Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

Problemas teórico-científicos y metodológicos de la investigación clínico-psicoanalítica : (tercera parte)

Tanto en la primera como en la segunda parte del trabajo se argumenta sobre la planificación de investigaciones y sobre los métodos en el Psicoanálisis. En esta tercera parte se expone las distintas formas de la explicación y su aplicación en el Psicoanálisis, inmediatamente se discurre sobre el estatus de la predicción en la teoría psicoanalítica y la práctica investigativa. Se aborda ¨la profecía autocumplida¨ en la interpretación y amplificando desde otras disciplinas el problema de ¨cirularidad¨, su relación con la psicogénesis, la transferencia y la contratransferencia. Se contrastan las afirmaciones popperianas con las del fundador del Psicoanálisis.

Thermal stress wave and spallation induced by an electron beam

Thermal stress wave and spallation in aluminium alloy exposed to a high fluency and low energy electron beams are studied theoretically. A simple model for the study of energy deposition of electrons in materials is presented on the basis of some empirical formulae. Under the stress wave induced by energy deposition, microcracks and/or microvoids may appear in target materials, and in this case, the inelastic volume deformation should not vanish. The viscoplastic model proposed by Bodner and Partom with corresponding Gurson's yield function requires modification for this situation. The new constitutive model contains a scalar field variable description of the material damage which is taken as the void volume fraction of the polycrystalline material. Incorporation of the damage parameter permits description of rate-dependent, compressible, inelastic deformation and ductile fracture. The melting phenomenon has been observed in the experiment, therefore one needs to take into account the melting process in the intermediate energy deposition range. A three-phase equation of state used in the paper provides a more detailed and thermodynamical description of metals, particularly, in the melting region. The computational results based on the suggested model are compared with the experimental test for aluminium alloy, which is subjected to a pulsed electron beam with high fluency and low energy. (C) 1997 Elsevier Science Ltd.

Dynamic damage and failure in viscoplastic materials

In this paper, a dynamic damage model in ductile solids under the application of a dynamic mean tensile stress is developed. The proposed model considers void nucleation and growth as parts of the damage process under intense dynamic loading (strain rates epsilon greater than or equal to 10(3) s(-1)). The evolution equation of the ductile void has the closed form, in which work-hardening behavior, rate-dependent contribution and inertial effects are taken into account. Meanwhile, a plate impact test is performed for simulating the dynamic fracture process in LY12 aluminum alloy. The damage model is incorporated in a hydrodynamic computer code, to simulate the first few stress reverberations in the target as it spalls and postimpact porosity in the specimen. Fair agreement between computed and experimental results is obtained. Numerical analysis shows that the influence of inertial resistance on the initial void growth in the case of high loading rate can not be neglected. It is also indicated that the dynamic growth of voids is highly sensitive to the strain rates.

Magnetostatic relations including fluctuation fields - the local expansion

Using the approach of local expansion, we analyze the magnetostatic relations in the case of conventional turbulence. The turbulent relations are obtained consisten tly for themomentum equation and induction equation of both the average and fluctuation relations.In comparison with the magnetostatic relations as discussed usually, turbulent fluctuationfields produce forces, one of which 1/(4π)(α1×B0)×B0 may have parallel and perpendicular components in the direction of magnetic field, the other of which 1/(4π)K×B0 is introduced by the boundary value of turbulence and is perpendicular to the magnetic field. In the case of 2-dimensional configuration of magnetic field, the basic equation will be reduced into a second-order elliptic equation, which includes some linear and nonlinear terms introduced by turbulent fluctuation fields. Turbulent fields may change the configuration of magnetic field and even shear it non-uniformly. The study on the influence of turbulent fields is significant since they are observed in many astrophysical environments.

A Multiscale-Domain Decomposition Method for High Reynolds Number Flows

The high Reynolds number flow contains a wide range of length and time scales, and the flow domain can be divided into several sub-domains with different characteristic scales. In some sub-domains, the viscosity dissipation scale can only be considered in a certain direction; in some sub-domains, the viscosity dissipation scales need to be considered in all directions; in some sub-domains, the viscosity dissipation scales are unnecessary to be considered at all. For laminar boundary layer region, the characteristic length scales in the streamwise and normal directions are L and L Re-1/ 2 , respectively. The characteristic length scale and the velocity scale in the outer region of the boundary layer are L and U, respectively. In the neighborhood region of the separated point, the length scale l<of this reason there exists a great disparity of the grid Reynolds numbers RDxi between different cells in Navier-Stokes (NS) equations computations for high Reynolds number flows, an idea of solving the conservation equations for discrete cells was proposed and named the discrete fluid dynamics (DFD) algorithm. Analysis shows that the basic conservative equations for discrete cells are the Euler equations, NS- and diffusion parabolized (DP) NS equations. In this paper, a new multiscale-domain decomposition method is developed for the high Reynolds number flow. First, the whole domain is decomposed to different sub-domains with the different characteristic scales. Then the different dominant equation of all sub-domains is defined according to the diffusion parabolized (DP) theory of viscous flow. Finally these different equations are solved simultaneously in whole computational region. For numerical tests of high Reynolds numerical flows, two-dimensional supersonic flows over rearward and frontward steps as well as an interaction flow between shock wave and boundary layer were solved numerically. The pressure distributions and local coefficients of skin friction on the wall are given. The numerical results obtained by the multiscale-domain decomposition algorithm are well agreement with those by NS equations. Comparing with the usual method of solving the Navier-Stokes equations in the whole flow, under the same numerical accuracy, the present multiscale domain decomposition method decreases CPU consuming about 20% and reflects the physical mechanism of practical flow more accurately.

韧性材料裂纹尖端孔洞群体损伤演化的实验和模拟

长期以来，材料的孔洞损伤一直是力学家和材料学家所关注的焦点之一，相应的研究方法很多，所得到的成果也很丰富。但是这些研究大部分是基于单个孔洞或有限个孔洞来考虑的，很少将大量的孔洞损伤作为整体来探讨。本文就是考虑到在韧性金属合金材料的破坏和失效过程中，往往是有大量的孔洞损伤参与其中的。我们试图将这些作为整体来考虑，并着重对初始裂纹钝化扩展过程的裂尖前沿来进行研究和讨论。本文从微孔洞数密度守恒方程出发，讨论了裂尖前沿孔洞损伤数密度群体化的方程以及它的解，探讨了损伤各阶矩的分布形式和演化规律。并且对一个系列低碳合金钢样品的I型初始裂纹的钝化扩展和断口孔洞的观察和统计的结果与计算模拟的结果进行了比较，得到了相同的趋势。计算模拟和试验的结果表明，在裂尖前沿孔洞损伤的群体演化过程中，损伤矩的分布是随着离开裂尖距离增加而减少的，并且这种分布随时间增加而且增加，并且趋于稳定分布。最后根据实验中反映出来的由于材料内部的不均匀等造成的孔洞损伤演化的不均匀性，引入随机涨落的概念导出局域孔洞数密度演化守恒方程来探讨这种不均匀性，通过模拟计算得到平均场理论和局域孔洞数密度守恒理论的差异，并由全场孔洞数密度演化守恒方程的分析来证实这个差异。

On optimal message vector length for block single parallel partition algorithm in a three-dimensional ADI solver

It has long been recognized that many direct parallel tridiagonal solvers are only efficient for solving a single tridiagonal equation of large sizes, and they become inefficient when naively used in a three-dimensional ADI solver. In order to improve the parallel efficiency of an ADI solver using a direct parallel solver, we implement the single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication costs. The measured performances show that the longest allowable message vector length (MVL) is not necessarily the best choice. To understand this observation and optimize the performance, we propose an improved model that takes the cache effect into consideration. The optimal MVL for achieving the best performance is shown to depend on number of processors and grid sizes. Similar dependence of the optimal MVL is also found for the popular block pipelined method.

Sentence comprehension before and after 1970: Topics, debates and techniques

[EN] Language Down the Garden Path traces the lines of research that grew out of Bever's classic paper. Leading scientists review over 40 years of debates on the factors at play in language comprehension, production, and acquisition (the role of prediction, grammar, working memory, prosody, abstractness, syntax and semantics mapping); the current status of universals and narrow syntax; and virtually every topic relevant in psycholinguistics since 1970. Written in an accessible and engaging style, the book will appeal to all those interested in understanding the questions that shaped, and are still shaping, this field and the ways in which linguists, cognitive scientists, psychologists, and neuroscientists are seeking to answer them.

Boundary value problems for stochastic differential equations

A theory of two-point boundary value problems analogous to the theory of initial value problems for stochastic ordinary differential equations whose solutions form Markov processes is developed. The theory of initial value problems consists of three main parts: the proof that the solution process is markovian and diffusive; the construction of the Kolmogorov or Fokker-Planck equation of the process; and the proof that the transistion probability density of the process is a unique solution of the Fokker-Planck equation.

It is assumed here that the stochastic differential equation under consideration has, as an initial value problem, a diffusive markovian solution process. When a given boundary value problem for this stochastic equation almost surely has unique solutions, we show that the solution process of the boundary value problem is also a diffusive Markov process. Since a boundary value problem, unlike an initial value problem, has no preferred direction for the parameter set, we find that there are two Fokker-Planck equations, one for each direction. It is shown that the density of the solution process of the boundary value problem is the unique simultaneous solution of this pair of Fokker-Planck equations.

This theory is then applied to the problem of a vibrating string with stochastic density.

Mechanisms in fs-laser ablation in fused silica

A theoretical model is proposed to describe the microscopic processes involved in the ablation in fused silica induced by femtosecond-laser pulse. Conduction-band electron (CBE) can absorb laser energy, the rate is calculated by quantum mechanical method and classical method. CBE is produced via photoionization (PI) and impact ionization (II). The PI and II rates are calculated by using the Keldysh theory and double-flux model, respectively. Besides the CBE production, we investigate laser energy deposition and its distribution. The equation of energy diffusion in physical space is resolved numerically. Taking energy density E-dep=54 kJ/cm(3) as the criterion, we calculate damage threshold, ablation depth, and ablation volumes. It is found that if energy diffusion is considered, energy density near sample surface is reduced to 1/10, damage threshold is enhanced more than 30%, ablation depth is increased by a factor of 10. Our theoretical results agree well with experimental measurements. Several ultrafast phenomena in fused silica are also discussed. (C) 2004 American Institute of Physics.

Where Tori fear to tread : hypermassive neutron star remnants and absolute event horizons Or topics in computational general relativity

Computational general relativity is a field of study which has reached maturity only within the last decade. This thesis details several studies that elucidate phenomena related to the coalescence of compact object binaries. Chapters 2 and 3 recounts work towards developing new analytical tools for visualizing and reasoning about dynamics in strongly curved spacetimes. In both studies, the results employ analogies with the classical theory of electricity and magnitism, first (Ch. 2) in the post-Newtonian approximation to general relativity and then (Ch. 3) in full general relativity though in the absence of matter sources. In Chapter 4, we examine the topological structure of absolute event horizons during binary black hole merger simulations conducted with the SpEC code. Chapter 6 reports on the progress of the SpEC code in simulating the coalescence of neutron star-neutron star binaries, while Chapter 7 tests the effects of various numerical gauge conditions on the robustness of black hole formation from stellar collapse in SpEC. In Chapter 5, we examine the nature of pseudospectral expansions of non-smooth functions motivated by the need to simulate the stellar surface in Chapters 6 and 7. In Chapter 8, we study how thermal effects in the nuclear equation of state effect the equilibria and stability of hypermassive neutron stars. Chapter 9 presents supplements to the work in Chapter 8, including an examination of the stability question raised in Chapter 8 in greater mathematical detail.

Radiation damping effects on the ultrashort x-ray pulses generated by nonlinear Thomson backscattering

Nonlinear Thomson backscattering of an intense Gaussian laser pulse by a counterpropagating energetic electron is investigated by numerically solving the electron equation of motion taking into account the radiative damping force. The backscattered radiation characteristics are different for linearly and circularly polarized lasers because of a difference in their ponderomotive forces acting on the electron. The radiative electron energy loss weakens the backscattered power, breaks the symmetry of the backscattered-pulse profile, and prolongs the duration of the backscattered radiation. With the circularly polarized laser, an adjustable double-peaked backscattered pulse can be obtained. Such a profile has potential applications as a subfemtosecond x-ray pump and probe with adjustable time delay and power ratio. (c) 2006 American Institute of Physics.

Advanced density functional theory methods for materials science

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn₃P₂) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn₃P₂ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.