Method of an approximate solution of the Peierls-Nabarro equations for non-planar screw dislocation cores

A class of solutions of a system of three Peierls-Nabarro equations is found using the methods of complex variable. These solutions could be used for investigation of non-planar screw dislocation cores within the Peierls-Nabarro model where the cores are dissociated along three intersecting slip planes.     

Interface energy of semicoherent metal-ceramic interfaces

An ab initio based approach to determine energies and structures for semicoherent interfaces is developed and applied to the Fe(001)/VN(001) system. To account for elastic displacements resulting from the lattice misfit, we compare an atomistic approach using a model potential (embedded-atom method) with a continuum approach using the Peierls-Nabarro model. The total interface energy of the atomistic modeling is found to be well reproduced by the Peierls-Nabarro model, demonstrating that accurate interface energies of semicoherent interfaces can be obtained by combining first principles for the chemical part of the energy and a Peierls-Nabarro model to account for the elasticity of the media.     

On minimum of energy in the Peierls-Nabarro dislocation model

The variations up to the fourth order of the total energy in the Peierls-Nabarro dislocation model are studied. It is shown that the total energy reaches the local functional minimum for the functionf(x) (with positive df/dx) which is the solution of the Peierls-Nabarro integro-differential equation.     

Discrete breathers in the Peyrard-Bishop model of DNA

The Peyrard-Bishop model, which describes the dynamics of a DNA molecule, is considered. The solutions that represent discrete breathers are derived in the framework of the model. The dynamic stability of the stationary discrete breathers with respect to small perturbations is studied. The solutions can be interpreted as the experimentally observed opening of the base pairs in the DNA double strand at the initial stages of denaturation. It is also demonstrated that the model allows the existence of mobile breathers that move in the absence of perturbations in the environment. The interaction of the mobile breathers is numerically simulated. The Peierls-Nabarro barrier and the effective mass and velocity of the breather are estimated.     

Peierls-Nabarro model of planar dislocation cores in b.c.c. crystals

Planar dislocation cores on {110} and {112} planes in b.c.c. crystals are studied using the Peierls-Nabarro model with force laws derived from four different interatomic potentials. A numerical iterative method suitable for solution of the Peierls-Nabarro equation is developed. The cores are represented by a continuous distribution of dislocations. The discussion of the correlation between the force laws and corresponding dislocation densities is based on the properties of the Hilbert transform.     

Dissipative discrete breathers: periodic,quasiperiodic, chaotic,and mobile

The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations.     

The dissociated properties of dislocation in two-dimensional triangular lattice

The dissociated core structure of dislocation in two-dimensional triangular lattice is determined by the variational method within lattice theory. The dissociation effect leads to a narrower core width of partial dislocations than the compact one. The equilibrium separation between two partial dislocations is not very sensitive to the intrinsic stacking fault energy and there exists deviation from the intrinsic stacking fault energy criterion in the continuous elastic theory of dislocation. The relationship between the equilibrium separation and intrinsic stacking fault energy is analogous in lattice theory and the Peierls-Nabarro model. But the equilibrium separation obtained in lattice theory is wider than that obtained in the Peierls-Nabarro model for the same intrinsic stacking fault energy.      

Peierls-nabarro barrier and stress of a/2 〈111〉 edge dislocation in α-Fe

The Peierls-Nabarro barrier and stress of thea/2〈111〉 edge dislocation on {112} and {110} plane inα-Fe at O K is calculated within the Peierls-Nabarro model. The method proposed by Nabarro is used, however, the sine force law is replaced by more general force laws based on two central interionic potentials inα-Fe. The values of the Peierls-Nabarro stress corresponding to one of the chosen interionic potentials, 3·5×10^?4 μ and 1×10^?4 μ on {112} plane (in the twinning direction) and on {110} plane, respectively, seem to be good estimates of the stress necessary to move edge dislocations inα-Fe at O K.     

Peierls-Nabarro model of the core of edge dislocation in Sm A liquid crystal

The core structure of an edge dislocation in Sm A liquid crystal is analysed by using the Peierls-Nabarro method. The stress necessary for a glide motion of dislocation and the dislocation core energy are estimated.     

Peierls-Nabarro model of non-planar screw dislocation cores

The Peierls-Nabarro model originally developed for dislocations with planar cores is modified to describe the cores of screw dislocations extended along two or three intersecting slip planes, under the action of external stress. This concept generalizes the simplified concept of sessile splitting of screw dislocations into singular partials and enables an instructive interpretation of fully atomistic models of screw dislocation cores developed recently for b.c.c. metals. As an example, a numerical solution of the modified Peierls-Nabarro equation is given for the equilibrium configuration of a 1/2 [111] screw dislocation core in -Fe extended along three {110} planes.     

Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately defined Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss.     

Modulational Instability and Energy Localization in a Chain of Interacting Frenkel Excitons

The modulational instability in one-dimensional molecule chain of interacting Frenkel excitons is investigated. The formation of localized modes via modulational instability is predicted and the previous numerical and analytical results are explained. The Peierls-Nabarro (PN) potential barrier for the localized modes is also discussed.     

The effect of shear stress on the screw dislocation core in bcc metals

The screw dislocation core structure in bcc metals under an external shear stress is investigated using the model of generalized splitting as an approximation of the Peierls-Nabarro model of screw dislocation dissociated on three {110} slip planes. The shear stress for which the core structure in this model is unstable is found.     

Experimental examination of displacement field in an edge dislocation core in aluminum

The displacement field of an edge dislocation in aluminum was experimentally investigated. Three typical theoretical models were discussed. High-resolution transmission electron microscopy (HRTEM) and geometric phase analysis (GPA) were used to map the displacement field of an edge dislocation. The displacement field near the dislocation core was determined. The experimental show that Peierls-Nabarro model is the most appropriate theoretical model for displacement field of dislocation in aluminum.     

Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling

A two-dimensional nonlinear Schrödinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the mobility of localized excitations is very poor. This is attributed to a large separation in parameter space of the bifurcation points of the involved stationary modes. At these points the stability of the fundamental modes is changed and an asymmetric intermediate solution appears that connects the points. The control of the power flow across the array when excited with plane waves is also addressed and shown to exhibit great flexibility that may lead to applications for power-coupling devices. In certain parameter regimes, the direction of a stable propagating plane-wave current is shown to be continuously tunable by amplitude variation (with fixed phase gradient). More exotic effects of the nonlinear coupling terms like compact discrete breathers and vortices, and stationary complex modes with nontrivial phase relations are also briefly discussed. Regimes of dynamical linear stability are found for all these types of solutions.     

Line and planar singularities in an anisotropic medium

The problem of a line or planar singularity in an anisotropic medium is treated on the basis of Fourier transformation. Fourier transforms of all basic quantities are given as well as general integral formulae for the displacement and stress fields. The results are applied to the Peierls-Nabarro model of a dislocation in an anisotropic medium.The author is greatly indebted to Mrs. J. Gemperlová from the Institute of Physics of the Czechoslovak Academy of Sciences, Prague, for very valuable discussions and many helpful comments.     

非线性热弹耦合Sine-Gordon型系统的整体吸引子

研究受Peierls-Nabarro力作用的非线性热弹耦 合Sine-Gordon型系统的动力行为.利用算子半群理论证明了 在一定的初边界条件下系统存在连续解, 利用算子半群分解技巧构造了渐近紧的不变吸收集, 进而证明了系统存在整体吸引子.     

Interactions of discrete solitons with structural defects

We investigated the interaction of discrete solitons with defect states fabricated in arrays of coupled waveguides. We achieved attractive and repulsive defects by decreasing and increasing, respectively, the spacing of one pair of waveguides in an otherwise uniform array. Linear and nonlinear propagation in the same samples show distinctly different properties. The role of the Peierls-Nabarro potential in the interaction of the soliton with the defect is discussed.     

Quantitative measurement of displacement and strain by the numerical moiré method

The numerical moié method with sensitivity as high as 0.03 nm has been presented.A quantitative displacement and strai,analysis program has been proposed by using this method.It is applied to an edge dislocation and a stacking fault in aluminum.The measured strain of edge dislocation is compared with theoretical prediction given by Peierls-Nabarro dislocation model.The displacement of stacking fault is also obtained.