Polynomials of Degree-Based Indices for Three-Dimensional Mesh Network

In order to study the behavior and interconnection of network devices,graphs structures are used to formulate the properties in terms of mathematical models.Mesh network(meshnet)is a LAN topology in which devices are connected either directly or through some intermediate devices.These terminating and intermediate devices are considered as vertices of graph whereas wired or wireless connections among these devices are shown as edges of graph.Topological indices are used to reflect structural property of graphs in form of one real number.This structural invariant has revolutionized the field of chemistry to identify molecular descriptors of chemical compounds.These indices are extensively used for establishing relationships between the structure of nanotubes and their physico-chemical properties.In this paper a representation of sodium chloride(NaCl)is studied,because structure of NaCl is same as the Cartesian product of three paths of length exactly like a mesh network.In this way the general formula obtained in this paper can be used in chemistry as well as for any degree-based topological polynomials of three-dimensional mesh networks.

A BLOCK-CENTERED UPWIND APPROXIMATION OF THE SEMICONDUCTOR DEVICE PROBLEM ON A DYNAMICALLY CHANGING MESH

The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.

Three-dimensional interconnected Ni（Fe）OxHy nanosheets on stainless steel mesh as a robust integrated oxygen evolution electrode

The development of an electrocatalyst based on abundant elements for the oxygen evolution reaction （OER） is important for water splitting associated with renewable energy sources. In this study, we develop an interconnected Ni（Fe）OxHy nanosheet array on a stainless steel mesh （SSNNi） as an integrated OER electrode, without using any polymer binder. Benefiting from the well- defined three-dimensional （3D） architecture with highly exposed surface area, intimate contact between the active species and conductive substrate improved electron and mass transport capacity, facilitated electrolyte penetration, and improved mechanical stability. The SSNNi electrode also has excellent OER performance, including low overpotential, a small Tafel slope, and long-term durability in the alkaline electrolyte, making it one of the most promising OER electrodes developed.

High Order Schemes on Three-Dimensional General Polyhedral Meshes—Application to the Level Set Method

In this article,we detail the methodology developed to construct arbitrarily high order schemes—linear and WENO—on 3D mixed-element unstructured meshes made up of general convex polyhedral elements.The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems.The construction of WENO schemes on 3D unstructured meshes is notoriously difficult,as it involves a much higher level of complexity than 2D approaches.This due to the multiplicity of geometrical considerations introduced by the extra dimension,especially on mixed-element meshes.Therefore,we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces.The contribution of this work concerns several areas of interest:the formulation of an improved methodology in 3D,the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations,the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.

MODELING UNCONFINED SEEPAGE FLOW USING THREE-DIMENSIONAL NUMERICAL MANIFOLD METHOD

Three-dimensional numerical manifold method for unconfined seepage analysis is proposed in this article.By constructing hydraulic potential functions of the manifold element,the element conductivity matrix and the global simultaneous equations for unconfined seepage analysis are derived in detail.The algorithm of locating the free surface and the formula for seepage forces are also given.Three-dimensional manifold method employs the tetrahedral mathematical meshes to cover the whole material volume.In the iterative process for locating the free surface,the manifold method can achieve an accurate seepage analysis of the saturated domain below the free surface with mathematical meshes unchanged.Since the shape of manifold elements can be arbitrary,the disadvantage of changing the permeability of transitional elements cut by the free surface in the conventional Finite Element Method（FEM） is removed,and the accuracy of locating the free surface can be ensured.Furthermore,the seepage force acting on the transitional elements can be accurately calculated by the simplex integration.Numerical results for a typical example demonstrate the validity of the proposed method.

Overview of 3D Scene Viewpoints evaluation method

The research on 3D scene viewpoints has been a frontier problem in computer graphics and virtual reality technology.In a pioneering study,it had been extensively used in virtual scene understanding,image-based modeling,and visualization computing.With the development of computer graphics and the human-computer interaction,the viewpoint evaluation becomes more significant for the comprehensive understanding of complex scenes.The high-quality viewpoints could navigate observers to the region of interest,help subjects to seek the hidden relations of hierarchical structure,and improve the efficiency of virtual exploration.These studies later contributed to research such as robot vision,dynamic scene planning,virtual driving and artificial intelligence navigation.The introduction of visual perception had The introduction of visual perception had contributed to the inspiration of viewpoints research,and the combination with machine learning made significant progress in the viewpoints selection.The viewpoints research also has been significant in the optimization of global lighting,visualization calculation,3D supervising rendering,and reconstruction of a virtual scene.Additionally,it has a huge potential in novel fields such as 3D model retrieval,virtual tactile analysis,human visual perception research,salient point calculation,ray tracing optimization,molecular visualization,and intelligent scene computing.

A blind watermarking algorithm for 3D mesh models based on vertex curvature

We propose a robust blind watermarking algorithm for three-dimensional(3D)mesh models based on vertex curvature to maintain good robustness and improve visual masking in 3D mesh models.In the embedding process,by using the local window of vertex,the root mean square curvature is calculated for every vertex of the 3D mesh model and an ordered set of fluctuation values is obtained.According to the ordered fluctuation values,the vertices are separated into bins.In each bin the fluctuation values are normalized.Finally,the mean of the root mean square curvature fluctuation values of the vertices in each bin is modulated to embed watermark information.In watermark detection,the algorithm uses a blind watermark extraction technique to extract the watermark information.The experimental results show that the algorithm has a very good performance for visual masking of the embedded model and that it can resist a variety of common attacks such as vertex rearrangement,rotation,translating,uniform scaling,noise,smoothing,quantization,and simplification.

A Hybrid FETD-FDTD Method with Nonconforming Meshes

A quasi non-overlapping hybrid scheme that combines the finite-difference time-domain(FDTD)method and the finite-element time-domain(FETD)method with nonconforming meshes is developed for time-domain solutions of Maxwell’s equations.The FETD method uses mixed-order basis functions for electric and magnetic fields,while the FDTD method uses the traditional Yee’s grid;the two methods are joined by a buffer zone with the FETD method and the discontinuous Galerkin method is used for the domain decomposition in the FETD subdomains.The main features of this technique is that it allows non-conforming meshes and an arbitrary numbers of FETD and FDTD subdomains.The hybrid method is completely stable for the time steps up to the stability limit for the FDTD method and FETD method.Numerical results demonstrate the validity of this technique.

Numerical Methods for Fluid-Structure Interaction—A Review

The interactions between incompressible fluid flows and immersed structures are nonlinearmulti-physics phenomena that have applications to a wide range of scientific and engineering disciplines.In this article,we review representative numericalmethods based on conforming and non-conformingmeshes that are currently available for computing fluid-structure interaction problems,with an emphasis on some of the recent developments in the field.A goal is to categorize the selected methods and assess their accuracy and efficiency.We discuss challenges faced by researchers in this field,and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interactions.