Evaluation of holonomic quantum computation: Adiabatic versus nonadiabatic

Based on the analytical solution to the time-dependent Schrodinger equations, we evaluate the holonomic quantum computation beyond the adiabatic limit. Besides providing rigorous confirmation of the geometrical prediction of holonomies, the present dynamical resolution offers also a practical means to study the nonadiabaticity induced effects for the universal qubit operations.

New algorithms of the TSM and TOM methods for calibrating microwave test fixtures

Based on the conventional through-short-match (TSM) method, an improved TSM method has been proposed in this Letter. This method gives an analytical solution and has almost all the advantages of conventional TSM methods. For example, it has no phase uncertainty and no bandwidth limitation. The experimental results show that the accuracy can be significantly improved with this method. The proposed theory can be applied to the through-open-match (TOM) method. (C) 2002 Wiley Periodicals. Inc.

Modelling of submarine landslides and generated water waves

The slide of unstable sedimentary bodies and their hydraulic effects are studied by numerical means. A two-dimensional fluid mechanics model based on Navier-Stokes equations has been developed considering the sediments and water as a mixture. Viscoplastic and diffusion laws for the sediments have been introduced into the model. The numerical model is validated with an analytical solution for a Bingham flow. Laboratory experiments consisting in the slide of gravel mass have been carried out. The results of these experiments have shown the importance of the sediment rheology and the diffusion. The model parameters are adjusted by trial and error to match the observed “sandflow”.

On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.

Absorbance kinetics of dye-doped systems with photochemical first order kinetics

Often it is assumed that absorbance decays in photochromic materials with the time dependence of the photochemical kinetics, i.e. exponentially for first order kinetics. Although this may hold in the limiting case of vanishing absorbance, deviations are to be expected for realistic samples, because the local photochemical kinetics slows down with increasing initial absorption and penetration depth of the radiation. We discuss the theory of the kinetics of initially homogeneous photochromic samples and derive analytical solutions. In extension of Tomlinson's theory we find an analytical solution that holds with good approximation even for samples that exhibit a small residual absorption in the saturation limit. The theoretical time dependence of the absorbance originating from photochemical first order kinetics of dye-doped systems is compared with experimental data published by Lafond et al. for fulgides doped in different polymer matrices. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

AlGaInAs-InPMicrocylinder Lasers Connected With an Output Waveguide

AlGaInAs-InPmicrocylinder lasers connected with an output waveguide are fabricated by planar technology. Room-temperature continuous-wave operation with a threshold current of 8 mA is realized for a microcylinder laser with the radius of 10 mu m and the output waveguide width of 2 mu m. The mode Q-factor of 1.2 x 10(4) is measured from the laser spectrum at the threshold. Coupled mode characteristics are analyzed by 2-D finite-difference time-domain simulation and the analytical solution of whispering-gallery modes. The calculated mode Q-factors of coupled modes are in the same order as the measured value.

Particle transfer and fusion cross-section for super-heavy nuclei in dinuclear system

Within the dinuclear system (DNS) conception, instead of solving the Fokker-Planck equation (FPE) analytically, the master equation is solved numerically to calculate the fusion probability of super-heavy nuclei, so that the harmonic oscillator approximation to the potential energy of the DNS is avoided. The relative motion concerning the energy, the angular momentum and the fragment deformation relaxations is explicitly treated to couple with the diffusion process. The nucleon transition probabilities, which are derived microscopically, are related with the energy dissipation of the relative motion. Thus they are time dependent. Comparing with the analytical solution of FPE at the equilibrium, our time-dependent results preserve more dynamical effects. The calculated evaporation residue cross-sections for one-neutron emission channel of Pb-based reactions are basically in agreement with the known experimental data within one order of magnitude.

THE VARIATION AND MOVEMENT OF A KIND OF EDDIES IN SHELF SLOPE WATER

Considering the characteristics of the time and space scales of the eddies we established a quasi-static and quasi-geostrophic model to describe their variation and movement in shelf slope water. The analytical solution revealed the main properties of the variation: slow expansion and fast stagnation processes and the law of the eddy motion affected under the background field. All theoretical results are proved by satellite image measurements.

基于介电泳的电极阵列电场仿真研究

介电泳方法被广泛地应用于微纳颗粒的分离和操纵中,实现介电泳操作的关键是设计满足所需电场分布的电极阵列。针对目前在微电极阵列设计中尚缺乏简单有效的电场解析方法的现状,提出一种基于格林公式的电极阵列电场的解析方法。首先介绍了传统介电泳和行波介电泳的概念和计算模型,分析了介电泳过程与电极上所施加的交变电压的频率和幅度的关系,然后在确立电极电势的边界条件的基础上,采用基于格林公式的电场解析方法,建立了非均匀电场的解析模型,得出不同条件下的电极阵列电场分布的仿真结果,最后利用FEMLAB有限元仿真软件对解析模型进行了对比仿真,验证了该解析模型的可行性。基于格林公式的电场解析求解方法能够有效地提高电极阵列设计中的针对性以及缩短电极设计的时间。

基于广义Lippmann-Schwinger方程的地震波场模拟算法与应用

In the last several decades, due to the fast development of computer, numerical simulation has been an indispensable tool in scientific research. Numerical simulation methods which based on partial difference operators such as Finite Difference Method (FDM) and Finite Element Method (FEM) have been widely used. However, in the realm of seismology and seismic prospecting, one usually meets with geological models which have piece-wise heterogeneous structures as well as volume heterogeneities between layers, the continuity of displacement and stress across the irregular layers and seismic wave scattering induced by the perturbation of the volume usually bring in error when using conventional methods based on difference operators. The method discussed in this paper is based on elastic theory and integral theory. Seismic wave equation in the frequency domain is transformed into a generalized Lippmann-Schwinger equation, in which the seismic wavefield contributed by the background is expressed by the boundary integral equation and the scattering by the volume heterogeneities is considered. Boundary element-volume integral method based on this equation has advantages of Boundary Element Method (BEM), such as reducing one dimension of the model, explicit use the displacement and stress continuity across irregular interfaces, high precision, satisfying the boundary at infinite, etc. Also, this method could accurately simulate the seismic scattering by the volume heterogeneities. In this paper, the concrete Lippmann-Schwinger equation is specifically given according to the real geological models. Also, the complete coefficients of the non-smooth point for the integral equation are introduced. Because Boundary Element-Volume integral equation method uses fundamental solutions which are singular when the source point and the field are very close，both in the two dimensional and the three dimensional case, the treatment of the singular kernel affects the precision of this method. The method based on integral transform and integration by parts could treat the points on the boundary and inside the domain. It could transform the singular integral into an analytical one both in two dimensional and in three dimensional cases and thus it could eliminate the singularity. In order to analyze the elastic seismic wave scattering due to regional irregular topographies, the analytical solution for problems of this type is discussed and the analytical solution of P waves by multiple canyons is given. For the boundary reflection, the method used here is infinite boundary element absorbing boundary developed by a pervious researcher. The comparison between the analytical solutions and concrete numerical examples validate the efficiency of this method. We thoroughly discussed the sampling frequency in elastic wave simulation and find that, for a general case, three elements per wavelength is sufficient, however, when the problem is too complex, more elements per wavelength are necessary. Also, the seismic response in the frequency domain of the canyons with different types of random heterogeneities is illustrated. We analyzed the model of the random media, the horizontal and vertical correlation length, the standard deviation, and the dimensionless frequency how to affect the seismic wave amplification on the ground, and thus provide a basis for the choice of the parameter of random media during numerical simulation.

中强地震震源的破裂过程

With the large developments of the seismic sources theory, computing technologies and survey instruments, we can model and rebuild the rupture process of earthquakes more realistically. On which earthquake sources' properties and tectonic activities law are realized more clearly. The researches in this domain have been done in this paper as follows. Based on the generalized ray method, expressions for displacement on the surface of a half-space due to an arbitrary oriented shear and tensile dislocation are also obtained. Kinematically, fault-normal motion is equivalent to tensile faulting. There is some evidence that such motion occurs in many earthquakes. The expressions for static displacements on the surface of a layered half-space due to static point moment tensor source are given in terms of the generalized reflection and transmission coefficient matrix method. The validity and precision of the new method is illustrated by comparing the consistency of our results with the analytical solution given by Okada's code employing same point source and homogenous half-space model. The computed vertical ground displacement using the moment tensor solution of the Lanchang_Gengma earthquake displays considerable difference with that of a double couple component .The effect of a soft layer at the top of the homogenous half-space on a shallow normal-faulting earthquake is also analyzed. Our results show that more seismic information would be obtained utilizing seismic moment tensor source and layered half-space model. The rupture process of 1999 Chi-Chi, Taiwan, earthquake investigated by using co-seismic surface displacement GPS observations and far field P-wave records. In according to the tectonic analysis and distributions of aftershock, we introduce a three-segment bending fault planes into our model. Both elastic half-space models and layered-earth models to invert the distribution of co-seismic slip along the Chi-Chi earthquake rupture. The results indicate that the shear slip model can not fit horizontal and vertical co-seismic displacements together, unless we add the fault-normal motion (tensile component) in inversions. And then, the Chi Chi earthquake rupture process was obtained by inversion using the seismograms and GPS observations. Fault normal motions determined by inversion, concentrate on the shallow northern bending fault from Fengyuan to Shuangji where the surface earthquake ruptures reveal more complexity and the developed flexural slip folding structures than the other portions of the rupture zone For understanding the perturbation of surface displacements caused by near-surface complex structures, We have taken a numeric test to synthesize and inverse the surface displacements for a pop-up structure that is composed of a main thrust and a back thrust. Our result indicates that the pop-up structure, the typical shallow complex rupture that occurred in the northern bending fault zone form Fengyuan to Shuangji, can be modeled better by a thrust fault added negative tensile component than by a simple thrust fault. We interpret the negative tensile distributions, that concentrate on the shallow northern bending fault from Fengyuan to Shuangji, as a the synthetic effect including the complexities of property and geometry of rupture. The earthquake rupture process also reveal the more spatial and temporal complexities form Fenyuan to SHuangji. According to the three-components teleseismic records, the S-wave velocity structure beneath the 59 teleseismic stations of Taiwan obtained by using the transform function method and the SA techniques. The integrated results, the 3D crustal structure of Taiwan reveal that the thickest part of crustal local in the western Central Range. This conclusion is consistent with the result form the Bouguer gravity anomaly. The orogenic evolution of Taiwan is young period, and the developing foot of Central Range dose not in static balancing. The crustal of Taiwan stays in the course of dynamic equilibrium. The rupture process of 2003)2,24,Jiashi, Xinjiang earthquake was estimated by the finite fault model using far field broadband P wave records of CDSN and IRIS. The results indicate that the earthquake focal is north dip trust fault including some left-lateral strike slip. The focal mechanism of this earthquake is different form that of earthquakes occurred in 1997 and 1998, but similar to that of 1996, Artux, Xinjiang earthquake. We interpreted that the earthquake caused trust fault due to the Tarim basin pushing northward and orogeny of Tianshan mountain. In the end, give a brief of future research subject: Building the Real Time Distribute System for rupture process of Large Earthquakes Based on Internet.

金川二矿区水平矿层灾变失稳问题研究

This dissertation is mainly composed of seven chapters. Specifically, a preface which introduces the background and significance of the dissertation, the present state of study relating to the dissertation, the methods and frame of the study in the dissertation is presented in the first chapter. The second chapter is mainly focused on the present theories and methods about the study on the Problems of Catastrophic Destabilization which are induced by deep mining. In the third chapter, basic conditions of Jinchuan Deposit II are introduced, which include regional geological background, engineering geological conditions, in-situ stress, hydrological geological conditions, mining methods and the present state of the horizontal ole layer. The fourth chapter analysizes the problem of Catastrophic Destabilization of the horizontal ole layer with theoretical methods and gives an analytical solution of elastic foundation beam which two ends are fixed and a catastrophic model of the horizontal ole layer. With FLAC3D, the Problem of Catastrophic Destabilization is analyzed, the variation of displacement and stress of the horizontal ole layer is described, and a development of plastic zone in ore layer is given out. The contents in the sixth chapter is a preliminary design of monitoring system for the horizontal ole layer. At the end of the text, several comprehensive conclusions are given in the seventh chapter.

PROPAGATION OF SONIC BOOMS THROUGH A REAL, STRATIFIED ATMOSPHERE

Sonic boom propagation in a quiet) stratified) lossy atmosphere is the subject of this dissertation. Two questions are considered in detail: (1) Does waveform freezing occur? (2) Are sonic booms shocks in steady state? Both assumptions have been invoked in the past to predict sonic boom waveforms at the ground. A very general form of the Burgers equation is derived and used as the model for the problem. The derivation begins with the basic conservation equations. The effects of nonlinearity) attenuation and dispersion due to multiple relaxations) viscosity) and heat conduction) geometrical spreading) and stratification of the medium are included. When the absorption and dispersion terms are neglected) an analytical solution is available. The analytical solution is used to answer the first question. Geometrical spreading and stratification of the medium are found to slow down the nonlinear distortion of finite-amplitude waves. In certain cases the distortion reaches an absolute limit) a phenomenon called waveform freezing. Judging by the maturity of the distortion mechanism, sonic booms generated by aircraft at 18 km altitude are not frozen when they reach the ground. On the other hand, judging by the approach of the waveform to its asymptotic shape, N waves generated by aircraft at 18 km altitude are frozen when they reach the ground. To answer the second question we solve the full Burgers equation and for this purpose develop a new computer code, THOR. The code is based on an algorithm by Lee and Hamilton (J. Acoust. Soc. Am. 97, 906-917, 1995) and has the novel feature that all its calculations are done in the time domain, including absorption and dispersion. Results from the code compare very well with analytical solutions. In a NASA exercise to compare sonic boom computer programs, THOR gave results that agree well with those of other participants and ran faster. We show that sonic booms are not steady state waves because they travel through a varying medium, suffer spreading, and fail to approximate step shocks closely enough. Although developed to predict sonic boom propagation, THOR can solve other problems for which the extended Burgers equation is a good propagation model.

Correlations in low dimensional quantum systems

In this thesis I present the work done during my PhD in the area of low dimensional quantum gases. The chapters of this thesis are self contained and represent individual projects which have been peer reviewed and accepted for publication in respected international journals. Various systems are considered, the first of which is a two particle model which possesses an exact analytical solution. I investigate the non-classical correlations that exist between the particles as a function of the tunable properties of the system. In the second work I consider the coherences and out of equilibrium dynamics of a one-dimensional Tonks-Girardeau gas. I show how the coherence of the gas can be inferred from various properties of the reduced state and how this may be observed in experiments. I then present a model which can be used to probe a one-dimensional Fermi gas by performing a measurement on an impurity which interacts with the gas. I show how this system can be used to observe the so-called orthogonality catastrophe using modern interferometry techniques. In the next chapter I present a simple scheme to create superposition states of particles with special emphasis on the NOON state. I explore the effect of inter-particle interactions in the process and then characterise the usefulness of these states for interferometry. Finally I present my contribution to a project on long distance entanglement generation in ion chains. I show how carefully tuning the environment can create decoherence-free subspaces which allows one to create and preserve entanglement.

Buoyancy driven flow and its stability in a horizontal rectangular channel with an arbitrary oriented transversal magnetic field

An MHD flow is considered which is relevant to horizontal Bridgman technique for crystal growth from a melt. In the unidirectional parallel flow approximation an analytical solution is found accounting for the finite rectangular cross section of the channel in the case of a vertical magnetic field. Numerical pseudo-spectral solutions are used in the cases of arbitrary magnetic field and gravity vector orientations. The vertical magnetic field (parallel to the gravity) is found to be he most effective to damp the flow, however, complicated flow profiles with "overvelocities" in the comers are typical in the case of a finite cross-section channel. The temperature distribution is shown to be dependent on the flow profile. The linear stability of the flow is investigated by use of the Chebyshev pseudospectral method. For the case of an infinite width channel the transversal rolls instability is investigated, and for the finite cross-section channel the longitudinal rolls instability is considered. The critical Gr number values are computed in the dependence of the Ha number and the wave number or the aspect ratio in the case of finite section.