Second-order Elements Research Articles

Solid rocket motor propellant grain burnback simulation based on fast minimum distance function calculation and improved marching tetrahedron method

To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor, a unified framework of burning surface regression simulation has been developed based on minimum distance function. In order to speed up the computation of the mini-mum distance between grid nodes of grain and the triangular mesh of burning surface, a fast distance querying method based on the equal size cube voxel structure was employed. An improved marching tetrahedron method based on piecewise linear approximation was carried out on second-order tetrahedral elements, achieved high-efficiency and adequate accuracy of burning surface extraction simultaneously. The cases of star grain, finocyl grain, and non-uniform tube grain were studied to verify the proposed method. The observed result indicates that the grain burnback computation method could realize the accurate simulation on unstructured tetrahedral mesh with a desirable performance on computational time.

Third-order nanocircuit elements for neuromorphic engineering.

Current hardware approaches to biomimetic or neuromorphic artificial intelligence rely on elaborate transistor circuits to simulate biological functions. However, these can instead be more faithfully emulated by higher-order circuit elements that naturally express neuromorphic nonlinear dynamics1-4. Generating neuromorphic action potentials in a circuit element theoretically requires a minimum of third-order complexity (for example, three dynamical electrophysical processes)5, but there have been few examples of second-order neuromorphic elements, and no previous demonstration of any isolated third-order element6-8. Using both experiments and modelling, here we show how multiple electrophysical processes-including Mott transition dynamics-form a nanoscale third-order circuit element. We demonstrate simple transistorless networks of third-order elements that perform Boolean operations and find analogue solutions to a computationally hard graph-partitioning problem. This work paves a way towards very compact and densely functional neuromorphic computing primitives, and energy-efficient validation of neuroscientific models.

Discrete phase space, relativistic quantum electrodynamics, and a non-singular Coulomb potential

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent relativistic quantum electrodynamics, the corresponding Feynman diagrams and [Formula: see text]-matrix elements are derived. In the special case of electron–electron scattering (Møller scattering), the explicit second-order element [Formula: see text] is deduced. Moreover, assuming the slow motions for two external electrons, the approximation of [Formula: see text] yields a divergence-free Coulomb potential.

Subwavelength gratings for creation and focusing of cylindrical vector beams

In this paper we derive the equations for the subwavelength grating vector of polarization element that creates the arbitrary order radially polarized beam. We show that the element can be implemented with different shape for different orientations of the input and output polarization. There are under consideration different essential cases of the first and the second order polarization. The second-order element can be sun- or mira- shape and axicon shape. Intermediate shapes are also possible.

How cybernetics explains institutional failure: A case of Greenland's open-air fish markets

Understanding why institutions fail is a major concern for natural resource governance. In systems where resources are managed locally, failure is often attributed to the rules poorly fitting the social-ecological system. But what might also bring failure is the manner with which the rules are ‘fitted’ to the system. This paper argues that the conceptual development of institutional failure could be made more tenable with cybernetics – the science of control and feedback. In our case study and process tracing of a ‘market’ institution (an open-air fish market in Greenland), we show how recently implemented European food safety regulations have generated unintended negative consequences, limiting Inuit access to marine foodstuffs, altering the social characteristics of food exchange, and giving rise to underground markets for marine foods. These outcomes signal the failure of reforms to this market institution, but not necessarily why it failed. We show how cybernetic orders explain institutional failure, focusing on how command-and-control-style decisions to intervene in marine food trading and handling (considered as the first-order cybernetics) fostered public doubt for the scientific expertise underpinning the reforms, and ultimately led to a public rejection and closure of a new, hygienic, multi-million-dollar marketplace for marine foods. We clarify how second-order cybernetic elements — such as legitimacy, reflexivity, co-design, and interaction among governance actors — could have prevented the observed outcome. Our case expands the conceptual development of institutional failure and clarifies how the lens of cybernetics can inform the study and practice of institutional change in fisheries governance.

Computational mechanics of the paddlefish rostrum

PurposeThe rostrum of a paddlefish provides hydrodynamic stability during feeding process in addition to detect the food using receptors that are randomly distributed in the rostrum. The exterior tissue of the rostrum covers the cartilage that surrounds the bones forming interlocking star shaped bones.Design/methodology/approachThe aim of this work is to assess the mechanical behavior of four finite element models varying the type of formulation as follows: linear-reduced integration, linear-full integration, quadratic-reduced integration and quadratic-full integration. The paper also presents the load transfer mechanisms of the bone structure of the rostrum. The base material used in the study was steel with elastic–plastic behavior as a homogeneous material before applying materials properties that represents the behavior of bones, cartilages and tissues.FindingsConclusions are based on comparison among the four models. There is no significant difference between integration orders for similar type of elements. Quadratic-reduced integration formulation resulted in lower structural stiffness compared with linear formulation as seen by higher displacements and stresses than using linearly formulated elements. It is concluded that second-order elements with reduced integration are the alternative to analyze biological structures as they can better adapt to the complex natural contours and can model accurately stress concentrations and distributions without over stiffening their general response.Originality/valueThe use of advanced computational mechanics techniques to analyze the complex geometry and components of the paddlefish rostrum provides a viable avenue to gain fundamental understanding of the proper finite element formulation needed to successfully obtain the system behavior and hot spot locations.

Identification of fan dynamics in a spray booth using genetic algorithms

Abstract An important element in the design of automation systems is the identification of the dynamics of the control object. There are many analytical methods for determining object dynamics models. This article presents the results of identifying the dynamics of a fan installed in a spray booth using genetic algorithms. A model of changes in the volume of air stream from the fan was created depending on the frequency of the current supplying the fan motor. The fan with ventilation channels is a system with non-linear and non-stationary dynamics. A linear model of such a system was adopted in the form of a second-order inertial element with coefficients depending on the frequency of the fan supply current. Calculations were carried out based on the results of measurements in a real object.

Second-harmonic generation and its nonlinear depolarization from lithium niobate thin films

In this Letter, we present systematic studies of the second-harmonic generation (SHG) behaviors of lithium niobate (LN) thin film, including comprehensively evaluating its second-order nonlinear susceptibility elements and characterizing the SH polarization states as functions of fundamental wavelengths and polarizations. Moreover, the film shows an advantage of SH enhancement resulting from Fabry–Perot resonance compared with its bulk counterpart. We further show a type of nonlinear effect from LN film, called the nonlinear depolarization effect, in which the degree of polarization (DOP) of SH is nonlinearly dependent on the intensity of the fundamental frequency wave. Such a nonlinear effect would enable novel light sources with controllable DOP. Our results would be useful in developing compact SHG devices and the related multi-functional monolithic integrated LN photonic chips.

Exact solutions for second-order effect of imperfect beams and frames based on matrix structural analysis

Initial member imperfections play important roles in the second-order effect of structures, and thus it is helpful to find ways for engineers to easily model the member imperfections in the analysis. Based on the matrix structural analysis (MSA), this paper presents a method for the exact second-order solutions of imperfect frame structures, which allows the use of one element per member for the exact solution. To develop the second-order MSA method, the fixed-end force vector is formulated in simplified forms to account for the effect of the member initial imperfections and the intermediate loads. Based on the equilibrium analysis of an imperfect axial-loaded beam–column, the element-end displacements and forces are solved exactly from the governing differential equation. The equilibrium relationship between the element-end displacements and forces is developed in a matrix form, which includes a second-order element stiffness matrix and the fixed-end force vector. Some intuitive plots of the fixed-end force vector are presented for convenient applications to typical engineering situations. The established formulations and the intuitive plots are readily coded in an easy-to-use computer program given in the Appendix for analyzing the exact second-order effect of general frames with initial imperfections and intermediate loads. Two illustrative examples are presented to demonstrate the simplicity of the developed second-order MSA approach for a systematic analysis of imperfect frames.

Higher-order finite elements for lumped-mass explicit modeling of high-speed impacts

This paper describes recent advances in higher-order finite elements for lumped-mass explicit approaches typically needed for high-rate impact modeling. Topics include benefits of 2nd order tetrahedral, wedge, hexahedral, and new pyramid element formulations to improve modeling and facilitate meshing, including the important class of applications, ogive nose-shaped projectiles impacting concrete at up to 1200 m/s. These 2nd order elements eliminate the need for hourglass control and provide higher resolution with fewer elements, since a single element can inherently capture curvature and flexural modes. Second-order elements can also simplify meshing, since in contrast to certain types of 1st order elements, they are less prone to volumetric locking associated with near incompressibility, such as what occurs in metal plasticity, and thus do not require special structures for these element types. Methods to avoid severe locking are available at the element level so as to permit unstructured meshing, e.g., all-tetrahedral methods or hexahedral-dominant methods. These technologies were developed within the U.S. Army Engineer Research and Development Center Geotechnical and Structures Laboratory (ERDC-GSL) in-house meshing (ProMesher), parallel analysis (ParaAble), and visualization (PenView) codes as well as placed into popular production software for meshing (Cubit), parallel analysis (EPIC), and visualization (ParaView). Examples using all-tetrahedral and hexahedral-dominant meshes demonstrate the ability of an unstructured 2nd order model using all four element types to accurately simulate high-rate impact problems. The benefits for shape optimization and large tradespace analyses are also demonstrated by the ability to automatically generate meshes.

Spectral element applications in complex nuclear reactor geometries: Tet-to-hex meshing

The spectral element code Nek5000 is an open-source, higher-order computational fluid dynamics code developed at Argonne National Laboratory. It is designed to solve incompressible Navier-Stokes equations, but it also has a low-Mach-number approximation feature available. Large eddy simulation is approached by explicit filtering of the velocity field (and other fields) to mimic the effect of dissipation due to the unresolved scale. The computational domain is decomposed into second-order hexahedral elements that conform to the boundaries. However, generating a high-quality pure-hexahedral mesh can be challenging for some problems. For simple geometries, traditional blocking methods can be used to decompose the domain into smaller blocks to generate a so-called structural mesh. A structural mesh can maintain good orthogonality but can have a highly skewed mesh to conform to the geometry, as well as unnecessary refinement in the far field. Moreover, for geometries with relative complexity, blocking the geometry becomes impossible. To address these issues, we adopted a tet-to-hex strategy to generate a pure hexahedral mesh for Nek5000. First, we generate a pure tetrahedral mesh for the geometry; then we divide one tetrahedral element into four hexahedral elements. A pure tetrahedral mesh could be easily generated for complex geometries by using many current meshing codes. In this paper, we use the commercial codes ANSYS meshing and ANSYS ICEM to generate the pure tetrahedral mesh and then convert it to a pure hexahedral mesh. Boundary layers are extruded in ANSYSICEM to maintain near-wall resolution.

Theoretical Foundations of Memristor Cellular Nonlinear Networks: Memcomputing With Bistable-Like Memristors

This paper presents the theory of a novel memcomputing paradigm based upon a memristive version of standard Cellular Nonlinear Networks. The insertion of a nonvolatile memristor in the circuit of each cell endows the dynamic array with the capability to store and retrieve data into and from the resistance switching memories, obviating the current need for extra memory blocks. Choosing the parameters of each cell circuit so that the memristors may undergo solely sharp transitions between two states, each processing element may be approximately described at any time as one of two first-order systems. Under this assumption, the classical Dynamic Route Map may be employed to synthesise and analyse the data storage and retrieval genes. A new system-theoretic methodology, called Second-Order Dynamic Route Map , is also introduced for the first time in this paper. This technique allows to study the operating principles of arrays with second-order processing elements, as is the case, in the proposed network, if the set up of cell circuit parameters induces analogue memristive dynamics. This paper shows how the novel tool may be adopted to investigate the operating mechanisms of a cellular array with second-order cells, which compute the element-wise logical OR between two binary images.

Mixed multiscale three-node triangular elements for incompressible elasticity

Purpose This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable mixed formulation for incompressible linear elasticity which circumvents the need to satisfy inf-sup condition. Design/methodology/approach Using the hybrid FE–meshfree method, the displacement and pressure are interpolated conveniently with the same order so that a continuous pressure field can be obtained with low-order elements. The multiscale variational principle is then introduced into the Galerkin form to obtain stable and convergent results. Findings The present method is capable of overcoming volume locking and does not exhibit unphysical oscillations near the incompressible limit. Moreover, there are no extra unknowns introduced in the present method because the fine-scale unknowns are eliminated using the static condensation technique, and there is no need to evaluate any user-defined stability parameter as the classical stabilization methods do. The shape functions constructed in the present model possess continuous derivatives at nodes, which gives a continuous and more precise stress field with no need of an additional smooth process. The shape functions in the present model also possess the Kronecker delta property, so that it is convenient to impose essential boundary conditions. Originality/value The proposed model can be implemented easily. Its convergence rates and accuracy in displacement, energy and pressure are even comparable to those of second-order mixed elements.

The Solution of a Problem of Speed of Response on Output Coordinate for Linear Dynamic Systems

The solution of the so-called problem of speed of response in one coordinate, which has important theoretical and practical importance, is investigated. It is formulated with reference to linear one-dimensional high-order control objects described by a system of ordinary differential equations in a certain phase space. The transient time tnn of the system designed is understood in a sense of the classical control theory in reference to one (output) coordinate of the object and is determined by using the zone Δ = σ* = 4.321 %, which equals the given (desirable) value of the overshoot of the system synthesized. This overshoot corresponds with the speed of response oscillating second-order element with a damping coefficient ζ= = 2 2 0,7071 / . It is indispensable to mention here that the equation Δ = σ is one of the necessary conditions for the maximum speed of response of the system with the oscillating character of transient processes. In accordance to this the task of the speed of response by one coordinate can be described by the following generalized formulation: one must find the linear algorithm of the feedback signal, which provides a preset order of the astatism na for the closed-loop control system and converts the control object from a zero state into a final state, which is determined by the constant signal of the input, with a minimal time value of the transient processes of the system tnn and the preset value of the overshoot σ m σ* while fulfilling the constraint of the control signal |u(t)| m umax. Nowadays the task mentioned is approximately solved by the algebraic method of the synthesis of linear control systems with the determination of a desirable transfer function of the designed closed-loop system based on model normalized transfer functions (NTF). In the works by Kim D. P. there was carried out the analysis of four types of normalized transfer functions characterized by the increased speed of response. In this work two additional types of normalized transfer functions are suggested, in comparison with mentioned NTF they have the increased speed of response in case of the preset value of the overregulation σ* = 4.321 %. On their basis and using the methodology of the modal control the method of the synthesis of the controller is suggested; this method ensures the transient time of the designed system to be close to the minimum in case of the preset constraint of the overregulation and the value of the control signal. It needs to be emphasized that in contrast to the algebraic method of the synthesis, this method is applied to a wider range of control objects: as to minimal-phased objects as to non-minimum-phased ones; as to the objects containing zeros as to those without them. The method is illustrated by an example of synthesis of control system speed of response of the fourth order, containing the results of its modeling.

Scalable Microring-Based Silicon Clos Switch Fabric With Switch-and-Select Stages

We propose and analyze a scalable microring-based Clos switch fabric architecture constructed with switch-and-select switching stages. A silicon 4 × 4 building block that was designed and fabricated through American Institute for Manufacturing Integrated Photonics is used for the proof-of-principle demonstration of a 16 × 16 Clos switch fabric. By fully blocking the first-order crosstalk, the 4 × 4 device is measured to show a crosstalk ratio in the range of –57 to –48.5 dB, enabling better than –39 dB crosstalk for the 16 × 16 switch. Our study shows that the three-stage Clos design enables up to a factor of 4 in the reduction of the number of switching cells compared to single-stage switch-and-select fabrics. We further explore the design space for both first-order and second-order switching elements using the foundry-validated parameters and how these factors impact the performance and scalability of the three-stage Clos switch. A detailed power penalty map is drawn for Clos switch fabrics with various scales, which reveals that the ultimate key limiting factor is the shuffle insertion loss. An optimized 32-port Clos switch fabric using foundry-enabled parameters is shown to have a less than 10-dB power penalty.

Polarization of gravitational waves in symmetric teleparallel theories of gravity and their modifications

Symmetric teleparallel gravity (STG) offers an interesting avenue to formulate a theory of gravitation that relies neither on curvature nor torsion but only on nonmetricity $Q$. Given the growing number of confirmed observations of gravitational waves (GWs) and their use to explore gravitational theories, in this work we investigate the GWs in various extensions of STG, focusing on their speed and polarization. We explore the plethora of theories that this new framework opens up, that is, as general relativity can be modified, so can the symmetric teleparallel equivalent of general relativity (STEGR). In this work, we investigate the fate of GWs in the generalized irreducible decomposition of STEGR, generalizations of the STEGR Lagrangian, $f(Q)$, a scalar field nonminimally coupled to the STEGR Lagrangian, and the general setup of $f(Q,B)$ theory where $B$ is the boundary term difference between the Ricci scalar and the STEGR Lagrangian. Coincidentally, $f(Q,B)$ forms a more general theory than $f(R)$ gravity since $Q$ embodies the second-order elements of the Ricci scalar while $B$ takes on its fourth-order boundary terms. Our work deals mainly with the resulting scalar-vector-tensor polarization modes of the plethora of STG theories, and how they effect their respective speeds of propagation.

Determination of installation sites for anti-adhesive devices on the bucket of an EK-18 excavator

3D rigid-body model of a bucket of power shovel EK-18 was built using modern CAD-software. A tetrahedral grid with 10-node second-order elements was chosen, and the given model was imported to APM WinMachine - model preparation preprocessor for finite element analysis. A finite element model was based on the geometrical model, imported from KOMPAS-3D to APM Studio. Calculation of stressed-strained state of the bucket was carried out under the forces emerging while digging with “back hoe” equipment. Shift, deformation and tension charts were planned and the most and the least strained areas were pointed out. Wet coherent soil excavation deals with soil adhesion to working bodies of power shovels and leads to reduced performance. Performance decrease is caused by reduction of useful bucket capacity and partial unloading, increased front resistance to cutting (digging) caused by wet soil adhesion to a working body, increased bucket entry resistance, increased idle time caused by necessity to clean working bodies. Also energy losses increase and quality of work drops because friction forces go up. Friction force while digging and levelling account for 30…70 percent of total digging resistance while performance decreases 1.2…2 times and more. However, the question of actuators location on the excavator bucket needs to be dealt with. The most suitable spots for mounting devices for reducing soil adhesion to the excavator bucket were defined. Such devices eliminates soil adhesion to bucket and increases efficiency of using power shovels with wet coherent soils.

Thermo-mechanical stability analysis of functionally graded shells

In this paper, the thermo-elastic nonlinear analysis of various Functionally Graded (FG) shells under different loading conditions is studied. A second-order isoparametric triangular shell element is presented for this purpose. The element is six-noded, and each node has all six independent degrees of freedom in space. It should be added, the first-order shear deformation theory is induced. Furthermore, Voigt’s model is adopted to define the FG material properties, which are considered to change gradually from one surface to another. The critical temperature is predicted. Both the pre-buckling and post-buckling equilibrium paths are traced. Since the linear eigenvalue analysis leads to wrong responses in the problems with strong nonlinearity, the suggested procedure is performed based on the FEM and more exact estimations are achieved using equilibrium path.

Extraordinary Second Harmonic Generation in ReS2 Atomic Crystals

We report the observations of unexpected layer-dependent, strong, and anisotropic second harmonic generations (SHGs) in atomically thin ReS2. Appreciable (negligible) SHGs are obtained from even (odd) numbers of ReS2 layers, which is opposite to the layer-dependence of SHGs in group VI transition metal dichalcogenides, such as MoS2 and WS2. The results are analyzed from ReS2's crystal structure, implying second harmonic polarizations generated from the interlayer coupling. Pumped by a telecomband laser, SHG from the bilayer ReS2 is almost one order of magnitude larger than that from the monolayer WS2. The estimated second-order nonlinear susceptibility of 900 pm/V is remarkably high among those reported in two-dimensional materials. The laser polarization dependence of ReS2's SHG is strongly anisotropic and indicates its distorted lattice structure with more unequal and non-zero second-order susceptibility elements.

Mixed-Order Finite-Element Modeling of Magnetic Material Degradation Due to Cutting

As a part of manufacturing of electrical machines, electrical sheets are cut to the desired shape by various cutting techniques, such as punching and laser cutting. This cutting process degrades the magnetic material near the cut edge, which should be included in the finite-element modeling of electrical machines. However, due to the nature of the cutting effects, the existing finite-element modeling of the cutting effect results in computationally heavy simulations. This paper investigates the application of mixed-order elements to model the cutting effect. The second-order nodal triangular elements are used near the cut edge, whereas transition/first-order elements are applied in the remaining solution domain. Furthermore, the accuracy of the presented method is analyzed with the traditional method. According to the simulations, the mixed-order elements returned accurate results significantly faster than the traditional finite-element-based approaches. Furthermore, the effect of the cutting on the machine performance is also studied by comparing its results briefly.