Arbitrary 2D Research Articles

Efficient prediction of crack initiation from arbitrary 2D notches

An efficient two-scale approach for predicting mode I crack initiation from 2D notches based on the Coupled Criterion is proposed. On the scale of the local model, a voxel model containing the notch simulates the displacement field. The crack model is introduced on the smaller scale and is defined in an image space. Based on the notch curvature, the precomputed crack model can be transformed to any position on the notch surface. The displacement field of the local model is fitted at the boundaries of the transformed crack model by predefined deformation modes and results can be obtained by a superposition of precomputed crack model results. By introducing the crack in the crack model, the stiffness of this model is reduced and thus, the incremental energy release rate can be inaccurate. Therefore, a boundary relaxation approach is used to obtain more accurate energy release rates. It is shown that the method is very efficient as it requires only 3:20 min to analyze 50 positions on a notch compared to 2:21 h of a conventional approach using full FEM simulations. Thereby, the method is reliable in identifying the critical position. The predicted failure index at this position deviates by at most 10.8%. Since the crack model limits the length of initiating cracks, Irwin’s length KIc2/σc2 of the material must lie below 2.53 times the radius of a circular hole under uniaxial tension. For a brittle material like Al2O3, notches with a curvature radius above 31μm can thus be analyzed.

Ray tracing in metasurfaces

Ray tracing in a metasurface is the process to obtain the three-dimensional (3D) light path under reflection and transmission, which may be helpful in the optical design of metalenses and other metaoptical devices. In this work, first we deduce the 3D vector form of Snell's law for metasurfaces by using a geometric approach. And then, we deduce the general equations to calculate the direction of the reflected and refracted beams in any metasurface, and for any incident beam. In other words, we derive vector form equations for the 3D direction of transmitted and reflected beams at a metasurface with arbitrary 2D phase profile, and for any 3D direction of incident light.

Determining the Phase Gradient Parameter of Three-Dimensional Polymorphic Beams

Three-dimensional polymorphic beams (3D PBs) with arbitrary 3D curves have drawn increasing attention. In this paper, we introduce the concept of phase gradient parameter (PGP) to describe the accumulation of phase along the curvilinear trajectory of a PB. To determine the magnitude and sign of the integral and fractional PGP of 3D PBs, we present an effective method called slightly defocused interference (SDI). The idea is based on the coaxial interference of two polymorphic beams of the same shape but various PGP. One of the interfered beams is slightly defocused, enabling the identification of the sign of the PGP. The efficiency of the reported method has been demonstrated with numerical simulations and experimental measurements by applying it to determining the PGP of various types of polymorphic beams. The results show high quality, indicating great potential in the applications of beam shaping.

Mean arc theorem for exploring domains with randomly distributed arbitrary closed trajectories

A remarkable result from integral geometry is Cauchy’s formula, which relates the mean path length of ballistic trajectories randomly crossing a convex 2D domain, to the ratio between the region area and its perimeter. This theorem has been generalized for non-convex domains and extended to the case of Brownian motion to find many applications in various fields including biological locomotion and wave physics. Here, we generalize the theorem to arbitrary closed trajectories exploring arbitrary domains. We demonstrate that, regardless of the complexity of this trajectory, the mean arc length still satisfies Cauchy’s formula provided that no closed trajectory is entirely contained in the domain. Below this threshold, the mean arc length decreases with the size of the closed trajectory. In this case, an approximate analytical formula can still be given for convex closed trajectories intersecting convex domains provided they are small in comparison. To validate our analysis, we performed numerical simulations of different types of trajectories exploring arbitrary 2D domains. Our results could be applied to retrieve geometric information of bounded domains from the mean first entrance–exit length.

Retrieving the Talbot length of arbitrary 2D gratings.

The Talbot effect has been revived in many fields of modern optics. As a key number of self-imaging, the fundamental Talbot length plays a crucial role in many applications. However, the inspection of the Talbot carpet for determining the Talbot length is applicable only if the 2D field distribution behind the grating is represented by a 1D cross section. In this Letter, we show an effective way to overcome this limitation to explore the self-imaging of gratings with complex 2D periodicities. For that purpose, the near-field diffraction is analyzed using the Pearson correlation coefficient of the intensity distribution in Fourier space. We report results on linear, ring, and spiral gratings.

Programming 2D Supramolecular Assemblies with Wireframe DNA Origami.

Wireframe DNA origami offers the ability to program nearly arbitrary 2D and 3D nanoscale geometries, with six-helix bundle (6HB) edge designs providing both geometric versatility and fidelity with respect to the target origami shape. Because individual DNA origami objects are limited in size by the length of the DNA scaffold, here, we introduce a hierarchical self-assembly strategy to overcome this limitation by programming supramolecular assemblies and periodic arrays using wireframe DNA origami objects as building blocks. Parallel half-crossovers are used together with lateral cohesive interactions between staples and the scaffold to introduce symmetry into supramolecular assemblies constructed from single DNA origami units that cannot be self-assembled directly using base-stacking or conventional antiparallel crossover designs. This hierarchical design approach can be applied readily to 2D wireframe DNA origami designed using the top-down sequence design strategy METIS without any prerequisites on scaffold and staple routing. We demonstrate the utility of our strategy by fabricating dimers and self-limiting hexameric superstructures using both triangular and hexagonal wireframe origami building blocks. We generalize our self-assembly approach to fabricate close-packed and non-close-packed periodic 2D arrays. Visualization using atomic force microscopy and transmission electron microscopy demonstrates that superstructures exhibit similar structural integrity to that of the individual origami building blocks designed using METIS. Our results offer a general platform for the design and fabrication of 2D materials for a variety of applications.

Translational surface coupling along a line with non-conforming meshes

In the modelling of large-scale metal structures, comprising plated components intersecting along weld lines, the meshing efficiency and flexibility are limited by the requirements of nodal alignment and compliance of element size, shape and edge orientation throughout the domain. Such limitations necessitate the use of complex transitional meshes in intersection regions and result in highly complex global mesh configurations. This paper presents an original and systematic methodology for surface coupling along an arbitrary 1D interface, which is applicable to any type of 2D and 3D FEs, and which provides a systematic framework for: (i) geometric modelling of weld lines; (ii) coupling of regions with different levels of discretisation detail or element types within a system; and (iii) domain partitioning problems involving computationally heterogeneous partitions. The strategy is based upon a novel coupling element formulation, which uses the fundamental principles of the mortar method and an augmented Lagrangian Multiplier optimisation approach. Particular consideration is given to an element formulation that enforces rigid translational coupling, which has been implemented for employment with co-rotational Reissner-Mindlin shell elements. Various numerical examples are presented to demonstrate the accuracy, versatility and substantial computational benefits of the developed methodology for modelling large-scale metal structural systems.

Machine‐Learning‐Enabled Vectorial Opto‐Magnetization Orientation

AbstractManipulation of light‐induced magnetization has become a fundamentally hot topic with a potentially high impact for atom trapping, confocal and magnetic resonance microscopy, and data storage. The control of the magnetization orientation mainly relies on the direct methods composed of amplitude, phase, and polarization modulations of the incident light under the tight focusing condition, leaving the achievement of arbitrary desirable 3D magnetization orientation complicated, inflexible, and inefficient. Here, a facile approach called machine learning inverse design to achieve expected vectorial opto‐magnetization orientation is proposed. This pathway is time‐efficient and accurate to produce the demanded incident beam for arbitrary prescribed 3D magnetization orientation. It is highlighted that the machine learning method is not only applied for magnetization orientations, but also widely used in the control of magnetization structures.

Theory of light propagation in arbitrary two-dimensional curved space

As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has received increasing attention in the past decade. Here, in light of the Huygens–Fresnel principle, we propose a theoretical frame to study light propagation along arbitrary geodesics on any 2D curved surfaces. This theory not only enables us to solve the enigma of “infinite intensity” that existed previously at artificial singularities on surfaces of revolution but also makes it possible to study light propagation on arbitrary 2D curved surfaces. Based on this theory, we investigate the effects of light propagation on a typical surface of revolution, Flamm’s paraboloid, as an example, from which one can understand the behavior of light in the curved geometry of Schwarzschild black holes. Our theory provides a convenient and powerful tool for investigations of radiation in curved space.

Variational, stable, and self-consistent coupling of 3D electromagnetics to 1D transmission lines in the time domain

This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrary-geometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. We propose a self-consistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient O-wave in a rectilinear prism and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole convolute.

3D Printing Nano‐Architected Semiconductors Based on Versatile and Customizable Metal‐Bound Composite Photoresins

AbstractSemiconductors are the cornerstones of the current information age. Next‐generation integrated optoelectronics calls for ultrahigh‐resolution manufacturing of sophisticated three‐dimensional (3D) semiconductor products, which introduces tremendous challenges for conventional planar lithography techniques. State‐of‐the‐art 3D printing techniques are promising but hampered by the absence of functional precursors for semiconductor formation. Here, a facile method to synthesize versatile and customizable metal‐bound composite photoresins for 3D printing various nano‐architected metal oxide semiconductors is reported. These photoresins can be readily synthesized using metal‐organic framework (MOF) precursors and commercially available monomers, which are free of the nanoparticle‐induced scattering effect. Arbitrary 3D architectures of metal oxide semiconductors (e.g., ZnO and Co3O4) are additively manufactured with a high resolution of 170 nm, high shape fidelity, and high surface quality. A ZnO‐based micro‐ultraviolet photodetector is fabricated to demonstrate its potential applications in optoelectronic devices. The versatile photoresins are expected to have broad applicability for various functional materials and pave the way for the fabrication of 3D integrated functional devices.

Node generation in complex 3D domains for heat conduction problems solved by RBF-FD meshless method

A novel algorithm is presented and employed for the fast generation of meshless node distributions over arbitrary 3D domains defined by using the stereolithography (STL) file format. The algorithm is based on the node-repel approach where nodes move according to the mutual repulsion of the neighboring nodes. The iterative node-repel approach is coupled with an octree-based technique for the efficient projection of the nodes on the external surface in order to constrain the node distribution inside the domain. Several tests are carried out on three different mechanical components of practical engineering interest and characterized by complexity of their geometry. The generated node distributions are then employed to solve a steady-state heat conduction test problem by using the Radial Basis Function-generated Finite Differences (RBF-FD) meshless method. Excellent results are obtained in terms of both quality of the generated node distributions and accuracy of the numerical solutions.

Strain-Enabled Phase Transition of Periodic Metasurfaces.

Phase transitions are universal in solid-state matters, as well as in periodic electromagnetic metasurfaces-the photonic analogues of crystals. Although such transitions dictate the properties of active metasurfaces, universal ways to describe the structure transition of periodic metasurfaces have not yet been established. Here, the authors report the strain-enabled phase transition (or lattice deformation) of stretchable metasurfaces with the crystallographic description. They analytically and experimentally demonstrate the phase transition of plasmonic lattices between two arbitrary 2D Bravais lattices under certain strain configurations. The strain-induced symmetry lowering of the structures gives rise to optical anisotropy upon polarization, namely, linearly and circularly polarized dichroism. They further demonstrate the potential of phase transition in information decoding with applied strain. Interpreting the phase transition of metasurfaces from a standpoint of symmetry would accelerate the discovery of emergent properties, and provide a generalizable approach to designing active metasurfaces.

A semi-analytical method to simulate hydroelastic slamming of 2D structural sections by coupling Wagner theory with the finite element method

A semi-analytical method based on coupling Wagner theory with the finite element method is applied to numerically simulate hydroelastic slamming of arbitrary symmetric 2D structural sections subject to a constant impact velocity or to free fall motion. The averaged elastic velocity method is adopted to consider the influence of the elastic response on the distribution of the slamming load. A coupled dynamic equation is established to govern the fluid-structural interaction. The nonlinear pressure term improves accuracy. To validate the method, numerically predicted structural deformations and the associated strains during impact for several wedge-shaped sections and a cylindrical shell are compared with published results. The results show that the averaged elastic velocity method is efficient in estimating the structure dynamics. The effect of the nonlinear pressure term on hydroelastic structural dynamics is parametrically studied by considering wedge sections with different deadrise angles and with the elastic bottom plating under different end constraints. This nonlinear pressure term ensures reliably predicted hydroelastic structural responses, especially for wedges of larger deadrise angles and smaller hydroelastic properties. The proposed method provides an efficient tool to estimate structural strength under slamming during the initial design stage of the marine or aerospace structure.

Reconfiguring Non-Convex Holes in Pivoting Modular Cube Robots

We present an algorithm for self-reconfiguration of admissible 3D configurations of pivoting modular cube robots with holes of arbitrary shape and number. Cube modules move across the surface of configurations by pivoting about shared edges, enabling configurations to reshape themselves. Previous work provides a reconfiguration algorithm for admissible 3D configurations containing no non-convex holes; we improve upon this by handling arbitrary admissible 3D configurations. The key insight specifies a point in the deconstruction of layers enclosing non-convex holes at which we can pause and move inner modules out of the hole. We prove this happens early enough to maintain connectivity, but late enough to open enough room in the enclosing layer for modules to escape the hole. Our algorithm gives reconfiguration plans with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) moves for n modules.

Force modeling for 2D freeform grinding with infinitesimal method

A universal method of grinding force modeling in arbitrary 2D freeform grinding is proposed, which is based on the infinitesimal approach. The main idea of this method is to discretize the freeform surface into a group of surfaces with very small widths along the profile of the surface cross section, which can be considered as flat surfaces inclined at different angles. The form grinding process can be considered as a series of inclined flat surface grinding, where the normal grinding force of each flat inclined surface is divided into portions along specific directions. The process of inclined flat surface grinding at certain angle is equivalently converted to flat surface grinding in terms of the same abrasive wheel peripheral velocity and workpiece velocity but different cutting depth and contacting curvature in inclined view plane. A mathematical model of grinding force in flat surface grinding (FSG) is established, where the sliding stage, plowing stage and chip formation stage are considered respectively with 9 coefficients which are determined with linear regression from the grinding experiments. The forces in form grinding are then obtained by summing the individual inclined surfaces grinding forces, which are verified via rail form grinding (RFG). The algorithm was validated by means of the grinding experiments with average relative percentage errors of 6.08% and 7.01% respectively on tangential grinding force and normal grinding force in FSG and average relative percentage errors of 8.47% and 10.37% respectively on longitudinal grinding force and vertical grinding force in RFG.

Krylov complexity in conformal field theory

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.

All-optical synthesis of an arbitrary linear transformation using diffractive surfaces

Spatially-engineered diffractive surfaces have emerged as a powerful framework to control light-matter interactions for statistical inference and the design of task-specific optical components. Here, we report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (Ni) and output (No), where Ni and No represent the number of pixels at the input and output fields-of-view (FOVs), respectively. First, we consider a single diffractive surface and use a matrix pseudoinverse-based method to determine the complex-valued transmission coefficients of the diffractive features/neurons to all-optically perform a desired/target linear transformation. In addition to this data-free design approach, we also consider a deep learning-based design method to optimize the transmission coefficients of diffractive surfaces by using examples of input/output fields corresponding to the target transformation. We compared the all-optical transformation errors and diffraction efficiencies achieved using data-free designs as well as data-driven (deep learning-based) diffractive designs to all-optically perform (i) arbitrarily-chosen complex-valued transformations including unitary, nonunitary, and noninvertible transforms, (ii) 2D discrete Fourier transformation, (iii) arbitrary 2D permutation operations, and (iv) high-pass filtered coherent imaging. Our analyses reveal that if the total number (N) of spatially-engineered diffractive features/neurons is ≥Ni × No, both design methods succeed in all-optical implementation of the target transformation, achieving negligible error. However, compared to data-free designs, deep learning-based diffractive designs are found to achieve significantly larger diffraction efficiencies for a given N and their all-optical transformations are more accurate for N < Ni × No. These conclusions are generally applicable to various optical processors that employ spatially-engineered diffractive surfaces.

Adaptive Finite Element Model for Simulating Crack Growth in the Presence of Holes.

This study presents a developed finite element code written by Visual Fortran to computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant amplitude loading, using the linear elastic fracture mechanics (LEFM) concept. Accordingly, optimizing an FCG analysis, it is necessary to describe all the characteristics of the 2D model of the cracked component, including loads, support conditions, and material characteristics. The advancing front method has been used to generate the finite element mesh. The equivalent stress intensity factor was used as the onset criteria of crack propagation, since it is the main significant parameter that must be precisely predicted. As such, a criterion premised on direction (maximum circumferential stress theory) was implemented. After pre-processing, the analysis continues with incremental analysis of the crack growth, which is discretized into short straight segments. The adaptive mesh finite element method was used to perform the stress analysis for each increment. The displacement extrapolation technique was employed at each crack extension increment to compute the SIFs, which are then assessed by the maximum circumferential stress theory to determine the direction of the crack growth and predict the fatigue life as a function of crack length using a modified form of Paris’ law. The application examples demonstrate the developed program’s capability and performance.

3D electron-beam writing at sub-15\u2009nm resolution using spider silk as a resist

Electron beam lithography (EBL) is renowned to provide fabrication resolution in the deep nanometer scale. One major limitation of current EBL techniques is their incapability of arbitrary 3d nanofabrication. Resolution, structure integrity and functionalization are among the most important factors. Here we report all-aqueous-based, high-fidelity manufacturing of functional, arbitrary 3d nanostructures at a resolution of sub-15 nm using our developed voltage-regulated 3d EBL. Creating arbitrary 3d structures of high resolution and high strength at nanoscale is enabled by genetically engineering recombinant spider silk proteins as the resist. The ability to quantitatively define structural transitions with energetic electrons at different depths within the 3d protein matrix enables polymorphic spider silk proteins to be shaped approaching the molecular level. Furthermore, genetic or mesoscopic modification of spider silk proteins provides the opportunity to embed and stabilize physiochemical and/or biological functions within as-fabricated 3d nanostructures. Our approach empowers the rapid and flexible fabrication of heterogeneously functionalized and hierarchically structured 3d nanocomponents and nanodevices, offering opportunities in biomimetics, therapeutic devices and nanoscale robotics.