Rectangular Cuboids Research Articles

Modeling magnetically levitated superconducting ellipsoids, cylinders, and cuboids for quantum magnetomechanics

We theoretically investigate the properties of magnetically levitated superconducting elements confined in anti-Helmholtz traps, for application in magnetomechanical experiments. We study both the translational modes and the librational mode. The librational mode gives an additional degree of freedom that levitated spheres do not have access to. We compare levitated particles of different shapes: ellipsoids (with analytical and numerical treatment), cylinders, and rectangular cuboids (numerical treatment). We find that the stable orientations of the particles depend on their aspect ratios. Published by the American Physical Society 2024

Exploring the influence of silicon oxide microchips shape on cellular uptake using imaging flow cytometry

Nano- and micro-carriers of therapeutic molecules offer numerous advantages for drug delivery, and the shape of these particles plays a vital role in their biodistribution and their interaction with cells. However, analysing how microparticles are taken up by cells presents methodological challenges. Qualitative methods like microscopy provide detailed imaging but are time-consuming, whereas quantitative methods such as flow cytometry enable high-throughput analysis but struggle to differentiate between internalised and surface-bound particles. Instead, imaging flow cytometry combines the best of both worlds, offering high-resolution imaging with the efficiency of flow cytometry, allowing for quantitative analysis at the single-cell level. This study focuses on fluorescently labelled silicon oxide microchips of various morphologies but related surface areas and volumes: rectangular cuboids and apex-truncated square pyramid microchips fabricated using photolithography techniques, offering a reliable basis for comparison with the more commonly studied spherical particles. Imaging flow cytometry was utilised to evaluate the effect of particle shape on cellular uptake using RAW 264.7 cells and revealed phagocytosis of particles with all shapes. Increasing the particle dose enhanced the uptake, while macrophage stimulation had minimal effect. Using a ratio particle:cell of 10:1 cuboids and spheres showed an uptake rate of approximately 50%, in terms of the percentage of cells with internalised particles, and the average number of particles taken up per cell ranging from about 1–1.5 particle/cell for all the different shapes. This study indicates how differently shaped micro-carriers offer insights into particle uptake variations, demonstrating the potential of non-spherical micro-carriers for precise drug delivery applications.Graphical

Imaging n-Dimensional Spaces Within m-Dimensional Spaces: An Extension of Hinton’s Method

We derive a Euclidean manifold that is virtually cyclic using a simple equation based on a Euclidean geometry and related to Hinton’s method. The derived equation is simple to understand, but able to project n-dimensional spaces into m-dimensional spaces. In addition, the method produces exact images of rectangular cuboids as elements of a vector space, implying that information is a vector and not a scalar.

The effect of unloading and ejection conditions on the properties of pharmaceutical tablets

This study investigates decompression and ejection conditions on tablet characteristics by comparing compact densities and tensile strengths made using regular rigid dies and custom-built die systems that enable triaxial decompression. Die-wall pressure evolution during decompression and ejection stresses did not meaningfully impact the density and tensile strength of the materials tested: microcrystalline cellulose, crystalline lactose monohydrate, and mannitol. Furthermore, the apparent differences in tensile strength between rectangular cuboids and cylindrical compacts are unrelated to decompression and ejection conditions, but rather a consequence of their shapes and of the test configurations. This suggests that elastic and plastic deformations that may occur during decompression and ejection are not significantly influenced by die-wall pressure evolution. We thus conclude that while triaxial decompression and constraint-free ejection may allow the production of defect-free compacts for materials that otherwise are defect prone using a rigid die, they seem to pose no benefits when the materials already produce defect-free compacts using a rigid die.

A generalized interface reaction kinetic model for describing heterogeneous processes driven by contracting mechanisms

The correct determination of the kinetic model and the kinetic parameters that describe a heterogeneous process is key to accurately predicting its progress within a wide range of conditions, which is one of the main purposes of kinetic analysis. Albeit ideal kinetic models continue to be used to gain insight about the process mechanism, they are constrained by certain assumptions that are rarely met in real experiments and limit their applicability. This is the case of contracting (or interface) kinetic models, which are one of the most commonly used. Thus, the ideal kinetic model R2 is derived by assuming a cylindrical contraction in the radial direction but not contemplating the possibility of a contraction in the direction of the axis of the cylinder. Moreover, in the case of the ideal model R3, it is assumed that contraction takes place simultaneously in particles of identical dimensions in all three directions of space (spheres or cubes). Here, it is revisited this type of model, and it is considered the contraction of particles with different geometries, namely cylinders with different aspect ratios and rectangular cuboids. Besides, a novel generalized interface reaction model is proposed, which covers all the studied cases and broadens the range of applicability to more complex situations involving different geometries and inhomogeneous particle sizes. Finally, the proposed model is applied to the analysis of the experimental thermal dissociation of ammonium nitrate, previously described in the literature as a sublimation process. It is proved that the novel kinetic model provides a more accurate description of the kinetics of the reaction and better prediction capabilities.

Technical note: Commissioning of a low-cost system for directly 3D printed flexible bolus.

To present the commissioning process of a low-cost solution for directly 3D printed flexible patient specific bolus. The 3D printing solution used in this study consisted of a resin stereolithography 3D printer and a flexible curing resin. To test the dimensional accuracy of the 3D printer, rectangular cuboids with varying dimensions were 3D printed and their measured dimensions were compared to the designed dimensions. Percent Depth Dose (PDD) profiles were measured by irradiating film embedded in a 3D printed phantom made of the flexible material. A CT of the phantom was acquired and used to replicate the irradiation setup in the treatment planning system. PDDs were calculated for both the native HU of the phantom, and with the phantom HU overridden to 300 HU to match its physical density. Dosimetric agreement was characterized by comparing calculated to measured depths of R90, R80, and R50. Upon completion of the commissioning process, a bolus was 3D printed for a clinical case study for treatment of the nose. Dimensional accuracy of the printer and material combination was found to be good, with all measured dimensions of test cuboids within 0.5mm of designed. PDD measurements demonstrated the best dosimetric agreement when the material was overridden to 300 HU, corresponding to the measured physical density of the material of 1.18g/cc. Calculated and measured depths of R90, R80, and R50 all agreed within 1mm. The bolus printed for the clinical case was free from defects, highly conformal, and led to a clinically acceptable plan. The results of the commissioning measurements performed indicate that the 3D printer and material solution are suitable for clinical use. The 3D printer and material combination can provide a low-cost solution a clinic can implement in-house to directly 3D print flexible bolus.

Cascades of Fano resonances in light scattering by dielectric particles

Fano lineshapes are fundamental spectroscopic signatures that quantitatively characterize the structural and dynamic properties of physical objects, from nuclei to three-dimensional solids and liquids. The study of cascades of Fano resonances is a fresh approach to the classical problem that greatly expands our knowledge and the scope of practical applications. Here it is demonstrated that in solid state physics cascades of Fano resonance can be considered as a general property of light scattering by dielectric particles with the Mie and Fabry-Perot manifold of narrow photonic eigenmodes. A general picture of Fano resonance cascades in the spectra of all basic elementary scatterers (spheres, cylinders, rings, split rings, rectangular cuboids) is presented. For rings, split rings, and cuboids, the scattering spectrum is divided into separate spectral regions, which begin with a broad transverse resonance of the Lorentz-type or Fano-type lineshape, genetically related to the modes of the disk that generates the ring, and continue with a gallery of longitudinal modes with exponentially increasing Q factors. The alternation of a cascade of transverse modes in a strict sequence of Lorentz-Fano-Lorentz-Fano-… is shown theoretically, as well as experimentally in the case of a ring. This picture opens the door to new fundamental phenomena and extended functionality of dielectric elementary scatterers due to the highly asymmetric controllable shape of the Fano line, periodically repeating in the scattering spectrum.

Rational design of BiFeO3 nanostructures for efficient charge carrier transfer and consumption for photocatalytic water oxidation

Crystal surfaces play significant role in controlling the photocatalytic properties of a semiconductor material. In this work, we report the controlled synthesis of various BiFeO3 nanostructures and validate the influence of various crystal surfaces towards photocatalytic properties for water oxidation. The synthesis of BiFeO3 nanostructures including hexagons, rectangular cuboids and nanoplates is achieved in NaOH aqueous solutions with various concentrations via a facile hydrothermal method. High-resolution transmission electron microscopy (HRTEM) revealed NaOH concentration dependent growth direction of various BiFeO3 nanostructures. BiFeO3 rectangular cuboids dominated with (102) crystal facets exhibited higher surface photovoltage (SPV) response confirming efficient charge carrier separation compared to hexagons and nanoplates. Furthermore, the photoelectrochemical measurements also confirmed the improved photocurrent density and positive shift in flat band potential for BiFeO3 rectangular cuboids studied via Mott-Schottky plots. Resultantly, BiFeO3 rectangular cuboids demonstrated superior photocatalytic O2 evolution activity of 82.2 µmol h−1 g−1 compared to 42.6 µmol h−1 g−1 and 53 µmol h−1 g−1 for hexagons and nanoplates, respectively, without any cocatalyst under visible light irradiation.

BiFeO3 bandgap engineering by dopants and defects control for efficient photocatalytic water oxidation

Tuning the electronic structure of a semiconductor via defects engineering is an effective strategy to modulate its band structure and charge carrier transport for superior photocatalytic properties. Herein, we report visible-light driven photocatalytic water oxidation on BiFeO3 nanoplates with Ti-dopants and oxygen vacancies, synthesized via facile hydrothermal method followed by thermal treatment in H2 atmosphere. The gradual increase of Ti-dopants progressively changes BiFeO3 morphology from rectangular cuboids to nanoplates. The introduction of Ti-dopants and oxygen vacancies tuned the band-gap of BiFeO3, enhanced visible light absorption, improved photogenerated charge-carrier dynamics, and higher driving force for O2 evolution to demonstrate excellent O2 evolution at a rate of 274 µmol h−1 g−1 which is 2.6 times higher compared to pristine BiFeO3. Furthermore, threefold higher photocurrent density and superior surface photovoltage (SPV) results confirm improved charge carrier dynamics in BiFeO3 with Ti- dopants and oxygen vacancies, which make BiFeO3-based nanoplates promising material for photocatalytic applications.

Method for C/N ratio estimation using Mask R-CNN and a depth camera for organic fraction of municipal solid wastes

Fast assessment of the initial carbon to nitrogen ratio (C/N) of organic fraction of municipal solid waste (OFMSW) is an important prerequisite for automatic composting control to improve efficiency and stability of the bioconversion process. In this study, a novel approach was proposed to estimate the C/N of OFMSW, where an instance segmentation model was applied to predict the masks for the waste images. Then, by combining the instance segmentation model with the depth-camera-based volume calculation algorithm, the volumes occupied by each type of waste were obtained, therefore the C/N could be estimated based on the properties of each type of waste. First, an instance segmentation dataset including three common classes of OFMSW was built to train mask region-based convolutional neural networks (Mask R-CNN) model. Second, a volume measurement algorithm was proposed, where the measurement result of the object was derived by accumulating the volumes of small rectangular cuboids whose bottom area was calculated with the projection property. Then the calculated volume was corrected with linear regression models. The results showed that the trained instance segmentation model performed well with average precision scores AP50 = 82.9, AP75 = 72.5, and mask intersection over unit (Mask IoU) = 45.1. A high correlation was found between the estimated C/N and the ground truth with a coefficient of determination R2=0.97 and root mean square error RMSE = 0.10. The relative average error was 0.42% and the maximum error was only 1.71%, which indicated this approach has potential for practical applications. Keywords: carbon to nitrogen ratio, estimation, volume measurement, organic fraction of municipal solid waste, depth camera, instance segmentation DOI: 10.25165/j.ijabe.20211405.6382 Citation: Huang J J, Zhang H D, Xiao X, Huang J Q, Xie J X, Zhang L, et al. Method for C/N ratio estimation using Mask R-CNN and a depth camera for organic fraction of municipal solid wastes. Int J Agric & Biol Eng, 2021; 14(5): 222–229.

Method for C/N ratio estimation using Mask R-CNN and a depth camera for organic fraction of municipal solid wastes

Fast assessment of the initial carbon to nitrogen ratio (C/N) of organic fraction of municipal solid waste (OFMSW) is an important prerequisite for automatic composting control to improve efficiency and stability of the bioconversion process. In this study, a novel approach was proposed to estimate the C/N of OFMSW, where an instance segmentation model was applied to predict the masks for the waste images. Then, by combining the instance segmentation model with the depth-camera-based volume calculation algorithm, the volumes occupied by each type of waste were obtained, therefore the C/N could be estimated based on the properties of each type of waste. First, an instance segmentation dataset including three common classes of OFMSW was built to train mask region-based convolutional neural networks (Mask R-CNN) model. Second, a volume measurement algorithm was proposed, where the measurement result of the object was derived by accumulating the volumes of small rectangular cuboids whose bottom area was calculated with the projection property. Then the calculated volume was corrected with linear regression models. The results showed that the trained instance segmentation model performed well with average precision scores AP50 = 82.9, AP75 = 72.5, and mask intersection over unit (Mask IoU) = 45.1. A high correlation was found between the estimated C/N and the ground truth with a coefficient of determination R2=0.97 and root mean square error RMSE = 0.10. The relative average error was 0.42% and the maximum error was only 1.71%, which indicated this approach has potential for practical applications. Keywords: carbon to nitrogen ratio, estimation, volume measurement, organic fraction of municipal solid waste, depth camera, instance segmentation DOI: 10.25165/j.ijabe.20211405.6382 Citation: Huang J J, Zhang H D, Xiao X, Huang J Q, Xie J X, Zhang L, et al. Method for C/N ratio estimation using Mask R-CNN and a depth camera for organic fraction of municipal solid wastes. Int J Agric & Biol Eng, 2021; 14(5): 222–229.

Fully-coupled numerical model for ballasted track analysis – Field measurements and predictions

This paper proposes a three-dimensional fully-coupled numerical model intended for the simulation of the dynamic behavior of ballasted railway tracks under real excitation. It is employed to reproduce the response of a French site located at the high-speed line connecting the two regions Bretagne and Pays de la Loire. The equation of motion is solved in the time domain by means of the finite difference method in which the rails and sleepers are represented by rectilinear beam elements which are rigidly attached to a spatial grid composed of rectangular cuboids. An adaptive meshing scheme based on the creation of load-attached moving nodes is adopted to model the moving train loads which are supposed to be time-independent. To validate the numerical simulations, a measuring campaign is performed in which tow aligned deflectometers are used to measure the displacement of the railway foundation just below the ballast layer under the track centerline. The velocity range of the high-speed passenger trains is covered in which four cases are taken into consideration ranging from 162 to 342 km/h. An excellent agreement between measurements and predictions is found. Therefore, the presented model can be considered reliable for the design of new high-speed lines.

A physicist’s guide to explicit summation formulas involving zeros of Bessel functions and related spectral sums

In this pedagogical review, we summarize the mathematical basis and practical hints for the explicit analytical computation of spectral sums that involve the eigenvalues of the Laplace operator in simple domains such as [Formula: see text]-dimensional balls (with [Formula: see text]), an annulus, a spherical shell, right circular cylinders, rectangles and rectangular cuboids. Such sums appear as spectral expansions of heat kernels, survival probabilities, first-passage time densities, and reaction rates in many diffusion-oriented applications. As the eigenvalues are determined by zeros of an appropriate linear combination of a Bessel function and its derivative, there are powerful analytical tools for computing such spectral sums. We discuss three main strategies: representations of meromorphic functions as sums of partial fractions, Fourier–Bessel and Dini series, and direct evaluation of the Laplace-transformed heat kernels. The major emphasis is put on a pedagogic introduction, the practical aspects of these strategies, their advantages and limitations. The review gathers many summation formulas for spectral sums that are dispersed in the literature.

Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes

Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating total magnetic moment by integrating the magnetic induction obtained from a full three dimensional solution of the Maxwell equations using adaptive mesh. The results are relevant for superconductors (and conductors in AC fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. Simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse field as well as infinite rectangular and elliptical cross-section strips.

Approximating Smallest Containers for Packing Three-Dimensional Convex Objects

We investigate the problem of computing a minimal-volume container for the non-overlapping packing of a given set of three-dimensional convex objects. Already the simplest versions of the problem are [Formula: see text]-hard so that we cannot expect to find polynomial time algorithms to determine the exact solution. We give constant ratio approximation algorithms for packing axis-parallel (rectangular) cuboids under translation into an axis-parallel (rectangular) cuboid as container, for packing cuboids under rigid motions into an axis-parallel cuboid or into an arbitrary convex container, and for packing convex polyhedra under rigid motions into an axis-parallel cuboid or arbitrary convex container. This work gives the first approximability results for the computation of minimum volume containers for the objects described.

Effect of process parameters on the Selective Laser Melting (SLM) of tungsten

Selective Laser Melting (SLM) is a promising technique for the fabrication of complex net shaped parts of many metals. However, the high melting temperature of tungsten makes fabricating complex parts via SLM difficult. A study was undertaken to understand the effect of process parameters like hatch spacing and scan speed on the densification of tungsten by the SLM technique. Experiments were conducted at hatch spacing of 15 and 30μm and scan speeds in the range 200–1400mm/s. A constant laser power of 90W and a powder layer thickness of 30μm were used. Rectangular cuboids of 7.8±1.4mm×10.1±0.1mm×10.1±0.04mm were printed using various process parameters and analyzed for densification. The densification of tungsten was found to increase with an increase in energy density. A maximum density of 75% theoretical was achieved at energy density of 1000J/mm3.

Optical Effects at projection measurements for Terahertz tomography

Abstract Optical effects like refraction, diffraction and edge effects have an influence on Terahertz measurements. They can result in image artifacts which makes it difficult to detect and resolve material defects inside the samples. We used a geometrical optical ray tracing approach to analyze the optical effects at Terahertz projection measurements which can be used to perform 2D or 3D THz images. We measured rectangular and cylindrical samples made of PEEK (Polyetheretherketon), POM (Polyoxymethylen), and PMMA (Polymethylmethacrylat) and compared the results to simulations that are realized with the software ZEMAX. We were able to simulate the measured Fresnel refraction and transmission behavior for rectangular cuboids with a length of 25 mm and cylinders with diameter of 25 mm. We showed the influence of diffraction and edge effects at samples with different sizes made of PMMA. Thus, the optical effect of refraction was significant and observable for cylinders with diameters greater than 1.5 mm and holes with diameter greater than 2.5 mm.

RMAP: a rectangular cuboid approximation framework for 3D environment mapping

This paper presents a rectangular cuboid approximation framework (RMAP) for 3D mapping. The goal of RMAP is to provide computational and memory efficient environment representations for 3D robotic mapping using axis aligned rectangular cuboids (RC). This paper focuses on two aspects of the RMAP framework: (i) An occupancy grid approach and (ii) A RC approximation of 3D environments based on point cloud density. The RMAP occupancy grid is based on the Rtree data structure which is composed of a hierarchy of RC. The proposed approach is capable of generating probabilistic 3D representations with multiresolution capabilities. It reduces the memory complexity in large scale 3D occupancy grids by avoiding explicit modelling of free space. In contrast to point cloud and fixed resolution cell representations based on beam end point observations, an approximation approach using point cloud density is presented. The proposed approach generates variable sized RC approximations that are memory efficient for axis aligned surfaces. Evaluation of the RMAP occupancy grid and approximation approach based on computational and memory complexity on different datasets shows the effectiveness of this framework for 3D mapping.

Tungsten oxide nanostructures based on laser ablation in water and a hydrothermal route

Well-dispersed and surface-stepped tungsten oxide nanostructures can be obtained via stacking of nanosized rectangular cuboids during hydrothermal treatment of LAL obtained precursors.

ON THE EXPONENTIAL CONVERGENCE OF THE METHOD OF FUNDAMENTAL SOLUTIONS

It is well known that the method of fundamental solutions (MFS) is a numerical method of exponential convergence. In other words, the logarithmic error is proportional to the node number of spatial discretization. In this study, the exponential convergence of the MFS is demonstrated by solving the Laplace equation in domains of rectangles, ellipses, amoeba-like shapes, and rectangular cuboids. In the solution procedure, the sources of the MFS are located as far as possible and the instability resulted from the ill-conditioning of system matrix is avoided by using the multiple precision floating-point reliable (MPFR) library. The results converge faster for the cases of smoother boundary conditions and larger area/perimeter ratios. For problems with discontinuous boundary data, the exponential convergence is also accomplished using the enriched method of fundamental solutions (EMFS), which is constructed by the fundamental solutions and the local singular solutions. The computation is scalable in the sense that the required time increases only algebraically.