Effects of Inclined Interface Angle on Compressible Rayleigh-Taylor Instability: A Numerical Study Based on the Discrete Boltzmann Method.

Rayleigh-Taylor (RT) instability is a basic fluid interface instability that widely exists in nature and in the engineering field. To investigate the impact of the initial inclined interface on compressible RT instability, the two-component discrete Boltzmann method is employed. Both the thermodynamic non-equilibrium (TNE) and hydrodynamic non-equilibrium (HNE) effects are studied. It can be found that the global average density gradient in the horizontal direction, the non-organized energy fluxes, the global average non-equilibrium intensity and the proportion of the non-equilibrium region first increase and then reduce with time. However, the global average density gradient in the vertical direction and the non-organized moment fluxes first descend, then rise, and finally descend. Furthermore, the global average density gradient, the typical TNE intensity and the proportion of non-equilibrium region increase with increasing angle of the initial inclined interface. Physically, there are three competitive mechanisms: (1) As the perturbed interface elongates, the contact area between the two fluids expands, which results in an increasing gradient of macroscopic physical quantities and leads to a strengthening of the TNE effects. (2) Under the influence of viscosity, the perturbation pressure waves on both sides of the material interface decrease with time, which makes the gradient of the macroscopic physical quantity decrease, resulting in a weakening of the TNE strength. (3) Due to dissipation and/or mutual penetration of the two fluids, the gradient of macroscopic physical quantities gradually diminishes, resulting in a decrease in the intensity of the TNE.

Domain-Aware Dual Attention for Generalized Medical Image Segmentation on Unseen Domains.

Recently, there has been significant progress in medical image segmentation utilizing deep learning techniques. However, these achievements largely rely on the supposition that the source and target domain data are identically distributed, and the direct application of related methods without addressing the distribution shift results in dramatic degradation in realistic clinical environments. Current approaches concerning the distribution shift either require the target domain data in advance for adaptation, or focus only on the distribution shift across domains while ignoring the intra-domain data variation. This paper proposes a domain-aware dual attention network for the generalized medical image segmentation task on unseen target domains. To alleviate the severe distribution shift between the source and target domains, an Extrinsic Attention (EA) module is designed to learn image features with knowledge originating from multi-source domains. Moreover, an Intrinsic Attention (IA) module is also proposed to handle the intra-domain variation by individually modeling the pixel-region relations derived from an image. The EA and IA modules complement each other well in terms of modeling the extrinsic and intrinsic domain relationships, respectively. To validate the model effectiveness, comprehensive experiments are conducted on various benchmark datasets, including the prostate segmentation in magnetic resonance imaging (MRI) scans and the optic cup/disc segmentation in fundus images. The experimental results demonstrate that our proposed model effectively generalizes to unseen domains and exceeds the existing advanced approaches.

Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects.

A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law, and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate nonequilibrium behaviors of the compressible Kelvin-Helmholtz instability (KHI). The entropy of mixing, the mixing area, the mixing width, the kinetic and internal energies, and the maximum and minimum temperatures are investigated during the dynamic KHI process. It is found that the mixing degree and fluid flow are similar in the KHI process for cases with various thermal conductivity and initial temperature configurations, while the maximum and minimum temperatures show different trends in cases with or without initial temperature gradients. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI morphological structure.

Knudsen Number Effects on Two-Dimensional Rayleigh-Taylor Instability in Compressible Fluid: Based on a Discrete Boltzmann Method.

Based on the framework of our previous work [H.L. Lai et al., Phys. Rev. E, 94, 023106 (2016)], we continue to study the effects of Knudsen number on two-dimensional Rayleigh-Taylor (RT) instability in compressible fluid via the discrete Boltzmann method. It is found that the Knudsen number effects strongly inhibit the RT instability but always enormously strengthen both the global hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) effects. Moreover, when Knudsen number increases, the Kelvin-Helmholtz instability induced by the development of the RT instability is difficult to sufficiently develop in the later stage. Different from the traditional computational fluid dynamics, the discrete Boltzmann method further presents a wealth of non-equilibrium information. Specifically, the two-dimensional TNE quantities demonstrate that, far from the disturbance interface, the value of TNE strength is basically zero; the TNE effects are mainly concentrated on both sides of the interface, which is closely related to the gradient of macroscopic quantities. The global TNE first decreases then increases with evolution. The relevant physical mechanisms are analyzed and discussed.

Total-Factor Eco-Efficiency and Its Influencing Factors in the Yangtze River Delta Urban Agglomeration, China.

Urban agglomerations are not only the core areas leading economic growth but also the fronts facing severe resource and environmental challenges. This paper aimed to increase our understanding of urban eco-efficiency and its influencing factors and thus provide the scientific basis for green development. We developed a model that incorporates super-efficiency, slacks-based-measure, and global-frontier technology to calculate the total-factor eco-efficiency (TFEE) and used a spatial panel Tobit model to take into account spatial spillover effects. An empirical study was conducted utilizing a prefecture-level dataset in the Yangtze River Delta Urban Agglomeration (YRDUA) from 2003 to 2016. The main findings reveal that significant spatial differences exist in TFEE in the YRDUA: high-TFEE cities were majorly located in the coastal areas, while low-TFEE cities were mostly situated inland. Overall, TFEE shows a trend of "decline first and then rise with fluctuation"; the disparity between inland and coastal regions has expanded. Further regression analysis suggests that industrial structure, environmental regulation, and innovation were positively related to TFEE, while foreign direct investment was not conducive to the growth in TFEE. The relationship between population intensity and urban eco-efficiency is an inverted U-shaped curve. Finally, several specific policy implications were raised based on the results.

Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model.

In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon.

Mesoscopic Simulation of the Two-Component System of Coupled Sine-Gordon Equations with Lattice Boltzmann Method.

In this paper, a new lattice Boltzmann model for the two-component system of coupled sine-Gordon equations is presented by using the coupled mesoscopic Boltzmann equations. Via the Chapman-Enskog multiscale expansion, the macroscopical governing evolution system can be recovered correctly by selecting suitable discrete equilibrium distribution functions and the amending functions. The mesoscopic model has been validated by several related issues where analytic solutions are available. The experimental results show that the numerical results are consistent with the analytic solutions. From the mesoscopic point of view, the present approach provides a new way for studying the complex nonlinear partial differential equations arising in natural nonlinear phenomena of engineering and science.

Nonequilibrium thermohydrodynamic effects on the Rayleigh-Taylor instability in compressible flows.

The effects of compressibility on Rayleigh-Taylor instability (RTI) are investigated by inspecting the interplay between thermodynamic and hydrodynamic nonequilibrium phenomena (TNE, HNE, respectively) via a discrete Boltzmann model. Two effective approaches are presented, one tracking the evolution of the local TNE effects and the other focusing on the evolution of the mean temperature of the fluid, to track the complex interfaces separating the bubble and the spike regions of the flow. It is found that both the compressibility effects and the global TNE intensity show opposite trends in the initial and the later stages of the RTI. Compressibility delays the initial stage of RTI and accelerates the later stage. Meanwhile, the TNE characteristics are generally enhanced by the compressibility, especially in the later stage. The global or mean thermodynamic nonequilibrium indicators provide physical criteria to discriminate between the two stages of the RTI.

Crystal structure and genetic modifications of FI-CMCase from Aspergillus aculeatus F-50.

Cellulose is the major component of the plant cell wall and the most abundant renewable biomass on earth, and its decomposition has proven to be very useful in many commercial applications. Endo-1,4-ß-d-glucanase (EC 3.2.1.4; endoglucanase), which catalyzes the random hydrolysis of 1,4-ß-glycosidic bonds of the cellulose main chain to cleave cellulose into smaller fragments, is the key cellulolytic enzyme. An endoglucanase isolated from Aspergillus aculeatus F-50 (FI-CMCase), which is classified into the glycoside hydrolase (GH) family 12, was demonstrated to be effectively expressed in the industrial strain Pichia pastoris. Here, the crystal structure and complex structures of P. pastoris-expressed FI-CMCase were solved to high resolution. The overall structure is analyzed and compared to other GH12 members. In addition, the substrate-surrounding residues were engineered to search for variants with improved enzymatic activity. Among 14 mutants constructed, one with two-fold increase in protein expression was identified, which possesses a potential to be further developed as a commercial enzyme product.

Functional and structural analysis of Pichia pastoris-expressed Aspergillus niger 1,4-ß-endoglucanase.

Eukaryotic 1,4-ß-endoglucanases (EC 3.2.1.4) have shown great potentials in many commercial applications because they effectively catalyze hydrolysis of cellulose, the main component of the plant cell wall. Here we expressed a glycoside hydrolase family (GH) 5 1,4-ß-endoglucanase from Aspergillus niger (AnCel5A) in Pichia pastoris, which exhibits outstanding pH and heat stability. In order to further investigate the molecular mechanism of AnCel5A, apo-form and cellotetraose (CTT) complex enzyme crystal structures were solved to high resolution. AnCel5A folds into a typical (ß/α)8-TIM barrel architecture, resembling other GH5 members. In the substrate binding cavity, CTT is found to bind to -4 - -1 subsites, and several polyethylene glycol molecules are found in positive subsites. In addition, several unique N-glycosylation motifs that may contribute to protein higher stability were observed from crystal structures. These results are of great importance for understanding the molecular mechanism of AnCel5A, and also provide guidance for further applications of the enzyme.

Improving specific activity and thermostability of Escherichia coli phytase by structure-based rational design.

Escherichia coli phytase (EcAppA) which hydrolyzes phytate has been widely applied in the feed industry, but the need to improve the enzyme activity and thermostability remains. Here, we conduct rational design with two strategies to enhance the EcAppA performance. First, residues near the substrate binding pocket of EcAppA were modified according to the consensus sequence of two highly active Citrobacter phytases. One out of the eleven mutants, V89T, exhibited 17.5% increase in catalytic activity, which might be a result of stabilized protein folding. Second, the EcAppA glycosylation pattern was modified in accordance with the Citrobacter phytases. An N-glycosylation motif near the substrate binding site was disrupted to remove spatial hindrance for phytate entry and product departure. The de-glycosylated mutants showed 9.6% increase in specific activity. On the other hand, the EcAppA mutants that adopt N-glycosylation motifs from CbAppA showed improved thermostability that three mutants carrying single N-glycosylation motif exhibited 5.6-9.5% residual activity after treatment at 80°C (1.8% for wild type). Furthermore, the mutant carrying all three glycosylation motifs exhibited 27% residual activity. In conclusion, a successful rational design was performed to obtain several useful EcAppA mutants with better properties for further applications.

Rational design to improve thermostability and specific activity of the truncated Fibrobacter succinogenes 1,3-1,4-ß-D-glucanase.

1,3-1,4-ß-D-Glucanase has been widely used as a feed additive to help non-ruminant animals digest plant fibers, with potential in increasing nutrition turnover rate and reducing sanitary problems. Engineering of enzymes for better thermostability is of great importance because it not only can broaden their industrial applications, but also facilitate exploring the mechanism of enzyme stability from structural point of view. To obtain enzyme with higher thermostability and specific activity, structure-based rational design was carried out in this study. Eleven mutants of Fibrobacter succinogenes 1,3-1,4-ß-D-glucanase were constructed in attempt to improve the enzyme properties. In particular, the crude proteins expressed in Pichia pastoris were examined firstly to ensure that the protein productions meet the need for industrial fermentation. The crude protein of V18Y mutant showed a 2 °C increment of Tm and W203Y showed ∼30% increment of the specific activity. To further investigate the structure-function relationship, some mutants were expressed and purified from P. pastoris and Escherichia coli. Notably, the specific activity of purified W203Y which was expressed in E. coli was 63% higher than the wild-type protein. The double mutant V18Y/W203Y showed the same increments of Tm and specific activity as the single mutants did. When expressed and purified from E. coli, V18Y/W203Y showed similar pattern of thermostability increment and 75% higher specific activity. Furthermore, the apo-form and substrate complex structures of V18Y/W203Y were solved by X-ray crystallography. Analyzing protein structure of V18Y/W203Y helps elucidate how the mutations could enhance the protein stability and enzyme activity.

Lattice Boltzmann model for generalized nonlinear wave equations.

In this paper, a lattice Boltzmann model is developed to solve a class of the nonlinear wave equations. Through selecting equilibrium distribution function and an amending function properly, the governing evolution equation can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. We validate the algorithm on some problems where analytic solutions are available, including the second-order telegraph equation, the nonlinear Klein-Gordon equation, and the damped, driven sine-Gordon equation. It is found that the numerical results agree well with the analytic solutions, which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems.

Diverse substrate recognition mechanism revealed by Thermotoga maritima Cel5A structures in complex with cellotetraose, cellobiose and mannotriose.

The hyperthermophilic endoglucanase Cel5A from Thermotoga maritima can find applications in lignocellulosic biofuel production, because it catalyzes the hydrolysis of glucan- and mannan-based polysaccharides. Here, we report the crystal structures in apo-form and in complex with three ligands, cellotetraose, cellobiose and mannotriose, at 1.29Å to 2.40Å resolution. The open carbohydrate-binding cavity which can accommodate oligosaccharide substrates with extensively branched chains explained the dual specificity of the enzyme. Combining our structural information and the previous kinetic data, it is suggested that this enzyme prefers ß-glucosyl and ß-mannosyl moieties at the reducing end and uses two conserved catalytic residues, E253 (nucleophile) and E136 (general acid/base), to hydrolyze the glycosidic bonds. Moreover, our results also suggest that the wide spectrum of Tm_Cel5A substrates might be due to the lack of steric hindrance around the C2-hydroxyl group of the glucose or mannose unit from active-site residues.

Crystal structures of Bacillus alkaline phytase in complex with divalent metal ions and inositol hexasulfate.

Alkaline phytases from Bacillus species, which hydrolyze phytate to less phosphorylated myo-inositols and inorganic phosphate, have great potential as additives to animal feed. The thermostability and neutral optimum pH of Bacillus phytase are attributed largely to the presence of calcium ions. Nonetheless, no report has demonstrated directly how the metal ions coordinate phytase and its substrate to facilitate the catalytic reaction. In this study, the interactions between a phytate analog (myo-inositol hexasulfate) and divalent metal ions in Bacillus subtilis phytase were revealed by the crystal structure at 1.25 Å resolution. We found all, except the first, sulfates on the substrate analog have direct or indirect interactions with amino acid residues in the enzyme active site. The structures also unraveled two active site-associated metal ions that were not explored in earlier studies. Significantly, one metal ion could be crucial to substrate binding. In addition, binding of the fourth sulfate of the substrate analog to the active site appears to be stronger than that of the others. These results indicate that alkaline phytase starts by cleaving the fourth phosphate, instead of the third or the sixth that were proposed earlier. Our high-resolution, structural representation of Bacillus phytase in complex with a substrate analog and divalent metal ions provides new insight into the catalytic mechanism of alkaline phytases in general.

Crystal structure and substrate-binding mode of cellulase 12A from Thermotoga maritima.

Cellulases have been used in many applications to treat various carbohydrate-containing materials. Thermotoga maritima cellulase 12A (TmCel12A) belongs to the GH12 family of glycoside hydrolases. It is a ß-1,4-endoglucanase that degrades cellulose molecules into smaller fragments, facilitating further utilization of the carbohydrate. Because of its hyperthermophilic nature, the enzyme is especially suitable for industrial applications. Here the crystal structure of TmCel12A was determined by using an active-site mutant E134C and its mercury-containing derivatives. It adopts a ß-jellyroll protein fold typical of the GH12-family enzymes, with two curved ß-sheets A and B and a central active-site cleft. Structural comparison with other GH12 enzymes shows significant differences, as found in two longer and highly twisted ß-strands B8 and B9 and several loops. A unique Loop A3-B3 that contains Arg60 and Tyr61 stabilizes the substrate by hydrogen bonding and stacking, as observed in the complex crystals with cellotetraose and cellobiose. The high-resolution structures allow clear elucidation of the network of interactions between the enzyme and its substrate. The sugar residues bound to the enzyme appear to be more ordered in the -2 and -1 subsites than in the +1, +2 and -3 subsites. In the E134C crystals the bound -1 sugar at the cleavage site consistently show the α-anomeric configuration, implicating an intermediate-like structure.

Structures of Selenomonas ruminantium phytase in complex with persulfated phytate: DSP phytase fold and mechanism for sequential substrate hydrolysis.

Various inositide phosphatases participate in the regulation of inositol polyphosphate signaling molecules. Plant phytases are phosphatases that hydrolyze phytate to less-phosphorylated myo-inositol derivatives and phosphate. The phytase from Selenomonas ruminantium shares no sequence homology with other microbial phytases. Its crystal structure revealed a phytase fold of the dual-specificity phosphatase type. The active site is located near a conserved cysteine-containing (Cys241) P loop. We also solved two other crystal forms in which an inhibitor, myo-inositol hexasulfate, is cocrystallized with the enzyme. In the "standby" and the "inhibited" crystal forms, the inhibitor is bound, respectively, in a pocket slightly away from Cys241 and at the substrate binding site where the phosphate group to be hydrolyzed is held close to the -SH group of Cys241. Our structural and mutagenesis studies allow us to visualize the way in which the P loop-containing phytase attracts and hydrolyzes the substrate (phytate) sequentially.