The statistics of the second order response of an FPSO in spreading seas

An expression for the probability density function of the second order response of a general FPSO in spreading seas is derived by using the Kac-Siegert approach. Various approximations of the second order force transfer functions are investigated for a ship-shaped FPSO. It is found that, when expressed in non-dimensional form, the probability density function of the response is not particularly sensitive to wave spreading, although the mean squared response and the resulting dimensional extreme values can be sensitive. The analysis is then applied to a Sevan FPSO, which is a large cylindrical buoy-like structure. The second order force transfer functions are derived by using an efficient semi-analytical hydrodynamic approach, and these are then employed to yield the extreme response. However, a significant effect of wave spreading on the statistics for a Sevan FPSO is found even in non-dimensional form. It implies that the exact statistics of a general ship-shaped FPSO may be sensitive to the wave direction, which needs to be verified in future work. It is also pointed out that the Newman's approximation regarding the frequency dependency of force transfer function is acceptable even for the spreading seas. An improvement on the results may be attained when considering the angular dependency exactly. Copyright © 2009 by ASME.

Difference schemes on non-uniform mesh and their application

High order accurate schemes are needed to simulate the multi-scale complex flow fields to get fine structures in simulation of the complex flows with large gradient of fluid parameters near the wall, and schemes on non-uniform mesh are desirable for many CFD (computational fluid dynamics) workers. The construction methods of difference approximations and several difference approximations on non-uniform mesh are presented. The accuracy of the methods and the influence of stretch ratio of the neighbor mesh increment on accuracy are discussed. Some comments on these methods are given, and comparison of the accuracy of the results obtained by schemes based on both non-uniform mesh and coordinate transformation is made, and some numerical examples with non-uniform mesh are presented.

Ghosts of order on the frontier of chaos

What kinds of motion can occur in classical mechanics? We address this question by looking at the structures traced out by trajectories in phase space; the most orderly, completely integrable systems are characterized by phase trajectories confined to low-dimensional, invariant tori. The KAM theory examines what happens to the tori when an integrable system is subjected to a small perturbation and finds that, for small enough perturbations, most of them survive.

The KAM theory is mute about the disrupted tori, but, for two-dimensional systems, Aubry and Mather discovered an astonishing picture: the broken tori are replaced by "cantori," tattered, Cantor-set remnants of the original invariant curves. We seek to extend Aubry and Mather's picture to higher dimensional systems and report two kinds of studies; both concern perturbations of a completely integrable, four-dimensional symplectic map. In the first study we compute some numerical approximations to Birkhoff periodic orbits; sequences of such orbits should approximate any higher dimensional analogs of the cantori. In the second study we prove converse KAM theorems; that is, we use a combination of analytic arguments and rigorous, machine-assisted computations to find perturbations so large that no KAM tori survive. We are able to show that the last few of our Birkhoff orbits exist in a regime where there are no tori.

Methods of multiparameter inversion of seismic data using the acoustic and elastic born approximations

This thesis presents two different forms of the Born approximations for acoustic and elastic wavefields and discusses their application to the inversion of seismic data. The Born approximation is valid for small amplitude heterogeneities superimposed over a slowly varying background. The first method is related to frequency-wavenumber migration methods. It is shown to properly recover two independent acoustic parameters within the bandpass of the source time function of the experiment for contrasts of about 5 percent from data generated using an exact theory for flat interfaces. The independent determination of two parameters is shown to depend on the angle coverage of the medium. For surface data, the impedance profile is well recovered.

The second method explored is mathematically similar to iterative tomographic methods recently introduced in the geophysical literature. Its basis is an integral relation between the scattered wavefield and the medium parameters obtained after applying a far-field approximation to the first-order Born approximation. The Davidon-Fletcher-Powell algorithm is used since it converges faster than the steepest descent method. It consists essentially of successive backprojections of the recorded wavefield, with angular and propagation weighing coefficients for density and bulk modulus. After each backprojection, the forward problem is computed and the residual evaluated. Each backprojection is similar to a before-stack Kirchhoff migration and is therefore readily applicable to seismic data. Several examples of reconstruction for simple point scatterer models are performed. Recovery of the amplitudes of the anomalies are improved with successive iterations. Iterations also improve the sharpness of the images.

The elastic Born approximation, with the addition of a far-field approximation is shown to correspond physically to a sum of WKBJ-asymptotic scattered rays. Four types of scattered rays enter in the sum, corresponding to P-P, P-S, S-P and S-S pairs of incident-scattered rays. Incident rays propagate in the background medium, interacting only once with the scatterers. Scattered rays propagate as if in the background medium, with no interaction with the scatterers. An example of P-wave impedance inversion is performed on a VSP data set consisting of three offsets recorded in two wells.

Ortho-positronium annihilation: steps toward computing the first order radiative corrections

The 0.2% experimental accuracy of the 1968 Beers and Hughes measurement of the annihilation lifetime of ortho-positronium motivates the attempt to compute the first order quantum electrodynamic corrections to this lifetime. The theoretical problems arising in this computation are here studied in detail up to the point of preparing the necessary computer programs and using them to carry out some of the less demanding steps -- but the computation has not yet been completed. Analytic evaluation of the contributing Feynman diagrams is superior to numerical evaluation, and for this process can be carried out with the aid of the Reduce algebra manipulation computer program.

The relation of the positronium decay rate to the electronpositron annihilation-in-flight amplitude is derived in detail, and it is shown that at threshold annihilation-in-flight, Coulomb divergences appear while infrared divergences vanish. The threshold Coulomb divergences in the amplitude cancel against like divergences in the modulating continuum wave function.

Using the lowest order diagrams of electron-positron annihilation into three photons as a test case, various pitfalls of computer algebraic manipulation are discussed along with ways of avoiding them. The computer manipulation of artificial polynomial expressions is preferable to the direct treatment of rational expressions, even though redundant variables may have to be introduced.

Special properties of the contributing Feynman diagrams are discussed, including the need to restore gauge invariance to the sum of the virtual photon-photon scattering box diagrams by means of a finite subtraction.

A systematic approach to the Feynman-Brown method of Decomposition of single loop diagram integrals with spin-related tensor numerators is developed in detail. This approach allows the Feynman-Brown method to be straightforwardly programmed in the Reduce algebra manipulation language.

The fundamental integrals needed in the wake of the application of the Feynman-Brown decomposition are exhibited and the methods which were used to evaluate them -- primarily dis persion techniques are briefly discussed.

Finally, it is pointed out that while the techniques discussed have permitted the computation of a fair number of the simpler integrals and diagrams contributing to the first order correction of the ortho-positronium annihilation rate, further progress with the more complicated diagrams and with the evaluation of traces is heavily contingent on obtaining access to adequate computer time and core capacity.

I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations

Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)¹S, (1s2s)³S, and (1s2s)¹S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z² +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z²)a.u.

Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0 x 10(-4) corresponding to 1 degrees C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10(-8) rad. (c) 2007 Elsevier Ltd. All rights reserved.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

Elimination of zero-order diffraction in digital holography

A simple method to suppress the zero-order diffraction in the reconstructed image of digital holography is presented. In this method, the Laplacian of a detected hologram is used instead of the hologram itself for numerical reconstruction by computing the discrete Fresnel integral. This method can significantly improve the image quality and give better resolution and higher accuracy of the reconstructed image. The main advantages of this method are its simplicity in experimental requirements and convenience in data processing. (C) 2002 Society of Photo-optical Instrumentation Engineers.

High-accuracy same-beam VLBI observations using Shanghai and Urumqi telescopes

The same-beam VLBI observations of Rstar and Vstar, which were two small satellites of Japanese lunar mission, SELENE, were successfully performed by using Shanghai and Urumqi 25-m telescopes. When the separation angle between Rstar and Vstar was less than 0.1 deg, the differential phase delay of the X-band signals between Rstar and Vstar on Shanghai-Urumqi baseline was obtained with a very small error of 0.15 mm rms, which was reduced by 1-2 order compared with the former VLBI results. When the separation angle was less than 0.56 deg, the differential phase delay of the S-band signals was also obtained with a very small error of several mm rms. The orbit determination for Rstar and Vstar was performed, and the accuracy was improved to a level of several meters by using VLBI and Doppler data. The high-accuracy same-beam differential VLBI technique is very useful in orbit determination for a spacecraft, and will be used in orbit determination for Mars missions of China Yinghuo-1 and Russia Phobos-grunt.

Analysis of the practical force accuracy of electromagnet-based nanoindenters

Two important factors that influence the force accuracy of the electromagnet-based nano-indenters but have not yet attracted much attention are analyzed, and a more reasonable way to estimate the force accuracy is presented in this paper. MTS Nano Indenter (R), with the characteristics of a coil suspended in a uniform magnetic field by two sets of springs acting as an actuator and force measuring unit, is used as an example. One of the two factors is the uniformity of the magnetic field. The other is the stiffness of the supporting spring. Consequently, the practical force accuracy varies considerably from test to test because it firmly depends on the working position of the coil and the displacement stroke. A reasonable estimated accuracy value is of the order of 10 degrees mu N for typical indentation tests with a 10(2) nm indentation depth or a 10 degrees mN test force. (C) 2010 Elsevier Ltd. All rights reserved.

Impact of difference accuracy on computational properties of vertical grids for a nonhydrostatic model

Starting from nonhydrostatic Boussinesq approximation equations, a general method is introduced to deduce the dispersion relationships. A comparative investigation is performed on inertia-gravity wave with horizontal lengths of 100, 10 and 1 km. These are examined using the second-order central difference scheme and the fourth-order compact difference scheme on vertical grids that are currently available from the perspectives of frequency, horizontal and vertical component of group velocity. These findings are compared to analytical solutions. The obtained results suggest that whether for the second-order central difference scheme or for the fourth-order compact difference scheme, Charny-Phillips and Lorenz ( L) grids are suitable for studying waves at the above-mentioned horizontal scales; the Lorenz time-staggered and Charny-Phillips time staggered (CPTS) grids are applicable only to the horizontal scales of less than 10 km, and N grid ( unstaggered grid) is unsuitable for simulating waves at any horizontal scale. Furthermore, by using fourth-order compact difference scheme with higher difference precision, the errors of frequency and group velocity in horizontal and vertical directions produced on all vertical grids in describing the waves with horizontal lengths of 1, 10 and 100 km cannot inevitably be decreased. So in developing a numerical model, the higher-order finite difference scheme, like fourth-order compact difference scheme, should be avoided as much as possible, typically on L and CPTS grids, since it will not only take many efforts to design program but also make the calculated group velocity in horizontal and vertical directions even worse in accuracy.

Impact of spatial resolution and spatial difference accuracy on the performance of Arakawa A-D grids

This paper alms at illustrating the impact of spatial difference scheme and spatial resolution on the performance of Arakawa A-D grids in physical space. Linear shallow water equations are discretized and forecasted on Arakawa A-D grids for 120-minute using the ordinary second-order (M and fourth-order (C4) finite difference schemes with the grid spacing being 100 km, 10 km and I km, respectively. Then the forecasted results are compared with the exact solution, the result indicates that when the grid spacing is I kin, the inertial gravity wave can be simulated on any grid with the same results from C2 scheme or C4 scheme, namely the impact of variable configuration is neglectable; while the inertial gravity wave is simulated with lengthened grid spacing, the effects of different variable configurations are different. However, whether for C2 scheme or for C4 scheme, the RMS is minimal (maximal) on C (D) grid. At the same time it is also shown that when the difference accuracy increases from C2 scheme to C4 scheme, the resulted forecasts do not uniformly decrease, which is validated by the change of the group A velocity relative error from C2 scheme to C4 scheme. Therefore, the impact of the grid spacing is more important than that of the difference accuracy on the performance of Arakawa A-D grid.

复杂介质边界元法数值模拟研究

A major impetus to study the rough surface and complex structure in near surface model is because accuracy of seismic observation and geophysical prospecting can be improved. Wave theory study about fluid-satuated porous media has important significance for some scientific problems, such as explore underground resources, study of earth's internal structure, and structure response of multi-phase porous soil under dynamic and seismic effect. Seismic wave numerical modeling is one of the effective methods which understand seismic propagation rules in complex media. As a numerical simulation method, boundary element methods had been widely used in seismic wave field study. This paper mainly studies randomly rough surface scattering which used some approximation solutions based on boundary element method. In addition, I developed a boundary element solution for fluid saturated porous media. In this paper, we used boundary element methods which based on integral expression of wave equation to study the free rough surface scattering effects of Kirchhoff approximation method, Perturbation approximation method, Rytov approximation method and Born series approximation method. Gaussian spectrum model of randomly rough surfaces was chosen as the benchmark model. The approximation methods result were compared with exact results which obtained by boundary element methods, we study that the above approximation methods were applicable how rough surfaces and it is founded that this depends on and ( here is the wavenumber of the incident field, is the RMS height and is the surface correlation length ). In general, Kirchhoff approximation which ignores multiple scatterings between any two surface points has been considered valid for the large-scale roughness components. Perturbation theory based on Taylor series expansion is valid for the small-scale roughness components, as and are .Tests with the Gaussian topographies show that the Rytov approximation methods improves the Kirchhoff approximation in both amplitude and phase but at the cost of an extra treatment of transformation for the wave fields. The realistic methods for the multiscale surfaces come with the Born series approximation and the second-order Born series approximation might be sufficient to guarantee the accuracy of randomly rough surfaces. It could be an appropriate choice that a complex rough surface can be divided into large-, medium-, and small-scale roughness components with their scattering features be studied by the Kirchhoff or Rytov phase approximations, the Born series approximation, and the perturbation theory, respectively. For this purpose, it is important to select appropriate parameters that separate these different scale roughness components to guarantee the divided surfaces satisfy the physical assumptions of the used approximations, respectively. In addition, in this paper, the boundary element methods are used for solving the porous elastic wave propagation and carry out the numerical simulation. Based on the fluid-saturated porous model, this paper analyses and presents the dynamic equation of elastic wave propagation and boundary integral equation formulation of fluid saturated porous media in frequency domain. The fundamental solutions of the elastic wave equations are obtained according to the similarity between thermoelasticity and poroelasticity. At last, the numerical simulation of the elastic wave propagation in the two-phase isotropic media is carried out by using the boundary element method. The results show that a slow quasi P-wave can be seen in both solid and fluid wave-field synthetic seismograms. The boundary element method is effective and feasible.

Efficient Nearest Neighbor Classification Using a Cascade of Approximate Similarity Measures

Nearest neighbor classification using shape context can yield highly accurate results in a number of recognition problems. Unfortunately, the approach can be too slow for practical applications, and thus approximation strategies are needed to make shape context practical. This paper proposes a method for efficient and accurate nearest neighbor classification in non-Euclidean spaces, such as the space induced by the shape context measure. First, a method is introduced for constructing a Euclidean embedding that is optimized for nearest neighbor classification accuracy. Using that embedding, multiple approximations of the underlying non-Euclidean similarity measure are obtained, at different levels of accuracy and efficiency. The approximations are automatically combined to form a cascade classifier, which applies the slower approximations only to the hardest cases. Unlike typical cascade-of-classifiers approaches, that are applied to binary classification problems, our method constructs a cascade for a multiclass problem. Experiments with a standard shape data set indicate that a two-to-three order of magnitude speed up is gained over the standard shape context classifier, with minimal losses in classification accuracy.