Geometrical Restrictions Research Articles

Excitation and Tuning of Spin Waves in Magnonic Crystals by Magnetic Coupling

Magnonic crystals with artificial micro/nanomagnetic pattern act as low‐loss information carriers in many microwave devices. The excitation and control of spin waves inside is essential and fundamental in magnonic crystal applications. Herein, permalloy micro‐disk patterns are constructed on a continuous permalloy film, and they succeed in exciting spin waves in this bilayer‐structured magnonic crystal. The spin‐wave modes can be effectively tuned by varying the periodic parameter (P) of upper‐layer disk pattern, which is confirmed by the transition from single‐peak to multi‐peak in ferromagnetic resonance (FMR) spectra with P decreased from 4 to 0.5 μm. The split in FMR spectra is reconstructed by micromagnetic simulation, revealing that three spin‐wave modes are respectively excited by the domain walls of below‐layer continuous film, geometrical restriction of permalloy micro‐disk, and magnetic coupling between neighboring permalloy micro‐disks. The tunable spin‐wave behavior in this bilayer‐structured magnonic crystal presents broad application prospect in programmable spintronic devices at micro/nanoscale.

Constrained many-to-many point matching in two dimensions

In the minimum-weight many-to-many point matching problem, we are given a set R of red points and a set B of blue points in the plane, of total size N, and we want to pair up each point in R to one or more points in B and vice versa so that the sum of distances between the paired points is minimized. This problem can be solved in O(N3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(N^3)$$\\end{document} time by using a reduction to the minimum-weight perfect matching problem, and thus, it is not fast enough to be used for on-line systems where a large number of tunes need to be compared. Motivated by similarity problems in music theory, in this paper we study several constrained minimum-weight many-to-many point matching problems in which the allowed pairings are given by geometric restrictions, i.e., a bichromatic pair can be matched if and only if the corresponding points satisfy a specific condition of closeness. We provide algorithms to solve these constrained versions in O(N) time when the sets R and B are given ordered by abscissa.

FIKA: A Conformal Geometric Algebra Approach to a Fast Inverse Kinematics Algorithm for an Anthropomorphic Robotic Arm

This paper presents a geometric approach to solve the inverse kinematics for an anthropomorphic robotic arm with seven degrees of freedom (DoF). The proposal is based on conformal geometric algebra (CGA), by which many geometric primitives can be operated naturally and directly. CGA allows for the intersection of geometric entities such as two or more spheres or a plane’s projection over a sphere. Rigid transformations of such geometric entities are performed using only one operation through another geometric entity called a motor. CGA imposes geometric restrictions on the inverse kinematics solution, which avoids computation of the forward kinematics or other numerical solutions, unlike traditional approaches. Comparisons with state-of-the-art algorithms are included to prove our algorithm’s superior performance: such as decreased execution time and errors of the end-effector for a series of desired poses.

Modeling and Simulation of Parametric Nonlinear Focused Ultrasound in Three-Dimensional Bubbly Liquids with Axial Symmetry by a Finite-Element Model

This paper presents the development of a numerical model able to track in time the behavior of nonlinear focused ultrasound when interacting with tiny gas bubbles in a liquid. Our goal here is to analyze the frequency components of the waves by developing a model that can easily be adapted to the geometrical restrictions and complexities that come out in several application frameworks (sonochemistry, medicine, and engineering). We thus model the behavior of nonlinear focused ultrasound propagating in a liquid with gas bubbles by means of the finite-element method in an axisymmetric three-dimensional domain and the generalized-α method in the time domain. The model solves a differential system derived for the nonlinear interaction of acoustic waves and gas bubble oscillations. The high nonlinearity and dispersion of the bubbly medium hugely affect the behavior of the finite-amplitude waves. These characteristics are used here to generate frequency components of the signals that do not exist at the source through nonlinear mixing (parametric antenna). The ability of the model to work with complex geometries, which is the main advantage of the method, is illustrated through the simulation of nonlinear focused ultrasound in a medium excited from two spherical sources in opposite directions.

Vibrational Spectroscopic, 13C NMR, DFT Studies on Chlorofullerene (C60Cl6): A Potential Bioactive Agent

Abstract. The present work comprises the systematic computational chemical findings on Chlorofullerene (C60Cl6). The molecular structure of C60Cl6 was optimized by density function theory (DFT)/B3LYP model of 6-31G(d,p) basis set using Gaussian 09 program. The infrared and Raman spectra were simulated and assigned for C60Cl6 molecule. Carbon – chlorine stretching vibrations are found to be in the range 150-900 cm-1 and the chains are strongly affected with the radial vibrations of the carbon sphere. The optimized geometries at ground-state of the molecules are calculated without any geometrical restriction, except those enforced by symmetry and the molecules are found to be minima on their respective potential energy surfaces. The optimized structures have been subjected to Gauge including atomic orbital (GIAO), the chemical shielding tensors using B3LYP/6-31G(d,p) in solvent phase with the aim of calculating 13C chemical shift values with respect to trimethylsilane (TMS) as computational reference. Molecular acuteness and stability were investigated using the Frontier molecular orbitals (FMO) analysis. The molecular electrostatic potential (MEP) mapping provides a valuable information regarding the net electrostatic effect produced by net charge distribution of the molecule. Chlorofullerenes are considered to be promising compounds for the investigation of biological action which show pronounced anti-HIV action and low toxicity. Hence, these results set goal in scheming the biocompatible molecules which will be useful in the field of carbon nano medicine and drug delivery application.

A two-dimensional void fraction distribution fast prediction model and application to a rod bundle

Accurate prediction of void fraction distribution is essential for system optimization, design, and safety analysis which involves gas-liquid two-phase flow. This paper introduces a novel conceptual two-dimensional Void Fraction Distribution Fast Prediction model (VDFP) designed to rapidly predict the void fraction distribution of fully developed two-phase pipe flow. By achieving this, the N-S equations were simplified into a readily solvable Laplacian form. The simplification was based on two assumptions: 1) For the steady simulation of fully developed pipe flow, the convective and axial diffusion terms in the time-averaged N-S equations are negligible; 2) The pressure field can be predefined as linearly decreasing along the axial direction while ignoring the radial pressure difference. After determining the axial velocity distribution, the void fraction distribution can be calculated through the balance of interfacial forces (lift force, wall lubrication force, and turbulent dispersion force) in the radial direction, which has a solid physical foundation and is applicable across a wide range of operating conditions. The feasibility of the VDFP model was validated by comparing the predicted results with experimental data of air-water two-phase flow in a rod bundle channel with a rod diameter of 25 mm and a rod pitch of 34 mm. Additionally, considering the constraints imposed by the rod bundle subchannel, the impact of bubble geometric restrictions on void fraction prediction was also evaluated. The validation results indicate that the VDFP model predicts the wall peak and core peak void fraction distribution results with satisfactory accuracy, and its solving time is <3 s, showing considerable potential for further reduction.

Indirect Determination of the Internal Diameter of Glass Conical Volumetric Instruments

Purpose: To determine the values of the internal diameter in conical-shaped glass volumetric instruments using height measurements, without needing to measure the wall thickness of the volumetric container, which will allow calculating the contribution to the uncertainty of volume measurement due to the adjustment of the meniscus. Methodological design: The proposed method approximates volume by a series of truncated cones bounded by instrument graduation lines. The series of truncated cones thus defined is subject to comply with a geometric restriction. Then, for the graduation lines of the volumetric instrument that did not adhere to the constraint, a power regression model allows approximation of the value of the internal diameter. Results: The proposed approach could be used as an alternative method to determine the internal diameter of glass conical volumetric instruments in cases where using a vernier caliper or optical comparator is not an option, either because the geometry of the conical instrument does not allow it or because higher cost instruments are not available. Research limitations: Only two types of conical volumetric instruments were tested: an Imhoff cone and a centrifuge tube, with scopes of 1 L and 100 mL, respectively, from only two commercial brands of laboratory glassware. The volume of the tip of the instrument was modeled up to the first graduation mark, always as a semi-ellipsoid of revolution. Findings: Comparing the direct measurement of the internal diameter of the volumetric instruments with an optical comparator, there is an average relative error below 10 %, with a maximum value below 20 % for the two different conical glass instruments studied.

Design and characterisation of a 3-D microphone array for windtunnel measurements

A three-dimensional (3-D) array of GRAS 40PH-10 CCP Free-field Array Microphones has been designed for use in the UNSW anechoic wind tunnel (UAT) for aeroacoustic measurements. The array consists of 192 microphones split into three identical planar arrays of 64 microphones which are placed on both sides and above the potential core of the open-jet that issues into the wind tunnel test section. The planar arrays feature an Underbrink spiral comprised of eight arms of eight microphones each. The spiral configuration was selected to maximize signal-to-noise ratio (SNR) and minimize the beamwidth given the geometrical restrictions of the UAT. A white noise speaker was placed at a range of locations within the testing domain to characterize the source localization abilities of the array as a function of position and frequency. Furthermore, a pair of independent white noise speakers were placed at various separation distances to determine the array’s capability to identify multiple sources within the domain. A 3-D implementation of conventional cross-spectral beamforming and Clean-SC deconvolution algorithms was used, and the performance of each was compared. It was determined that Clean-SC was the preferred method for 3-D beamforming in terms of source localization accuracy, SNR, and beamwidth, despite the higher computational cost.

Prevention of enclosed voids in topology optimization using a cumulative sum flood fill algorithm

Topology optimization has seen increased interest with the rise of additive manufacturing (AM) as a fabrication method, because of its ability to exploit the geometric complexity that AM offers. However, AM still imposes some geometric restrictions on the design, most notably on minimum feature size, overhang angles, and enclosed voids. Enclosed voids are problematic because for many AM methods it is impossible to remove supports, unmelted powder or uncured liquid from them. This paper introduces a filter based on a cumulative sum flood fill algorithm to alleviate this issue in a flexible manner. This filter produces a density field where every enclosed void element is rendered solid. It successfully eliminates enclosed voids in both 2D and 3D problems, with low computational cost due to its geometric nature. In addition we demonstrate direct control over the location, amount, and size of powder removal features by varying boundary conditions for the filter, running additional flood fills, and adding morphology operators, respectively.

A local simplex spline basis for C3 quartic splines on arbitrary triangulations

We deal with the problem of constructing, representing, and manipulating C3 quartic splines on a given arbitrary triangulation T, where every triangle of T is equipped with the quartic Wang–Shi macro-structure. The resulting C3 quartic spline space has a stable dimension and any function in the space can be locally built via Hermite interpolation on each of the macro-triangles separately, without any geometrical restriction on T. We provide a simplex spline basis for the space of C3 quartics defined on a single macro-triangle which behaves like a B-spline basis within the triangle and like a Bernstein basis for imposing smoothness across the edges of the triangle. The basis functions form a nonnegative partition of unity, inherit recurrence relations and differentiation formulas from the simplex spline construction, and enjoy a Marsden-like identity.

Modelling of Peristaltic Pumps with Respect to Viscoelastic Tube Material Properties and Fatigue Effects

Peristaltic pump technology is widely used wherever relatively low, highly accurately dosed volumetric flow rates are required and where fluid contamination must be excluded. Thus, typical fields of application include food, pharmaceuticals, medical technology, and analytics. In certain cases, when applied in conjunction with polymer-based tubing material, supplied peristaltic flow rates are reported to be significantly lower than the expected set flow rates. Said flow rate reductions are related to (i) the chosen tube material, (ii) tube material fatigue effects, and (iii) the applied pump frequency. This work presents a fast, dynamic, multiphysics, 1D peristaltic pump solver, which is demonstrated to capture all qualitatively relevant effects in terms of peristaltic flow rate reduction within linear peristaltic pumps. The numerical solver encompasses laminar fluid dynamics, geometric restrictions provided by peristaltic pump operation, as well as viscoelastic tube material properties and tube material fatigue effects. A variety of validation experiments were conducted within this work. The experiments point to the high degree of quantitative accuracy of the novel software and qualify it as the basis for elaborating an a priori drive correction.

A hole-filling based approach to controlling structural complexity in topology optimization

Shape and topology optimization problems are usually associated with geometrical restrictions. Effective control of structural complexity during the optimization process is important for various considerations, e.g., functionality, manufacturability, and aesthetics. Most existing approaches characterize structural complexity as the number of cavities. However, for three-dimensional structures, the genus (i.e., the number of tunnels) should also be considered as an additional topological constraint. In this paper, a hole-filling method is integrated into the bi-directional evolutionary structural optimization (BESO) computational framework to control the number and size of existing cavities and tunnels during the form-finding process. In the hole-filling method, excess cavities are filled with solid material and excess tunnels are covered by building sheet-like patches. The minimum size of the truss-like components and the minimum thickness of the sheet-like components can be controlled separately. Several two- and three-dimensional compliance minimization problems are presented to demonstrate the effectiveness and potential applications of the proposed approach. The structural performances of the optimized structures with and without complexity control are compared and analyzed. The results show that the developed methodology can produce structurally efficient designs with controllable topologies. It is also demonstrated that the generation of sheet-like components can considerably increase the stiffness of the optimized structure. The proposed approach is capable of generating diverse and competitive designs for architects and engineers to achieve a fine balance between architectural novelty and structural efficiency.

Complementation of analytical solutions for the quantitative roof stability analysis of rock cavities and tunnels

This study revisited a well-founded analytical solution describing the collapse profiles of tunnel roofs and estimated traditional stability measures to be used for quantitative safety assessment and practical engineering design. The original analytical approach was proposed by Fraldi and Guarracino based on a variational approach in the context of limit analysis, and subsequently extended to account for pore-pressure, seismic excitation, shallow buried depth, and axis-symmetric analysis, etc. In this study, the optimal bounds for the stability number, shear strength-based factor of safety, and support pressure were derived from the available original and extended analytical expressions of the failed block in both rectangular and circular tunnels. The computational results were in good agreement with those obtained with semi-analytical and numerical approaches but were obtained with much less computational effort. Regarding the tunnel at a shallow depth, a revised profile function was suggested by employing a different boundary condition that allowed the geometric restriction in the previous study to be eliminated; as a result, improved solutions could be obtained. All computation outcomes, including those of the extensions, were validated with those based on the piecewise linear failure mechanisms. The obtained failure mechanisms demonstrated an identical shape of the profile function in terms of curvature, and differences in safety measures were attributed to the dimension of the failed blocks. The proposed techniques in this study enrich the existing theoretical method while retaining its extreme simplicity.

Curved channels with constant cross sections may support trapped surface waves

Curved channels with constant cross sections are constructed which support a trapped surface wave. Since corresponding eigenvalues are embedded in the continuous spectrum of the water wave problem and therefore possess the natural instability, the construction procedure requires “fine-tuning” of several parameters in the (small) curvature of the channel as well as geometrical restrictions on the cross section. In particular, the mirror symmetry of the cross section with respect to the vertical axis disrupts the procedure, but examples of suitable non-symmetric cross sections are provided.

Evaporation of vertical and pendant ethanol droplets and internal Marangoni convections

Understanding droplet evaporation has broad implications for science and industry. Over the past decades, theoretical models concerning this topic have been extensively studied for better prediction of this process. Although the existing models have shown reliable accuracy both in qualitative and quantitative analysis, most focus on specific physical scenarios and therefore consider only part of the transport mechanisms in the process, e.g., a diffusion-based model. In this study, we numerically investigated the evaporation of vertical and pendant ethanol droplets in an open space and developed a novel comprehensive model for simulation. The model incorporated vapor diffusion, thermal conduction, evaporative cooling, natural convection, and Marangoni stress, showing excellent accuracy in three-dimensional scenes. A sessile droplet evaporating on top of a horizontal substrate was compared. Our analysis started with the temperature distribution surrounding and inside the droplet, from which a complex multi-mechanism coupling behind the concerned issues was implied. We then studied the vapor diffusion and flow features in the gas domain and revealed geometric restriction as an important influencing factor. Next, we focused on the internal flows, demonstrating the dominance of Marangoni convections within the droplet and the characteristics of flow behaviors. The local evaporation flux was identified. Finally, we compared lifetimes in different cases and discussed the effects of droplet volume during evaporation. Overall, a vertical droplet had higher evaporation intensity and internal convection, while pendant and sessile droplets were similar. Our study hopes to provide a reference for ethanol droplet evaporation and possible applications based on such a phenomenon.

De Rham compatible Deep Neural Network FEM

On general regular simplicial partitions T of bounded polytopal domains Ω⊂Rd, d∈{2,3}, we construct exact neural network (NN) emulations of all lowest order finite element spaces in the discrete de Rham complex. These include the spaces of piecewise constant functions, continuous piecewise linear (CPwL) functions, the classical “Raviart–Thomas element”, and the “Nédélec edge element”. For all but the CPwL case, our network architectures employ both ReLU (rectified linear unit) and BiSU (binary step unit) activations to capture discontinuities. In the important case of CPwL functions, we prove that it suffices to work with pure ReLU nets. Our construction and DNN architecture generalizes previous results in that no geometric restrictions on the regular simplicial partitions T of Ω are required for DNN emulation. In addition, for CPwL functions our DNN construction is valid in any dimension d≥2. Our “FE-Nets” are required in the variationally correct, structure-preserving approximation of boundary value problems of electromagnetism in nonconvex polyhedra Ω⊂R3. They are thus an essential ingredient in the application of e.g., the methodology of “physics-informed NNs” or “deep Ritz methods” to electromagnetic field simulation via deep learning techniques. We indicate generalizations of our constructions to higher-order compatible spaces and other, non-compatible classes of discretizations, in particular the “Crouzeix–Raviart” elements and Hybridized, Higher Order (HHO) methods.

A novel beam stopper-based approach for scatter correction in digital planar radiography

X-ray scatter in planar radiography degrades the contrast resolution of the image, thus reducing its diagnostic utility. Antiscatter grids partially block scattered photons at the cost of increasing the dose delivered by two- to four-fold and posing geometrical restrictions that hinder their use for other acquisition settings, such as portable radiography. The few software-based approaches investigated for planar radiography mainly estimate the scatter map from a low-frequency version of the image. We present a novel method for scatter correction in planar imaging based on direct patient measurements. Samples from the shadowed regions of an additional partially obstructed projection acquired with a beam stopper placed between the X-ray source and the patient are used to estimate the scatter map. Evaluation with simulated and real data showed an increase in contrast resolution for both lung and spine and recovery of ground truth values superior to those of three recently proposed methods. Our method avoids the biases of post-processing methods and yields results similar to those for an antiscatter grid while removing geometrical restrictions at around half the radiation dose. It can be used in unconventional imaging techniques, such as portable radiography, where training datasets needed for deep-learning approaches would be very difficult to obtain.

Freestanding region-responsive bilayer for functional packaging of ingestible devices

Ingestible capsules have the potential to become an attractive alternative to traditional means of treating and detecting gastrointestinal (GI) disease. As device complexity increases, so too does the demand for more effective capsule packaging technologies to elegantly target specific GI locations. While pH-responsive coatings have been traditionally used for the passive targeting of specific GI regions, their application is limited due to the geometric restrictions imposed by standard coating methods. Dip, pan, and spray coating methods only enable the protection of microscale unsupported openings against the harsh GI environment. However, some emerging technologies have millimeter-scale components for performing functions such as sensing and drug delivery. To this end, we present the freestanding region-responsive bilayer (FRRB), a packaging technology for ingestible capsules that can be readily applied for various functional ingestible capsule components. The bilayer is composed of rigid polyethylene glycol (PEG) under a flexible pH-responsive Eudragit® FL 30 D 55, which protects the contents of the capsule until it arrives in the targeted intestinal environment. The FRRB can be fabricated in a multitude of shapes that facilitate various functional packaging mechanisms, some of which are demonstrated here. In this paper, we characterize and validate the use of this technology in a simulated intestinal environment, confirming that the FRRB can be tuned for small intestinal release. We also show a case example where the FRRB is used to protect and expose a thermomechanical actuator for targeted drug delivery.

Identification of IL-2 inducible tyrosine kinase inhibitors by quantum mechanics and ligand based virtual screening approaches

Interleukin-2-inducible T-cell kinase (ITK) is a crucial intracellular signaling mediator in normal and malignant T-cells and natural killer cells. Selective inhibition of ITK might be useful for treating a variety of disorders including; autoimmune, inflammatory, and neoplastic disorders. Over the past two decades, the clinical management of ITK inhibitors has progressed dramatically. So far, specific inhibitor with no off-target effects against ITK is available. Herein, we aim to discover potential virtual hits to fasten the process of drug design and development against ITK. In this regard, the key chemical characteristics of ITK inhibitors were identified using ligand-based pharmacophore modeling. The validated pharmacophore comprises one hydrogen bond donor and three hydrogen bond acceptors and was utilized as a 3D query in virtual screening using ZINC, Covalent, and in-house databases. A total of 12 hit compounds were chosen on the basis of their critical interactions with the significant amino acids of ITK. The orbital energies such as HOMO and LUMO of the hit compounds were calculated to evaluate the inhibitor’s potencies. Further, molecular dynamics simulation demonstrated the stability of ITK upon binding of selected virtual hits. Binding energy using the MMGBSA method showed the potential binding affinity of all the hits with ITK. The research identifies key chemical characteristics with geometric restrictions that lead to ITK inhibition. Communicated by Ramaswamy H. Sarma

Inverse problem for a random Schrödinger equation with unknown source and potential

In this paper, we study an inverse scattering problem associated with the time-harmonic Schrödinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random distribution of the microlocally isotropic type, whereas the potential function is assumed to be deterministic. The well-posedness of the forward scattering problem is first established in a proper sense. It is then proved that the rough strength of the random source can be uniquely recovered, independent of the unknown potential, by a single realisation of the passive scattering measurement. In addition to the use of a single sample of the passive measurement for two unknowns, another significant feature of our result is that there is no geometric restriction on the supports of the source and the potential: they can be separated, or overlapped, or one containing the other.