bcc Fe的刃型位错中氦-空位团的稳定性

 采用周期性原子阵列方法建立bcc Fe中的刃型位错,利用分子动力学计算了0 K时bcc Fe的位错芯里氦-空位团的稳定性,并与理想Fe晶体里氦-空位团的稳定性进行比较发现,位错的作用导致氦-空位团不稳定。点缺陷（He、空位与自间隙Fe原子）与氦-空位团的结合能与团中氦-空位比例密切相关,当氦与空位数之比在3~6时,结合能趋于稳定。     

Stable equidistant step trains during crystallization of insulin

Bunching of growth steps plagues layerwise crystallization of materials in laboratory, industrial, and geological environments, and theory predicts that equidistant step trains are unstable under a variety of conditions. Searching for an example of stable equidistant step trains, we monitored the generation and spatiotemporal evolution of step trains on length scales from 100 nm to 1 mm during the crystallization of insulin, using atomic force microscopy and phase-shifting interferometry. We show that near-equidistant step trains are generated by single and cooperating screw dislocation. The lack of step-step interaction and the overall transport-controlled growth regime further regularize the step train and ensure the stability of the obtained equidistant arrangement.     

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明：对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明：对于正耗散的情况,该冲击波是稳定的.     

Elastic energy of a straight dislocation and contribution from core tractions

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach–Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than those gliding in {112} planes.     

KdV-Burgers方程行波解的稳定性

对KdV-Burgers方程的行波解进行线性稳定性分析,数值结果表明：对于正耗散情形,其行波解是稳定的;对于负耗散情形,其行波解是不稳定的.其次构造有限差分法对其行波解进行非线性动力学演化,结果表明：对于正耗散情形,KdV-Burgers方程的行波解是稳定的.本文结果修正和完善了相关文献中所得结论.     

Nonlinear quantum shock waves in fractional quantum Hall edge states

Using the Calogero model as an example, we show that the transport in interacting nondissipative electronic systems is essentially nonlinear and unstable. Nonlinear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for nonlinear systems, a propagating semiclassical wave packet develops a shock wave at a finite time. A wave packet collapses into oscillatory features which further evolve into regularly structured localized pulses carrying a fractionally quantized charge. The Calogero model can be used to describe fractional quantum Hall edge states. We discuss perspectives of observation of quantum shock waves and a direct measurement of the fractional charge in fractional quantum Hall edge states.     

Osher Flux with Entropy Fix for Two-Dimensional Euler Equations

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: a first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.     

Continuum modeling of the equilibrium and stability of animal flocks

Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where the density goes continuously to zero at a well-defined flock edge, and we discuss conditions on the model that allow for such solutions. We also demonstrate conditions under which, as the flock size increases, the interior density in our equilibria tends to an approximately uniform value. Motivated by observations of starling flocks that are relatively thin in a direction transverse to the direction of flight, we investigate the stability of infinite, planar-sheet flock equilibria. We find that long-wavelength perturbations along the sheet are unstable for the class of models that we investigate. This has the conjectured consequence that sheet-like flocks of arbitrarily large transverse extent relative to their thickness do not occur. However, we also show that our model admits approximately sheet-like, ‘pancake-shaped’, three-dimensional ellipsoidal equilibria with definite aspect ratios (transverse length-scale to flock thickness) determined by anisotropic perceptual/response characteristics of the flocking individuals, and we argue that these pancake-like equilibria are stable to the previously mentioned sheet instability.     

Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators

Unstable attractors are a novel type of attractor with local unstable dynamics, but with positive measures of basins.Here, we introduce local contracting dynamics by slightly modifying the function which mediates the interactions among the oscillators. Thus, the property of unstable attractors can be controlled through the cooperation of expanding and contracting dynamics. We demonstrate that one certain type of unstable attractor is successfully controlled through this simple modification. Specifically, the staying time for unstable attractors can be prolonged, and we can even turn the unstable attractors into stable attractors with predictable basin sizes. As an application, we demonstrate how to realize the switching dynamics that is only sensitive to the finite size perturbations.     

Positive energy without supersymmetry

Witten's positive energy theorem and its generalizations can be viewed as stating that supersymmetric solutions of any supergravity theory are stable. In this paper we give a criterion to test the stability of non-supersymmetric solutions of supergravity theories and solutions of theories which cannot be embedded in a supergravity theory. Previously some of these solutions might have been considered to be unstable. In particular, we show that the non-supersymmetric stationary point of the scalar potential of the gauged N = 5 supergravity theory is stable. We also give an elegant derivation of the Breitenlohner-Freedman condition for (small fluctuation) stability.     

Image forces on edge dislocations: a revisit of the fundamental concept with special regard to nanocrystals

Two conditions under which image forces become significant are when a dislocation is close to a surface (or interface) or when the dislocation is in a nanocrystal. This investigation pertains to the calculation of image forces under these circumstances. A simple edge dislocation is simulated using finite element method (FEM) by feeding-in the appropriate stress-free strains in idealised domains, corresponding to the introduction of an extra half-plane of atoms. Following basic validation of the new model, the energy of the system as a function of the position of the simulated dislocation is plotted and the gradient of the curve gives the image force. The reduction in energy of the system arises from two aspects: firstly, due to the position of the dislocation in the domain and, secondly, due to deformations to the domain (/surfaces). The second aspect becomes important when the dislocation is positioned near a free-surface or in nanocrystals and can be calculated using the current methodology without constructing fictitious images. It is to be noted that domain deformations have been ignored in the standard theories for the calculation of image forces and, hence, they give erroneous results (magnitude and/or direction) whenever image forces play an important role. An important point to be noted is that, under certain circumstances, where domain deformations occur in the presence of an edge dislocation, the ‘image' can be negative (attractive), zero or even positive (repulsive). The current model is extended to calculate image forces based on the usual concept of an ‘image dislocation’.     

On the linearization of nonlinear langevin-type stochastic differential equations

We show that a logical extension of the piecewise optimal linearization procedure leads to the Gaussian decoupling scheme, where no iteration is required. The scheme is equivalent to solving a few coupled equations. The method is applied to models which represent (a) a single steady state, (b) passage from an initial unstable state to a final preferred stable state by virtue of a finite displacement from the unstable state, and (c) a bivariate case of passage from an unstable state to a final stable state. The results are shown to be in very good agreement with the Monte Carlo calculations carried out for these cases. The method should be of much value in multidimensional cases.     

Elastic interaction between a dislocation and a near-by inclusion

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.     

Controlling chaos in power system based on finite-time stability theory

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.     

Existence and stability analysis of spiky solutions for the Gierer-Meinhardt system with large reaction rates

We study the Gierer-Meinhardt system in one dimension in the limit of large reaction rates. First we construct three types of solution: (i) an interior spike; (ii) a boundary spike and (iii) two boundary spikes. Second we prove results on their stability. It is found that an interior spike is always unstable; a boundary spike is always stable. The two boundary spike configuration can be either stable or unstable, depending on the parameters. We fully classify the stability in this case. We characterize the destabilizing eigenfunctions in all cases. Numerical simulations are shown which are in full agreement with the analytical results.     

Unfolding of an unstable singularity point into a ring

It is well known that phase singularities, in general lines in space, are topologically stable features of a wave field. An exception is a pointlike singularity, which is unstable and deforms into a ring or disappears when a small perturbation is applied. Recently, Nye showed how such an event can be understood as an unfolding of a higher-order dislocation [J. Opt. Soc. Am. A (to be published)]. We present an optical implementation of this model and show experimentally that the focal region of a lens contains points of zero intensity on the optical axis that deform into rings when a small amount of spherical aberration is applied to the system.     

Multiscale dislocation dynamics simulations of shock-induced plasticity in small volumes

Multiscale dislocation dynamics plasticity (MDDP) was used to investigate shock-induced deformation in monocrystalline copper. In order to enhance the numerical simulations, a periodic boundary condition was implemented in the continuum finite element (FE) scale so that the uniaxial compression of shocks could be attained. Additionally, lattice rotation was accounted for by modifying the dislocation dynamics (DD) code to update the dislocations’ slip systems. The dislocation microstructures were examined in detail and a mechanism of microband formation is proposed for single- and multiple-slip deformation. The simulation results show that lattice rotation enhances microband formation in single slip by locally reorienting the slip plane. It is also illustrated that both confined and periodic boundary conditions can be used to achieve uniaxial compression; however, a periodic boundary condition yields a disturbed wave profile due to edge effects. Moreover, the boundary conditions and the loading rise time show no significant effects on shock–dislocations interaction and the resulting microstructures. MDDP results of high strain rate calculations are also compared with the predictions of the Armstrong–Zerilli model of dislocation generation and movement. This work confirms that the effect of resident dislocations on the strain rate can be neglected when a homogeneous nucleation mechanism is included.     

Surface stress mediated image force and torque on an edge dislocation

The proximity of interfaces gives prominence to image forces experienced by dislocations. The presence of surface stress alters the traction-free boundary conditions existing on free-surfaces and hence is expected to alter the magnitude of the image force. In the current work, using a combined simulation of surface stress and an edge dislocation in a semi-infinite body, we evaluate the configurational effects on the system. We demonstrate that if the extra half-plane of the edge dislocation is parallel to the surface, the image force (glide) is not altered due to surface stress; however, the dislocation experiences a torque. The surface stress breaks the ‘climb image force’ symmetry, thus leading to non-equivalence between positive and negative climb. We discover an equilibrium position for the edge dislocation in the positive ‘climb geometry’, arising due to a competition between the interaction of the dislocation stress fields with the surface stress and the image dislocation. Torque in the climb configuration is not affected by surface stress (remains zero). Surface stress is computed using a recently developed two-scale model based on Shuttleworth’s idea and image forces using a finite element model developed earlier. The effect of surface stress on the image force and torque experienced by the dislocation monopole is analysed using illustrative 3D models.     

Stability of Symmetric Solitary Wave Solutions of a Forced Korteweg-de Vries Equation and the Polynomial Chaos

In this paper, we consider the numerical stability of gravity-capillary waves generated by a localized pressure in water of finite depth based on the forced Korteweg-de Vries (FKdV) framework and the polynomial chaos. The stability studies are focused on the symmetric solitary wave for the subcritical flow with the Bond number greater than one third. When its steady symmetric solitary-wave-like solutions are randomly perturbed, the evolutions of some waves show stability in time regardless of the randomness while other waves produce unstable fluctuations. By representing the perturbation with a random variable, the governing FKdV equation is interpreted as a stochastic equation. The polynomial chaos expansion of the random solution has been used for the study of stability in two ways. Firstly, it allows us to identify the stable solution of the stochastic governing equation. Secondly, it is used to construct upper and lower bounding surfaces for unstable solutions, which encompass the fluctuations of waves.     

Steps on the smectic a liquid crystal surface and their interaction with an edge dislocation

The step on the smectic A surface is modelled using a part of an edge dislocation solution. Then a step-edge dislocation interaction in a finite smectic A sample is calculated and discussed.