Geometric Behavior Research Articles

Introducing hafnium to atomically small- and medium-sized tin clusters (HfSnn0/-/2- (n = 4–17)): A computational investigation of geometrical and growth behavior, spectral properties, electronic configuration and thermochemistry

The global and local minimum configurations of single Hf atom doped Sn clusters are conducted via density function theory (DFT) combined with artificial bee colony algorithm (ABCluster). Furthermore, DFT method is also used to systematically investigate on their structural growth evolution, spectral and electronic information, thermochemical properties following the size of tin clusters doped Hf atom. Structurally, the ground-state geometries of neutral, anion and di-anion are discovered that, from n = 4, the number of Sn atoms in cluster, HfSnn0/-/2- adsorb additional Sn atom on the prior architecture one by one until forming n = 17 for HfSnn-10/-, as well as forming n = 16 for HfSnn-12-. And for the HfSn110/- and HfSn102- as beginning the species veritably develop sealed architectures. The strongest vibrational modes of sealed nanoclusters are stretching modes of Hf atom with infrared actives and breathing modes of the Sn cage framework with Raman actives, respectively. The natural population analysis (NPA) elucidates the stronger relationship between the Hf atoms and the tin frameworks in sealed clusters than that in unsealed clusters. The results of thermochemical properties, molecular orbital shell (MOs), adaptive natural density partitioning (AdNDP) and ultraviolet visible absorption spectrum (UV–Vis) indicate that, the HfSn16 with high symmetry of Td exhibits thermochemical stability and optoelectronic properties, which is utilized potentially as zero-dimensional unit of self-assembling fluorescent nanomaterials.

Generalised scaled boundary isogeometric analysis – a method for structural analysis of naturally shaped timber structures

ABSTRACT Natural building materials, such as naturally shaped tree trunks, have been used in construction since ancient times. Wood is primarily processed as a long, thin product due to its growth and structure, leaving many parts unused. These neglected parts, like branches, can be used for load-bearing structures. However, they require a new parametric description due to material and geometric behaviour differences. It's crucial to transfer these geometries into the calculation model accurately. The surface is described using NURBS based on image data to realise this. Applying the Scaled Boundary Isogeometric Analysis (SBIGA) can directly use these geometries for structural analysis. This method combines the concepts from the scaled boundary finite element method (SBFEM) with the isogeometric analysis (IGA). In this technique, two-dimensional surfaces are scaled to a centre point. When used in the context of thin, long structures, obtuse-angled polyhedrons occur within a patch, leading to numerical condition problems. This motivates this contribution to modify the conventional SBIGA towards a generalised scheme. This work introduces a generalised SBIGA approach, employing a scaling centre line instead of a scaling centre point. This enables the analysis of slender, curved objects without additional structure partitioning, simplifying the preprocessing while improving the performance.

Non-Linear Behavior of Double-Layered Grids

Abstract This study presents a numerical approach to an analysis of the mechanical behavior of double-layered tensegrity grids. We present a comparative study on the behavior of tensegrity grids through geometric nonlinear analysis (GNA) and combined nonlinear analysis (CNLA) (geometric and material), considering the possible effect of evolution in the elasto-plastic domain of the cable elements. The effect of the relaxation of cable on the amplification of the displacement of these grids was taken into account. The updated Lagrangian formulation, which modifies the Newton-Raphson iterative scheme with incremental loading, was adopted. We have developed a numerical computational model specific to tensegrity structures that simulates the geometric and material nonlinear behavior. The reliability of the calculation tool developed has been validated. Additionally, the results of the application of the numerical model on a grid, which was generated based on demi-cuboctahedral tensegrity cells, are presented.

Non-Linear Behaviour and Analysis of Innovative Suspension Steel Roof Structures

Suspension structures are one of the most effective roof load-bearing structures for medium to long spans. Their shape under symmetric loads is usually a square parabola or a curve close to it. The biggest drawback of such structures is their increased deformability under asymmetric loads. So-called rigid cables are used to solve this problem. However, the production of such rigid cables with a curvilinear shape is complicated, and their maintenance also has drawbacks due to the above-mentioned shape. To avoid these shortcomings, straight-line suspension structures have been used. This paper proposes a new form of combined suspension roof structures consisting of main load-bearing straight suspension elements supported by cable struts. For the main suspension elements, the bending stiffness is accepted, taking into account the operational requirements of the structure. This article analyses the behaviour of such a combined suspension structural system in symmetric conditions with an innovative approach. The arrangements of this system are discussed. The calculation of the forces and displacements of this structure and its elements is presented, taking into account the geometrical nonlinear behaviour. The distribution of the forces in the rigid elements and node displacements of the structure are discussed. The proposed new form of a combined cable-supported roof structure was shown to be more effective in terms of weight than the standard parabolic-shaped suspension structure.

Robust Two-Layer Control of DC Microgrids With Fluctuating Constant Power Load Demand

This paper proposes a cascaded control structure for the regulation of DC Microgrids (MG). It is well-known that the negative impedance characteristics of a constant power load (CPL) adversely affect the stability of the network, and can cause problems such as voltage collapse or damage the electronic components. To mitigate this, we propose a two-layer control structure, where at the inner layer, the proposed controller achieves fast tracking of the supplied reference points and ultimate boundedness of the trajectories in a desired set. The outer layer generates the inner layer reference points, accounts for system constraints, and introduces robustness of the voltage dynamics to unknown perturbations of the CPL demand. For the first time, an investigation of the nonlinear geometric behaviour of the CPL is carried out to derive necessary conditions that ensure boundedness of the network dynamics and feasible regulation to a desired equilibrium set. Finally, Control Lyapunov functions are formulated to prove the stability and estimate the region of attraction of the closed loop dynamics. A simulated scenario of a meshed MG network is presented to confirm the validity of the results.

Assessment on flexural performance of monolithic glass considering spatial and depth characteristics of scratches

Glass products are widely used in building envelopes. Fracture can be triggered accidentally from the glass surface damage such as scratch. This study proposed an approach to assess the flexural performance of the aged monolithic glass panel, which has scratch with spatial and depth information detected via non-contact sensing. The coaxial double ring (CDR) test was conducted for experimentally evaluating the flexural strength on a total number of 160 scratched annealed (AN) and fully tempered (FT) glass specimens. Finite element (FE) analysis was performed to find the exact stress state by considering the geometric non-linear behaviour of glass panel under large deflection. Test and numerical results demonstrate that the scratch depth characterized by a confocal microscope and spatial location can both influence the failure load of FT glass, whereas AN glass is only sensitive to the latter. With combining linear elastic fracture mechanics (LEFM) theory, the relationship between the scratch depth and the residual strength of FT glass can be accurately determined. The spatial and depth characteristics of scratch can then be integrated for the failure load assessment of monolithic FT glass panel. The assessment framework can contribute to the accurate non-destructive assessment on aged architectural glass.

Kinematics modeling of the gear-based crank mechanism engine regardless of the compressions ratio variations.

In this work, geometric and kinematic modeling of the gear-based crank mechanism engine (GBCM) was performed. To this aim, a mechanical approach based on projective computational methods and mechanism theory laws is applied, to which a parametric study has allowed a conclusion on the geometrical and kinematic behaviors of the moving links. The study concluded that the kinematic quantities at connecting rod head are one-half of those at the piston top head. The extrinsic behavior like the stroke of the connecting rod head is twice the crank radius and the piston kinematic are identical to the conventional engine with the same crankshaft ratio regardless of the compression ratio and any gear wheel radius. Hence, all the extrinsic kinematic properties of a classic crankshaft mechanism of the fixed compression ratio engine remain valid for a gear-based crank mechanism engine and can be used for dynamic calculation purposes.

A geometry dependent directivity analysis of an optical structure based on NV center in diamond

We present and investigate a highly directional diamond based optical nanostructure embedded with an elliptical solid immersion lens (e-SIL). An in depth analysis of the far field evolution is elucidated with respect to geometrical modification. This design is capable of producing a maximum directivity of ∼11 dB at its optimized position. Geometrical tolerance and directional behavior has been studied within a wide range of dipole variation. The incident light source noise is neutralized with the manipulation of e-SIL geometry by considering an experimental simulation environment. Enhancement in directivity near NV center zero phonon line (ZPL) region with reduced excitation light source noise can improve the overall efficiency of the NV single photon emitter and can be useful for multiple photonic applications.

Enantioselective merged gold/organocatalysis.

Gold complexes, because of their unique carbophilic nature, have evolved as efficient catalysts for catalyzing various functionalization reactions of C-C multiple bonds. However, the realization of enantioselective transformations via gold catalysis remains challenging due to the geometrical constraints and coordination behaviors of gold complexes. In this context, merged gold/organocatalysis has emerged as one of the intriguing strategies to achieve enantioselective transformations which could not be possible by using a single catalytic system. Historically, in 2009, this field started with the merging of gold with axially chiral Brønsted acids and chiral amines to achieve enantioselective transformations. Since then, based on the unique reactivity profiles offered by each catalyst, several reports utilizing gold in conjunction with various chiral organocatalysts such as amines, Brønsted acids, N-heterocyclic carbenes, hydrogen-bonding and phosphine catalysts have been documented in the literature. This article demonstrates an up-to-date development in this field, especially focusing on the mechanistic interplay of gold catalysts with chiral organocatalysts.

Comparative evaluation of methods for obtaining the stress-free geometry of keratoconus corneas with different levels of severity

A biomechanical model that simulates the physiological pressure load on the cornea without considering the stresses in vivo will result in an overstress or underestimation of the stress field and incorrect deformation of the corneal structure. Therefore, it is essential to propose numerical models that consider the stress-free geometry of the cornea. In this study, the Displacement and Pre-stress methods were compared to obtain the stress-free geometry (S-FG) and the physiological estimated geometry (P-EG), based on the patient-specific geometric behavior and the computational time required to reach each geometry. The same shape and contour conditions were considered in the models obtained from both methods for each of the pathological scenarios analyzed. Both methods behaved differently to obtain the free geometry, and this difference increased with the severity grade of the disease. However, they behaved in a similar way to reach the physiological estimated geometry. The Displacement method required a lower computational cost to reach the free geometry, with both methods presenting a similar computational cost to obtain the physiological geometry. The stress-free geometries obtained by both methods allowed to characterize the existing biomechanical decompensation during the progression of the diseases. In conclusion, the calculation of the stress-free corneal geometry associated to the clinically measured intraocular pressure with the Displacement and Prestress Methods in keratoconus eyes allows the development of accurate and useable models in clinical practice in real time. This displacement method shows some benefits in terms of computational cost.

Molecular structure, spectroscopic analysis and theoretical investigations of new organic chloride salt containing 3,3’-diammoniumbiphenylsulfone cation

A new organic chloride salt with the general formula [C12H14N2O2S.2Cl.2H2O] was synthesized by slow evaporation method. The examined chemical compound crystallizes in the P21/c monoclinic space group. The infrared and UV-visible spectroscopies were used to analyze the identified structure once again. It was discovered that strong hydrogen connections between organic cations, chloride anions, and water molecules dominate crystal packing. The intermolecular interactions in this salt were studied using Hirshfeld surface analysis. The optimized geometrical parameters, vibrational assignments, optical behavior and thermodynamic properties of the title compound were performed using density functional theory (DFT/B3LYP) method with 6-31 G (d) as basis set. Moreover, peaks observed on the NMR of solid state 13C are identified.

Authoring Moving Parts of Objects in AR, VR and the Desktop

Creating digital twins of real objects is becoming more popular, with smartphones providing 3D scanning capabilities. Adding semantics to the reconstructed virtual objects is important to possibly reproduce training scenarios that otherwise could demand significant resources or happen in dangerous scenarios in some cases. The aim of this work is to evaluate the usability of authoring object component behaviors in immersive and non-immersive approaches. Therefore, we present an evaluation of the perceived ease of use to author moving parts of objects under three different conditions: desktop, augmented reality (AR) and virtual reality (VR). This paper provides insights into the perceived benefits and issues that domain experts might encounter when authoring geometrical component behaviors across each interface. A within-subject study is the major contribution of this work, from which is presented an analysis based on the usability, workload and user interface preferences of participants in the study. To reduce confounding variables in the study, we ensured that the virtual objects and the environment used for the evaluation were digital twins of the real objects and the environment that the experiment took place in. Results show that the desktop interface was perceived as more efficient and easier to use based on usability and workload measures. The desktop was preferred for performing component selection but no difference was found in the preference for defining a behavior and visualizing it. Based on these results, a set of recommendations and future directions are provided to achieve a more usable, immersive authoring experience.

Memeplex-based memetic algorithm for the multi-objective optimal design of composite structures

Hybrid construction is proposed to decrease costs in lightweight structures using fiber-reinforced plastics (FRP) composite materials. Minimum weight, minimum strain energy (stiffness), and minimum energy variability of the structural system response are the objectives of the robust design optimization approach applied to composite shell structures with stiffeners. The trade-off depends on given stress, displacement, and buckling constraints imposed on composite structures considering non-linear geometric behavior. The design variables are ply angles and ply thicknesses of shell laminates, the cross-section dimensions of stiffeners, and the variables related to the selection of materials and their distribution at the laminate level and subsequently of the laminates along the structure. A Multi-Objective Memetic Algorithm (MOMA) applies multiple learning procedures exploring the synergy of different cultural transmission rules. An enlarged virtual population with a dual age-dominance nature captures and updates the Pareto curve. The concept of memeplex controls the meme selection and their propagation along the hybrid genetic and cultural evolution path. The success of memetic learning procedures is analyzed by measuring each meme's relative and absolute success events according to different approaches, depending on the reference time used in evolutionary history. Results show that MOMA is promising in multi-objective optimization of composite hybrid structures.

Probing the impact of process variables in laser-welded aluminum alloys: A machine learning study

This paper presents a pioneering approach, Bayesian machine learning (ML), for the estimation and characterization of critical laser welding features in Aluminum alloys, encompassing peak temperature, heat-affected zone width, and bead aspect ratio. The methodology involved constructing a laser welding database utilizing finite element simulations (FEM). The distinctive advantage of the Bayesian ML model lies in its capability to address challenges associated with excessive approximation and to account for uncertainties in parameters. This results in precise and resilient predictions of laser weld parameters across a spectrum of aluminum alloys. The findings underscored the model's efficacy in forecasting output targets, although regression analysis unveiled unique characteristics in data distribution and outliers specific to aluminum alloys. These outliers were primarily linked with the melting range of aluminum alloys, leading to the Al7075 alloy having the lowest prediction, and the Al1100 alloy the highest within the ML model. Additionally, the normalized average weight functions of input parameters were illustrated, clarifying their differing importance concerning diverse types of Al alloys in precisely forecasting output objectives. In light of these explanations, it remains consistent that laser power (LP) and welding speed (WS) inputs hold substantial sway across all alloys, while workpiece thickness (WT), beam diameter (BD), and initial temperature (IT) played comparatively lesser roles. Ultimately, this work contributes to a more profound comprehension of the relationships between input features and the geometrical and thermal behavior of laser-welded Al joints.

Phase transition of Bianchi-type I cosmological model in [formula omitted] gravity

In the context of the f(T) theory of gravity, where T represents as a torsion scalar, we explore the Locally Rotational Symmetric Bianchi type-I dark energy model. An effective cosmological model is used, and its isotropization is examined, producing a conclusion that accurately depicts the evolution of our Universe. We looked at dark energy (DE) and dark matter (DM) in both interacting and non-interacting forms. The exact solution of the field equations was achieved by using special form of the time-varying deceleration parameter in terms of the Hubble parameter. The dark matter energy density (Ω(dm)) decreases with redshift while dark energy density (Ω(de)) grow with redshift. The physical and geometrical behaviour of the models are examined in both forms. A combination of dark matter and dark energy can eliminate the coincidence issue in the ΛCDM model. Using the most recent observations, we also discussed the physical characteristics of the generated models about the early Universe and late-time acceleration. It has been noted that this model has an initial singularity, initial decelerating growth and late-time transitions to an accelerating expansion phase.

Equiform rectifying curves in Galilean space [formula omitted

This research paper presents the equiform rectifying curves in Galilean space G4, and establish the relation between equiform curves and their equiform curvature functions. The proposed methodology involves studying the necessary and sufficient conditions for the curve α(σ) with non zero curvatures K1(σ),K2(σ), and K3(σ) to be congruent to an equiform rectifying curve. By employing this approach we derive various characterizations of these curves, also deduce that there are no equiform rectifying curves in G4 with zero constant equiform curvature functions K2(σ), and K3(σ). The findings contribute to a deeper understanding of the geometric properties and behaviour of equiform rectifying curves in Galilean space G4. Thereby offering potential applications in fields such as mathematical physics and differential geometry.

ANALYTICAL SOLUTIONS OF TIME FRACTIONAL NEGATIVE ORDER KdV-CALOGERO-BOGOYAVLENSKII-SCHIFF EQUATION

In this work, we obtain the exact solutions of negative-order forms for KDV-Calogero-Bogoyavlenskii-Schiff equation (nKdV-nCBS) with conformable fractional derivative by using method. Chain rule and wave transform are used for transforming nonlinear fractional partial differential equation into nonlinear integer order ordinary differential equation. By this way, we don’t need any normalization or reduction formulas which have complex calculation procedures. Moroever 3D graphical simulations are presented to show the geometrical behaviour of derived solutions.

Restriction of irreducible unitary representations of 𝑆𝑝𝑖𝑛(𝑁,1) to parabolic subgroups

In this paper, we obtain explicit branching laws for all irreducible unitary representations of G = Spin ⁡ ( N , 1 ) G=\operatorname {Spin}(N,1) when restricted to a parabolic subgroup P P . The restriction turns out to be a finite direct sum of irreducible unitary representations of P P . We also verify Duflo’s conjecture for the branching laws of discrete series representations of G G with respect to P P . That is to show: in the framework of the orbit method, the branching law of a discrete series representation is determined by some geometric behavior of the moment map for the corresponding coadjoint orbit.

On the influence of free space in topology optimization of electro-active polymers

This study investigates the impact of the surrounding free space on the topology optimization (TO) of electro-active polymers (EAPs). It is well understood that, under the application of an electric field, the deformation of an EAP is not solely determined by the field distribution within the body, but also by the distribution in the free space surrounding it. This is particularly true for electronic EAP, which are emerging as leading candidates for developing artificial muscles. Our study specifically focuses on understanding the influence of the free space in the context of density-based TO. We model the free space as an extended void region around the design domain. Our numerical experiments focus on EAP actuators and take into account their geometrical nonlinear behavior. The results show that incorporating the surrounding free space has a significant impact on the performance of the optimized EAPs with low electric permittivity. This makes it essential to consider in real-world applications.

Nonlinear Stress-Free-State Forward Analysis Method of Long-Span Cable-Stayed Bridges Constructed in Stages

Structural analysis and construction control of staged-construction processes are major subjects in the context of modern long-span bridges. Although the forward and backward analysis methods are able to simulate situations, their main disadvantage is that they usually apply the stage superposition principle. In the actual construction process, due to changes made to the plan, the construction process needs to be adjusted at any time, and it is difficult to implement the construction process in complete accordance with the established plan. As a result, the existing simulation method based on the incremental structural analysis of each construction stage has poor adaptability to such adjustments. In this study, considering the strong geometric nonlinear behavior of the long-span cable-stayed bridge construction process, the geometrically nonlinear mechanical equations of the staged-construction bar system structure were derived. The minimum potential energy theorem was used by introducing the concept of the stress-free-state variable of the structural elements. The equation reflects the influence of the change in the stress-free-state variables of structural elements on the completion state of the structure. From the analysis of the geometrical condition that the equilibrium equation holds, the stress-free installation condition of the closing section of the planar beam element structure was obtained. A new simulation method for long-span cable-stayed bridge construction has been proposed, which is called the stress-free-state forward analysis. This method can directly obtain the intermediate process state of cable-stayed bridge construction without performing stage-by-stage demolition calculations, and causing the internal force and deformation of the completion state to reach the design target state. This method can realize the simulation of multi-process parallel operation in construction, and solves the problem of automatic filtering of temporary loads. To illustrate the application of the method, a long-span cable-stayed bridge was analyzed.