A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

Buckling Optimization of Curved Grid Stiffeners through the Level Set Based Density Method

Stiffened structures have great potential for improvingmechanical performance,and the study of their stability is of great interest.In this paper,the optimization of the critical buckling load factor for curved grid stiffeners is solved by using the level set based density method,where the shape and cross section(including thickness and width)of the stiffeners can be optimized simultaneously.The grid stiffeners are a combination ofmany single stiffenerswhich are projected by the corresponding level set functions.The thickness and width of each stiffener are designed to be independent variables in the projection applied to each level set function.Besides,the path of each single stiffener is described by the zero iso-contour of the level set function.All the single stiffeners are combined together by using the p-norm method to obtain the stiffener grid.The proposed method is validated by several numerical examples to optimize the critical buckling load factor.

Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems

In real space density functional theory calculations,the effective potential depends on the electron density,requiring self-consistent iterations,and numerous integrals at each step,making the process time-consuming.In our research,we propose an optimization method to expedite density functional theory(DFT)calculations for systems with large aspect ratios,such as metallic nanorods,nanowires,or scanning tunneling microscope tips.This method focuses on employing basis set to expand the electron density,Coulomb potential,and exchange-correlation potential.By precomputing integrals and caching redundant results,this expansion streamlines the integration process,significantly accelerating DFT computations.As a case study,we have applied this optimization to metallic nanorod systems of various radii and lengths,obtaining corresponding ground-state electron densities and potentials.

Topological and Shape Optimization of Flexure Hinges for Designing Compliant Mechanisms Using the Level Set Method

A flexure hinge is a major component in designing compliant mechanisms that o ers unique possibilities in a wide range of application fields in which high positioning accuracy is required. Although various flexure hinges with di erent configurations have been successively proposed, they are often designed based on designers' experiences and inspirations. This study presents a systematic method for topological optimization of flexure hinges by using the level set method. Optimization formulations are developed by considering the functional requirements and geometrical constraints of flexure hinges. The functional requirements are first constructed by maximizing the compliance in the desired direction while minimizing the compliances in the other directions. The weighting sum method is used to construct an objective function in which a self-adjust method is used to set the weighting factors. A constraint on the symmetry of the obtained configuration is developed. Several numerical examples are presented to demonstrate the validity of the proposed method. The obtained results reveal that the design of a flexure hinge starting from the topology level can yield more choices for compliant mechanism design and obtain better designs that achieve higher performance.

Surface and Content Validity of the Mentoring Function Scale for Novice Nurses

This study aimed to examine the surface and content validity of the Mentoring Function Scale for Novice Nurses, used to assess the mentoring of entry-level nurses, and to refine the scale items. In Study 1, six nurse education researchers, selected using convenience sampling, with five or more years of nursing experience and experience teaching novice nurses, were invited to an expert meeting in July 2015. A group interview was conducted that lasted approximately 120 minutes. Study 2 examined the content validity index. Between September and November 2015, we distributed a self-administered questionnaire survey to 11 participants selected by convenience sampling. The participants included five nurse education researchers with a minimum of five years of nursing experience and experience teaching novice nurses, as well as six clinical nurses with a master’s degree or higher. Finally, 81 questionnaire items were retained from the initial 125 items. The 81-item Mentoring Function Scale for Novice Nurses had higher content validity than the original scale. To further increase the scale’s applicability, future studies should assess its reliability, construct validity, and criterion-related validity.

An Improved Level Set Approach to the Simulation of Drop and Bubble Motion

An improved level set approach for computing the incompressibletwo-phase flow with significantly de- formed free interface ispresented. The control volume formulation with the semi-implicitmethod for pressure-linked equations consistent (SIMPLEC) algorithmincorporated is used to solve the governing equations on a staggeredgrid. Several improvements concerning the computational grid,interface update, reinitialization procedure etc. are tested Andfound to be effective in promoting the convergence and numericalstability.

Simulation of Non-isothermal Injection Molding for a Non-Newtonian Fluid by Level Set Method

A non-isothermal injection molding process for a non-Newtonian viscous pseudoplastic fluid is simulated.A conservative interface capturing technique and the flow field solving method are coupled to perform a dynamic simulation.The validity of the numerical method is verified by a benchmark problem.The melt interface evolution versus time is captured and the physical quantities such as temperature,velocity and pressure at each time step are obtained with corresponding analysis.A"frozen skin"layer with the thickness increasing versus time during the injection process is found.The fact that the"frozen skin"layer can be reduced by increasing the injection velocity is numerically verified.The fountain flow phenomenon near the melt interface is also captured.Moreover,comparisons with the non-isothermal Newtonian case show that the curvatures of the interface arcs and the pressure contours near the horizontal mid-line of the cavity for the non-Newtonian pseudoplastic case is larger than that for the Newtonian case.The velocity profiles are different at different positions for the non-Newtonian pseudoplastic case,while in the case of Newtonian flow the velocity profiles are parabolic and almost the same at different positions.

Dietary energy sources and levels shift the multi-kingdom microbiota and functions in the rumen of lactating dairy cows

Background: Dietary energy source and level in lactation diets can profoundly affect milk yield and composition.Such dietary effects on lactation performance are underpinned by alteration of the rumen microbiota, of which bacteria, archaea, fungi, and protozoa may vary differently. However, few studies have examined all the four groups of rumen microbes. This study investigated the effect of both the level and source of dietary energy on rumen bacteria, archaea, fungi, and protozoa in the rumen of lactating dairy cows. A 2 × 2 factorial design resulted in four dietary treatments: low and high dietary energy levels(LE: 1.52–1.53;and HE: 1.71–1.72 Mcal/kg dry matter) and two dietary energy sources(GC: finely ground corn;and SFC: steam-flaked corn). We used a replicated 4 × 4 Latin square design using eight primiparous Chinese Holstein cows with each period lasting for 21 d. The rumen microbiota was analyzed using metataxonomics based on kingdom-specific phylogenetic markers [16 S r RNA gene for bacteria and archaea, 18 S r RNA gene for protozoa, and internally transcribed spacer 1(ITS1) for fungi] followed with subsequent functional prediction using PICRUSt2.Results: The GC resulted in a higher prokaryotic(bacterial and archaeal) species richness and Faith's phylogenetic diversity than SFC. For the eukaryotic(fungi and protozoa) microbiota, the LE diets led to significantly higher values of the above measurements than the HE diets. Among the major classified taxa, 23 genera across all the kingdoms differed in relative abundance between the two dietary energy levels, while only six genera(none being protozoal)were differentially abundant between the two energy sources. Based on prokaryotic amplicon sequence variants(ASVs) from all the samples, overall functional profiles predicted using PICRUSt2 differed significantly between LE and HE but not between the two energy sources. Fish Taco analysis identified Ruminococcus and Coprococcus as the taxa potentially contributing to the enriched KEGG pathways for biosynthesis of amino acids and to the metabolisms of pyruvate, glycerophospholipid, and nicotinate and nicotinamide in the rumen of HE-fed cows. The co-occurrence networks were also affected by the dietary treatments, especially the LE and GC diets, resulting in distinct co-occurrence networks. Several microbial genera appeared to be strongly correlated with one or more lactation traits.Conclusions: Dietary energy level affected the overall rumen multi-kingdom microbiota while little difference was noted between ground corn and steam-flaked corn. Some genera were also affected differently by the four dietary treatments, including genera that had been shown to be correlated with lactation performance or feed efficiency.The co-occurrence patterns among the genera exclusively found for each dietary treatment may suggest possible metabolic interactions specifically affected by the dietary treatment. Some of the major taxa were positively correlated to milk properties and may potentially serve as biomarkers of one or more lactation traits.

APPLICATION OF ROUGH SET THEORY TO MAINTENANCE LEVEL DECISION-MAKING FOR AERO-ENGINE MODULES BASED ON INCREMENTAL KNOWLEDGE LEARNING

The maintenance of an aero-engine usually includes three levels,and the maintenance cost and period greatly differ depending on the different maintenance levels.To plan a reasonable maintenance budget program, airlines would like to predict the maintenance level of aero-engine before repairing in terms of performance parameters,which can provide more economic benefits.The maintenance level decision rules are mined using the historical maintenance data of a civil aero-engine based on the rough set theory,and a variety of possible models of updating rules produced by newly increased maintenance cases added to the historical maintenance case database are investigated by the means of incremental machine learning.The continuously updated rules can provide reasonable guidance suggestions for engineers and decision support for planning a maintenance budget program before repairing. The results of an example show that the decision rules become more typical and robust,and they are more accurate to predict the maintenance level of an aero-engine module as the maintenance data increase,which illustrates the feasibility of the represented method.

Calculation of microscopic nuclear level densities based on covariant density functional theory

In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial method using single-particle level schemes obtained from the CDFT,and the level densities are then obtained by considering collective effects such as vibration and rotation.Our results are compared with those of other NLD models,including phenomenological,microstatisti-cal and nonrelativistic Hartree–Fock–Bogoliubov combinatorial models.This comparison suggests that the general trends among these models are essentially the same,except for some deviations among the different NLD models.In addition,the NLDs obtained using the CDFT combinatorial method with normalization are compared with experimental data,including the observed cumulative number of levels at low excitation energies and the measured NLDs.The CDFT combinatorial method yields results that are in reasonable agreement with the existing experimental data.

The shape optimization of the arterial graft design by level set methods

The goal of the arterial graft design problem is to find an optimal graft built on an occluded artery, which can be mathematically modeled by a fluid based shape optimization problem. The smoothness of the graft is one of the important aspects in the arterial graft design problem since it affects the flow of the blood significantly. As an attractive design tool for this problem, level set methods are quite efficient for obtaining better shape of the graft. In this paper, a cubic spline level set method and a radial basis function level set method are designed to solve the arterial graft design problem. In both approaches, the shape of the arterial graft is implicitly tracked by the zero-level contour of a level set function and a high level of smoothness of the graft is achieved. Numerical results show the efficiency of the algorithms in the arterial graft design.

The Uniqueness of Meromorphic Functions with Common Range Sets and Deficient Values

In this paper, the uniqueness of meromorphic functions with common range sets and deficient values are studied. This result is related to a question of Gross.

On the Differentiability of Vector Valued Additive Set Functions

The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets.?Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.

Topology and Shape Optimization of 2-D and 3-D Micro-ArchitecturedThermoelastic Metamaterials Using a Parametric Level Set Method

2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.

Big Data Audit of Banks Based on Fuzzy Set Theory to Evaluate Risk Level

The arrival of big data era has brought new opportunities and challenges to the development of various industries in China.The explosive growth of commercial bank data has brought great pressure on internal audit.The key audit of key products limited to key business areas can no longer meet the needs.It is difficult to find abnormal and exceptional risks only by sampling analysis and static analysis.Exploring the organic integration and business processing methods between big data and bank internal audit,Internal audit work can protect the stable and sustainable development of banks under the new situation.Therefore,based on fuzzy set theory,this paper determines the membership degree of audit data through membership function,and judges the risk level of audit data,and builds a risk level evaluation system.The main features of this paper are as follows.First,it analyzes the necessity of transformation of the bank auditing in the big data environment.The second is to combine the determination of the membership function in the fuzzy set theory with the bank audit analysis,and use the model to calculate the corresponding parameters,thus establishing a risk level assessment system.The third is to propose audit risk assessment recommendations,hoping to help bank audit risk management in the big data environment.There are some shortcomings in this paper.First,the amount of data acquired is not large enough.Second,due to the lack of author’knowledge,there are still some deficiencies in the analysis of audit risk of commercial banks.

Lipschitz continuity of the optimal value function and KKT solution set in indefinite quadratic programs

When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.

Investigation of analytical harmonic frequency and potential energy function, vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.

The Method of Flotation Froth Image Segmentation Based on Threshold Level Set

A novel flotation froth image segmentation based on threshold level set method is put forward in view of the problem of over-segmentation and under-segmentation which occurs when the existing method segmented the flotation froth images. Firstly, the proposed method adopts histogram equalization to improve the contrast of the image, and then chooses the upper threshold and lower threshold from grey value of histogram of the image equalization, and complete image segmentation using the level set method. In this paper, the model which integrates edge with region level set model is utilized, and the speed energy term is introduced to segment the target. Experimental results show that the proposed method has better segmentation results and higher segmentation efficiency on the images with under-segmentation and incorrect segmentation, and it is meaningful for ore dressing industrial.

NEW SET OF OPERATOR-VALUED BESSEL FUNCTIONS,THE HOLOMORPHIC DISCRETE SERIES AND ITS ANALYTIC CONTINUATION

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