Subspace Minimization Conjugate Gradient Method Based on Cubic Regularization Model for Unconstrained Optimization

Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

Immiscible water-alternating-gas（WAG） flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency.Nevertheless,considering the complicated phase behavior and various multiphase flow characteristics,gas tends to break through early in production wells in heterogeneous formations because of overriding,fingering,and channeling,which may result in unfavorable recovery performance.On the basis of phase behavior studies,minimum miscibility pressure measurements,and immiscible WAG coreflood experiments,the cubic B-spline model（CBM） was employed to describe the three-phase relative permeability curve.Using the Levenberg-Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially,optimization of production performance including pressure drop,water cut,and the cumulative gas-oil ratio was performed.A novel numerical inversion method was established for estimation of the water-oil-gas relative permeability curve during the immiscible WAG process.Based on the quantitative characterization of major recovery mechanisms,the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment.The proposed method is reliable and can meet engineering requirements.It provides a basic calculation theory for implicit estimation of oil-water-gas relative permeability curve.

Investigation of cost-effectiveness of highway asphalt pavement maintenance treatments based on rutting development analysis

To investigate the cost-effectiveness of different maintenance treatments of highways in Jiangsu Province, the historical pavement maintenance records, traffic load information and pavement performance data in the pavement management system （PMS） are recorded and analyzed. Compared with the growth model, the linear model, the logarithm model and the exponential model, the cubic model has higher regression accuracy R2 and it can capture the sigmoid shape of the deterioration curve. So it is selected to simulate the pavement rotting development. The benefit over cost ratio is calculated to quantify the treatment cost- effectiveness. The analysis results show that thin hot mix asphalt （HMA） overlays and micro surfacing are more cost- effective than the. other two treatments on light and moderate traffic roads. Hot in-place recycling and thick HMA overlays have much longer service lives and greater cost-effectiveness under heavy or extra heavy traffic.

Theoretical simulation of the effect of deformation on local gravity in a density gradient zone

We modeled the effect of the deformation of a Density Gradient Zone （DGZ） on a local gravity field using a cubical model and introduced a new method to simulate a complex DGZ （CDGZ）. Then, we analyzed the features of the model for the influence of the deformation of the DGZ on the local gravity field. We concluded that land-based gravity is not sensitive to the thickness of the DGZ and that the magnitude of the contribution of the DGZ is one order less than that of the volume strain with the same displacement.

3D Positional and Quantitative Prediction of the Xiaoqinling Gold Ore Belt in Tongguan, Shaanxi, China

Quantitative prediction of deep orebody based on 3D visualization technology is of great significance in mineral exploration. Based on the 2D traditional quantitative predicting method, the geoanomaly theory and the mineral exploration model idea, we constructed 3D models of the topography, strata, structure, magmatite and prospecting engineering of the study area using the commercial 3D modeling software Micromine, delineated eight prospective areas and estimated the gold resources amount with methods of Abundance Estimation and Volume Estimation. Then, we compared and counted the known ore blocks and the predicted blocks, which quantitatively explains this prediction＇s validity. The results show that Xiaoqinling gold belt in Tongguan has convincing potential for gold development and utilization and the prediction method based on 3D visualization technology proves to be effective.

Remote Sensing Retrieval of Surface Suspended Sediment Concentration in the Yellow River Estuary

Accurate assessment of surface suspended sediment concentration （SSSC） in estuary is essential to address several important issues： erosion, water pollution, human health risks, etc. In this study, an empirical cubic retrieval model was developed for the retrieval of SSSC from Yellow River Estuary. Based on sediments and seawater collected from the Yellow River and southeastern Laizhou Bay, SSSC conditions were reproduced in the laboratory at increasing concentrations within a range common to field observations. Continu- ous spectrum measurements of the various SSSCs ranging from 1 to 5700 mg/1 were carried out using an AvaField-3 spectrometer. The results indicated the good correlation between water SSSC and spectral reflectance （Rrs） was obtained in the spectral range of 726-900 nm. At SSSC greater than 2700 mg/L, the 740-900 nm spectral range was less susceptible to the effects of spectral reflectance saturation and more suitable for retrieval of high sediment concentrations. The best correlations were obtained for the reflectance ratio of 820 nm to 490 nm. Informed by the correlation between Rrs and SSSC, a retrieval model was developed （R2 = 0.992）. The novel cubic model, which used the ratio of a near-infrared （NIR） band （740-900 nm） to a visible band （400-600 nm） as factors, provided robust quantifica- tion of high SSSC water samples. Two high SSSC centers, with an order of 103 mg/1, were found in the inversion results around the abandoned Diaokou River mouth, the present Yellow River mouth to the abandoned Qingshuigou River mouth. There was little sedi- ment exchange between the two high SSSC centers due to the directions of the residual currents and vertical mixing.

Determining thresholds of low soil temperature for ecophysiological traits of black spruce and jack pine seedlings

Many studies have estimated approximately ranges of thresholds of low soil temperature in the growth and ecophysi-ological traits of trees, but difficultly determined the exact values. To resolve the problem, black spruce （Picea mariana） and jack pine （Pinus banksiana） seedlings were exposed to 5, 10, 15, 20, 25, 30 and 35℃ soil temperature in greenhouses. After 90 days of the treatment, net photosynthetic rate （A）, stomatal conductance （gs）, transpiration rate （E）, water use efficiency （WUE） and specific leaf area （SLA） were measured. This study showed that all the traits had an asymmetrical peak relationship with changing soil temperature, the relationship was well simulated using a cubic curvilinear model, and the exact thresholds could be derived from the second derivative of the model. The results revealed that the thresholds varied among ecophysiological traits and between tree species. In black spruce, the thresholds were 14.1, 14.7, 10.7, 14.4 and 16.2℃ forA, gs, E, WUE and SLA; 15.4, 10.4, 14.7, 16.9 and 10.5℃ for the corresponding traits in jack pine. The lowest thresholds of E in black spruce and gs in jack pine were an indicator representing the minimum requirement of soil temperature for the regular processes of ecophysiology. The highest thresholds of SLA in black spruce and WUE in jack pine suggest they are the most sensitive to decreasing soil temperature and may play an important role in the acclimation. The averaged thresholds were at 14.0 and 13.6℃ for black spruce and jack pine, suggesting that the sensitivity of both species to low soil temperature was quite close.

Numerical study of the flow in the Yellow River with non-monotonous banks

A 2-D depth averaged RNG k- ε model is developed to simulate the flow in a typical reach of the Upper Yellow River with non-monotonic banks. In order to take account of the effect of the secondary flow in a bend, the momentum equations are modified by adding an additional source term. A comparison between the numerical simulation and the field measurements indicates that the improved 2-D depth averaged RNG k- ε model can improve the accuracy of the numerical simulation. An arc spline interpolation method is developed to interpolate the non-monotonic river banks. The method can also be reasonably applied for the 2-D interpolation of the river bed level. Through a comparison of the water surface gradients simulated in the seven bends of the studied reach, some analytical formulae are improved to reasonably calculate the longitudinal and transverse gradients in meandering river reaches. Furthermore, the positions of the maximum water depth and the maximum velocity in a typical bend are discussed.