The behaviour of a dislocation pileup with a finite-strength source is investigated in the presence of various stress gradients within a continuum model where a free-dislocation region exists around the source. Expressions for dislocation density and stress field within the pileup are derived for the situation where there are first and second spatial gradients in applied stress. For a pileup configuration under an applied stress, yielding occurs when the force acting on the leading dislocations at the pileup tips reaches the obstacle strength, and at the same time, it is required that the source be at the threshold stress for dislocation production. A numerical methodology is presented to solve the underlying equations that represent the yielding conditions. The yield stress calculated for a pileup configuration is found to depend on stress gradients, obstacle spacing and source/obstacle strengths. It increases with increasing the first stress gradient, yet dependent on the second stress gradient. Furthermore, while the dependency of yield stress on the obstacle spacing intensifies with increasing the first stress gradient, it diminishes with an increase of second stress gradient. Therefore, the second stress gradient, as a newly introduced parameter, can provide a new physical insight into the size-dependent plasticity phenomena at small length scales. 相似文献
Understanding the factors that affect self-diffusion in isoreticular and multivariate (MTV) MOFs is key to their application in drug delivery, separations, and heterogeneous catalysis. Here, we measure the apparent self-diffusion of solvents saturated within the pores of large single crystals of MOF-5, IRMOF-3 (amino-functionalized MOF-5), and 17 MTV-MOF-5/IRMOF-3 materials at various mole fractions. We find that the apparent self-diffusion coefficient of N,N-dimethylformamide (DMF) may be tuned linearly between the diffusion coefficients of MOF-5 and IRMOF-3 as a function of the linker mole fraction. We compare a series of solvents at saturation in MOF-5 and IRMOF-3 to elucidate the mechanism by which the linker amino groups tune molecular diffusion. The ratio of the self-diffusion coefficients for solvents in MOF-5 to those in IRMOF-3 is similar across all solvents tested, regardless of solvent polarity. We conclude that average pore aperture, not solvent-linker chemical interactions, is the primary factor responsible for the different diffusion dynamics upon introduction of an amino group to the linker. 相似文献
The chromatographic elution process is a key step in the production of notoginseng total saponins. Due to quality variability of loading samples and resin capacity decreasing over cycle time, saponins, especially the five main saponins of notoginseng total saponins, need to be monitored in real time during the elution process. In this study, convolutional neural networks, one of the most popular deep learning methods, were used to develop quantitative calibration models based on in‐line near‐infrared spectroscopy for notoginsenoside R1, ginsenosides Rg1, Re, Rb1 and Rd, and their sum concentration, with root mean square error of prediction values of 0.87, 2.76, 0.60, 1.57, 0.28, and 4.99 mg/mL, respectively. Partial least squares calibration models were also developed for model performance comparison. Results show predicted concentration profiles outputted by both the convolutional neural network models and partial least squares models show agreements with the real trends defined by reference measurements, and can be used for elution process monitoring and endpoint determination. To the best of our knowledge, this is the first reported case study of combining convolutional neural networks and in‐line near‐infrared spectroscopy for monitoring of the chromatographic elution process in commercial production of botanical drug products. 相似文献
The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.
Applied Mathematics and Mechanics - The stress and the strain should be defined as statistical variables averaged over the representative volume elements for any real continuum system. It is shown... 相似文献