to the existence of two critical stresses: one for coupled shear/boundary motion and the other for grain boundary sliding. For the non-Σ boundaries, the critical stress for coupled shear/boundary motion is typically smaller than that for sliding; coupled shear/boundary motion occurs for all inclinations. For Σ5 boundaries, for which the critical stress is smaller and depends on boundary inclination, coupled shear/boundary motion occurs for some, but not all inclinations.     

Sinh-Gordon boundary TBA and boundary Liouville reflection amplitude

The ground state energy of the sinh-Gordon model defined on the strip is studied using the boundary thermodynamic Bethe ansatz equation. Its ultraviolet (small width of the strip) behavior is compared with the one obtained from the boundary Liouville reflection amplitude. The results are in perfect agreement in the allowable range of the parameters and provide convincing support for both approaches. We also describe how the ultraviolet limit of the effective central charge can exceed one in the parameter range when the Liouville zero mode forms a bound state.     

Spectrum of local boundary operators from boundary form factor bootstrap

Using the recently introduced boundary form factor bootstrap equations, we map the complete space of their solutions for the boundary version of the scaling Lee–Yang model and sinh-Gordon theory. We show that the complete space of solutions, graded by the ultraviolet behaviour of the form factors can be brought into correspondence with the spectrum of local boundary operators expected from boundary conformal field theory, which is a major evidence for the correctness of the boundary form factor bootstrap framework.     

The boundary of a boundary principle: A unified approach

The boundary of a boundary principle in field theories is described. The difference in treatment of the principle in electrodynamics and general relativity is pointed out and reformulated in terms of underlying mathematical structure of the theories. The problem of unifying the treatment is formulated and solved. The role of E. Cartan's concept of the moment of rotation associated with the curvature of a Levi-Civita connection on a frame bundle is shown to be crucial for the unification. The analysis of the boundary of a boundary principle in Kaluza-Klein theory is performed and the recipe for a unified treatment of the principle in electrodynamics and general relativity is shown to follow from the analysis. It is pointed out that the unification cand be extended to Yang-Mills fields easily.     

A kernel-free boundary integral method for elliptic boundary value problems

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green’s functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green’s functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GMRES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong.     

A kernel-free boundary integral method for elliptic boundary value problems

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green’s functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green’s functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GMRES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong.     

Spin-wave resonance spectrum of a ferromagnetic boundary layer with unsymmetrical boundary conditions

A study is presented on the effects of unsymmetrical (d₁ =–d₂) attachment of surface spins and regards the excitation spectrum for a conducting ferromagnetic layer with spin-system damping. The conductivity causes nonuniformity in the high-frequency field in the film, which alters the shape of the spin-wave spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 119–124, July, 1974.     

Grain boundary interdiffusion in the case of concentration-dependent grain boundary diffusion coefficient

The grain boundary diffusion in a binary system which exhibits a grain boundary phase transition is considered in the framework of Fisher's model. The kinetic law of the growth of the grain boundary phase and the distribution of the diffusant near the grain boundary are calculated. The method of determining of the concentration dependence of the grain boundary diffusion coefficient from the experimentally measured penetration profiles of the diffusant along the grain boundaries is suggested. The experimental results on Zn diffusion in Fe(Si) bicrystals, Ni diffusion in Cu bicrystals and grain boundary grooving in Al in the presence of liquid In are discussed in light of the suggested model.     

Symmetry boundary conditions

A simple approach to energy conserving boundary conditions using exact symmetries is described which is especially useful for numerical simulations using the finite difference method. Each field in the simulation is normally either symmetric (even) or antisymmetric (odd) with respect to the simulation boundary. Another possible boundary condition is an antisymmetric perturbation about a nonzero value. One of the most powerful aspects of this approach is that it can be easily implemented in curvilinear coordinates by making the scale factors of the coordinate transformation symmetric about the boundaries. The method is demonstrated for magnetohydrodynamics (MHD), reduced MHD, and a hybrid code with particle ions and fluid electrons. These boundary conditions yield exact energy conservation in the limit of infinite time and space resolution. Also discussed is the interpretation that the particle charge reverses sign at a conducting boundary with boundary normal perpendicular to the background magnetic field.     

Acoustic boundary layer

On the basis of the boundary-layer concept, a method is proposed for calculating the oscillation-velocity and temperature fields in a volume of arbitrary form, bounded by rigid walls and filled by a viscous heat-conducting fluid. It is shown that the potential part of the sound field may be determined as in an ideal non-heat-conducting fluid, while close to the wall there are not only potential waves but also eddy velocity waves and temperature waves moving out from the wall. A method of solving a broad class of problems is discussed in which the boundary conditions at a distorted surface may be replaced, without significant error, by conditions at a plane boundary.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 92–97, November, 1980.It remains to thank our colleagues in the acoustics faculty for participating in discussions of the work.     

Domain boundary engineering

We review the idea that domain boundaries, rather than domains, can carry information and act as memory devices. Domains are bulk objects; their large response to changing external fields is related to their change in volume, which implies the movement of domain boundaries. In many cases, the design of ‘optimal’ domain structures corresponds to ‘optimal’ domain boundaries with parameters such as the domain boundary mobility, pinning properties and the formation of specific boundaries such as curved boundaries or needle domains. This argument is enhanced further in this review: domain boundaries themselves can host properties which are absent in the bulk, they can be multiferroic, super- or semi-conductors while the matrix shows none of these properties. It is agued that multiferroic walls can be described formally as chiral whereby the chirality relates to state-vectors such as polarisation and magnetic moment and their (non-linear) coupling. Once such walls can be generated reliably, a new generation of devices with much higher storage density than ever produced before can be envisaged.     

Exact boundary condition for time-dependent wave equation based on boundary integral

An exact non-reflecting boundary conditions based on a boundary integral equation or a modified Kirchhoff-type formula is derived for exterior three-dimensional wave equations. The Kirchhoff-type non-reflecting boundary condition is originally proposed by L. Ting and M.J. Miksis [J. Acoust. Soc. Am. 80 (1986) 1825] and numerically tested by D. Givoli and D. Cohen [J. Comput. Phys. 117 (1995) 102] for a spherically symmetric problem. The computational advantage of Ting–Miksis boundary condition is that its temporal non-locality is limited to a fixed amount of past information. However, a long-time instability is exhibited in testing numerical solutions by using a standard non-dissipative finite-difference scheme. The main purpose of this work is to present a new exact boundary condition and to eliminate the long-time instability. The proposed exact boundary condition can be considered as a limit case of Ting–Miksis boundary condition when the two artificial boundaries used in their method approach each other. Our boundary condition is actually a boundary integral equation on a single artificial boundary for wave equations, which is to be solved in conjunction with the interior wave equation. The new boundary condition needs only one artificial boundary, which can be of any shape, i.e., sphere, cubic surface, etc. It keeps all merits of the original Kirchhoff boundary condition such as restricting the temporal non-locality, free of numerical evaluation of any special functions and so on. Numerical approximation to the artificial boundary condition on cubic surface is derived and three-dimensional numerical tests are carried out on the cubic computational domain.     

Significant decrease in interfacial energy of grain boundary through serrated grain boundary transition

The mechanism of serrated grain boundary formation and its effect on liquation behaviour have been studied in a wrought nickel-based superalloy – Alloy 263. It was newly discovered that grain boundaries are considerably serrated in the absence of γ?′-phase or M₂₃C₆ at the grain boundaries. An electron energy-loss spectroscopy study suggests that serration is triggered by the discontinuous segregation of C and Cr atoms at grain boundaries for the purpose of relieving the excessive elastic strain energy. The grain boundaries serrate to have specific segments approaching one {111} low-index plane at a boundary so that the interfacial free energy of the grain boundary can be decreased, which may be responsible for the driving force of the serration. The serrated grain boundaries effectively suppress grain coarsening and are highly resistant to liquation due to their lower wettability resulting from a lower interfacial energy of the grain boundary.     

The kinetic boundary layer for the Fokker-Planck equation with absorbing boundary

The Fokker-Planck equation for the distribution of position and velocity of a Brownian particle is a particularly simple linear transport equation. Its normal solutions and an apparently complete set of stationary boundary layer solutions can be determined explicitly. By a numerical algorithm we select linear combinations of them that approximately fulfill the boundary condition for a completely absorbing plane wall, and that approach a linearly increasing position space density far from the wall. Various aspects of these approximate solutions are discussed. In particular we find that the extrapolated asymptotic density reaches zero at a distance x_M beyond the wall. We find x_M=1.46 in units of the velocity persistence length of the Brownian particle. This study was motivated by certain problems in the theory of diffusion-controlled reactions, and the results might be used to test approximate theories employed in that field.     

Grain boundary structures in silicon carbide: Verification of the extended boundary concept

A grain boundary layer of ca. 0.5 nm in thickness is present in B+C added SiC and SiC without any sintering aids. Since these materials do not show a significant strength-decrease at high temperatures, Ikuhara et al. presumed that the layer is not a second phase of sintering aids or impurities but a reconstructed structure formed to reduce the high energy of the grain boundary, and they called such a boundary an extended boundary. The concept of the extended boundary, however, has not yet been generally accepted for lack of convincing evidence. In the present work, the elements analysis of the boundary layer was made and some additional collateral verifications were conducted in order to inspect the extended boundary concept.     

Numerical treatment of acoustic problems with boundary singularities by the singular boundary method

The singular boundary method (SBM) is a novel boundary-type meshless method based on the fundamental solution of the given governing equation. The SBM employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions. In this paper, we investigate the acoustic problems with boundary singularities using the SBM. This is achieved by combining the SBM with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution. The singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities. Then the regular solution is obtained by the SBM. Numerical examples show the excellent performance of the proposed technique.     

Thermodynamics of curved boundary layers

A thermodynamic treatment of curved boundary layers is given which closely parallels the conventional theory of curved interfacial layers. The boundary analogs to the Gibbs adsorption isotherm and the Gibbs-Tolman-Koenig-Buff equation are derived.     

The causal boundary of space-times

A definition of a causal boundary is given by assigning a future and a past endpoint to any non-extensible timelike or null line. A topology and a partial ordering can be introduced on . The usual conditions for the causal structure can be formulated as properties of . This boundary is compared with other types of boundaries.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General RelativityWork supported by the Deutsche Forschungsgemeinschaft.     

大气边界层的实验模拟

通过皮托管将模拟大气流动的风洞中的风速转换成气流的总静压差，再由压力传感器将其转换成电信号，输入到计算机中进行模／数转换处理，经过进一步处理，得到了风洞中风速边界层的模拟廓线．     

Ellipsometry of mass-transport boundary layers

The effect of mass-transport boundary layers, that are often associated with surface reactions proceeding at high rates, on ellipsometer measurements of the underlying surface has been investigated for typical transport conditions in liquids. The effect can be of significant extent and depends primarily on concentration difference across the boundary layer, angle of incidence and optical constants of the surface. A simplified method for predicting boundary-layer effects based on light refraction is introduced. Computations are in good agreement with experiments.