Variational analysis of ablation for variable properties

"Work was performed as part of a Cornell Aeronautical Laboratory Internal Research Project."

Research on the influence of fabrication parameters on the performance of buried ion-exchanged glass waveguides using the variational method

The variational method is proposed to analyze the influence of the fabrication parameters on the performance of buried K+-Na+ ion-exchanged Er3+-Yb3+ ions co-doped glass waveguide. The unknown parameters of the Hermite-Gaussian functions as the trial field distribution are determined based on the scalar variational principle. It is demonstrated that the results calculated in this paper agree with those measured in the experiment. The mode dimensions, the effective refractive index, and the overlap factor as the functions of the fabrication parameters are investigated. These results of the variational analysis are useful for the design and optimization of Er3+-Yb3+ ions co-doped waveguides.

A Variational Calculation of TE and TM Cutoff Wavenumbers in Circular Eccentric Guides by Conformal Mapping

The cutoff wavenumbers of higher order modes in circular eccentric guides are computed with the variational analysis combined with a conformal mapping. A conformal mapping is applied to the variational formulation, and the variational equation is solved by the finite-element method. Numerical results for TE and TM cutoff wavenumbers are presented for different distances between the centers and ratio of the radii. Comparisons with numerical results found in the literature validate the presented method

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

Variational and perturbative schemes for a spiked harmonic oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian operator - d2/dx2 + x2 + l(l + 1)/x2 + λ|x| -α, where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large coupling perturbative expansion is carried out and the contributions up to fourth-order to the ground state energy are explicitly evaluated. Numerical results are compared for the special case α = 5/2. © 1989 American Institute of Physics.

Local environmental structures of Mo in the superionic conducting glass (AgI)(0.6)(Ag2MoO4)(0.4) by anomalous X-ray scattering

The anomalous X-ray scattering (AXS) method using Mo K absorption edges has been employed for obtaining the local structural information of superionic conducting glass having the composition (AgI)(0.6)(Ag2MoO4)(0.4). The possible atomic arrangements in the near-neighbor region of this glass were estimated by coupling the results with the least-squares variational analysis so as to reproduce the differential intensity profile for Mo as well as the ordinary scattering profile. The coordination number of oxygen around Mo is found to be about 4 at the distance of 0.180 mn. This implies that the most probable structural entity in the glass is the MoO4 tetrahedral unit which has been proposed based on infrared spectroscopy. The value of the coordination number of I- around Ag+ is estimated as 4.4 at 0.287 nm, suggesting an arrangement similar to that of crystalline or molten AgI.

激光辐照热障涂层中平面应变问题的热弹性变分分析

针对激光辐照热障涂层材料的平面应变问题,提出热障涂层热弹性分析的基本方程,对定常温度场给出级数形式解析解,并用最小余能原理和变分法分析了结构的热弹性应力场,研究了最大应力和界面应力的分布特征,并就一些物理参数的影响进行了讨论.结果表明,热障涂层的主要破坏因素为表面拉伸应力,界面应力相对较小,但在自由边界有集中现象,剥落应力大于剪切应力,是导致涂层破坏的重要原因.涂层厚度增加会改变厚度方向上的应力分布,界面应力向中心集中.

Application of altimetry data assimilation on mesoscale eddies simulation

Mesoscale eddy plays an important role in the ocean circulation. In order to improve the simulation accuracy of the mesoscale eddies, a three-dimensional variation (3DVAR) data assimilation system called Ocean Variational Analysis System (OVALS) is coupled with a POM model to simulate the mesoscale eddies in the Northwest Pacific Ocean. In this system, the sea surface height anomaly (SSHA) data by satellite altimeters are assimilated and translated into pseudo temperature and salinity (T-S) profile data. Then, these profile data are taken as observation data to be assimilated again and produce the three-dimensional analysis T-S field. According to the characteristics of mesoscale eddy, the most appropriate assimilation parameters are set up and testified in this system. A ten years mesoscale eddies simulation and comparison experiment is made, which includes two schemes: assimilation and non-assimilation. The results of comparison between two schemes and the observation show that the simulation accuracy of the assimilation scheme is much better than that of non-assimilation, which verified that the altimetry data assimilation method can improve the simulation accuracy of the mesoscale dramatically and indicates that it is possible to use this system on the forecast of mesoscale eddies in the future.

Assessing levels of uncertainty in recent temperature time series

We examine to what degree we can expect to obtain accurate temperature trends for the last two decades near the surface and in the lower troposphere. We compare temperatures obtained from surface observations and radiosondes as well as satellite-based measurements from the Microwave Soundings Units (MSU), which have been adjusted for orbital decay and non-linear instrument-body effects, and reanalyses from the European Centre for Medium-Range Weather Forecasts (ERA) and the National Centre for Environmental Prediction (NCEP). In regions with abundant conventional data coverage, where the MSU has no major influence on the reanalysis, temperature anomalies obtained from microwave sounders, radiosondes and from both reanalyses agree reasonably. Where coverage is insufficient, in particular over the tropical oceans, large differences are found between the MSU and either reanalysis. These differences apparently relate to changes in the satellite data availability and to differing satellite retrieval methodologies, to which both reanalyses are quite sensitive over the oceans. For NCEP, this results from the use of raw radiances directly incorporated into the analysis, which make the reanalysis sensitive to changes in the underlying algorithms, e.g. those introduced in August 1992. For ERA, the bias-correction of the one-dimensional variational analysis may introduce an error when the satellite relative to which the correction is calculated is biased itself or when radiances change on a time scale longer than a couple of months, e.g. due to orbit decay. ERA inhomogeneities are apparent in April 1985, October/November 1986 and April 1989. These dates can be identified with the replacements of satellites. It is possible that a negative bias in the sea surface temperatures (SSTs) used in the reanalyses may have been introduced over the period of the satellite record. This could have resulted from a decrease in the number of ship measurements, a concomitant increase in the importance of satellite-derived SSTs, and a likely cold bias in the latter. Alternately, a warm bias in SSTs could have been caused by an increase in the percentage of buoy measurements (relative to deeper ship intake measurements) in the tropical Pacific. No indications for uncorrected inhomogeneities of land surface temperatures could be found. Near-surface temperatures have biases in the boundary layer in both reanalyses, presumably due to the incorrect treatment of snow cover. The increase of near-surface compared to lower tropospheric temperatures in the last two decades may be due to a combination of several factors, including high-latitude near-surface winter warming due to an enhanced NAO and upper-tropospheric cooling due to stratospheric ozone decrease.

A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical collapse in a degenerate binary fermion mixture using a hydrodynamic model

We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion-fermion mixture ( DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances, there cannot be a collapse for repulsive interspecies fermion fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion-fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model, we study different aspects of collapse in such a DFFM initiated by a jump in the interspecies fermion-fermion interaction ( scattering length) to a large negative ( attractive) value using a Feshbach resonance. Suggestion for experiments of collapse in a DFFM of distinct atoms is made.

Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)