Arbitrary Structures Research Articles

The Numerical Assembly Technique for arbitrary planar beam structures based on an improved homogeneous solution

AbstractThe Numerical Assembly Technique (NAT) is extended to investigate arbitrary planar frame structures with a focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial discretization. To this end, we systematically introduce a frame structure as a set of nodes, beams, bearings, springs, and external loads and formulate the corresponding boundary and coupling conditions. As the underlying homogeneous solution of the governing equations, we use a novel approach recently presented in the literature. This greatly improves the numerical stability and allows the stable computation of very high natural frequencies accurately. We show this improvement by investigating the condition number of the system matrix and also by the use of variable precision arithmetic.

Stability of drawing of microstructured optical fibres

We consider the stability of the drawing of a long and thin viscous thread with an arbitrary number of internal holes of arbitrary shape that evolves due to axial drawing, inertia and surface tension effects. Despite the complicated geometry of the boundaries, we use asymptotic techniques to determine a particularly convenient formulation of the equations of motion that is well-suited to stability calculations. We will determine an explicit asymptotic solution for steady states with (a) large surface tension and negligible inertia, and (b) large inertia. In both cases, we will show that complicated boundary layer structures can occur. We will use linear stability analysis to show that the presence of an axisymmetric hole destabilises the flow for finite capillary number and which answers a question raised in the literature. However, our formulation allows us to go much further and consider arbitrary hole structures or non-axisymmetric shapes, and show that any structure with holes will be less stable than the case of a solid axisymmetric thread. For a solid axisymmetric thread, we will also determine a closed-form expression that delineates the unconditional instability boundary in which case the thread is unstable for all draw ratios. We will determine how the detailed effects of the microstructure affect the stability, and show that they manifest themselves only via a single function that occurs in the stability problem and hence have a surprisingly limited effect on the stability.

Quantum kinetic theory of nonlinear optical currents: Finite Fermi surface and Fermi sea contributions

The quantum kinetic framework provides a versatile method for investigating the dynamical optical and transport currents of crystalline solids. In this paper, starting from the density-matrix equations of motion, we present a general theoretical path to obtain the nonlinear optical response in an elegant and transparent manner. We devise an extensive kinetic theory that can be applied to materials with arbitrary band structures and captures intraband and interband coherence effects, finite Fermi surfaces, and disorder effects. We present a classification of the nonlinear optical currents arising from the interference of the interband and intraband components of the density matrix with distinct symmetry and quantum geometrical origin for each contribution. In this context, we report the following four primary findings: (i) The Fermi golden rule approach is insufficient to derive the correct expression for the injection current, a shortcoming that we remedy in our theory while associating the injection current with the intraband-interband contribution to the second-order density matrix. (ii) The interband-intraband contribution yields a resonant current that survives irrespective of any symmetry constraint in addition to the well-known anomalous nonlinear current (nonresonant), which requires time-reversal symmetry. (iii) Quite generally, the nonlinear current is significantly enhanced by contributions arising from the finite Fermi surface. (iv) The finite Fermi surface and Fermi sea additionally lead to sizable novel nonlinear effects via contributions we term double resonant and higher-order pole. We investigate such effects in sum frequency and difference frequency generation. As an illustration, we compute the nonlinear response of the topological antiferromagnet CuMnAs and thin film tilted Weyl semimetals as model systems dominated by interband coherence contributions. We find that the nonlinear response of CuMnAs is responsive to the direction of the finite magnetization field and the response of Weyl semimetal to the tilt. In addition, the choice of the polarization angle of the beam is crucial to have a nonlinear current in CuMnAs, while it is not the case for Weyl semimetals.

Price Discrimination in Selection Markets

Abstract Should insurance prices vary with age? I consider competitive markets for lemons where a signal (e.g., age) partitions consumers (e.g., young and old). I study the continuum of policies from zero price-discrimination (zero- PD, equal prices) to full-PD (no restrictions). Restricting PD can increases welfare if high-cost markets exhibit greater adverse selection, or when the high-cost market “unravels.” I characterize optimal PD, and show how it is affected by changes in cost. In a calibration, optimal PD increases welfare by about $30/person-year. I extend the model to arbitrary signal structures, behavioral consumers, a monopolized industry, and multi-product firms.

On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation

This paper focuses on antenna modeling using wire-grid and surface triangulation as two of the most commonly used MoM-based approaches in this field. A comprehensive overview is provided for each of them, including their history, applications, and limitations. The mathematical background of these approaches is briefly presented. Two working algorithms were developed and described in detail, along with their implementations using acceleration techniques. The wire-grid-based algorithm enables modeling of arbitrary antenna solid structures using their equivalent grid of wires according to a specific modeling recommendation proposed in earlier work. On the other hand, the surface triangulation-based algorithm enables calculation of antenna characteristics using a novel excitation source model. Additionally, a new mesh generator based on the combined use of the considered algorithms is developed. These algorithms were used to estimate the characteristics of several antenna types with different levels of complexity. The algorithms computational complexities were also obtained. The results obtained using these algorithms were compared with those obtained using the finite difference time domain numerical method, as well as those calculated analytically and measured. The analysis and comparisons were performed on the example of a rectangle spiral, a spiral, rounded bow-tie planar antennas, biconical, and horn antennas. Furthermore, the validity of the proposed algorithms is verified using the Monte Carlo methodology.

Parallel beam splitting and controlling system based on cascaded acousto-optic modulators.

In recent years, ultrashort pulse lasers (lasers) have been already widely used for providing excellent laser machining quality for the electronics industry, replication tools, and other applications. However, the major drawback of this processing is low efficiency, especially for a large number of laser ablation demands. In this paper, a beam-splitting approach based on cascaded acousto-optic modulators (AOMs) is proposed and analyzed in detail. The cascaded AOMs can split a laser beam into several beamlets with the same propagation direction. These beamlets can be switched on and off individually, and the beam pitch can be changed independently. At the same time, the experimental setup of three cascaded AOM beam splittings is built up to verify the capability of the high-speed control (switching rate:1MHz), high-energy utilization rate (>96% at three AOMs), and high-energy splitting uniformity (nonuniformity: 3.3%). This scalable approach enables the processing of arbitrary surface structures with high quality and efficiency.

Active control of cure-induced distortion for composite parts using multi-zoned self-resistance electric heating method

High dimensional accuracy of the carbon fiber reinforced polymer (CFRP) composite parts has been a long-term challenge for manufacturers in the aerospace industry. Traditionally, the uneven curing temperature could aggravate the cure-induced distortion (CID) and should be avoided as much as possible. But even under an ideally uniform temperature field, the CID of curved parts still cannot be eliminated because of the anisotropic shrinkage nature of the CFRP laminate. In this work, a novel CID control method based on the multi-zoned heating methodology is proposed, which actively applies an optimized non-uniform temperature field in different zones of the part to counteract the CID influenced by geometric structures. The counteracting principle of the proposed method lies in that using the actively formed through-thickness temperature gradients in different zones generates numerous small local thermal deformations, and their combination can significantly reduce the overall CID of the CFRP part. A co-optimization framework combined with the numerical model and genetic algorithm is established to rapidly compute the optimized multi-zoned temperature field for the CFRP parts with arbitrary complex structures. A good agreement between the numerical and the previous experimental results shows the effectiveness of the numerical model, and the multi-zoned temperature field optimization case of a scaled air-intake CFRP part demonstrates the performance of the co-optimization framework. Finally, by using the multi-zoned self-resistance electrical heating method, the CID reduction of the proposed method is experimentally validated on a complex CFRP part, where the average displacement reduces by >60 % compared to that of the traditional oven process.

On the Bipolaronic Mechanism of High-Temperature Superconductivity in "Ginzburg Sandwiches" FeSe-SrTiO<sub>3</sub>; SrTiO<sub>3</sub>-FeSe-SrTiO<sub>3</sub>

The mechanism of experimentally observed high-temperature superconductivity (HTSC) in thin FeSe films on SrTiO₃-type substrates has been theoretically investigated. Applying the theory of large-radius bipolaronic states developed based on the exact Hamiltonian of electron-phonon interaction for arbitrary multilayer structures, the bipolaronic mechanism of Cooper pairing of polarons in FeSe monolayers on SrTiO₃ substrates is investigated and in three-layer structures SrTiO₃–FeSe–SrTiO₃, which are typical "Ginzburg sandwiches". Approach proposed by Ginzburg to enhance the electron-phonon interaction and achieve HTSС by separating the regions where electrons are located (forming Cooper pairs or bipolarons) with the regions in which excitons are excited (or inertial polarization is induced), made it possible to implement the criteria for the formation of bipolaronic states in multilayer structures with high binding energy, due to the possibility of selecting optimal geometric and material parameters (layer thicknesses, dielectric permittivity, optical frequencies, effective masses). It is shown that the binding energy of bipolarons (<i>E_bp</i>) in these structures is in the range of values for which bipolarons remain stable quasiparticles and can exist at temperatures significantly higher than their Bose condensation temperature. The formation of bipolarons with high binding energy in the FeSe monolayer on the SrTiO₃ substrate provides the emergence of a bipolaronic HTS with a critical temperature (<i>T_c</i>) more than an order of magnitude higher than <i>T_c</i> for massive FeSe crystals. At the same time, the binding energy of the bipolaron in the FeSe layer with thickness <i>d</i> on the SrTiO₃ substrate increases exponentially with decreasing <i>d</i> (<i>E_bp</i>~<i>exp</i>(-<i>d </i>/ <I>R<SUB>S</SUB></I>) <I>R<SUB>S</SUB></I> is the radius of the polaron) and reaches its maximum value in the limit of the multilayer film FeSe (d→0). The presented theory allows modeling a multilayer system and determining the range of values of the material and geometric parameters of layers forming a multilayer structure with a large number of FeSe layers in which <i>T_c</i> values in the room temperature range can be achieved.

Zygote structure enables pluripotent shape-transforming deployable structure.

We propose an algorithmic framework of a pluripotent structure evolving from a simple compact structure into diverse complex 3D structures for designing the shape-transformable, reconfigurable, and deployable structures and robots. Our algorithmic approach suggests a way of transforming a compact structure consisting of uniform building blocks into a large, desired 3D shape. Analogous to a fertilized egg cell that can grow into a preprogrammed shape according to coded information, compactly stacked panels named the zygote structure can evolve into arbitrary 3D structures by programming their connection path. Our stacking algorithm obtains this coded sequence by inversely stacking the voxelized surface of the desired structure into a tree. Applying the connection path obtained by the stacking algorithm, the compactly stacked panels named the zygote structure can be deployed into diverse large 3D structures. We conceptually demonstrated our pluripotent evolving structure by energy-releasing commercial spring hinges and thermally actuated shape memory alloy hinges, respectively. We also show that the proposed concept enables the fabrication of large structures in a significantly smaller workspace.

Uniform Asymptotic Estimate for the Ruin Probability in a Renewal Risk Model with Cox–Ingersoll–Ross Returns

Consider an insurance risk model with arbitrary dependence structures between the claim sizes. Suppose that the risky investment in the insurer can be established by the Cox–Ingersoll–Ross model. When the claim-size distribution is heavy-tailed, a uniform asymptotic formula for ruin probability is obtained.

Graph Fusion Network-Based Multimodal Learning for Freezing of Gait Detection.

Freezing of gait (FoG) is identified as a sudden and brief episode of movement cessation despite the intention to continue walking. It is one of the most disabling symptoms of Parkinson's disease (PD) and often leads to falls and injuries. Many computer-aided FoG detection methods have been proposed to use data collected from unimodal sources, such as motion sensors, pressure sensors, and video cameras. However, there are limited efforts of multimodal-based methods to maximize the value of all the information collected from different modalities in clinical assessments and improve the FoG detection performance. Therefore, in this study, a novel end-to-end deep architecture, namely graph fusion neural network (GFN), is proposed for multimodal learning-based FoG detection by combining footstep pressure maps and video recordings. GFN constructs multimodal graphs by treating the encoded features of each modality as vertex-level inputs and measures their adjacency patterns to construct complementary FoG representations, thus reducing the representation redundancy among different modalities. In addition, since GFN is devised to process multimodal graphs of arbitrary structures, it is expected to achieve superior performance with inputs containing missing modalities, compared to the alternative unimodal methods. A multimodal FoG dataset was collected, which included clinical assessment videos and footstep pressure sequences of 340 trials from 20 PD patients. Our proposed GFN demonstrates a great promise of multimodal FoG detection with an area under the curve (AUC) of 0.882. To the best of our knowledge, this is one of the first studies to utilize multimodal learning for automated FoG detection, which offers significant opportunities for better patient assessments and clinical trials in the future.

Carbazole‐Based Anion Ionic Water‐Soluble Two‐Photon Initiator for Achieving 3D Hydrogel Structures

Abstract3D hydrogel structures fabricated by two‐photon polymerization (TPP) have become attractive in biomedical fields. Generally, conventional organic solvents are toxic and the residues left in the fabricated 3D structures are harmful to cells. Hence, anion ionic carbazole‐based water‐soluble two‐photon initiator (TPI) 3,6‐bis[2‐(1‐methylpyridinium)vinyl]‐9‐methylcarbazole ditosylate (BT) is proposed to construct arbitrary 3D hydrogel structures. Cucurbit[7]uril (CB7) and BT form a host‐guest complex (CB7/BT) with a binding ratio of 1:1, which further improves the water solubility, biocompatibility and nonlinear absorption property of TPI. A water‐soluble photoresist consisting of photoinitiator CB7/BT and monomer poly(ethylene glycol) diacrylate is prepared to explore the TPP fabrication capacity. The electron paramagnetic resonance measurement shows that CB7/BT initiates photopolymerization by alkyl radicals. The laser threshold power of the photoresist is 6.3 mW and the feature size is 127 nm in TPP at 780 nm. The initiator with p‐toluenesulfonate anion exhibits higher binding energy, larger two‐photon absorption cross‐section and two‐photon fabrication resolution compared with the previous work using iodide as an anion, indicating a promising way to improve the fabrication capacity of water‐soluble TPI through changing the anion ionic group. The proposed strategy will provide high potential for the further application in the biomedical field.

Module intersection and uniform formula for iterative reduction of one-loop integrals

In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov representation and auxiliary vector for tensor structure. Using this strategy we have studied the reduction of general one-loop integrals, i.e., integrals having arbitrary tensor structures and arbitrary power for propagators. Inspired by these studies, a uniform and compact formula that iteratively reduces all one-loop integrals has been written down, where messy polynomials in integration-by-parts (IBP) relations have organized themselves to Gram determinants.

Discovering block structure in networks

A generalisation of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network structures can be compared and an optimal block matrix can be determined. Some simple algorithms for optimising block modularity are described and applied on networks with planted structure. In many cases the planted structure is recovered. Cases where it is not are analysed and it is found that strong degree-correlations explain the planted structure so that the discovered pattern is more ‘surprising’ than the planted one under the configuration model. Some well studied networks are analysed with this new method, which is found to automatically deconstruct the network in a very useful way for creating a summary of its key features.

A comprehensive model of nitrogen-free ordered carbon quantum dots

We propose and demonstrate a novel range of models to accurately determine the optical properties of nitrogen-free carbon quantum dots (CQDs) with ordered graphene layered structures. We confirm the results of our models against the full range of experimental results for CQDs available from an extensive review of the literature. The models can be equally applied to CQDs with varied sizes and with different oxygen contents in the basal planes of the constituent graphenic sheets. We demonstrate that the experimentally observed blue fluorescent emission of nitrogen-free CQDs can be associated with either small oxidised areas on the periphery of the graphenic sheets, or with sub-nanometre non-functionalised islands of sp2-hybridised carbon with high symmetry confined in the centres of oxidised graphene sheets. Larger and/or less symmetric non-functionalised regions in the centre of functionalised graphene sheet are found to be sources of green and even red fluorescent emission from nitrogen-free CQDs. We also demonstrate an approach to simplify the modelling of the discussed sp2-islands by substitution with equivalent strained polycyclic aromatic hydrocarbons. Additionally, we show that the bandgaps (and photoluminescence) of CQDs are not dependent on either out-of-plane corrugation of the graphene sheet or the spacing between sp2-islands. Advantageously, our proposed models show that there is no need to involve light-emitting polycyclic aromatic molecules (nanographenes) with arbitrary structures grafted to the particle periphery to explain the plethora of optical phenomena observed for CQDs across the full range of experimental works.

Interaction structures of multi localized waves within the Kadomtsev–Petviashvili I equation

This paper investigates a (2+1)-dimensional Kadomtsev–Petviashvili I (KP I) equation, which describes the long waves in water with weak surface tension. The KP I equation can be reduced to a (1+1)-dimensional system consisting of a generalized multi component nonlinear Schrödinger (NLS) equation and a modified Korteweg–de Vries (mKdV) equation by using constraints the potential function of the KP I equation to its squared eigenfunction. So, any solution of the (1+1)-dimensional integrable system gives rise to a localized solution of the KP I equation. Then, according to the Lax pairs of the above (1+1)-dimensional system, the generalized (m,N−m)-fold Darboux transformation is adopted to explore various solutions. These solutions include single structure solutions, such as lump-chains, (N-1)-th degenerate lump-chains and Nth-order lump, and especially interaction solutions of arbitrary structures formed on the basis of single structure solutions. As a consequence, the corresponding single structure and mixed interaction solutions for the KP I equation can be obtained by solving the (1+1)-dimensional system with generalized DT. Moreover, all these structure solutions are discussed analytically and shown graphically. Finally, we also sum up various mathematical features of mixed localized wave solutions. The results obtained in this paper may be helpful to understand the interaction phenomena of localized nonlinear waves in KP I equation.

ElecTra code: Full-band electronic transport properties of materials

This paper introduces ElecTra, an open-source code which solves the linearized Boltzmann transport equation in the relaxation time approximation for charge carriers in a full-band electronic structure of arbitrary complexity, including their energy, momentum, and band-index dependence. ElecTra stands for ‘ELECtronic TRAnsport’ and computes the electronic and thermoelectric transport coefficients electrical conductivity, Seebeck coefficient, electronic thermal conductivity, and mobility, for semiconductor materials, for both unipolar and bipolar (small bandgap) materials. The code uses computed full-bands and relevant scattering parameters as inputs and considers single crystal materials in 3D and 2D. The present version of the code (v1) considers: i) elastic scattering with acoustic phonons and inelastic scattering with non-polar optical phonons in the deformation potential approximation, ii) inelastic scattering with polar phonons, iii) scattering with ionized dopants, and iv) alloy scattering. The user is given the option of intra- and inter-band scattering considerations. The simulation output also includes relevant relaxation times and mean-free-paths. The transport quantities are computed as a function of Fermi level position, doping density, and temperature. ElecTra can interface with any DFT code which saves the electronic structure in the ‘.bxsf’ format. In this paper ElecTra is validated against ideal electronic transport situations of known analytical solutions, existing codes employing the constant relaxation time approximation, as well as experimentally well-assessed materials such as Si, Ge, SiGe, and GaAs. Program summaryProgram title: ElecTra – Electronic Transport simulation labCPC Library link to program files:https://doi.org/10.17632/ycgx2fjzb6.1Licensing provisions: GPLv3Programming Language: MATLAB®Nature of the problem: computing the electronic and thermoelectric charge transport coefficients of materials with arbitrary complex full-band electronic structures, considering the carrier energy-, momentum-, and band-dependence of the scattering rates.Solution method: Semiclassical Linearized Boltzmann transport equation, with electronic structures (DFT or analytical) as input, formed into constant-energy surfaces, with scattering rates evaluated using Fermi's Golden Rule.Additional comments including restrictions and unusual features:•Programming interface: any DFT code which saves data in the ‘.bxsf’ format.•RAM: a case study for a half-Heusler bandstructure on a 51×51×51k-mesh, 2 Gb per processor is needed•Running time: for the example above, depending on the number and complexity of the scattering mechanisms and the number of simulated Fermi levels and temperatures considered, the time needed varies from ∼ 1 hour on a desktop PC or laptop (light simulations), to 5-10 hours on an HPC with 30-45 cores (heavy simulations). Using the constant relaxation time and constant mean-free-path approximations on a desktop PC or laptop, the running time is of the order of minutes.

Automatic generation of Grover quantum oracles for arbitrary data structures

The steadily growing research interest in quantum computing—together with the accompanying technological advances in the realization of quantum hardware—fuels the development of meaningful real-world applications, as well as implementations for well-known quantum algorithms. One of the most prominent examples till today is Grover’s algorithm, which can be used for efficient search in unstructured databases. Quantum oracles that are frequently masked as black boxes play an important role in Grover’s algorithm. Hence, the automatic generation of oracles is of paramount importance. Moreover, the automatic generation of the corresponding circuits for a Grover quantum oracle is deeply linked to the synthesis of reversible quantum logic, which—despite numerous advances in the field—still remains a challenge till today in terms of synthesizing efficient and scalable circuits for complex Boolean functions. In this paper, we present a flexible method for automatically encoding unstructured databases into oracles, which can then be efficiently searched with Grover’s algorithm. Furthermore, we develop a tailor-made method for quantum logic synthesis, which vastly improves circuit complexity over other current approaches. Finally, we present another logic synthesis method that considers the requirements of scaling onto real world backends. We compare our method with other approaches through evaluating the oracle generation for random databases and analyzing the resulting circuit complexities using various metrics.

Are Human Learners Capable of Learning Arbitrary Language Structures

The artificial grammar learning paradigm is a classic method of investigating the influence of universal constraints on shaping learning biases on language acquisition. While this method has been used extensively by linguists to test theoretical claims in generative grammar, one of the most prevalent frameworks in language acquisition, several studies have questioned whether artificial grammar learning reflects language acquisition enough to allow us to use it to draw inferences about the validity of universal constraints, particularly those arising from phonetic naturalness. The current study tests whether artificial grammar learning shows the effect of one robust phonetic naturalness constraint: the restriction on nasal harmony patterns arising from the sonority hierarchy. Nasal harmony is of particular interest because it is one of the few types of harmony that occurs between consonants and vowels, which is an under-researched topic. The results, contrary to the skeptical concerns, showed that participants (n = 120) could learn an artificial grammar involving a natural pattern, but could not learn one corresponding to an arbitrary/phonetically unmotivated pattern in the same way or to the same degree. This study contributes epistemic support to the large body of work using artificial grammar experiments to test phonological operations.

Multi-dimensional hypercomplex continuous orthogonal moments for light-field images

Image moments have always been topical in the domain of image processing, and the proposed hypercomplex moments and multi-channel moments have greatly broadened the application of image moments in recent years. However, the hypercomplex moments are limited by the specific number of imaginary parts of the hypercomplex number, and the redundancy of imaginary parts or the overflow of image channels will occur when the number of imaginary parts does not fit the image structure. The multi-channel moments allow flexible adjustment of the number of channels, but their loose structure will result in the loss of correlation between multiple channels of images. Moreover, the hypercomplex moments and multi-channel moments cannot handle images with multi-dimensional structures such as light-field (LF) images. For the purpose of addressing the above problems, this paper proposes generalized hypercomplex continuous orthogonal moments (HCOMs) and extends them to multi-dimensional hypercomplex continuous orthogonal moments (MHCOMs) in multi-dimensional space. MHCOMs can be used to process images with arbitrary multi-dimensional structures, and when they are used for LF image processing, there is no need to map the LF images to two-dimensional space to change the multi-dimensional structural properties of LF images. By calculating MHCOMs of LF images, a set of multi-dimensional hypercomplex tensors containing robust feature information of LF images can be obtained, and the original LF images can be reconstructed using this information. Furthermore, the MHCOMs-based zero-watermarking scheme is designed for LF images, which has excellent robustness and can achieve lossless copyright protection for LF images.