Optimisation of damping treatments based on big bang–big crunch and modal strain energy methods

A cost-effective methodology is needed in various applications in order to optimise damping treatments for structures. Although some methods appear to be applicable for structures with relatively simple geometries, it is still difficult to utilise them for general structures. This paper presents an efficient approach for optimisation of passive damping treatments that can be applied to general structures. First, an optimisation procedure based on big bang–big crunch optimisation method is introduced and its effectiveness for damping optimisation is evaluated. Then, a procedure based on modal strain energy method is presented for the prediction of modal damping levels for structures with damping treatments and its performance is assessed. After that, for validation purposes, the proposed optimisation methodology is used to maximise modal damping for a single mode of a structure whose optimised configurations are known for the individual modes. Finally, the performance of the proposed optimisation procedure is demonstrated for the maximisation of damping levels for multiple modes at the same time and the applicability of the approach for general structures with passive damping treatments is demonstrated.     

Beyond Einstein's radiation theory

Einstein's radiation mechanism is generalized to account for the possibility of population inversion by placing a nonlinear bound on the growth of an unstable perturbation. The nonstationary linear mechanism of relaxation to blackbody radiation below threshold is studied. The nonstationary photon distribution is the negative binomial distribution, and casting it as a law of error, for which the most probable value is the mean value, gives the expression for the statistical entropy. The second law yields a nonequilibrium generalization of Planck's radiation law. The nonlinear mechanism leading to the transformation from the negative binomial probability distribution, for chaotic light, to a Poisson probability distribution, for coherent light, is then analyzed. A criterion for lasing is given in terms of the chemical potential of radiation which is compared to the inequality for the transition from quantum to classical statistics.     

Emissivity estimates

A variational expression is developed to estimate the overall and angular emissivities for a halfspace geometry described by the equation of transfer. In contrast to the usual variational procedure of postulating a functional and then proving correctness, the appropriate functional is derived using a Lagrange multiplier technique. With asymptotic trial functions, simple expressions for the emissivities result. This variational estimate of the overall emissivity is exceeding accurate when compared to exact results for an isotropic phase function. The angular emissivity, a more detailed quantity, is estimated with less accuracy. The formalism is not restricted to an isotropic phase function, but is valid for general anisotropic scattering. As an example of an anisotropic phase function, the case of Thomson scattering is considered. The emissivity for this phase function is found to be slightly larger than that for isotropic scattering.     

PMD统计模型的改进

对于PMD的研究,分段模型是较优的选择.原始模型经过数学推导, 可转化为迭代模型.转化后的模型物理意义明晰,在直观上便于看出PMD随光纤分段增加的累积过程,具有较强的移植性.理论分析指明了数值方法产生误差的缘由,给出了实用数值计算的迭代模式,对于PMD补偿具有指导意义,同时使计算变得简洁.     

Ab Initio investigation of the Elliott-Yafet electron-phonon mechanism in laser-induced ultrafast demagnetization

The spin-flip (SF) Eliashberg function is calculated from first principles for ferromagnetic Ni to accurately establish the contribution of Elliott-Yafet electron-phonon SF scattering to Ni's femtosecond laser-driven demagnetization. This is used to compute the SF probability and demagnetization rate for laser-created thermalized as well as nonequilibrium electron distributions. Increased SF probabilities are found for thermalized electrons, but the induced demagnetization rate is extremely small. A larger demagnetization rate is obtained for nonequilibrium electron distributions, but its contribution is too small to account for femtosecond demagnetization.     

Inverse of the volume attenuation coefficient for soft particles

An integral equation of the first kind is considered, which relates the distribution function for the absorbing particles to the bulk aerosol attenuation coefficient (for single scattering). An inversion formula for the distribution function is derived. Schemes A and B for regularizing the problem are described for the case of tabulated absorption. The regularization is performed by introducing operators calculated from the optical information at the input. It is shown that scheme A is applicable only to transparent particles, while scheme B is applicable to any particle. A realization of scheme B is presented.     

INHOMOGENEOUS WAVES IN ANISOTROPIC POROUS LAYER OVERLYING SOLID BEDROCK

The problem of propagation of inhomogeneous waves in anisotropic porous layered medium is studied using transfer matrix. Firstly, transfer matrix for an anisotropic porous layer is derived. Biot's poro-elastic theory is incorporated to model the acoustics of anisotropic porous layer. The interface between porous layer and elastic half-space is considered as imperfect and modified boundary conditions are applied for this more realistic situation. The theory of transfer matrix is used to derive the analytical expression for the surface impedance. Numerical computation of results is done for different degrees of bonding in the low as well as high-frequency range. In the first case, which is relevant to geophysical studies, the surface impedance is predicted for low-frequency range and surface impedance for second model is computed in high-frequency range. It is observed that loose bondedness is accompanied by the loss of energy at the interface. The technique of transfer matrix is utilized to compute the surface impedance in both cases. The role of surface impedance in seismological studies and in the study of composites is discussed.     

Optical conductivity of solitons in polyacetylene

The soliton lattice solution of the continuum model for polyacetylene is used to derive the frequency dependent conductivity of charged solitons. The limit of low soliton density is explicitly evaluated and shown to be free of singularities. The conductivity sum rule is proven for the model Hamiltonian, and is shown to be satisfied by the explicit solution. Implications for polyacetylene and for TTF-TCNQ are discussed.     

Routes to nonsequential double ionization

A method is proposed for the calculation of the S matrix for many-electron processes in intense-laser atom physics, in close analogy to the strong-field approximation for one-electron processes. Given a scenario of how some process evolves, corresponding approximations to the classical action are made which allow for the evaluation of the quantum-mechanical S matrix. The method is applied to the distribution of the total electronic momentum in nonsequential double ionization, and the results are compared to recent measurements. Good agreement is obtained for neon for a rescattering scenario. There is no comparable agreement for helium and argon, and possible alternative scenarios are discussed.     

Semiclassical functional integrals for self-dual gauge fields

The semiclassical approximation to the functional integral for four-dimensional Euclidean gauge theories is discussed in detail for general stationary points of the action. It is shown how to take the limit from a compact space to flat space, and the zero modes corresponding to global gauge transformations are carefully discussed. The results are specialised to general self-dual multi-instanton gauge fields given by the general construction of Atiyah et al. It is shown how the normalization matrix of the zero modes can be determined and the complete expression for the functional measure is given for the two instanton case. This is shown to factorise for well-separated instantons. Some technical matters are discussed in an appendix and a resume of results for multi-instanton functional determinants is included.     

Solutions of a fourth order Bethe Salpeter equation

A Bethe Salpeter equation with interaction up to the fourth order is solved numerically for a bound state with energy equal to zero. It is found that the fourth order term is important even for very heavy exchanged mesons, and for angular momentum equal to 1. The correction found is to be considered the highest limit for the corrections with energy different from zero.     

高斯分布及截断和抽样

 详细推论了高斯分布的轴对称电子束的截断方法和确定截断因子的表达式。结果表明在截断因子为0.9时,电子束发射度等于均方根发射度的二倍, 而当电子束发射度等于均方根发射度时, 截断因子仅为0.59。给出了四维坐标变量的几率密度函数公式, 并简述了相应的抽样方法。     

Non-linear free vibrations of buckled plates with deformable loaded edges

In the great majority of papers dealing with non-linear dynamic buckling of plates it is assumed that the edge at which the in-plane load is applied is not deformable (rigid). In those few references in which buckling with deformable edges is examined normally a variational approach is used, based on “trial” functions for the in-plane displacements, which approach often leads to incorrect results. In this paper an exact form of the solution is found for the in-plane displacements, it being assumed that the membrane force is, at all times, exactly equal to the load applied at the corresponding loaded edge. As is well known, when the plate is buckled through a rigid beam these two forces are only on average equal to each other. It is shown here that the deformability of the loaded edges for plates undergoing large deformations should be taken into account for square-shaped plates, especially for those close to the so-called “golden-cut” shape (the aspect ratio between the edges equal to √2), while for long rectangular plates this effect may be disregarded.     

Wave-induced bed flows by a Lagrangian vortex scheme

Nominally 2-dimensional viscous flow induced by gravity waves over a spatially periodic bed is simulated by a Lagrangian vortex scheme. A vortex sheet is introduced on the surface at each time step to satisfy the zero velocity conditions. The sheet is discretised; the vortex-in-cell method is used to convect vorticity and random walks are added to effect viscous diffusion. Good agreement with analytical theory is obtained for velocity profiles in uniform sinusoidal flow and for mass transport due to linear waves. Mass transport for finite amplitude waves is also obtained. For separated flow over rippled beds, which is still liminar, a vortex decay factor is required to produce agreement with experiment and is thought to compensate for large scale 3-dimensional effects.     

Sound radiation from perforated plates

A practical engineering noise control measure that can often be used for plate-like structures is to construct them from perforates. This can dramatically reduce the sound radiation from such structures. Here, a prediction model is developed to quantify this effect. It is an extension of Laulagnet's model for the radiation from an unbaffled plate, which expresses the surface pressure difference as well as the plate velocity as a sum over plate modes. The perforation is included in terms of a continuously distributed surface impedance, which for moderately sized holes is predominantly inertial. Results show that the radiation efficiency reduces, not only as the perforation ratio increases but also as the hole size reduces for a given perforation ratio. Experimental validation is given which shows a good agreement with the predictions. An approximate formula is also proposed for the effect of perforation which corresponds well with the analytical calculations up to half the critical frequency and could be used for an engineering application to predict the noise reduction due to perforation. A model for the case of a perforated plate embedded in an equally perforated baffle is also discussed for comparison.     

Dimensional resonances and second-harmonic generation in a semibounded nonlinear layered periodic medium

A theory for the nonlinear interaction of electromagnetic waves in a semibounded periodic dielectric structure is developed using the example of second-harmonic generation. One of the layers forming a period is assumed to have nonlinear polarization. The theory is an improved perturbation theory based on the Green theorem. The phase-matching conditions for interacting waves are shown to correspond to dimensional resonances for individual layers or for the structure period. The interaction efficiency is maximum at passband edges for the case of resonance for the entire period. For this resonance, the phase-matching conditions are met for a frequency spectrum rather than for a single frequency. This feature makes it possible to convert spectra from one frequency range to another.     

Statistical Estimates for the Navier–Stokes Equations and the Kraichnan Theory of 2-D Fully Developed Turbulence

A mathematical formulation of the Kraichnan theory for 2-D fully developed turbulence is given in terms of ensemble averages of solutions to the Navier–Stokes equations. A simple condition is given for the enstrophy cascade to hold for wavenumbers just beyond the highest wavenumber of the force up to a fixed fraction of the dissipation wavenumber, up to a logarithmic correction. This is followed by partial rigorous support for Kraichnan's eddy breakup mechanism. A rigorous estimate for the total energy is found to be consistent with Kraichnan's theory. Finally, it is shown that under our conditions for fully developed turbulence the fractal dimension of the attractor obeys a sharper upper bound than in the general case.     

The Generation of Current in Tokamaks by the Absorption of Waves in the Electron Cyclotron Frequency Range

The theory of current generation due to the absorption of high-frequency waves is developed for the case in which the propagation of the waves is described in the geometrical optics approximation. An expression for the current generated is obtained which is similar in fornn to the expression for the rate of energy deposition. This expression is incorporated in a toroidal ray tracing code to study current generation due to the absorption of waves in the electron cyclotron frequency range. The dependence of the current generated on temperature and angle of injection for the joint Naval Research Laboratory-Oak Ridge National Laboratory experiment on ISXB is studied.