Triangular Structure Research Articles

Solving Perturbed Dynamic Systems Using Schur Decomposition

This work introduces a methodology for the generation of an approximate analytical solution to perturbed ordinary differential equations using Schur decomposition. This methodology is based on the use of operator theory to find a linear approximation to the ordinary differential equation in an expanded space of configuration. Once this linearization is performed, the Schur decomposition is used to transform the resultant differential equation into an upper triangular system that can be solved sequentially following the upper triangular structure. Based on these results, a perturbation technique is also proposed to study these problems. Finally, this work provides a set of algorithms to automate all the methodologies presented, with a special focus on polynomial differential equations and the use of Legendre polynomials to represent the dynamical system. Several examples of application are provided, including the Duffing oscillator, the Van der Pol oscillator, and the zonal harmonics problem around the moon.

From Walking to Running: 3D Humanoid Gait Generation via MPC.

We present a real time algorithm for humanoid 3D walking and/or running based on a Model Predictive Control (MPC) approach. The objective is to generate a stable gait that replicates a footstep plan as closely as possible, that is, a sequence of candidate footstep positions and orientations with associated timings. For each footstep, the plan also specifies an associated reference height for the Center of Mass (CoM) and whether the robot should reach the footstep by walking or running. The scheme makes use of the Variable-Height Inverted Pendulum (VH-IP) as a prediction model, generating in real time both a CoM trajectory and adapted footsteps. The VH-IP model relates the position of the CoM to that of the Zero Moment Point (ZMP); to avoid falling, the ZMP must be inside a properly defined support region (a 3D extension of the 2D support polygon) whenever the robot is in contact with the ground. The nonlinearity of the VH-IP is handled by splitting the gait generation into two consecutive stages, both requiring to solve a quadratic program. Thanks to a particular triangular structure of the VH-IP dynamics, the first stage deals with the vertical dynamics using the Ground Reaction Force (GRF) as a decision variable. Using the prediction given by the first stage, the horizontal dynamics become linear time-varying. During the flight phases, the VH-IP collapses to a free-falling mass model. The proposed formulation incorporates constraints in order to maintain physically meaningful values of the GRF, keep the ZMP in the support region during contact phases, and ensure that the adapted footsteps are kinematically realizable. Most importantly, a stability constraint is enforced on the time-varying horizontal dynamics to guarantee a bounded evolution of the CoM with respect to the ZMP. Furthermore, we show how to extend the technique in order to perform running on tilted surfaces. We also describe a simple technique that receives input high-level velocity commands and generates a footstep plan in the form required by the proposed MPC scheme. The algorithm is validated via dynamic simulations on the full-scale humanoid robot HRP-4, as well as experiments on the small-sized robot OP3.

In Vitro and In Vivo Analysis of the Effects of 3D-Printed Porous Titanium Alloy Scaffold Structure on Osteogenic Activity.

The effect of titanium scaffold geometry on the bone regeneration ability of the scaffold remains unclear. Here, selective laser melting as a 3D printing technology was used to create porous titanium alloy scaffolds with two unit structures: a hollow hexagonal prism (group A) and a hollow triangular prism (group B). The structures and morphologies of the scaffolds were characterized before mechanical properties were simulated. Cell adhesion behaviors, osteoblast activity and proliferation, and alkaline phosphatase (ALP) activity were evaluated, in addition to in vivo testing in an animal model. The results showed that the two scaffolds made of Ti6Al4V had compression moduli similar to that of human cortical bone (116.91 ± 0.01 and 174.29 ± 2.21 MPa vs. 89–164 MPa). The two scaffolds were nontoxic to cells and had good biocompatibility, while group A scaffolds facilitated cell adhesion. The number of cells increased gradually in culture. The ALP activity of cells on group A scaffolds demonstrated higher osteogenic ability than that of group B scaffolds. The in vivo tests showed that all scaffolds retained their shape well after implantation, and no obvious inflammatory reaction or infection in surrounding tissues was found. Based on fluorescence staining, mature new bone formation was found at week 12. Group A scaffolds showed better bone integration ability compared with group B scaffolds. The percentage of new bone area in group A (7.5%) was higher than that in group B (6.5%). This research suggests that the hollow hexagonal prism structure of porous scaffolds can promote osteogenic differentiation and osseointegration better than the triangular prism structure.

Emergence of crystalline few-body correlations in mass-imbalanced Fermi polarons

Polarons can serve as an ideal platform to identify few-body correlations in tackling complex many-body problems. In this work, we reveal various crystalline few-body correlations smoothly emergent from the mass-imbalanced Fermi polarons in two dimensions. A unified variational approach up to three particle-hole excitations allows us to extract the dominant dimer, trimer, or tetramer correlation in a single framework. When the fermion-impurity mass ratio is beyond certain critical value, the Fermi polaron is found to undergo a smooth crossover, instead of a sharp transition, from the polaronic to trimer and tetramer regimes as the fermion-impurity attraction is increased. The emergent trimer and tetramer correlations result in the momentum-space crystallization of particle-hole excitations featuring a stable diagonal or triangular structure, as can be directly probed through the density-density correlation of majority fermions. Our results shed light on the intriguing quantum phases in the mass-imbalanced Fermi-Fermi mixtures beyond the pairing superfluid paradigm.

3D-printed lattice structures with SiC whiskers to strengthen thermal metamaterials

Recently, 3D-printed metamaterials have undergone rapid development; however, the preparation of most metamaterials requires the use of resin-based materials. Thus, multifunctional ceramic metamaterials, especially the introduction of other materials to optimize thermal metamaterials, must be investigated. Here, lattice structures with different units were prepared via stereolithography appearance (SLA) process. The SiC-reinforced phase was obtained by applying chemical vapor infiltration (CVI). The effects of the SiC content and unit type on the mechanical and thermal properties were studied. The results showed that the thermal expansion coefficient (CTE) of the structures decreased by 50% after one CVI cycle. Among the structures, the wave-shaped torsion flexible design reduced the instantaneous CTE to 3.67 × 10−6 K−1 at 150 °C, lower than that for the other structures. More importantly, the lattice structures strengthened with SiC whiskers exhibited outstanding mechanical performance. The compressive strengths of the triangular structure after sintering, one cycle of CVI, two cycles of CVI, and the introduction of SiC whiskers after one cycle of CVI were 3.23, 10.51, 27.38, and 39.4 MPa, respectively. The introduction of SiC increased the compressive strength of the structure by nearly 10 times, satisfying the requirements of high strength and low CTE. Thus, this method can considerably improve the thermal and mechanical properties of 3D-printed ceramic metamaterials, laying the foundation for an in-depth study on the design and preparation of thermal metamaterials.

Chemoproteomics reveals berberine directly binds to PKM2 to inhibit the progression of colorectal cancer

SummaryColorectal cancer is one of the most serious tumors and berberine can inhibit the recurrence and transformation of colorectal adenoma into colorectal cancer. However, the direct binding target proteins of berberine in inhibiting colorectal cancer remain unclear. In this study, the chemical proteomics method was used and demonstrated that berberine is directly bound to pyruvate kinase isozyme type M2 (PKM2) in colorectal cancer cells. The triangular N-O-O triangular structure of berberine contributed to hydrophobic interaction with I119 amino acid residues and π-π interaction with F244 amino acid residues of PKM2 protein. Moreover, berberine was shown to inhibit the reprogramming of glucose metabolism and the phosphorylation of STAT3, down regulate the expression of Bcl-2 and Cyclin D1 genes, ultimately inhibiting the progression of colorectal cancer. This study uncovered the direct binding target protein and mechanism of berberine to improve metabolic reprogramming in colorectal cancer, which is helpful to guide the optimization of berberine.

A study on the effects of internal architecture on the mechanical properties and mixed-mode fracture behavior of 3D printed CaCO3/ABS nanocomposite samples

PurposeThe purpose of this study was to investigate the effects of CaCO3 nanoparticles on the mechanical properties, and mixed-mode fracture behavior of acrylonitrile butadiene styrene 3D printed samples with different internal architectures.Design/methodology/approachThe nanocomposite filaments have been fabricated by a melt-blending technique. The standard tensile, compact tension and special fracture test samples, named Arcan specimens, have been printed at constant extrusion parameters and at four different internal patterns. A special fixture was used to carry out the mixed-mode fracture tests of Arcan samples. Finite element analyses using the J-integral method were performed to calculate the fracture toughness of such samples. The fractographic observations were used to evaluate the mechanism of fracture at different concentrations of nanoparticles.FindingsThe addition of CaCO3 nanoparticles has resulted in a significant increase in the fracture loading of the samples, although this increase was not consistent for all the filling patterns, being more significant for samples with linear and triangular structures. According to the fractographic observations, the creation of uniformly distributed microvoids due to the blunting effect of nanoparticles and 3D stress state at the crack tip in the samples with linear and triangular structures justify the enhancement in the fracture loading by the addition of CaCO3 nanoparticles in the matrix.Originality/valueThere is a significant gap in the knowledge of the effects of different nanoparticles in the polymer samples produced by the fused filament fabrication process. One of such nanoparticles is an inorganic CaCO3 nanoparticle that has been frequently used as nanofillers to improve the thermomechanical properties of thermoplastic polymers. Here, experimental and numerical studies have been conducted to investigate the effects of such nanoadditives on the mechanical and fracture behavior of 3D printed samples.

Simulation of the evolution of rough surfaces by sputtering using the binary collision approximation

The evolution of triangular surface structures with different sizes, the roughening of initially smooth surfaces, and the smoothing of initially rough surfaces were studied by computer simulations for sputtering by 5 keV argon on copper at normal incidence as a function of incident fluence. The program SDTrimSP-2D was used in binary collision approximation, diffusion was neglected. As already predicted by Sigmund [J. Mater. Sci. 1973, 8, 1545], a triangular ridge is relatively stable under bombardment at low fluences. However, at fluences above a critical fluence, it eventually flattens out and finally disappears. Initially smooth surfaces get rougher during bombardment, the roughness increases as the square root of incident fluence. This effect is more pronounced for larger metaparticle sizes. Initially rough surfaces get smoother by sputtering, the final smoothness depends on the initial degree of roughness. The smoothing process follows a characteristic pattern with smaller-scale roughness disappearing first and larger-scale roughness remaining stable until higher fluences. This effect gets visible in the Fourier-spectrum of the rough surface as damping of higher frequencies.

Investigating the strain controlled epitaxial growth of Mn3Ge films through thickness modulation

Mn3Ge, a typical member of the Heusler family, has a high spin polarization and large spin Hall angle, making it a potential material for spintronic devices. Regarded as a topological Weyl semi-metal, Mn3Ge could be applied in topological spintronics owing to its special Fermi-arc-type surface states and various spin transport properties. In this study, we grew high-quality perpendicularly magnetized Mn3Gefilms through magnetron sputtering. X-ray diffraction (XRD) showed that hexagonal antiferromagnetic Mn3Ge was mixed with tetragonal ferromagnetic Mn3Ge. Thickness-dependent double-phase Mn3Ge films with large magnetic anisotropy and robust anomalous Hall effect (AHE) were obtained. The triangular spin structure of hexagonal Mn3Ge enhances the AHE; however, it shrinks the coercivity of the tetragonal ferromagnetic property. This manipulation of coexisting multi-phases comes from the strain of the substrate during growth, achieved by controlling the film thickness. Structural, magnetic, and transport measurements demonstrated stress modulation of the defect pinning, magnetic anisotropy, and spin transport properties. The coexistence of antiferromagnetic and ferromagnetic Mn3Ge provides the possibility of a new generation of Mn3X-based devices for applications in spin-torque memories.

Sliding-Window-Based RNC Scheme in UAV Multicasting: Performance Analysis and Network Optimization

Unmanned aerial vehicles (UAVs)-enabled multicasting network has attracted significant attention in recent years. However, there are still some disadvantages of existing multicasting schemes used in these systems, such as low transmission efficiency and high feedback overhead. Accordingly, we propose a sliding coding window (SCW)-based random network coding (SCWRNC) scheme for a UAV multicasting network where one UAV base station is dispatched to the multicast data stream to multiple user equipments (UEs). The proposed scheme includes an SCW scheduling original packets for encoding, a lower triangular coding structure enabling UEs to decode out information even without receiving a full set of coded packets, and a feedback-compete mechanism requiring only one UE to send feedback information. The packet scheduling process is described as a five-tuple Markov decision process. Then, we give a theoretical analysis of the proposed scheme, based on which the sliding steps of SCW and the UAV hovering location are jointly optimized to maximize the system throughput. The optimal sliding steps are obtained by applying the Greedy scheduling technique, while the UAV optimal position is obtained by minimizing the maximum outage probability of all UEs. Furthermore, we also propose a flexible feedback mechanism, which enables more than one UE to send feedback for systems with sufficient resources and a “F-SCWRNC” scheme for systems where no UE is allowed to send feedback. Numerical results show that both the proposed SCWRNC scheme and F-SCWRNC scheme could achieve significant throughput gain over the existing ones.

Mechanism of improvement in the strength of para-aramid paper by polyphenylene sulfide pulp

Aramid paper has been widely applied in aerospace, rail transit, and other fields because of its outstanding mechanical properties, high-temperature resistance, and excellent insulation. We prepared para-aramid chopped fibers/polyphenylene sulfide (ACFs/PPS) composite paper, which has superior mechanical strength compared with other aramid papers. However, the mechanism of PPS pulp improving para-aramid paper is still unclear. Herein, the structure change and interface behavior of composite paper during hot pressing were studied. The surface of ACFs was modified by PPS pulp in-situ melting and self-wetting at high temperatures, which made the surface of ACFs rough and viscous. ACFs were staggered in three-dimensional space, and countless network nodes were formed at the staggered parts. With the node as the vertex and the ACF as the side length, countless stable triangular structures were formed. Under this structure, the tensile fracture surface of the composite paper showed the splitting of the bulk structure of aramid fiber, indicating that the paper had strong interfacial strength. More importantly, PPS pulp breaks the limitation of weak interfacial strength between ACFs and resin matrix. We can predict that PPS pulp can be made into advanced paper-based materials with other high-performance inert fibers.

Investigation of design and self-recovery characteristics of multicellular energy-absorbing structures manufactured via laser powder bed fusion

Direct structuring of three-dimensional structures by laser powder bed fusion (LPBF) offers a higher degree of freedom in structural design and solves the difficult problem of traditional machining for complex structural parts. Here, we report the energy absorption characteristics of different multicellular structures manufactured via LPBF. We evaluate the energy absorption properties for different multicellular structures [triangular multicellular structure, quadrilateral multicellular structure, pentagonal multicellular structure (PMS), hexagonal multicellular structure, and octagonal multicellular structure (OMS)] by experimental and numerical calculations. The accuracy of the simulation is verified by comparing the deformation and force–displacement curves of different structures. The PMS has the best overall performance, with specific energy absorption and crushing force efficiency being 3331 mJ and 3165.74 J/kg, respectively. At the same time, the shape memory effect of all structures under 15% deformations is more than 95%. However, partial failure of the OMS occurred within 15% of the deformation. Therefore, the problem of partial failure of the structure under low deformation is a critical problem to be solved urgently in the future.

New type of multiple lump and rogue wave solutions of the (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili equation

In this paper, a new version of the solution in form of Grammian for the (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili equation is obtained with the aid of the polynomial function. A family of multiple lump solutions are constructed. All the center points of the lumps form a triangular structure as the auxiliary variable tends to the negative or positive large values. A unified scheme for constructing the high-order rogue wave solutions is proposed. This new type of rogue wave reflects the appearance and disappearance of multiple lump waves in the background of N-kink solitons. The results can well mimic complex waves and explain complex dynamics in fluids.

Reflection Mechanism of Dielectric Corner Reflectors: The Role of the Diffraction of Evanescent Waves and the Goos-Hänchen Shift.

Nano- and microstructures have been developed for asymmetric light transmission (ALT) filters operating in a wide wavelength range. One of the most straightforward structures with ALT properties is a dielectric corner reflector (DCR) comprising a one-dimensional grating of a triangular shape on one surface. The DCR possesses strong reflection only for one-way light illumination due to multiple total internal reflections (TIRs) inside the triangular grating. For triangular structures being much larger than the wavelength of light, the reflection properties are expected to be fully described by geometrical optics. However, geometrical optics do not account for the Goos–Hänchen (GH) shift, which is caused by the evanescent wave of the TIR. In this work, the reflection mechanism of DCRs is elucidated using the finite element method and a quantitative model built by considering the GH shift. The reduction in reflection of the DCR is dominated by diffraction of the evanescent wave at the corner of the triangular structure. Our model is based on simple mathematics and can optimize the DCR geometry for applications addressing a wide wavelength range such as radiative cooling.

Implementation of Sacrificial Support Structures for Hybrid Manufacturing of Thin Walls

Thin-walled features can be difficult to produce with traditional machining methods which often rely on excess stock material for stiffness. This challenge is increased in hybrid manufacturing where the feature is already near net shape before machining. Significant workpiece deflection can result in poor geometric and surface finish tolerances on the finished part. A potential solution to this problem is to implement sacrificial support structures to the as-printed geometry. The supports are then machined away during the finishing portion of the hybrid process. In the present work, several different design parameters for these sacrificial supports were evaluated to determine their impact on the quality of representative thin wall geometry samples. The angle, height, and spacing of triangular support structures were varied for each sample and then machined and examined. The addition of these supports relative to an unsupported configuration provided a deflection reduction of around 0.2 mm. Surface roughness was improved by approximately 1.5 µm. Increasing values of support height were found to correspond to reduced wall deflection. Similarly, decreasing values of support angle and support spacing improved geometric accuracy. Efficiency comparisons showed that increases in print time corresponded to rapidly diminishing gains in geometric accuracy but continued to improve surface roughness. Implications for hybrid finishing of additively manufactured thin-walled structures is briefly discussed.

Ultrasonography and biochemical studies of hepatobiliary system in buffaloes

The present work was undertaken to study the ultrasonographic and clinico-biochemical parameters of hepatobiliary system in apparently healthy adult non gravid buffaloes. The present study revealed that, the hepatic parenchyma was homogenously coarse echogenic, interspersed with anechoic bands of hepatic vessels, with sharp margin and was hyperechoic relative to right renal cortex. It was imaged from just behind the last rib to the 6th intercostal space. The gallbladder was visualized between the 12th to 9th intercostal spaces, seen as a pear-shaped fluid-filled anechoic structure with hyperechoic wall, restricted to one to two intercostal spaces. The portal vein was seen as a stellate, branching, anechoic structure with hyperechoic wall and the hepatic vein as anechoic tubular structure with anechoic wall within the hepatic parenchyma. The caudal vena cava was observed as a triangular anechoic structure in transverse view and tubular in longitudinal view. It is concluded that the ultrasonography is a useful tool for the non-invasive examination of liver. Its sonographic appearance and parameters measured in healthy buffaloes can serve as reference values for the diagnosis of pathological changes in liver.

Overtopping volume of impulse waves in glacier lakes: Experimental and numerical investigation using rigid dams

Glacier lake outburst floods (GLOFs) that result from the breaching of moraine dams are typical disasters in high mountain regions of the Tibetan Plateau, which endanger vital infrastructures such as the Sichuan-Tibet Railway and Highway. Breaching can be caused by tsunami-type waves, resulting from glaciers calving and falling into impounded lakes, which overtop and destroy their natural boundaries. In this work, we develop an equation for the overtopping volume based on the simplified geometry of fluids running up an incline. Specifically, we propose that overtopping can be viewed in terms of the run-up of solitary waves impacting a structure from which relationships with the dam and wave properties can be established. This equation is tested and verified against physical experiments and numerical simulations of waves overtopping rigid, impermeable triangular structures which serve as idealized natural dams. The proposed equation is found to adequately account for the first-order dependencies of the overtopping volume on the different dam and wave properties. We extend the applicability of this analysis to erodible dams made up of glacier tills, wherein we show the basic dependence of the overtopping volume on the erodibility of the dams and flood scales.

Capturing the stereoconfiguration of (C6H6)2Ar by Coulomb-explosion imaging

The configurations of the ${({\mathrm{C}}_{6}{\mathrm{H}}_{6})}_{2}\mathrm{Ar}\phantom{\rule{4pt}{0ex}}({\mathrm{Bz}}_{2}\mathrm{Ar})$ complex are identified by femtosecond laser-induced Coulomb explosion, in which the produced three-body coincident ionic momenta $({\mathrm{Bz}}^{+}\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}{\mathrm{Bz}}^{+}\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}{\mathrm{Ar}}^{+})$ is measured. The triangular structure is clearly determined by coincident momenta combined with quantum chemistry calculations, arising from classical trajectory simulations of eight promising configurations. Additionally, the bond distances between Ar and two Bz molecules are retrieved from the measured coincident momenta. The good agreement between measurement and computational calculations strongly suggests the laser-induced Coulomb explosion is a powerful approach for imaging configurations of the weakly bound molecular clusters.

Silver Ion-Induced Formation of Unprecedented Thorium Nonamer Clusters via Lacuna-Construction Strategy

Silver Ion-Induced Formation of Unprecedented Thorium Nonamer Clusters via Lacuna-Construction Strategy

Partially pivoted ACA based acceleration of the energetic BEM for time-domain acoustic and elastic waves exterior problems

We consider acoustic and elastic wave propagation problems in 2D unbounded domains, reformulated in terms of space-time Boundary Integral Equations (BIEs). For their numerical solution, we employ a weak formulation related to the energy of the system and we discretize the weak problems by a Galerkin-type Boundary Element Method (BEM): this approach, called Energetic BEM, has revealed accurate and stable even on large time intervals of analysis. In particular, it results that, when standard Lagrangian basis functions are considered, the BEM matrices have Toeplitz lower triangular block structure, where blocks for growing time become fully populated; hence the overall memory cost of the energetic BEM is O(M2N), M and N being the number of the space degrees of freedom and the total number of performed time steps, respectively. This drawback prevents the application of such method to large scale problems. As a possible remedy, we propose a fast technique based on the Adaptive Cross Approximation (ACA). The core of this procedure is the approximation of sufficiently large time blocks of the energetic BEM matrix through the partially pivoted ACA algorithm, which allows to compute only few of the original entries. This leads to reduced assembly time, which for the energetic BEM is generally relevant, coupled with reduced memory storage requirements. Additionally, the consequent acceleration of the matrix/vector multiplication together with a marching on time procedure, leads to remarkable reduction of the computational solution time. The effectiveness of the proposed method is theoretically proved and several numerical results are presented and discussed.