3D analysis of interaction of Lamb waves with defects in loaded steel plates

The objective of the research presented here is the investigation of the interaction of guided waves with welds, defects and other non-uniformities in steel plates loaded by liquid. The investigation has been performed using numerical simulation for 2D and 3D cases by the finite differences method, finite element method and measurement of 3D distributions of acoustic fields. Propagation of the S(0) mode in a steel plate and its interaction with non-uniformities was investigated. It was shown that using the measured leaky wave signals in the water loading of the steel plate and by application of signal processing, the 3D ultrasonic field structure inside and outside of the plate can be reconstructed. The presence of leaky wave signals over the defect caused by the mode conversion of Lamb waves has been proved using the numerical modelling and experimental investigations. The developed signal and data processing enables to visualise dynamics of ultrasonic fields over the plate, and also to estimate spatial positions of defects inside the steel plates.     

An energy law preserving C finite element scheme for simulating the kinematic effects in liquid crystal dynamics

In this paper, we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain Ω. We reformulate the original model in the weak form which is consistent with the continuous dissipative energy law for the flow and director fields in W^1,2+σ(Ω) (σ > 0 is an arbitrarily small number). This enables us to use convenient conformal C⁰ finite elements in solving the problem. Moreover, a discrete energy law is derived for a modified midpoint time discretization scheme. A fixed iterative method is used to solve the resulted nonlinear system so that a matrix free time evolution may be achieved and velocity and director variables may be solved separately. A number of hydrodynamical liquid crystal examples are computed to demonstrate the effects of the parameters and the performance of the method.     

Scaling properties of dynamic response in orientational glasses

The freezing transition in dipolar and quadrupolar glasses is characterized by the presence of local random electric and strain fields generated by substitutional disorder. The dynamic response in the ergodic phase above the freezing temperature T_F is studied in terms of Langevin dynamics applied to the recently formulated symmetry-adapted random-bond-random-field (SARBRF) model of orientational glasses. Following the theory of spin glasses it is assumed that for T≥T_F the response can be written in a dynamic scaling form by introducing a scaling exponent v and a frequency scaling variable. The value of v(T) is explicitly evaluated for the quadrupolar (100) SARBRF model, and its relation to the experimentally observed effective exponent u_eFF(T) in dipolar and quadrupolar glasses is discussed.     

Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields

Rigorous upper bounds are derived for large-scale turbulent flame speeds in a prototypical model problem. This model problem consists of a reaction-diffusion equation with KPP chemistry with random advection consisting of a turbulent unidirectional shear flow. When this velocity field is fractal with a Hurst exponentH with 0<H<1, the almost sure upper bounds suggest that there is an accelerating large-scale turbulent flame front with the enhanced anomalous propagation lawy=C _H t ^1+H for large renormalized times. In contrast, a similar rigorous almost sure upper bound for velocity fields with finite energy yields the turbulent flame propagation law within logarithmic corrections. Furthermore, rigorous theorems are developed here which show that upper bounds for turbulent flame speeds with fractal velocity fields are not self-averaging, i.e., bounds for the ensemble-averaged turbulent flame speed can be extremely pessimistic and misleading when compared with the bounds for every realization.     

Global noise characteristics of a laser Doppler vibrometer-II. Experiments using beam dynamics

The use of a laser Doppler vibrometer to obtain velocity information from vibrating structures has gained wide acceptance in recent years. Although use of such an instrument can yield a spatially dense matrix of velocity information, several users have noted ‘noise’ at certain points in the spatial field. The technique by which the SLDV system operates results in occasional velocity ‘drop-outs’ which are unidirectional, always estimating the velocity response closer to zero than reality. These ‘drop-out’ areas occur more predominately at points of maximum velocity response with small rotational components. Alternatively, points exhibiting minimum velocity response with large rotational components are less susceptible to the ‘noise’. In this paper, an experiment to visualize the speckle pattern motions received by the photo-detectors during these vibration conditions is presented. Theories regarding the source(s) of the ‘noise’ are developed.     

Finite element-based large eddy simulation using a combination of the variational multiscale method and the dynamic Smagorinsky model

A finite element-based large eddy simulation (LES) is proposed using a combination of the residual-based variational multiscale (RBVMS) approach and the dynamic Smagorinsky eddy-viscosity model. In this combined model, the cross-stress terms are modelled using the RBVMS approach while the eddy-viscosity model is used to represent the Reynolds stresses. The eddy-viscosity is computed dynamically in a local fashion for which a localized version of the variational Germano identity is developed. To improve the robustness of the local dynamic procedure, two types of averaging schemes are considered. The first type employs spatial averaging over homogeneous direction(s) which is only applicable to turbulent flows with statistical homogeneity in at least one direction. The second type is based on Lagrangian averaging over fluid pathtubes, which is applicable to inhomogeneous turbulent flows. The predictions from the combined model are compared to the direct numerical simulation or experimental data and also to the predictions from the RBVMS model. This is done for two cases: turbulent flow in a channel (Re_τ = 590) and flow over a cylinder (Re_D = 3, 900). For the turbulent channel flow, predictions are similar between the RBVMS model and the combined model. For flow over a cylinder, the combined model provides better predictions, specifically for fluctuations in the streamwise velocity and lift.     

Flowfield vorticity calculation using PIV data

The simultaneous velocity measurement at different flowfield locations is one of the key advantages of a PIV system. This allows a straightforward calculation of derived flow magnitudes including spatial correlations. Thus, postprocessing techniques need further attention in order to assure maximum feature extraction with minimum error, among other issues. This paper is devoted to expand the capability of calculating vorticity in a PIV sampled flow field. The methodology proposed is based on linear algorithms (FIR filters) able to obtain the first spatial derivative of a grid sampled magnitude containing random noise. Generalization to other flow magnitudes based on spatial derivatives is immediate. Been this a widely used method, the main objective of the study is to develop new filters from families already documented. The relevant performance parameters of these filters are evaluated and commented. Synthetic data fields are used to test the basic metrological attributes in a controlled way. As a result of the study, algorithms with better performances than the usual ones are proposed and strong points are highlighted. Finally, results of the application to real PIV data are exhibited and commented.     

Glauber dynamics of the asymmetric SK-model

We solve the Glauber dynamics of the fully asymmetric SK-model and some of its extensions: Incorporation of random external fields and additional storage of a finite number of patterns. An analytical expression for theT=0 autocorrelation function of the equilibrium dynamics is derived and compared with the asymptotic exponential decay. The dynamical behaviour of the fully asymmetric SK-model is also investigated in a situation with nonequilibrium initial conditions. For weak correlations between the synaptic couplings a first order perturbation expansion is made yielding a finite relaxation time for the response function and a vanishing EA-order parameter if the asymmetry is high enough.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Discrete dislocation dynamics: an important recent break-through in the modelling of dislocation collective behaviour

Recent results obtained by 3D discrete Dislocation Dynamics (DD) simulations are reviewed. Firstly, in the case of fatigued AISI 316L stainless steel, it is shown how DD simulations can both explain the formation of persistent slip bands and give a criterion for crack initiation. The same study is performed in the case of precipitate hardened metals where the precipitate size plays a crucial role. Secondly, we show how molecular dynamics (MD) simulations can feed the DD simulations for two applications. The first concerns the modelling of BCC Fe for which the dislocation mobility is derived from MD simulations. The second considers the modelling of irradiated stainless steels (FCC), where MD is used to define the local rules of interactions between dislocations and Frank loops. To cite this article: M.C. Fivel, C. R. Physique 9 (2008).     

二维完全阻挫$lt;i$gt;XY$lt;/i$gt;模型的动力学指数

采用大规模动力学蒙特卡罗模拟方法,对二维完全阻挫XY模型的Kosterlitz-Thouless（KT）型相变展开数值研究.系统从有序初始态出发演化到高于KT相变的温度,以普适的动力学标度形式为基础,通过测量磁化和Binder累积量,得出动力学关联时间和平衡态空间关联长度,确定出更精确的动力学指数z.特别是建议并证实了一种在KT相变温度以上（T>T_KT）,独立判断动力学指数z的方法.模拟结果表明,动力学指数z≈2,这与在相变温度以下（T<T_KT）测量的结果一致. 关键词： 蒙特卡罗法 动力学指数 Kosterlitz-Thouless相变 XY模型')" href="#">二维完全阻挫XY模型     

Coherence theory and coherence phenomena in a closed spin‐1/2 system

A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence Ξ, and discuss in some detail a general coherence theory and its elementary results. As expected, decoherence is understood as a statistical process that is caused by the dynamics of the system, similar to the growth of entropy. It appears that coherence is an important measure that helps to understand quantum properties of a system, e.g., the decoherence time can be derived from the coherence function Ξ(t), but not from the entropy dynamics. Moreover, the concept of decoherence time is applicable in closed and finite systems. However, in most cases, the decay of off‐diagonal elements differs from the usual exp(‐t/τ_d) behaviour. For concreteness, we report the form of decoherence time τ_d in a finite Heisenberg model with respect to the number of particles N, density n_ρ, spatial dimension D and ? in a η/r^?‐type of potential.     

Bödeker’s effective theory: From Langevin dynamics to Dyson–Schwinger equations

The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|g²T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Bödeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: <hep-ph/9810313>; G.D. Moore, Phys. Rev. D62 (2000) 085011. Available from: <hep-ph/0001216>]. In this work we provide a complementary, more analytic approach based on Dyson–Schwinger equations. Using methods known from stochastic quantitation, we recast Bödeker’s Langevin equation in the form of a field theoretic path integral. We introduce gauge ghosts in order to help control possible gauge artefacts that might appear after truncation, and which leads to a BRST symmetric formulation and to corresponding Ward identities. A second set of Ward identities, reflecting the origin of the theory in a stochastic differential equation, is also obtained. Finally, Dyson–Schwinger equations are derived.     

Effective scaling behavior of magnetization and Hamming distance in Ising thin films under a surface field

The recent improvements on the technology for developing high-quality thin magnetic films has renewed the interest in the study of surface effects in both static and dynamic magnetic responses. In this work, we use a Monte-Carlo algorithm with Metropolis dynamics together with a spreading of damage technique to study the interplay between the effects of finite thickness and surface ordering field in thin ferromagnetic Ising (S=1/2) films. We calculate, near the bulk critical temperature and several values of the surface field, the dependence on the film thickness of the average magnetization M and Hamming distance D. We employ a finite size scaling analysis to show that both obey an effective one-parameter scaling but exhibit distinct characteristic surface fields. At their corresponding characteristic surface fields both M and D become roughly thickness independent and we estimate the critical exponent characterizing the behavior of the typical scaling lengths. Received 29 March 1999 and Received in final form 21 April 1999     

Relative Equilibria in Continuous Stellar Dynamics

We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non-radial stationary solutions whose supports are made of an arbitrarily large number of disjoint compact sets, in the low angular velocity and large scale limit. At first order, the solutions behave like point particles, thus making the link with the relative equilibria in N-body dynamics.     

Accurate identification of the frequency response functions for the rotor-bearing-foundation system using the modified pseudo mode shape method

In this paper, an identification technique in the dynamic analyses of rotor-bearing-foundation systems called the pseudo mode shape method (PMSM) was improved in order to enhance the accuracy of the identified dynamic characteristic matrices of its foundation models. Two procedures, namely, phase modification and numerical optimisation, were proposed in the algorithm of PMSM to effectively improve its accuracy. Generally, it is always necessary to build the whole foundation model in studying the dynamics of a rotor system through the finite element analysis method. This is either unfeasible or impractical when the foundation is too complicated. Instead, the PMSM uses the frequency response function (FRF) data of joint positions between the rotor and the foundation to establish the equivalent mass, damping, and stiffness matrices of the foundation without having to build the physical model. However, the accuracy of the obtained system's FRF is still unsatisfactory, especially at those higher modes. In order to demonstrate the effectiveness of the presented methods, a solid foundation was solved for its FRF by using both the original and modified PMSM, as well as the finite element (ANSYS) model for comparisons. The results showed that the accuracy of the obtained FRF was improved remarkably with the modified PMSM based on the results of the ANSYS. In addition, an induction motor resembling a rotor-bearing-foundation system, with its housing treated as the foundation, was taken as an example to verify the algorithm experimentally. The FRF curves at the bearing supports of the rotor (armature) were obtained through modal testing to estimate the above-mentioned equivalent matrices of the housing. The FRF of the housing, which was calculated from the equivalent matrices with the modified PMSM, showed satisfactory consistency with that from the modal testing.     

On coordination and continuous hawk-dove games on small-world networks

It is argued that small-world networks are more suitable than ordinary graphs in modelling the diffusion of a concept (e.g. a technology, a disease, a tradition, ...). The coordination game with two strategies is studied on small-world networks, and it is shown that the time needed for a concept to dominate almost all of the network is of order , where N is the number of vertices. This result is different from regular graphs and from a result obtained by Young. The reason for the difference is explained. Continuous hawk-dove game is defined and a corresponding dynamical system is derived. Its steady state and stability are studied. Replicator dynamics for continuous hawk-dove game is derived without the concept of population. The resulting finite difference equation is studied. Finally continuous hawk-dove is simulated on small-world networks using Nash updating rule. The system is 2-cyclic for all the studied range. Received 8 July 2000 and Received in final form 23 July 2000     

Theory of a FIR optical digital differentiator

Abstract

An optical realization of a proposed family of the finite impulse response (FIR) qth-order mth-derivative digital differentiators (under coherent operation), whose transfer functions are derived from the well-known numerical differentiation scheme (namely, the backward Taylor series expansion), using the amplified fiber optic transversal filters is presented. Several input pulse shapes, such as polynomials of various orders and the Gaussian and exponential pulses, are chosen as examples for illustration of the accuracy of the proposed optically realized differentiators. A mathematical model describing the dynamic (or transient) response of any optical discrete-time systems using the z-transform technique is proposed. The real-time performances of the proposed differentiators have been analyzed using both the steady-state and the dynamic analyses, Although the analysis is directed at fiber optic systems, the methodology and the results are applicable to other physical systems.     

Modelling nongrey gas-phase and soot radiation in luminous turbulent nonpremixed jet flames

Much progress has been made in radiative heat transfer modelling with respect to the treatment of nongrey radiation from both gas-phase species and soot particles, while radiation modelling in turbulent flame simulations is still in its infancy. Aiming at reducing this gap, this paper introduces state-of-the-art models of gas-phase and soot radiation to turbulent flame simulations. The full-spectrum k-distribution method (M.F. Modest, 2003, Journal of Quantitative Spectroscopy & Radiative Transfer, 76, 69–83) is implemented into a three-dimensional unstructured computational fluid dynamics (CFD) code for nongrey radiation modelling. The mixture full-spectrum k-distributions including nongrey absorbing soot particles are constructed from a narrow-band k-distribution database created for individual gas-phase species, and an efficient scheme is employed for their construction in CFD simulations. A detailed reaction mechanism including NO _x and soot kinetics is used to predict flame structure, and a detailed soot model using a method of moments is employed to determine soot particle size distributions. A spherical harmonic P₁ approximation is invoked to solve the radiative transfer equation. An oxygen-enriched, turbulent, nonpremixed jet flame is simulated, which features large concentrations of gas-phase radiating species and soot particles. Nongrey soot modelling is shown to be of greater importance than nongrey gas modelling in sooty flame simulations, with grey soot models producing large errors. The nongrey treatment of soot strongly influences flame temperatures in the upstream and the flame-tip region and is essential for accurate predictions of NO. The nongrey treatment of gases, however, weakly influences upstream flame temperatures and, therefore, has only a small effect on NO predictions. The effect of nongrey soot radiation on flame temperature is also substantial in downstream regions where the soot concentration is small. Limitations of the P₁ approximation are discussed for the jet flame configuration; the P₁ approximation yields large errors in the spatial distribution of the computed radiative heat flux for highly anisotropic radiation fields such as those in flames with localized, near-opaque soot regions.     

Retrieval and chaos in layeredQ-Ising neural networks

Using a probabilistic approach, we study the parallel dynamics of theQ-Ising layered networks for arbitraryQ. By introducing auxiliary thermal fields, we express the stochastic dynamics within the gain function formulation of the deterministic dynamics. Evolution equations are derived for arbitraryQ at both zero and finite temperatures. An explicit analysis of the fixed-point equations is carried out for bothQ=3 andQ. The retrieval properties are discussed in terms of the gain parameter, the storage capacity, and the temperature. Using the time evolution of the distance between two network configurations, we investigate the possibility of microscopic chaos. Chaotic behavior is always present for arbitrary finiteQ. However, in the limitQ the existence of chaos depends on the parameters of the system.