Uniform Square Research Articles

Study on energy absorption performance of variable thickness CFRP/aluminum hybrid square tubes under axial loading

Variable thickness hybrid square (VTHS) tubes which had variable thickness of CFRP to achieve the variation of axial crushing performance are proposed. To study the crushing characteristics and relative advantages of the VTHS, pure aluminum tube, uniform hybrid square tube and VTHS were manufactured firstly, and their axial crushing tests were conducted. Experimental results showed that, compared with uniform hybrid square tube, VTHS had lower initial peak crushing force. Finite element models were established and verified to explore the effect of parameters of the tubes on axial crushing performance further. Numerical results showed that the crushing force can be controlled by varying the thickness of CFRP. Compared with uniform thickness hybrid square tube, VTHS had an improvement of 24.5% in specific energy absorption and increase was greater for the VTHS with thinner metal. Effects of the mean thickness, thickness difference, and number of segments of CFRP on the energy absorption performance were studied. Finally, a theoretical model to predict the mean crushing force was proposed and its accuracy was verified by tests. Results demonstrate that theory can be used to obtain the mean crushing force of each segment of VTHS accurately.

A Biomimetic, SoC-Based Neural Stimulator for Novel Arbitrary-Waveform Stimulation Protocols.

Novel neural stimulation protocols mimicking biological signals and patterns have demonstrated significant advantages as compared to traditional protocols based on uniform periodic square pulses. At the same time, the treatments for neural disorders which employ such protocols require the stimulator to be integrated into miniaturized wearable devices or implantable neural prostheses. Unfortunately, most miniaturized stimulator designs show none or very limited ability to deliver biomimetic protocols due to the architecture of their control logic, which generates the waveform. Most such designs are integrated into a single System-on-Chip (SoC) for the size reduction and the option to implement them as neural implants. But their on-chip stimulation controllers are fixed and limited in memory and computing power, preventing them from accommodating the amplitude and timing variances, and the waveform data parameters necessary to output biomimetic stimulation. To that end, a new stimulator architecture is proposed, which distributes the control logic over three component tiers – software, microcontroller firmware and digital circuits of the SoC, which is compatible with existing and future biomimetic protocols and with integration into implantable neural prosthetics. A portable prototype with the proposed architecture is designed and demonstrated in a bench-top test with various known biomimetic output waveforms. The prototype is also tested in vivo to deliver a complex, continuous biomimetic stimulation to a rat model of a spinal-cord injury. By delivering this unique biomimetic stimulation, the device is shown to successfully reestablish the connectivity of the spinal cord post-injury and thus restore motor outputs in the rat model.

Real-time control of dendritic propagation in rechargeable batteries using adaptive pulse relaxation.

The non-uniform growth of microstructures in dendritic form inside the battery during prolonged charge-discharge cycles causes short-circuit as well as capacity fade. We develop a feedback control framework for the real-time minimization of such microstructures. Due to the accelerating nature of the branched evolution, we focus on the early stages of growth, identify the critical ramified peaks, and compute the effective time for the dissipation of ions from the vicinity of those branching fingers. The control parameter is a function of the maximum interface curvature (i.e., minimum radius) where the rate of runaway is the highest. The minimization of the total charging time is performed for generating the most packed microstructures, which correlate closely with those of considerably higher charging periods, consisting of constant and uniform square waves. The developed framework could be utilized as a smart charging protocol for safe and sustainable operation of rechargeable batteries, where the branching of the microstructures could be correlated with the sudden variation in the current/voltage.

Simulated and experimental analysis of laser beam energy profiles to improve efficiency in wire-fed laser deposition

Laser cladding is a well-established technique, with the majority of prior numerical modelling work focused on delivery and melt pool behaviour of powder-based processes. This research presents new investigations into optimised laser beam shaping for the unique characteristics of wire-based processes, where direct substrate heating, as well as heat transfer between the wire and substrate, is important. The value of this subject is the improved deposition rates and dense metallic structures that can be achieved by wire-based deposition processes compared to powder-based material delivery. The within-wire temperature distribution (AISI 316 stainless steel), the heat transfer and direct heating of the substrate (mild steel) are modelled via heat transfer simulations, with three laser beam irradiance distributions. This analysis identified the removal of localised high-temperature regions typically associated to standard Gaussian distributions, and the improved substrate heating that a uniform square beam profile can provide. Experiments using pre-placed wire and a 1.2 kW CO2 laser were analysed using cross-sectional optical microscopy to provide model validation and evidence of improved wire-substrate wetting, while maintaining favourable austenitic metallurgy in the clad material. A key finding of this work is a reduction, from 480 to 190 W/mm2, in the required irradiance for effective melt pool formation when changing from a Gaussian distribution to a uniform square distribution. This also provided a 50% reduction in total energy. The potential improvements to energy efficiency, cost reductions and sustainability improvements are recognised and discussed.

Revisiting the discrete planar Laplacian: exact results for the lattice Green function and continuum limit

The paper deals with the discrete Laplacian on a uniform infinite square lattice. The definition of its fundamental solution or lattice Green function (LGF) is clarified as the Fourier coefficients of a certain generalized periodic function g. Such a functional must be regularized and gives the LGF up to a constant equal to \({<}g{>}\), the mean value of g. For \({<}g{>}=0\), the LGF may be expressed in an exact analytic form in terms of hypergeometric and gamma functions. The continuum limit of the LGF is finally studied requiring an appropriate renormalization of \({<}g{>}\) in order to obtain the logarithmic Coulomb potential.

Study on Strain Rate Effect and Size Effect of Dynamic Response Characteristics of Granite

Under impact load, the dynamic mechanical properties of rock are complex and changeable. The Split Hopkinson Pressure Bar (SHPB) system was used to change the impact load to carry out different strain rate loading tests on granite with different aspect ratios, and to analyze the influence of strain rate and aspect ratio on the dynamic energy consumption of granite crushing. The results show that at an impact velocity of 14 m/s, the granite with an aspect ratio of 1.4 appears to be strip-shaped fragments after being broken; the granite with an aspect ratio of 1.0 uniform square fragments after being broken; the granite with an aspect ratio of 0.6 appears to be a large number of flat fragments after being broken. When the load strain rate of the granite with an aspect ratio of 0.6 increases from 50 s-1 to 150 s-1, the energy-time density index increases significantly; when the load strain rate exceeds 150 s-1, the energy-time density index decreases. When the strain rate of granite with an aspect ratio of 1.0 exceeds 80 s-1, the energy-time density increases significantly. When the strain rate of the granite with an aspect ratio of 1.4 exceeds 60 s-1, the rate of increase of the energy-time density of the rock increases significantly.

SNR of the coded aperture imaging system

In this paper, the expression for the SNR has been developed through the imaging model. It is concluded that the image SNR decreases with the increase of the number of light-emitting points of the target under the same hardware conditions and experimental parameters. Using uniform bright squares of different sizes as the target, the SNR of the reconstructed image is calculated. Simulation and prototype experiments have proved the correctness of the conclusion. Based on this conclusion, a method of segmented area imaging is proposed to improve the reconstructed image quality. The quality of all the images using this method with Wiener inverse filtering, R-Lucy deconvolution, and ADMM is better than the image quality obtained by full-area imaging.

Uniform semi-Latin squares and their pairwise-variance aberrations

For integers n>2 and k>0, an (n×n)∕ksemi-Latin square is an n×n array of k-subsets (called blocks) of an nk-set (of treatments), such that each treatment occurs once in each row and once in each column of the array. A semi-Latin square is uniform if every pair of blocks, not in the same row or column, intersect in the same positive number of treatments. It is known that a uniform (n×n)∕k semi-Latin square is Schur optimal in the class of all (n×n)∕k semi-Latin squares, and here we show that when a uniform (n×n)∕k semi-Latin square exists, the Schur optimal (n×n)∕k semi-Latin squares are precisely the uniform ones. We then compare uniform semi-Latin squares using the criterion of pairwise-variance (PV) aberration, introduced by J. P. Morgan for affine resolvable designs, and determine the uniform (n×n)∕k semi-Latin squares with minimum PV aberration when there exist n−1 mutually orthogonal Latin squares of order n. These do not exist when n=6, and the smallest uniform semi-Latin squares in this case have size (6×6)∕10. We present a complete classification of the uniform (6×6)∕10 semi-Latin squares, and display the one with least PV aberration. We give a construction producing a uniform ((n+1)×(n+1))∕((n−2)n) semi-Latin square when there exist n−1 mutually orthogonal Latin squares of order n, and determine the PV aberration of such a uniform semi-Latin square. Finally, we describe how certain affine resolvable designs and balanced incomplete-block designs can be constructed from uniform semi-Latin squares. From the uniform (6×6)∕10 semi-Latin squares we classified, we obtain (up to block design isomorphism) exactly 16875 affine resolvable designs for 72 treatments in 36 blocks of size 12 and 8615 balanced incomplete-block designs for 36 treatments in 84 blocks of size 6. In particular, this shows that there are at least 16875 pairwise non-isomorphic orthogonal arrays OA(72,6,6,2).

Efficient Simulation of Cuboid Object in Multiplanar Layered Medium by Improved Spectrum Integral Method

An efficient improved spectrum integral method (ISIM) is proposed to accelerate the scattering simulation of cuboid object by method of moment (MoM) in multiplanar layered medium (LM). The layered medium Green’s functions (LMGFs) are studied and decomposed into transmission and reflection terms, which hold the translational invariance and reverse translational invariance, respectively. By virtue of the (reverse) translational invariance of LMGF from the uniform square grids on the surface of the cuboid object, most of the coupling between the expanding basis functions and the testing basis functions can be represented by two kinds of submatrices, i.e., the Toeplitz matrix when transmission term is involved, and the conjugate Toeplitz matrix when reflection term is involved. Moreover, the submatrix coupling the expanding/testing basis functions defined on the edges with those defined on the parallel surfaces/edges is also extended to the (conjugate) Toeplitz matrixes. This will significantly alleviate the heavy computation and memory burden from the conventional SIM. With the improved operations on the basis functions associated with the edges of the cuboid object, the proposed ISIM in LM can reach the computational complexity as low as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${O}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N} ^{1.5}$ </tex-math></inline-formula> log( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N)) in the matrix vector production, while the computational complexity of matrix filling and the memory requirement are both <inline-formula> <tex-math notation="LaTeX">${O}$ </tex-math></inline-formula>(</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}^{1.5}$ </tex-math></inline-formula> ). Moreover, compared with conventional SIM, both theoretical analysis and numerical results demonstrate that the memory requirement and matrix filling time are dramatically decreased.

Mode selection and high-quality upconversion lasing from perovskite CsPb2Br5 microplates

In recent years, halide perovskite nanostructures have had great advances and have opened up a bright future for micro/nanolasers. However, upconversion lasing by two-photon excitation with mode selection and high quality factor in one device is still rarely reported. Herein, two lasing modes are demonstrated in the all-inorganic perovskite CsPb 2 Br 5 microplates with subwavelength thickness and uniform square shape. The net optical gain is quickly established in less than 1 ps and persists more than 30 ps, revealed by ultrafast transient absorption spectroscopy. The temperature-dependent low-threshold amplified spontaneous emission confirms the net gain for stimulated emission with a high characteristic temperature of 403 K, far surpassing the all-inorganic CsPbBr 3 semiconductor gain media. Remarkably, upconversion lasing based on two kinds of microcavity effects, Fabry–Pérot and whispering-gallery modes, from the microplates at room temperature is successfully achieved with a low threshold operating in multi- or single-mode, respectively. Surprisingly, the quality factor ( ∼ 3551 ) is among the best values obtained from perovskite micro/nanoplate upconversion lasers without an external cavity. Moreover, the highly stable chromaticity with color drift only less than 0.1 nm also outbalances the all-inorganic CsPbBr 3 ones. These superior performances of CsPb 2 Br 5 microplate lasing with a facile solution synthesis procedure will offer a feasible structure to fabricate specific functionalities for high-performance frequency upconversion micro/nanoscale photonic integrated devices.

Thermal Transport and Frequency Response of Localized Modes on Low-Stress Nanomechanical Silicon Nitride Drums Featuring a Phononic-Band-Gap Structure

Development of broadband thermal sensors for the detection of, among others, radiation, single nanoparticles, or single molecules is of great interest. In recent years, photothermal spectroscopy based on the shift of the resonance frequency of stressed nanomechanical resonators has been successfully demonstrated. Here, we show the application of soft-clamped phononic crystal membranes made of silicon nitride as thermal sensors. It is experimentally demonstrated how a quasi-bandgap remains even at very low tensile stress, in agreement with finite element method simulations. An increase of the relative responsivity of the fundamental defect mode is found when compared to that of uniform square membranes of equal size, with enhancement factors as large as an order of magnitude. We then show phononic crystals engineered inside nanomechanical trampolines, which results in additional reduction of the tensile stress and increased thermal isolation, resulting in further enhancement of the responsivity. Finally, defect mode and bandgap tuning is shown by laser heating of the defect to the point where the fundamental defect mode completely leaves the bandgap.

Toward the Highly Ordered Lamellar Hybrid Membrane for Molecular Sieving by One-Pot Self-Assembly of Hybrid Hyperbranched Polymer

Ordered lamellar hybrid membranes are of great interest, due to their application as functional materials, including molecular sieving, biosensors, optical devices, and drug, as well as gene delive...

New 25-point stencils with optimal accuracy for 2-D heat transfer problems. Comparison with the quadratic isogeometric elements

A new approach for the increase in the order of accuracy of high order elements used for the time dependent heat equation and for the time independent Poisson equation has been suggested on uniform square and rectangular meshes. It is based on the optimization of the coefficients of the corresponding discrete stencil equation with respect to the local truncation error. By a simple modification of the coefficients of 25-point stencils, the new approach exceeds the accuracy of the quadratic isogeometric elements by four orders for the heat equation and by twelve orders for the Poisson equation. Despite the significant increase in accuracy, the computational costs of the new technique are the same as those for the conventional quadratic isogeometric elements on a given mesh. The numerical examples are in a good agreement with the theoretical results for the new approach and also show that the new approach is much more accurate than the conventional isogeometric elements at the same number of degrees of freedom. Hybrid methods that combine the new stencils with the conventional isogeometric and finite elements and can be applied to irregular domains are also presented.

Structural Optimization for Asymmetric Framed Structures without Shear Walls

This paper proposes a method for the preliminary arrangement of columns having variable sizes on an asymmetric plan, such that the resulting structure will have minimum torsion. Asymmetry can be due to shape of the plan as well as arrangement of columns having variable sizes. This study shows the influence of first three modes in determining the structural behavior of RCC framed buildings during earthquake. The time periods were approximately calculated by using 3D-shear-torsion beam method. The optimization was done using Genetic algorithm in Matlab. The seismic performance of general asymmetric structures with uniform square columns were compared with optimized asymmetric structures having columns with variable sizes. The results from pushover analysis showed significant increase in strength and ductility along the direction having torsion.

Two-Dimensional Supramolecular Ionic Frameworks for Precise Membrane Separation of Small Nanoparticles

Supramolecular frameworks driven by intermolecular interactions represent a new type of porous materials differing from those driven by covalent or coordination bonding. The intermolecular interaction-induced flexible assembly structures display unique advantages in materials processing, structure stimuli-responses and recyclings. In this work, a two-dimensional (2D) supramolecular-ionic framework (SIF) was constructed through the initial ionic interaction between host cation and polyoxometalate polyanion and then the host-guest inclusion of the formed host ionic complex with a four-arm porphyrin guest molecule following a 2+4 reaction. Several prepared framework monolayer bearing orthometric grid structure constituted a nanosheet-like assembly with flexibility and exhibited processability, which provided the feasibility for further preparation of separation membrane via a simple suction procedure of their dispersed suspensions in mixed solvents. The nano-filtration based on the uniform square pores under a slightly reduced pressure successfully achieved a precise separation of several types of nanoparicles and molecular clusters in wide distribution at a cutting off value as small as 2.2 nm. These results also implied potentials of the present strategy for more separations at molecluar level and very fine nanoscale.

Square permutations are typically rectangular

We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. The starting point for all our results is a sampling procedure for asymptotically uniform square permutations. Building on that, we first describe the global behavior by showing that these permutations have a permuton limit which can be described by a random rectangle. We also explore fluctuations about this random rectangle, which we can describe through coupled Brownian motions. Second, we consider the limiting behavior of the neighborhood of a point in the permutation through local limits. As a byproduct, we also determine the random limits of the proportion of occurrences (and consecutive occurrences) of any given pattern in a uniform random square permutation.

Improved 2D Coprime Array Structure with the Difference and Sum Coarray Concept

Recently, the difference and sum (diff-sum) coarray has attracted much attention in one-dimensional direction-of-arrival estimation for its high degrees-of-freedom (DOFs). In this paper, we utilize both the spatial information and the temporal information to construct the diff-sum coarray for planar sparse arrays. The diff-sum coarray contains both the difference coarray and the sum coarray, which provides much higher DOFs than the difference coarray alone. We take a planar coprime array consisting of two uniform square subarrays as the array model. To fully use the aperture-extending ability of the diff-sum coarray, we propose two novel configurations to improve the planar coprime array. The first configuration compresses the inter-element spacing of one subarray and results in a larger consecutive area in the coarray. The second configuration rearranges the two subarrays and introduces a proper separation between them, which can significantly reduce the redundancy of the diff-sum coarray and increase the DOFs. Besides, we derive the closed-form expressions of the central consecutive ranges in the coarrays of the proposed array configurations. Simulations verify the superiority of the proposed array configurations.

Numerical Investigation of Incompressible Forced Convection in a Channel with a Rectangular Prism

The aim of the present study is to investigate the effects of the rectangular prism on forced convection in a channel with the Lattice Boltzmann Method (LBM). In this context, numerical analysis of steady and unsteady incompressible flow and heat transfer has been done in a two-dimensional straight parallel channel. Momentum and energy transport are modelled with LBM. This study is used as a single relaxation time rule with a uniform square lattice structure. Different Reynolds numbers (50 and 1000) and constant Prandtl number value (0.7) have been investigated. In this study Nusselt number has been calculated for channel flow with rectangular prism and it was compared with an empty channel. Streamlines and isotherms were presented for the above-mentioned cases. LBM results were validated by commercial CFD code with the same conditions. It is found from results that Nusselt number with a rectangular prism in a channel was increased and the flow goes to transient form at Re=1000. Also, LBM code results are similar accuracy with commercial CFD code.

Stability and boundedness of nonautonomous neutral differential equation with delay

We consider the nonautonomous neutral differential equation with delay h p(t) q(t) x(t) + b1x(t - r1) 0 0i0 + a(t) x 00(t) + b2x 00(t - r2) +b(t) x 0 (t) + b3x 0 (t - r3) + c(t)f(x(t - s)) = e(t, x, x0 , x 00). Using the method of Lyapunov, we give conditions for the uniform asymptotic stability and uniform boundedness and square integrability of solutions for the considered system. Our theorems generalize and extend some related results known in the literature. Example is given to show our resuls.

The synthesis of MAPbBr3 nanoplatelets with long-term stability and high photoluminescence quantum yield through controlling the synthetic temperature and dilution treatment

Organometal halide perovskite nanocrystals are very promising for optoelectronic applications due to their unique optical properties. However, the OHP nanocrystals generally suffer from problems such as nonuniform morphology and poor stability. This work reports the synthesis of MAPbBr3 nanoplatelets through dilution of the irregular colloidal MAPbBr3 nanocrystals prepared at 50 °C. The dilution followed by self-organization of the nanocrystals result in the production of uniform square nanoplatelets with long term stability up to 6 months and high photoluminescence quantum yield about 90%. Furthermore, by using bidentate coordination molecule pyrazole as co-ligand, regular 2D structural Nanocrystals with round edge and aggregation were produced. The aggregated nanoplatelets prepared at 50 °C show the same self-assembly process after dilution to form uniform square nanoplatelets.