Cosmological equations and thermodynamics on apparent horizon in thick braneworld

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the generalized Friedmann equation in some limits and demonstrate that the reductions but not the generalized Friedmann equation can be rewritten as the first law of equilibrium thermodynamics on the apparent horizon of thick braneworld.

The solution properties of phenolphthalein poly(arylether sulfone) .1. The solubility behavior and determination of M-II equations

A series of narrow molecular weight distribution fractions of phenolphthalein polyarylether sulfone(PES-C) had been prepared, The <(M) over bar (w)> of these fractions were determined by conventional light scattering method. The [eta] and the Huggins slope constant k' in DMF, CHCl3 and 1,2-dichloroethane were also determined. The Huggins constants are greater than 0.5 in all of these solvents showing a special solubility behavior. The Mark-Houwink equations of PES-C in these solvents at 25 degrees C are [eta] = 2.79 x 10(-2) <(M) over bar (0.615)(w)> (DMF); [eta] = 3.96 x 10(-2) <(M) over bar (0.58)(w)> (CHCl3); [eta] = 7.40 x 10(-2) <(M) over bar (0.52)(w)> (CH2ClCH2Cl).

Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa's results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa's (1999) results, and the applicable scope of water depth is deeper.

地震波模拟：非规则网格离散的数值解法、吸收边界及其实际应用

This dissertation presents a series of irregular-grid based numerical technique for modeling seismic wave propagation in heterogeneous media. The study involves the generation of the irregular numerical mesh corresponding to the irregular grid scheme, the discretized version of motion equations under the unstructured mesh, and irregular-grid absorbing boundary conditions. The resulting numerical technique has been used in generating the synthetic data sets on the realistic complex geologic models that can examine the migration schemes. The motion equation discretization and modeling are based on Grid Method. The key idea is to use the integral equilibrium principle to replace the operator at each grid in Finite Difference scheme and variational formulation in Finite Element Method. The irregular grids of complex geologic model is generated by the Paving Method, which allow varying grid spacing according to meshing constraints. The grids have great quality at domain boundaries and contain equal quantities of nodes at interfaces, which avoids the interpolation of parameters and variables. The irregular grid absorbing boundary conditions is developed by extending the Perfectly Matched Layer method to the rotated local coordinates. The splitted PML equations of the first-order system is derived by using integral equilibrium principle. The proposed scheme can build PML boundary of arbitrary geometry in the computational domain, avoiding the special treatment at corners in a standard PML method and saving considerable memory and computation cost. The numerical implementation demonstrates the desired qualities of irregular grid based modeling technique. In particular, (1) smaller memory requirements and computational time are needed by changing the grid spacing according to local velocity; (2) Arbitrary surfaces and interface topographies are described accurately, thus removing the artificial reflection resulting from the stair approximation of the curved or dipping interfaces; (3) computational domain is significantly reduced by flexibly building the curved artificial boundaries using the irregular-grid absorbing boundary conditions. The proposed irregular grid approach is apply to reverse time migration as the extrapolation algorithm. It can discretize the smoothed velocity model by irregular grid of variable scale, which contributes to reduce the computation cost. The topography. It can also handle data set of arbitrary topography and no field correction is needed.

Coordinate-Independent Computations on Differential Equations

This project investigates the computational representation of differentiable manifolds, with the primary goal of solving partial differential equations using multiple coordinate systems on general n- dimensional spaces. In the process, this abstraction is used to perform accurate integrations of ordinary differential equations using multiple coordinate systems. In the case of linear partial differential equations, however, unexpected difficulties arise even with the simplest equations.

Automatic Qualitative Analysis of Ordinary Differential Equations Using Piecewise Linear Approximations

This paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.

The Coupled Depth/Slope Approach to Surface Reconstruction

Reconstructing a surface from sparse sensory data is a well known problem in computer vision. Early vision modules typically supply sparse depth, orientation and discontinuity information. The surface reconstruction module incorporates these sparse and possibly conflicting measurements of a surface into a consistent, dense depth map. The coupled depth/slope model developed here provides a novel computational solution to the surface reconstruction problem. This method explicitly computes dense slope representation as well as dense depth representations. This marked change from previous surface reconstruction algorithms allows a natural integration of orientation constraints into the surface description, a feature not easily incorporated into earlier algorithms. In addition, the coupled depth/ slope model generalizes to allow for varying amounts of smoothness at different locations on the surface. This computational model helps conceptualize the problem and leads to two possible implementations- analog and digital. The model can be implemented as an electrical or biological analog network since the only computations required at each locally connected node are averages, additions and subtractions. A parallel digital algorithm can be derived by using finite difference approximations. The resulting system of coupled equations can be solved iteratively on a mesh-pf-processors computer, such as the Connection Machine. Furthermore, concurrent multi-grid methods are designed to speed the convergence of this digital algorithm.

The use of transvaginal synthetic mesh for anterior vaginal wall prolapse repair: a randomized controlled trial

The aim of the study was to compare the efficacy and safety of transvaginal trocar-guided polypropylene mesh insertion with traditional colporrhaphy for treatment of anterior vaginal wall prolapse.This is a randomized controlled trial in which women with advanced anterior vaginal wall prolapse, at least stage II with Ba a parts per thousand yenaEuro parts per thousand+1 cm according to the Pelvic Organ Prolapse Quantification (POP-Q) classification, were randomly assigned to have either anterior colporrhaphy (n = 39) or repair using trocar-guided transvaginal mesh (n = 40). the primary outcome was objective cure rate of the anterior compartment (point Ba) assessed at the 12-month follow-up visit, with stages 0 and I defined as anatomical success. Secondary outcomes included quantification of other vaginal compartments (POP-Q points), comparison of quality of life by the prolapse quality of life (P-QOL) questionnaire, and complication rate between the groups after 1 year. Study power was fixed as 80 % with 5 % cutoff point (p < 0.05) for statistical significance.The groups were similar regarding demographic and clinical preoperative parameters. Anatomical success rates for colporrhaphy and repair with mesh placement groups were 56.4 vs 82.5 % (95 % confidence interval 0.068-0.54), respectively, and the difference between the groups was statistically significant (p = 0.018). Similar total complication rates were observed in both groups, with tape exposure observed in 5 % of the patients. There was a significant improvement in all P-QOL domains as a result of both procedures (p < 0.001), but they were not distinct between groups (p > 0.05).Trocar-guided transvaginal synthetic mesh for advanced anterior POP repair is associated with a higher anatomical success rate for the anterior compartment compared with traditional colporrhaphy. Quality of life equally improved after both techniques. However, the trial failed to detect differences in P-QOL scores and complication rates between the groups.

Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode

Gough, John; Van Handel, R., (2007) 'Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode', Journal of Statistical Physics 127(3) pp.575-607 RAE2008

Hamilton?Jacobi?Bellman equations for quantum optimal feedback control

Gough, John; Belavkin, V.P.; Smolianov, O.G., (2005) 'Hamilton?Jacobi?Bellman equations for quantum optimal feedback control', Journal of Optics B: Quantum and Semiclassical Optics 7 pp.S237-S244 RAE2008

Stochastic Mesh-Based Multiview Reconstruction

A method for reconstruction of 3D polygonal models from multiple views is presented. The method uses sampling techniques to construct a texture-mapped semi-regular polygonal mesh of the object in question. Given a set of views and segmentation of the object in each view, constructive solid geometry is used to build a visual hull from silhouette prisms. The resulting polygonal mesh is simplified and subdivided to produce a semi-regular mesh. Regions of model fit inaccuracy are found by projecting the reference images onto the mesh from different views. The resulting error images for each view are used to compute a probability density function, and several points are sampled from it. Along the epipolar lines corresponding to these sampled points, photometric consistency is evaluated. The mesh surface is then pulled towards the regions of higher photometric consistency using free-form deformations. This sampling-based approach produces a photometrically consistent solution in much less time than possible with previous multi-view algorithms given arbitrary camera placement.

Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.