Valley evolution by meandering rivers

Fluvial systems form landscapes and sedimentary deposits with a rich hierarchy of structures that extend from grain- to valley scale. Large-scale pattern formation in fluvial systems is commonly attributed to forcing by external factors, including climate change, tectonic uplift, and sea-level change. Yet over geologic timescales, rivers may also develop large-scale erosional and depositional patterns that do not bear on environmental history. This dissertation uses a combination of numerical modeling and topographic analysis to identify and quantify patterns in river valleys that form as a consequence of river meandering alone, under constant external forcing. Chapter 2 identifies a numerical artifact in existing, grid-based models that represent the co-evolution of river channel migration and bank strength over geologic timescales. A new, vector-based technique for bank-material tracking is shown to improve predictions for the evolution of meander belts, floodplains, sedimentary deposits formed by aggrading channels, and bedrock river valleys, particularly when spatial contrasts in bank strength are strong. Chapters 3 and 4 apply this numerical technique to establishing valley topography formed by a vertically incising, meandering river subject to constant external forcing—which should serve as the null hypothesis for valley evolution. In Chapter 3, this scenario is shown to explain a variety of common bedrock river valley types and smaller-scale features within them—including entrenched channels, long-wavelength, arcuate scars in valley walls, and bedrock-cored river terraces. Chapter 4 describes the age and geometric statistics of river terraces formed by meandering with constant external forcing, and compares them to terraces in natural river valleys. The frequency of intrinsic terrace formation by meandering is shown to reflect a characteristic relief-generation timescale, and terrace length is identified as a key criterion for distinguishing these terraces from terraces formed by externally forced pulses of vertical incision. In a separate study, Chapter 5 utilizes image and topographic data from the Mars Reconnaissance Orbiter to quantitatively identify spatial structures in the polar layered deposits of Mars, and identifies sequences of beds, consistently 1-2 meters thick, that have accumulated hundreds of kilometers apart in the north polar layered deposits.

Gauge Invariant Spectral Cauchy Characteristic Extraction of Gravitational Waves in Computational General Relativity

We present a complete system for Spectral Cauchy characteristic extraction (Spectral CCE). Implemented in C++ within the Spectral Einstein Code (SpEC), the method employs numerous innovative algorithms to efficiently calculate the Bondi strain, news, and flux.

Spectral CCE was envisioned to ensure physically accurate gravitational wave-forms computed for the Laser Interferometer Gravitational wave Observatory (LIGO) and similar experiments, while working toward a template bank with more than a thousand waveforms to span the binary black hole (BBH) problem’s seven-dimensional parameter space.

The Bondi strain, news, and flux are physical quantities central to efforts to understand and detect astrophysical gravitational wave sources within the Simulations of eXtreme Spacetime (SXS) collaboration, with the ultimate aim of providing the first strong field probe of the Einstein field equation.

In a series of included papers, we demonstrate stability, convergence, and gauge invariance. We also demonstrate agreement between Spectral CCE and the legacy Pitt null code, while achieving a factor of 200 improvement in computational efficiency.

Spectral CCE represents a significant computational advance. It is the foundation upon which further capability will be built, specifically enabling the complete calculation of junk-free, gauge-free, and physically valid waveform data on the fly within SpEC.

星间激光通讯中的精跟踪研究

星间激光通讯中，精跟踪起着十分重要的作用，而精密偏转镜（FSM）是精跟踪系统中最为关键的部件．基于光学矢量反射定律，推导得到了FSM的精确光学特性，这一特性为精跟踪控制系统提供了精确的理论依据．设计了基于FSM精确光学特性的精跟踪控制系统，对系统整定所用的单纯形法进行了两点重要改进，并对所设计的精跟踪系统进行了数字模拟，由此实现了对FSM的精确控制，提高了精跟踪系统的精确性；将光学衍射超分辨原理应用到星间激光通讯中．利用三区位相光瞳滤波器的超分辨性能，改变光学系统的点扩散函数，从而改变接收端焦平面上的光强

Absorption characteristic and nonvolatile holographic recording in LiNbO3 : Cr : Cu crystals

The absorption characteristic of lithium niobate crystals doped with chromium and copper (Cr and Cu) is investigated. We find that there are two apparent absorption bands for LiNbO3:Cr:Cu crystal doped with 0.14 wt.% Cr2O3 and 0.011 wt.% CuO; one is around 480 nm, and the other is around 660 nm. With a decrease in the doping composition of Cr and an increase in the doping composition of Cu, no apparent absorption band in the shorter wavelength range exists. The higher the doping level of Cr, the larger the absorbance around 660 nm. Although a 633 nm red light is located in the absorption band around 660 nm, the absorption at 633 nm does not help the photorefractive process; i.e., unlike other doubly doped crystals, for example, LiNbO3:Fe:Mn crystal, a nonvolatile holographic recording can be realized by a 633 nm red light as the recording light and a 390 nm UV light as the sensitizing light. For LiNbO3:Cr:Cu crystals, by changing the recording light from a 633 nm red light to a 514 nm green light, sensitizing with a 390 nm UV light and a 488 nm blue light, respectively, a nonvolatile holographic recording can be realized. Doping the appropriate Cr (for example, N-Cr = 2.795 X 10(25)m(-3) and N-Cr/N-Cu = 1) benefits the improvement of holographic recording properties. (c) 2005 Optical Society of America.

Turbulent buoyant jets into stratified or flowing ambient fluids

Theoretical and experimental studies were made on two classes of buoyant jet problems, namely:

1) an inclined, round buoyant yet in a stagnant environment with linear density-stratification;

2) a round buoyant jet in a uniform cross stream of homogenous density.

Using the integral technique of analysis, assuming similarity, predictions can be made for jet trajectory, widths, and dilution ratios, in a density-stratified or flowing environment. Such information is of great importance in the design of disposal systems for sewage effluent into the ocean or waste gases into the atmosphere.

The present study of a buoyant jet in a stagnant environment has extended the Morton type of analysis to cover the effect of the initial angle of discharge. Numerical solutions have been presented for a range of initial conditions. Laboratory experiments were conducted for photographic observations of the trajectories of dyed jets. In general the observed jet forms agreed well with the calculated trajectories and nominal half widths when the value of the entrainment coefficient was taken to be α = 0.082, as previously suggested by Morton.

The problem of a buoyant jet in a uniform cross stream was analyzed by assuming an entrainment mechanism based upon the vector difference between the characteristic jet velocity and the ambient velocity. The effect of the unbalanced pressure field on the sides of the jet flow was approximated by a gross drag term. Laboratory flume experiments with sinking jets which are directly analogous to buoyant jets were performed. Salt solutions were injected into fresh water at the free surface in a flume. The jet trajectories, dilution ratios and jet half widths were determined by conductivity measurements. The entrainment coefficient, α, and drag coefficient, C_d, were found from the observed jet trajectories and dilution ratios. In the ten cases studied where jet Froude number ranged from 10 to 80 and velocity ratio (jet: current) K from 4 to 16, α varied from 0.4 to 0.5 and C_d from 1.7 to 0.1. The jet mixing motion for distance within 250D was found to be dominated by the self-generated turbulence, rather than the free-stream turbulence. Similarity of concentration profiles has also been discussed.

A multiple scattering problem

The present work deals with the problem of the interaction of the electromagnetic radiation with a statistical distribution of nonmagnetic dielectric particles immersed in an infinite homogeneous isotropic, non-magnetic medium. The wavelength of the incident radiation can be less, equal or greater than the linear dimension of a particle. The distance between any two particles is several wavelengths. A single particle in the absence of the others is assumed to scatter like a Rayleigh-Gans particle, i.e. interaction between the volume elements (self-interaction) is neglected. The interaction of the particles is taken into account (multiple scattering) and conditions are set up for the case of a lossless medium which guarantee that the multiple scattering contribution is more important than the self-interaction one. These conditions relate the wavelength λ and the linear dimensions of a particle a and of the region occupied by the particles D. It is found that for constant λ/a, D is proportional to λ and that |Δχ|, where Δχ is the difference in the dielectric susceptibilities between particle and medium, has to lie within a certain range.

The total scattering field is obtained as a series the several terms of which represent the corresponding multiple scattering orders. The first term is a single scattering term. The ensemble average of the total scattering intensity is then obtained as a series which does not involve terms due to products between terms of different orders. Thus the waves corresponding to different orders are independent and their Stokes parameters add.

The second and third order intensity terms are explicitly computed. The method used suggests a general approach for computing any order. It is found that in general the first order scattering intensity pattern (or phase function) peaks in the forward direction Θ = 0. The second order tends to smooth out the pattern giving a maximum in the Θ = π/2 direction and minima in the Θ = 0 , Θ = π directions. This ceases to be true if ka (where k = 2π/λ) becomes large (> 20). For large ka the forward direction is further enhanced. Similar features are expected from the higher orders even though the critical value of ka may increase with the order.

The first order polarization of the scattered wave is determined. The ensemble average of the Stokes parameters of the scattered wave is explicitly computed for the second order. A similar method can be applied for any order. It is found that the polarization of the scattered wave depends on the polarization of the incident wave. If the latter is elliptically polarized then the first order scattered wave is elliptically polarized, but in the Θ = π/2 direction is linearly polarized. If the incident wave is circularly polarized the first order scattered wave is elliptically polarized except for the directions Θ = π/2 (linearly polarized) and Θ = 0, π (circularly polarized). The handedness of the Θ = 0 wave is the same as that of the incident whereas the handedness of the Θ = π wave is opposite. If the incident wave is linearly polarized the first order scattered wave is also linearly polarized. The second order makes the total scattered wave to be elliptically polarized for any Θ no matter what the incident wave is. However, the handedness of the total scattered wave is not altered by the second order. Higher orders have similar effects as the second order.

If the medium is lossy the general approach employed for the lossless case is still valid. Only the algebra increases in complexity. It is found that the results of the lossless case are insensitive in the first order of k_imD where k_im = imaginary part of the wave vector k and D a linear characteristic dimension of the region occupied by the particles. Thus moderately extended regions and small losses make (k_imD)² ≪ 1 and the lossy character of the medium does not alter the results of the lossless case. In general the presence of the losses tends to reduce the forward scattering.

复折射率光纤传输特性分析的Davidenko方法

增益或损耗对光纤的传输特性影响很大。使用Davidenko方法对复折射率光纤的传输特性进行了分析。研究了复折射率纤芯或复折射率包层阶跃光纤,通过比较发现,使用Davidenko方法得到的解与精确解符合得很好。对于芯区为复折射介质的光纤,HE11模与LP01模增益值偏差约为0.6%;对于包层区为复折射率介质的光纤,HE11模与LP01模增益值偏差约为2%。实际研究工作中,为了得到更精确的结果,应该求解全矢量的复本征方程,尤其是包层具有增益或损耗的光纤。

Investigation on the static recording characteristic of super-resolution near-field structure with antimony mask layer

Static recording characteristic of super-resolution near-field structure with antimony (Sb) is investigated in this paper. The recording marks are observed by a scanning electron microscopy (SEM), a high-resolution optical microscopy with a CCD camera and an atomic force microscopy (AFM). The super-resolution mechanism is also analyzed based on these static recording marks. Results show that the light reaching on recording layer is composed of two parts, one is the linear transmissive light (propagating field) and the other is the nonlinear evanescent light in the optical near field. The evanescent light may be greatly enhanced in the center of the spot because Sb will transit from a semiconductor to a metal when it is melted under the high laser power irradiation. This local melted area in the spot center may be like a metal tip in the optical near field that can collect and enhance the information that is far beyond the diffraction limit, which leads to the super-resolution recording and readout. (c) 2005 Elsevier Ltd. All rights reserved.

Focusing properties of concentric piecewise cylindrical vector beam

The focusing properties of a concentric piecewise cylindrical vector beam is investigated theoretically in this paper. The beam consists of three portions with different and changeable phase retardation and polarization. Numerical simulations show that the evolution of the focal shape is very considerable by changing the radius and polarization rotation angle of each portion of the vector beam. And some interesting focal spots may occur, such as two- or three-peak focus, dark hollow focus, ring focus, and two-ring-peak focus. Corresponding gradient force patterns are also computed, and novel trap patterns, including cup shell shape trap with one trap at its each side along axis, rectangle shell shape trap with one trap at its each side, dumbbell optical trap, spherical shell optical trap, may occur, which shows that the concentric piecewise cylindrical vector beam can be used to construct controllable optical tweezers. (c) 2006 Elsevier GmbH. All rights reserved.