(5E)-Dimethyl 2-bromo­methyl-5-cyclo­hexyl­imino-2-phenyl-2,5-dihydro­furan-3,4-dicarboxyl­ate

The mol­ecule of the title compound, C21H24BrNO5, has a planar furan ring [maximum deviation = 0.025 (3) Å]. The carboxy­methyl group in the 3-position is nearly coplanar with this ring [dihedral angle = 7.9 (1)°], whereas that in the 4-position is nearly perpendicular to it [dihedral angle = 78.9 (1) Å]

Gaussian Smoothing and Asymptotic Convexity

Coordinated Science Laboratory was formerly known as Control Systems LaboratorySmoothing (say by a Guassian kernel) has been a very popular technique for optimizing a nonconvex objective function. The rationale behind smoothing is that the smoothed function has less spurious local minima than the original one. This technique has seen tremendous success in many real world tasks such as those arising in machine learning and computer vision. Despite its empirical success, there has been little theoretical understanding about the effect of smoothing in optimization. This work rigorously studies some of the fundamental properties of the smoothing technique. In particular, we present a formal definition for the functions that can eventually become convex by smoothing. We clarify the related necessary and sufficient conditions and present a closed-form expression for the minimizer of the resulted smoothed function, when it satisfies certain decay conditions.National Science Foundation / NSF IIS 11-1601

The influence of parent austenite characteristics on the intervariant boundary network in a lath martensitic steel

The influence of the parent austenite deformation state on the intervariant boundary network (i.e., population, plane orientation, and connectivity) of a lath martensitic microstructure was investigated using conventional EBSD mapping and five-parameter boundary analysis approach along with quantification of boundary connectivity using homology metrics. The lath martensite largely revealed a bimodal misorientation angle distribution, closely matched with the Kurdjumov–Sachs (K–S) orientation relationship. The application of deformation significantly changed the distribution, gradually reducing the intensity of the 60° misorientation angle peak. This was largely ascribed to substructure development within the parent austenite upon deformation, which stimulates particular variant/s having a habit plane (011)α′ closely parallel to the primary (111)γ and/or secondary (11¯¯¯1)γ slip plane. The interaction of these variants eventually promoted specific intervariant boundaries (e.g., 60°/[111], 10.5°/[011], and 49.5°/[110]) at the expense of 60°/[011]. The application of deformation in the parent austenite did not change the intervariant boundary plane character distribution, which mostly exhibited an anisotropic character terminated on {110} planes because of the displacive nature of the martensitic transformation. However, the extent of anisotropy progressively decreased with increasing strain in the austenite prior to transformation. The grain boundary network connectivity was markedly altered due to the local variant selection induced by the deformation. Deformation in the austenite regime generally decreased the connectivity of boundaries having a {110} plane orientation. The intervariant boundaries with the {110} twist character also displayed a similar trend, though the connectivity of {110} tilt boundaries progressively enhanced with increasing strain. The former was closely matched with a decrease in the population of 60°/[110] intervariant boundaries with the strain. The current findings suggest that the intervariant boundary network of lath martensite can be manipulated through changes in the parent austenite deformation state which, in turn, can be used to enhance key final product properties such as toughness.publishedVersio

Seeing Through the Blur

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryThis paper addresses the problem of image alignment using models such as affine and homography and by directly using pixel intensity values. Coarse-to-fine scheme has become a standard for direct intensity-based alignment. It is believed that such coarse-to-fine scale sampling (Gaussian blur) can improve region of convergence of the alignment optimization. Although, it has been proposed that such isotropic blur may not be optimal for some motion models, no rigorous derivation for such kernels has been known to date. In this work, we derive kernels for some of the common motion models such as affine and homography, which are able to smooth the alignment objective function. This is appealing because the smoothing process often removes poor local minima and thus reaches deeper solutions. Our derivation shows that these kernels coincide with Gaussian blur of the image only for displacement motion.National Science Foundation / NSF IIS 11-1601

Flow properties of an intact MPL from nano-tomography and pore network modelling

Adding a hydrophobic micro-porous layer (MPL) between a gas diffusion layer (GDL) and a catalyst layer (CL) at the cathode of a PEM fuel cell was found capable of improving cell performance. However, how an MPL does this is not well-understood because current techniques are limited in measuring, observing and simulating multiphase pore fluid flow across the full range of pores that vary to a great extent in geometry, topology, surface morphology. In this work, we focused our investigation on estimating flow properties of an MPL volume to assess the limiting effect of strongly hydrophobic sub-micron pores on water transports. We adopted a nano-tomography and pore network flow modelling approach. A pore-structure model, purposely reconstructed from an intact MPL sample using Focused Ion Beam milling and Scanning Electron Microscope (FIB/SEM) previously, was used to extract a realistic pore network. A two-phase pore network flow model, developed recently for simulating the flow of gas, liquid or their mixture in both micrometre and nanometre pores, was applied to the pore network. We firstly tested the validity of the constructed pore network, and then calculated the properties: permeability for both water and selected gases, water entry pressure, and relative permeability. Knudsen diffusion was taken into consideration in calculations when appropriate. Our calculations showed that the water permeability was three orders of magnitude smaller than experimentally measured results reported in the literature, and when the water contact angle increased from 95° to 150°, the water-entry pressure increased from 2.5 MPa to 28 MPa. Thus our results revealed that for a strongly hydrophobic MPL that contains nanometre pores only it would behave like a buffer to water, and therefore the structural preferential paths in an MPL, such as cracks, are likely to be responsible for significant liquid water transport from the CL to the GDL that has been observed experimentally recently. We highlighted the needs for multi-scale modelling of the interplays of liquid water and gas transfer in MPLs that contain variable pores

Flow simulation of artificially induced microfractures using digital rock and lattice boltzmann methods

Microfractures have great significance in the study of reservoir development because they are an effective reserving space and main contributor to permeability in a large amount of reservoirs. Usually, microfractures are divided into natural microfractures and induced microfractures. Artificially induced rough microfractures are our research objects, the existence of which will affect the fluid-flow system (expand the production radius of production wells), and act as a flow path for the leakage of fluids injected to the wells, and even facilitate depletion in tight reservoirs. Therefore, the characteristic of the flow in artificially induced fractures is of great significance. The Lattice Boltzmann Method (LBM) was used to calculate the equivalent permeability of artificially induced three-dimensional (3D) fractures. The 3D box fractal dimensions and porosity of artificially induced fractures in Berea sandstone were calculated based on the fractal theory and image-segmentation method, respectively. The geometrical parameters (surface roughness, minimum fracture aperture, and mean fracture aperture), were also calculated on the base of digital cores of fractures. According to the results, the permeability lies between 0.071–3.759 (dimensionless LB units) in artificially induced fractures. The wide range of permeability indicates that artificially induced fractures have complex structures and connectivity. It was also found that 3D fractal dimensions of artificially induced fractures in Berea sandstone are between 2.247 and 2.367, which shows that the artificially induced fractures have the characteristics of self-similarity. Finally, the following relations were studied: (a) exponentially increasing permeability with increasing 3D box fractal dimension, (b) linearly increasing permeability with increasing square of mean fracture aperture, (c) indistinct relationship between permeability and surface roughness, and (d) linearly increasing 3D box fractal dimension with increasing porosity